1 Exoplanets Introduction Planets and Astrobiology (2016-2017) G. Vladilo Importance of the study of extrasolar planets • Main scientific motivations – Setting our understanding of planetary physics in a global co ntext Planetary physics so far only based on the Solar System Testing models of formation and evolution of planetary systems – Understanding how typical are the Solar System properties Four smaller planets interior to four larger planets Nearly circular and aligned orbits – Setting terrestrial life in a universal context Quantifying the frequency of planets that have suitable conditions for hosting life (habitable planets) 2 Importance of the study of extrasolar planets • Technological and scientific spin-offs – Exoplanet observations are driving huge technological improvements to classical astronomical instrumentation Imaging, coronagraphy, high resolution spectroscopy, photometry, interferometry, etc. – Stellar physics strongly benefits from exoplanet observations A huge amount of high quality stellar measurements is becoming available Exoplanet science is providing fresh motivation to improve our understanding of stellar physics and stellar chemical abundances – In turn, exoplanet studies will benefit from the higher level of understanding of stellar properties 3 4 Basic concepts of celestial mechanics derived from the study of the Solar System useful for studying exoplanet systems
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Exoplanets � Introduction
Planets and Astrobiology (2016-2017)G. Vladilo
Importance of the study of extrasolar planets
• Main scientific motivations– Setting our understanding of planetary physics in a global context
Planetary physics so far only based on the Solar SystemTesting models of formation and evolution of planetary systems
– Understanding how typical are the Solar System properties Four smaller planets interior to four larger planetsNearly circular and aligned orbits
– Setting terrestrial life in a universal contextQuantifying the frequency of planets that have suitable conditions for hosting life (�habitable planets�)
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Importance of the study of extrasolar planets
• Technological and scientific spin-offs– Exoplanet observations are driving huge technological improvements
to classical astronomical instrumentationImaging, coronagraphy, high resolution spectroscopy, photometry, interferometry, etc.
– Stellar physics strongly benefits from exoplanet observationsA huge amount of high quality stellar measurements is becoming availableExoplanet science is providing fresh motivation to improve our understanding of stellar physics and stellar chemical abundances
– In turn, exoplanet studies will benefit from the higher level of understanding of stellar properties
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Basic concepts of celestial mechanics �derived from the study of the Solar System�
useful for studying exoplanet systems
• Kozai resonance– In a two-body system with a small body in a highly inclined
orbit, angular momentum exchange between the secondary and primary body results in the body’s inclination and eccentricity oscillating synchronously, i.e. increasing one at the expense of the other, whilst conserving the integral of motion
– The eccentricity and inclination oscillate with the same periodicity, but 180o out of phase
– In the Solar System affects the long-term evolution of long-period comets
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Basic concepts of celestial mechanics �derived from the study of the Solar System
• Lagrangian points– Lagrangian points are constant-pattern solutions of the
restricted three-body problem– Given two massive bodies in orbits around their common
barycenter, there are five positions in space where a third body, of comparatively negligible mass, could be placed so as to maintain its position relative to the two massive bodies
– These five positions, labeled L1 to L5 Lagrangian points, lie in the orbital plane of the two large bodies
– In these 5 positions, the gravitational fields of two massive bodies combined with the minor body's centrifugal force are in balance, allowing the smaller body to be relatively stationary with respect to the first two
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Basic concepts of celestial mechanics �derived from the study of the Solar System
• Location of the Lagrangian points– L1, L2 and L3 are on the line connecting the two large bodies. – L4 and L5 form an equilateral triangle with the two large bodies
Bodies in L4 and L5 are in 1:1 resonance with the smaller of the two large bodies
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Basic concepts of celestial mechanics �derived from the study of the Solar System
• Stability of the Lagrangian points– L1, L2 and L3 are not stable, but it is possible to find quasi periodic
orbits around these points, at least in the restricted three-body problem– L4 and L5 are stable, which implies that objects can orbit around them
in a rotating coordinate system tied to the two large bodies
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Basic concepts of celestial mechanics �derived from the study of the Solar System
Spaceflight applications
Natural bodies
• Natural Solar System bodies in Lagrangian points– It is common to find objects at or orbiting the L4 and L5 points of
natural orbital systems– These objects are generically called “Trojans”, after the names of the
family of asteroids found in the Sun-Jupiter L4 and L5 points– The Sun–Earth L4 and L5 points contain interplanetary dust and at
least one asteroid– Recent observations suggest that the Sun–Neptune L4 and L5 points
may be thickly populated– Other examples of population of L4 and L5 are found, at the level of
minor bodies orbiting Saturn’s moons
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Basic concepts of celestial mechanics �derived from the study of the Solar System
• Hill radius– Radius within which the gravity of one object dominates
that of other bodies within the system– For a planet with mass Mp in a circular orbit of radius ap
around a central star with mass M*, the Hill radius is
– This expression can be derived as a special case of the calculation of L1 and L2 for Mp << M*
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Basic concepts of celestial mechanics �derived from the study of the Solar System
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Planet definition for extrasolar systems• The definition of planet adopted for the Solar System cannot be
fully applied to extrasolar planetary systems– We can test whether its mass is below the deuterium burning
limit (M~13 MJ), but we cannot experimentally determine whether the exoplanet has cleared its orbit
• Orbiting sub-stellar objects are referred as planets is their mass is less than ~13 MJ
• Attempts to formulate a precise definition of a planet face a number of difficulties– (Basri & Brown 2006, Ann. Rev. Earth Plan. Sci., 34, 193)
• A definition free of upper and lower mass limits is:– A planet is an end product of disk accretion around a primary
star of substar
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Planet definition for extrasolar systems
A simple metric has been proposed to determine whether a planet can clear its orbital zone during a characteristic time scale, t*,
such as the main-sequence life time of its central star (Margot 2015) The feeding zone must have a size C RH where RH is the Hill radius
From this, and requiring that the planet has cleared its orbit in a time scale less than the age of the planetary system, the following expression can be derived
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Test of the clearing mass algorithm in the Solar System Margot (2015)
Planet definition for extrasolar systems
The top two lines show clearing to 5 Hill radii in
either 10 billion years (dashed line) or 4.6 billion
years (dotted line)
The solid line shows clearing of the feeding
zone (2 √3 Hill radii) in 10 billion years
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Application of the clearing mass algorithm to Kepler exoplanetst*=t* (M*) stellar age (Margot 2015)
Planet definition for extrasolar systems
Extrasolar planetary systems �Generalization of planetary orbits to the case of binary stars
• Solar System planets orbit a single star• Many stars occur in binary or multiple star systems
– Nearby G-K dwarfs, for example, are known to occur more often in binary or multiple systems than they do in isolation
• Many young binaries are known to possess disks, either around one of the star (circumstellar disk) or surrounding both stars (circumbinary disk) which, in analogy to single stars, may provide the accretion material necessary for planet formation
• The presence of one or more planets around a binary or multiple star system is limited by considerations of dynamical stability
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Stable planetary orbits around binary stars
Several types of stable orbits around binary stars are possible in principle
• S-type orbits– The planet lies in a circumstellar orbit, i.e. orbiting either the
primary or the secondary star
• P-type orbits– The planet lies in a circumbinary orbit, i.e. orbiting both stars
• L-type orbits– The planet lies in a 1:1 “Trojan” resonance around L4 or L5
Lagrange points
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P-type orbits
• P-type orbits– The planet lies in a circumbinary
orbit, i.e. orbiting both stars– Numerical simulations indicate
that the P-type planetary orbit is stable for semimajor axes exceeding a critical value
Only wide P-type orbits are stable
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S-type orbits
• S-type orbits– The planet orbits either the primary or
the secondary star– The gravitational force of the secondary
induces orbital perturbationsThe perturbative effect varies with the companion star mass and according to the eccentricity and semimajor axis of the binary which together determine the closest approach of the planet to the secondary
– Simulations indicate that the S-type planetary orbit is stable for semimajor axes below a critical value
Stable S-type orbits must be close to the planet’s central star
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S-type orbits
Kozai resonance in S-type orbits– Numerical simulations of
S-type binaries indicate that, if the planet’s orbit is significantly inclined, the planet and the secondary star exchange angular momentum
– As a result, the planet undergoes a Kozai resonance, with an oscillation of its inclination and eccentricity
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Detection methods of exoplanets
• Direct methods– Direct imaging of the planet
• Indirect methods– Mostly based on effects induced on the host star
Gravitational perturbation of the stellar motionVariations of the stellar luminosity
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Exoplanet detection methods
Detection of exoplanets:�Geometric configuration of the observation
We call i the angle between the orbital spin and the line of sight (i.e., the angle between the orbital plane and the plane of the sky)
i= 0o � face on i=90o � edge on
With this convention, the velocity vector of the motion of the central star in the orbital plane is projected along the line of sight with a factor sin i
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Detection of exoplanets:�Derivation of the orbital period and semi-major axis
– We use the third Kepler’s law
– We assume that the planet mass is negligible compared to the mass of the central star: mp<< M*
– We estimate the mass of the central star, M*, from a spectroscopic study of the star and models of stellar evolution
– In most cases we obtain a measurement of the orbital period, P using indirect methods. We then use the third Kepler’s law to estimate the semimajor axis, a
– If the detection method provides a direct measurement of the semimajor axis, a, we use the third Kepler’s law to estimate the orbital period, P
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Detection of exoplanets:�Indirect methods: temporal baseline of the observations
• Temporal baseline of the observations with indirect methods
– The orbital period P is measured from the time variability of a stellar signal that bears signatures of the presence of a planetDifferent types of signal can be employed:stellar pulses, spectroscopy, photometry or angular position of the star
– In order to measure P (and to derive a from the third Kepler’s law), the star should be observed over a temporal baseline covering at least a few orbital periods
– This leads to an observational selection bias: planets with short orbital periods will require a shorter temporal baseline of observations
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– The orbital periods of the Solar System planets show that a temporal baseline in the order of tens of years would be required to prove the existence of periodicity for planets with a � 5 AU
• This observational bias affects all indirect methods of exoplanet detection and favours the discovery of planets with short orbital periods, very close to the host star - This is (one of the reasons) why most
detected exoplanets have orbital period of a few days and a � 0.1 AU
Detection of exoplanets:�Indirect methods: temporal baseline of the observations
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Planet naming, catalogs
• Planets around star X are denoted as X b, c, … in alphabetic order according to the discovery sequence, rather than according to the semi-major axis, which would demand constant revision as additional planets are discovered around the same star
• Exoplanets catalogs– www.exoplanet.eu
Extrasolar planet encyclopediaReference catalog and bibliography
– www.exoplanets.orgExoplanet Orbit Database (Jones et al. 2008)
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Histogram of number of exoplanet detections versus
