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Astronomy 110: SURVEY OF ASTRONOMY 9. Properties of Stars 1. Distances & other parameters 2. The Hertzsprung-Russell diagram 3. Star clusters & stellar evolution
Astronomy 110: SURVEY OF ASTRONOMY
9. Properties of Stars
1. Distances & other parameters
2. The Hertzsprung-Russell diagram
3. Star clusters & stellar evolution
Distance measurements are critical to understanding stellar properties. Stars span an enormous range of luminosity, temperature, and size, and these parameters are profoundly related to each other. Studying clusters of stars born at the same time provides clues to the lives of stars.
1. DISTANCES & OTHER PARAMETERS
a. The Scale of the Solar System
b. How Far to the Stars?
c. Luminosity and Brightness
The Scale of the Solar System
Kepler and later astronomers made good scale models of the Solar System, but they didn’t know its true size.
S
Planet a (AU) P (yr)Mercury 0.387 0.241Venus 0.723 0.615Earth 1.000 1.000Mars 1.524 1.881
Jupiter 5.203 11.857Saturn 9.537 29.424
To find the value of one AU, a measurement of the actual distance (in km) to any planet would suffice.
Parallax Method: Theory
P
D
Observe P from points 1, 2 separated by baseline, b.
2
1
to distant star
θ
Suppose that from point 1 the planet lines up with a distant star, while from point 2 the angle between the planet and star is θ.
θb
Parallax Method: Theory
P
D
θ
How many triangles?
N = θ360°
Circumference C of big circle?
Radius of big circle?
C ≃ θ360° b
D ≃ θ360°b2π
1 That’s the distance to P!
C b
θ
The Distance to Mars
On October 1, 1672, Mars lined up with a bright star:
Wikipedia: Giovanni Cassini
Mars was then 0.43 AU from Earth. Cassini used the known distance between the two observing points and the measured parallax angle to find this distance in km:
DMars ≃ 6.0×107 km ⇒ 1 AU ≃ 1.38×108 km
Cayenne (South America)Paris (Europe)
Measuring the AU
1. Transits of Venus: 1761, 1769, 1874, 1882
2. Observations of Mars: 1877
3. Observations of Eros: 1930
4. Radar measurements: 1958 and since
— inconclusive due to effects of atmosphere
1 AU = 1.49×108 km
1 AU = 1.4960×108 km
1 AU = 1.49597871×108 km
How Far to the Stars?
JuneDec
We need a much larger baseline to measure stellar distances! The Earth’s orbit gives a baseline of
b = 2 AU
Stellar Parallax
Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the Sun.
Parallax of a Nearby Star
Stellar Parallax
Over the course of a year, nearby stars seem to move in small ovals as a result of Earth’s motion about the Sun.
2p Dec JuneD ≃ p
360°AU2π1
p
D
AU
Parallax Calculations
The parallax angle p is half the total shift:
Stars are far away, so p is measured in arc-sec (1˝ = 1°/3600).
Define a new distance unit, the parsec (pc):
1 pc = 360 × 3600AU = 3.09×1013 km2π⇒ D ≃ p
1˝ pc
1. Suppose star B is twice as far away as star A.
A. Star B has 4 times the parallax angle of star A.B. Star B has 2 times the parallax angle of star A.C. Both stars have the same parallax angle.D. Star A has 2 times the parallax angle of star B.E. Star A has 4 times the parallax angle of star B.
2. If we could measure stellar parallaxes from Mars instead of Earth, would nearby stars move in ovals which are
A. the same size as seen from Earth, because the stars are just about as far from Mars.
B. larger than seen from Earth, because Mars has a larger orbit.
C. smaller than seen from Earth, because Mars is a smaller planet.
Nearest Known Stars
Wikipedia: Nearest stars
Most too dim to see without a telescope!
1.32 pc = 4.3 ly
2.63 pc = 8.6 ly
3.22 pc = 10.5 ly3.50 pc = 11.4 ly
3.65 pc = 11.9 ly
3.62 pc = 11.8 ly
3.50 pc = 11.4 ly
A Stellar Distance Scale
1. Distances on Earth are determined by surveying techniques.
2. Parallax measurements at two points on Earth yield distances to other planets (now checked by radar).
3. These distances set the scale for the Solar System, and fix our distance to the Sun: 1 AU = 1.496×108 km.
4. Parallax measurements at two (or more) points on Earth’s orbit yield distances to nearby stars.
At each step, known distances are used to find unknown distances.
3. Suppose we found an error in our calculation of the AU, and the correct value was 10% larger. How would this change our values for stellar distances?
A. Stellar distances would be unchanged.B. Stellar distances would increase by 10%.C. Stellar distances would decrease by 10%.
Luminosity and Brightness
Absolute Luminosity (L) is the energy a star radiates per unit time.
L⊙ = 3.8×1026 watt
Apparent Brightness (B) is the energy received per unit time and unit area.
B⊙ = 1366 watt / m2
Brightness: Inverse-Square Law
Energy conservation implies that the same luminosity passes through each sphere.
Sphere of radius D has area
A = 4πD2
B = LAL
4πD2=
Thus, brightness is inversely proportional to (distance)2:
The Sun and αCen Compared
B⊙ = 1366 watt / m2
Bα = 2.8×10-8 watt / m2
αCen appears much fainter: αCen is much further away:
Dα = 1.32 pc = 4.1×1016 m
D⊙ = 1 AU = 1.49×1011 m
What about their luminosities?
Lα = Bα (4πDα2) = 5.9×1026 watt
L⊙ = B⊙ (4πD⊙2) = 3.8×1026 watt
αCen is about 50% more luminous than the Sun!
4. How would αCen’s apparent brightness change if it was 3 times further away?
A. It would be 1/3 as bright.B. It would be 1/6 as bright.C. It would be 1/9 as bright.D. It would appear the same.E. It would be 3 times as bright.
Neighbors of the Sun
A few nearby stars are more luminous than the Sun, butmost are much less luminous; of the 150 nearest stars:
From (L⊙) To (L⊙) Number of Stars
Examples
10 100 4 Vega: 50 L⊙1 10 14 αCen: 1.5 L⊙
0.1 1 25 τCet: 0.46 L⊙0.01 0.1 21
0.001 0.01 57
0.0001 0.001 29
DISTANCES & OTHER PARAMETERS: REVIEW
D ≃ θ360°b2π
1
1. Parallax equation: (a) number of triangles, (b) circumference of circle, (c) radius of circle.
2. Brightness and luminosity:
— brightness is what we observe; it has units of energy per unit time per unit area.
— luminosity is what a star puts out; it has units of energy per unit time.
P
D
θb
2. THE HERTZSPRUNG-RUSSELL DIAGRAM
a. Interpreting Stellar Spectra
b. The Main Sequence
c. Beyond the Main Sequence
SWEEPS ACS/WFC Color Composite
Stars have different luminosities and colors.
— luminous stars may be red or blue
— dim stars are generally red
Types of Spectra: ReviewBlack Body Spectrum
Black-Body (Thermal) Radiation
Any opaque object (black body) with a temperature T > 0 K emits light (radiation). As the temperature goes up, this light gets brighter and bluer.
Relationship Between Temperature and Luminosity
Properties of Thermal Radiation
• Higher temperature ⇒ more light at all wavelengths
• Higher temperature ⇒ peak shifts towards blue
Types of Spectra: ReviewBlack Body Spectrum
Black Body + Absorption Spectrum
Emission Spectrum
Spectral Lines: Review
Each electron orbit has a definite energy level.
To jump from orbit to orbit takes a photon with exactly the right amount of energy. n = 2 10.2 eV
n = 3 12.1 eV
n = 4 12.8 eV
n = ∞ 13.6 eV
n = 5 13.1 eV
n = 6 13.2 eV
656 nm
1.9 eV486 nm
2.6 eV 434 nm
2.9 eV
In hydrogen, orbit n has energy1n2En = 1 - ( )× 13.6 eV
where an eV is an energy unit.
Stellar Spectra
Black Body + Absorption Spectrum
In stars, the lower photosphere produces a black-body spectrum, while cooler gas above creates dark lines.
Stars exhibit a tremendous variety of spectra — why?
Text
Stellar Spectra
Interpreting Stellar Spectra
Stars have different spectra almost entirely because they have different surface temperatures!
Composition plays a minor role — almost all stars are mostly hydrogen and helium, just like the Sun.
Stellar Spectra and Temperatures
O
B
A
F
G
K
M
Hydrogen
Ionized Calcium
SodiumTitanium Oxide
Titanium Oxide
T > 30000 K
T ~ 20000 K
T ~ 9000 K
T ~ 6800 K
T ~ 5500 K
T ~ 4200 K
T < 3500 K
Old
Bread
And
Fruit
Get
Kinda
Moldy
Spectral Types
Hydrogen
Ionized Calcium
SodiumTitanium Oxide
Titanium Oxide
T > 30000 K
T ~ 20000 K
T ~ 9000 K
T ~ 6800 K
T ~ 5500 K
T ~ 4200 K
T < 3500 K
Spectral Types
Most H atoms at n = 2 level.
Most H atoms are ionized.
Most H atoms at n = 1 level.
Plotting the HR Diagram
The HR diagram shows surface temperature on the horizontal axis and luminosity on the vertical axis.
The Main Sequence
Most stars in the Sun’s neighborhood fall along a roughly diagonal line on an HR diagram.
This line is called the main sequence.
Nature of the Main Sequence
All main-sequence stars produce energy in the same way as the Sun, by fusing hydrogen to form helium in their cores.
A star’s place along the main sequence is fixed by its mass.
Measuring Stellar Masses: Review
For any two masses M and m orbiting each other, Newton’s version of Kepler’s Law III states:
P2
a3 G(M + m)4π2
=
This provides a way of ‘weighing’ stars — we observe a pair of stars orbiting each other (a double-star) and solve this equation to get their masses.
Wikipedia: Kepler’s Laws
M
m
Stellar Lifetimes Along the Main Sequence
The main sequence is also a sequence of life-times.
High-mass stars must have hotter cores to balance gravity, so they use up hydrogen faster.
The Main Sequence: Summary
Mass is the key property of a main-sequence star: other basic properties are all determined by mass.
Low Mass High Mass
low luminosity
low temperature
long lifetime
high luminosity
high temperature
short lifetime
Giants and Supergiants
Some stars are not part of the main sequence; they are relatively cool but very luminous.
These stars must have enormous radii to give off so much energy.
Other stars are hot but very dim.
These stars must have tiny radii to give off so little energy.
White Dwarfs
Stellar Radii
THE H-R DIAGRAM: SUMMARY
c. Beyond the Main Sequence
a. Interpreting Stellar Spectra
b. The Main Sequence
— spectra differ mostly because of temperature.
— on the main sequence, stars are arranged by mass.
— giants and dwarfs have very different radii.
Main Sequence Lifetimes
• 1 M⊙ star: L = L⊙— lifetime: T⊙ ≈ 1010 yr
• 10 M⊙ star: L ≈ 104 L⊙10 × fuel; use at 104 × rate
⇒ T ≈ (10/104) T⊙ ≈ 107 yr
• 0.1 M⊙ star: L ≈ 0.003 L⊙0.1 × fuel; use at 0.003 × rate
⇒ T ≈ (0.1/0.003) T⊙ ≈ 3×1011 yr
3. STAR CLUSTERS & STELLAR EVOLUTION
a. Nature of Star Clusters
b. Cluster HR Diagrams
c. Cluster Distances
Open clusters Globular clusters
Nature of Star Clusters
Two Types of Clusters
2. Open Clusters
1. Globular Clusters
— young, ‘metal’-rich stars
— contain 100 to 104 stars
— found in disk of Milky Way
— old, ‘metal’-poor stars
— contain 105 to 106 stars
— found in halo of Milky Way
Cluster Formation
Star Cluster R136 Bursts Out
Star clusters form in massive interstellar gas clouds.
— rapid formation ⇒ stars have similar ages
— cloud well-mixed ⇒ stars have similar composition
Clusters are held together by mutual gravity of stars.
High-mass cluster stars tend to form pairs and eject smaller stars. This eventually disrupts open clusters.
Star Cluster Dynamics
Simulated Star Cluster
Cluster HR Diagrams
The Pleiades (M45)All the stars in a cluster have the same age, so HR diagrams for cluster stars tell us about:
• cluster ages
• stellar evolution
• cluster distances
Evolution of HR Diagrams
So as a cluster ages, the main sequence ‘burns down’ in order.
lifetime: 107 yr
lifetime: 108 yr
lifetime: 109 yr
lifetime: 1010 yr
High-mass stars burn out first; low-mass stars die later.
(Note: this animation also shows stars after they leave the main sequence.)
Using the H-R Diagram to Determine the Age of a Star Cluster
Evolution of HR Diagrams
So as a cluster ages, the main sequence ‘burns down’ in order.
High-mass stars burn out first; low-mass stars die later.
Instead of plotting stars, we represent them with a line of constant age.
Using the H-R Diagram to Determine the Age of a Star Cluster
The Pleiades: A Young Cluster
Pleiades and Stardust
Using the H-R Diagram to Determine the Age of a Star Cluster
Star Cluster Messier 67
M67: An Older Cluster
Using the H-R Diagram to Determine the Age of a Star Cluster
Cluster HR Diagrams Compared
Globular Cluster M4
Clusters have a range of ages; giant and dwarf stars appear at different stages of cluster aging process.
Cluster Distances
106
All stars in a cluster are at the same distance.
Plot apparent brightness instead of luminosity.
30001000030000
surface temperature
106
105
104
103
102
10
1
0.1
10-2
10-3
10-4
10-5
appa
rent
bri
ghtn
ess
Pleiades
Hyades
Main seq. in Hyades appears ~9 × brighter than in Pleiades; why?
Pleiades are ~3 × more distant than Hyades!
A Cluster Distance Scale
1. Parallax measurements at two (or more) points on Earth’s orbit yield distances to nearby stars.
2. Nearby stars are used to measure luminosity of main sequence.
3. Main sequence luminosity is used to get distance to Hyades & Pleiades (also checked by parallax).
4. Improved main sequence luminosities yield distances to other clusters throughout galaxy (and beyond!).
At each step, known distances are used to find unknown distances.
