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Chapter 15 Surveying the Stars Properties of Stars
• Distances • Luminosities • Temperatures • Radii • Masses
Distance Use radar in Solar System, but stars are so far we use parallax: apparent shift of a nearby object against a background of more distant objects
Parallax and Distance
• Nearest star: Alpha Centauri at 1.3 parsecs
• Works well out to 200 parsecs (pc)
• The local 10 pc neighborhood (Adric Riedel, GSU): https://www.youtube.com/watch?v=up_MqNBv0FE
Luminosity Power radiated by star = surface area x rate/unit area = 4πR 2 x σ T 4
where R = radius T = temperature σ = Stefan-Boltzmann constant
Apparent brightness:
Amount of starlight that reaches Earth
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With increasing distance, luminosity is spread over a larger area
Area of sphere = 4π (distance)2
Divide luminosity by area to get brightness
Inverse-Square Law: brightness proportional to 1/distance2
Thought Question
How would the apparent brightness of Alpha Centauri change if it were three times farther away?
A. It would be only 1/3 as bright B. It would be only 1/6 as bright C. It would be only 1/9 as bright D. It would be three times brighter
Magnitude Scale
Magnitude Scale
Given apparent magnitude m and distance d, we can find absolute magnitude M = apparent magnitude if moved to d = 10 pc
m – M = 5 log d – 5
Sun: M = 5
Recall: log 1 = 0, log 10 = 1, log 100 = 2, …
Suppose star has absolute mag M = –5, d = 1000: What is apparent mag m?
m = – 5 + 5x3 – 5 = 5
Temperature: Thermal Radiation 1. Hotter objects emit more light per unit area at all
frequencies. 2. Hotter objects emit photons with a higher average
energy.
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The color of a star is indicative of its temperature (compare blue B and visual (yellow) V magnitudes)
Red stars are relatively cool, while blue ones are hotter.
Solid
Molecules
Neutral Gas
Ionized Gas (Plasma)
Temperature Level of ionization seen in spectral absorption lines; spectral classification
10 K
102 K
103 K
104 K
105 K
106 K
Pioneers of Spectral Classification
• Annie Jump Cannon and the “calculators” at Harvard laid the foundation of modern stellar classification
Temperature and Spectral Classification
Stellar spectra are much more informative than the blackbody curves.
There are seven (ten) general categories corresponding to different temperatures.
From highest to lowest, those categories are:
O B A F G K M (L T Y)
Oh, Be A Fine Girl/Guy, Kiss Me
Radii Angular radius and distance give radius. Most stars are pin-points, but we are starting to measure their sizes using interferometry; GSU CHARA Array at Mt Wilson – Regulus
0.0014 arcsec
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Stellar Radii from Eclipsing Binary Stars Duration of light dips related to size (radius)
Mass
Many stars are in binary pairs; measurement of their orbital motion allows determination of the masses of the stars.
Kepler’s Third Law:
(M1 + M2) P2 = a3
where M1 and M2 are the masses (MSUN), P is the period (years), and a is the separation or “semimajor axis” (AU)
Types of Binary Star Systems
• Visual Binary • Eclipsing Binary • Spectroscopic Binary
About half of all stars are in binary systems
Mass from Visual Binaries
Orbital motion can be measured directly
Kruger 60
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Mass from Spectroscopic Binaries: Motion detected by Doppler shifts
http://astrosun2.astro.cornell.edu/academics/courses/astro101/herter/java/binary/binary.htm
Masses from Eclipsing Binaries
Combine light curve and Doppler shift curve: + radii, temperatures, system inclination, masses
Temperature
Lum
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Hertzsprung-Russell diagram plots the luminosity and temperature of stars
Positions of stars in the HRD
Most stars occupy the main sequence where stars create energy by H fusion (like the Sun).
Higher mass stars have larger luminosities and shorter lives.
For given T, stars with higher L have larger radii: giants and supergiants.
Older stars where core H fusion done.
Large radius
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Small radius
For given T, stars with lower L have lower radii: white dwarfs.
Very old stars, all nuclear fusion complete.
Full spectral classification includes spectral type and luminosity class:
I - supergiant II - bright giant III - giant IV - subgiant V - main sequence
Examples: Sun - G2 V Sirius - A1 V Proxima Centauri - M5.5 V Betelgeuse - M2 I
Extending the Cosmic Distance Scale
We can estimate a star’s luminosity if we know its spectral type and luminosity class
Extending the Cosmic Distance Scale
Distance from “spectroscopic parallax”
1. Measure the star’s apparent magnitude m and spectral classification
2. Use spectral classification to estimate luminosity (absolute magnitude M) from HRD
3. Apply inverse-square law to find distance Magnitude version: m – M = 5 log d - 5
Extending the Cosmic Distance Scale
Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs:
Temperature
Lum
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H-R diagram depicts:
Temperature
Color
Spectral Type
Luminosity
Radius
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Temperature
Lum
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Which star is the hottest?
A
B C
D
Temperature
Lum
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Which star is the most luminous?
A
B C
D
Temperature
Lum
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Which star is a main-sequence star?
A
B C
D
Temperature
Lum
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Which star has the largest radius?
A
B C
D
Stellar Properties Review Luminosity: from brightness and distance
10-4 LSun - 106 LSun
Temperature: from color and spectral type
3,000 K - 50,000 K
Mass: from period (p) and average separation (a) of binary-star orbit
0.08 MSun - 100 MSun
Stellar Properties Review Luminosity: from brightness and distance
10-4 LSun - 106 LSun
Temperature: from color and spectral type
3,000 K - 50,000 K
Mass: from period (p) and average separation (a) of binary-star orbit
0.08 MSun - 100 MSun
(0.08 MSun) (100 MSun)
(100 MSun) (0.08 MSun)
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Lifetime
Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 billion years x 10 / 104 ~ 10 million years
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
10 billion years x 0.1 / 0.01 ~ 100 billion years
Until core hydrogen (10% of total) is used up
Main-Sequence Star Summary High Mass:
High Luminosity Short-Lived Large Radius Blue
Low Mass:
Low Luminosity Long-Lived Small Radius Red
Temperature
Lum
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Which star is most like our Sun?
A
B
C
D
Temperature
Lum
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Which of these stars will have changed the least 10 billion years from now?
A
B
C
D
Temperature
Lum
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Which of these stars can be no more than 10 million years old?
A
B
C
D
Star clusters: groups of same age stars
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Open cluster: A few thousand loosely packed stars (Pleiades) Globular cluster: Up to a million or more stars in a dense ball (M80)
Massive blue stars die first, followed by lower mass stars (white, yellow, orange, and red)
In HRD, stars die away first at the top end (massive stars) of main sequence.
Find cluster age by determining the turn-off point, the most massive stars still on main sequence.
Oldest globular clusters are 13 billion years old