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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

inos

ity

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

inos

ity

H-R diagram depicts:

Temperature

Color

Spectral Type

Luminosity

Radius

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Temperature

Lum

inos

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Which star is the hottest?

A

B C

D

Temperature

Lum

inos

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Which star is the most luminous?

A

B C

D

Temperature

Lum

inos

ity

Which star is a main-sequence star?

A

B C

D

Temperature

Lum

inos

ity

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

inos

ity

Which star is most like our Sun?

A

B

C

D

Temperature

Lum

inos

ity

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