Post on 01-Apr-2021
transcript
Exoplanets
Edge on
Face on
Detecting Exoplanet Transit
Lab 5 Detecting Exoplanet Transit
bull Due March 13 (Wed) 1159pm (e-submission)
bull Target GJ 1214 b
bull Data from ACAM on the William Herschel Telescope
bull Lectures on Exoplanets and Differential Photometry
bull Group Presentations Preferred Dates amp Format
Lab 5 Detecting Exoplanet Transit
Exoplanets
How Do We Detect
Extra-solar Planets (Exoplanets)
Exoplanet discoveries per year
2000 confirmed exoplanets discovered so far
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Lab 5 Detecting Exoplanet Transit
bull Due March 13 (Wed) 1159pm (e-submission)
bull Target GJ 1214 b
bull Data from ACAM on the William Herschel Telescope
bull Lectures on Exoplanets and Differential Photometry
bull Group Presentations Preferred Dates amp Format
Lab 5 Detecting Exoplanet Transit
Exoplanets
How Do We Detect
Extra-solar Planets (Exoplanets)
Exoplanet discoveries per year
2000 confirmed exoplanets discovered so far
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
bull Due March 13 (Wed) 1159pm (e-submission)
bull Target GJ 1214 b
bull Data from ACAM on the William Herschel Telescope
bull Lectures on Exoplanets and Differential Photometry
bull Group Presentations Preferred Dates amp Format
Lab 5 Detecting Exoplanet Transit
Exoplanets
How Do We Detect
Extra-solar Planets (Exoplanets)
Exoplanet discoveries per year
2000 confirmed exoplanets discovered so far
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How Do We Detect
Extra-solar Planets (Exoplanets)
Exoplanet discoveries per year
2000 confirmed exoplanets discovered so far
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanet discoveries per year
2000 confirmed exoplanets discovered so far
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
So how do we detect them
Exoplanets
Direct Imaging
Stellar Motions minus velocities timing astrometry
Light curve minus transient planets
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Direct Imaging
bull Currently heating up with adaptive optics high contrast imaging systems
bull Earth-like planet around a sun-like star is 10 billion times fainter than its star
bull Need to find a faint object very close to a bright star
HR 8799
Beta Pictoris
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
bull Only about ~ 20 planets directly imaged (2017)
bull Technically challenging
Direct Imaging
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Stellar Motions
bull Radial velocity timing astrometry
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Radial Velocity Comparisons
bull Best measurements now at a level of 05 ms (a slow walk)
1995
Stellar Motions
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
bull 51 Pegasi b ndash First planet around sun-like star
bull P = 423 days Hot Jupiter
Stellar Motions
Radial Velocity Comparisons
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet radius and
star radius
Transit probability in terms of star radius and
distance between the planet and star
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Eclipse depth in terms of planet and star
radii
Transit probability in terms of star radius and
distance between the planet and star
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Light Curve ndash Transiting Planets
HD 209458
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Orbital Period
Transit Transit
Secondary
Eclipse
Can reach 10 parts-per-million accuracy for
the brightest stars from space
Precision Photometry
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Light Curve Method Transient PlanetsA transient planet changes blocks the light from a star = eclipse
Challenges and Advantages of
Detecting Transient Planets
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Light Curve Method Transient Planets
Large Transit Planet Survey OGLE Kepler Corot hellip
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
The Kepler Project
Exoplanets
How do we detect exoplanets
Transient Planets
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
FOV
The Kepler Mission Field
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
The Kepler Mission
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
The Kepler Mission
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
The Kepler
Mission
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
Small telescope discovery Hubble Space Telescope data
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Example HD209458b (1999)
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Transient Planets
Example HD209458b (1999)
ldquoInformation on planet atmosphererdquo
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanets
How do we detect exoplanets
Transient Planets ldquoInformation on planet atmosphererdquo
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Density measurement Useful Diagrams
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Kepler-78
Star KIC 8435766 (Kepler-78)
Constellation Cygnus
Right ascension (α) 19h
34m
58s
Declination (δ) +44deg 26prime 54Prime
Apparent magnitude (mV) 12
Radius (r) 073plusmn015 R
Temperature (T) 5143 (plusmn 70) K
Metallicity [FeH] -008 (plusmn 013)
Density measurement Example
A planet was discovered in 2013 by analyzing
data from Kepler space telescope The planet
was found not only transiting the star but its
occultation and reflected light from the parent star
due to orbital phases were also detected
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Kepler-78b (formerly
known as KIC 8435766 b)
is an exoplanet orbiting
around the star Kepler-78
Mass (m) 169-185 Moplus
Radius (r) 112 Roplus
Bond Albedo () 20-60
Density (ρ) 53-56 g cm-3
Density measurement Example
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Exoplanet Density Measurement
o Density is critical to understanding
the nature of planets
o Part of Lab 5 is to measure the
density of a transiting planet
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
What do we learn from transit
light curve analyses
o Transit Probability Depth Duration and
Period
o Limb Darkening Effect Ingress and Egress
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
o Transit Probability Ra
o Transit Depth (RpR )2
o Transit Duration (Ra)P
Geometrical
Configuration
Geometry amp Time ( Mass)
Transit Probability Depth Duration
Simple Case
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Blue Circles two extreme planet-orbit
inclinations above and below which the
planet does not transit
2Ra angle separation
between the two extreme orbits
Solid angle traced out by
the two extreme transit
configurations =
Transit Probability =
Transit Probability Depth Duration
Simple Case
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Condition for full transit
Condition for grazing transit
(i inclination ndash see next slides)
Transit Probability Depth Duration
Simple Case
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
True Anomaly () angle
between direction of
periapsis (B) and the current
position of a planet (P) on an
ellipse (= angular parameter
that defines the position of a
planet in a Keplerian orbit)
Keplerian Planet Orbit
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Larger star andor closer planet
gives a high transit probability
For an eccentric orbit (e eccentricity)
Higher probability with a large
eccentricity
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Edge on (i = 90) so
always transit
Face on (i = 0) so
no transit
Observer
i the angle between the angular-momentum vector of the planetrsquos orbit and the line of sight
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Transit Duration time during which any part
of the planet obscures the disc of the star
depends on how the planet transits the host
star
Transit Length length the planet has to
travel across the disk of the star
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Transit
Depth
Limb
Darkening
Ingress Egress
Transit Depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth
Transit Depth
A small planet (eg Earth) requires high-precision photometry
for the planet to be detected due to its shallow transit depth