The Spectra of Stars and Binary Stars (Masses and Radii)

The Spectra of Stars and Binary Stars (Masses and Radii)

Colors of Stars Stars are made of hot, dense gas Con$nuous spectrum from the lowest visible layers ( photosphere ). Approximates a blackbody spectrum. From Wien s Law, we expect: hojer stars appear BLUE (T=10,000 50,000 K) middle stars appear YELLOW (T~6000K) cool stars appear RED (T~3000K)

Spectra of Stars Hot, dense lower photosphere of a star is surrounded by thinner (but szll fairly hot) atmosphere. Produces an Absorp$on Line spectrum. Lines come from the elements in the stellar atmosphere.

Spectral ClassificaZon of Stars Astronomers nozced that stellar spectra showed many similarizes. Can stars be classified by their spectra? Draper Survey at Harvard (1886 1897): ObjecZve Prism Photography obtained spectra of >100,000 stars hired women as computers to analyze spectra

ObjecZve Prism Spectra

Harvard ClassificaZon Edward Pickering s first ajempt at a systemazc spectral classificazon: Sort by Hydrogen absorpzon line strength Spectral Type A = strongest Hydrogen lines followed by types B, C, D, etc. (weaker) Problem: Other lines followed no discernible pajerns.

Edward Pickering Harvard Computers (c. 1900)

Annie Jump Cannon Leader of Pickering s computers, she nozced subtle pajerns among metal lines. Re arranged Pickering s ABC spectral types, throwing out most as redundant. Lef 7 primary and 3 secondary classes: O B A F G K M (R N S) Unifying factor: Temperature

Annie Jump Cannon

The Spectral Sequence O B A F G K M L T Hotter Cooler 50,000K 2000K Bluer Redder Spectral Sequence is a Temperature Sequence

Spectral Types

The Spectral Sequence is a Temperature Sequence Gross differences among the spectral types are due to differences in Temperature. ComposiZon differences are minor at best. Why? Demonstrated by Cecilia Payne Gaposhkin in 1920 s What lines you see depends on the state of excita$on and ioniza$on of the gas.

Example: Hydrogen Lines Visible Hydrogen absorpzon lines come from the second excited state. B Stars (15 30,000 K): Most of H is ionized, so only very weak H lines. A Stars (10,000 K): Ideal excitazon condizons, strongest H lines. G Stars (6000 K): Too cool, lijle excited H, so only weak H lines.

O Stars HoJest Stars: T>30,000 K Strong lines of He + No lines of H

B Stars T=15,000 30,000 K Strong lines of He Very weak lines of H

A Stars T = 10,000 7500 K Strong lines of H Weak lines of Ca+

F Stars T = 7500 6000 K weaker lines of H Ca + lines growing stronger first weak metal lines appear

G Stars T = 6000 5000 K Strong lines of Ca +, Fe +, & other metals much weaker H lines The Sun is a G type Star

K Stars Cool Stars: T = 5000 3500 K Strongest metal lines H lines praczcally gone first weak CH & CN molecular bands

M Stars Very cool stars: T = 2000 3500 K Strong molecular bands (especially TiO) No lines of H

L & T Stars Coolest stars: T < 2000 K Discovered in 1999 Strong molecular bands Metal hydride (CrH & FeH) Methane (CH4) in T stars Probably not stars at all

Modern Synthesis: The M K System An understanding of atomic physics and bejer techniques permit finer disznczons. Morgan Keenan (M K) ClassificaZon System: Start with Harvard classes: O B A F G K M L T Subdivide each class into numbered subclasses: A0 A1 A2 A3... A9

Examples: The Sun: G2 star Other Bright Stars: Betelgeuse: M2 star (Orion) Rigel: B8 star (Orion) Sirius: A1 star (Canis Major) Aldebaran: K5 star (Taurus)

Binary Stars Apparent Binaries Chance projeczon of two disznct stars along the line of sight. Ofen at very different distances. True Binary Stars: A pair of stars bound by gravity. Orbit each other about their center of mass. Between 20% and 80% of all stars are binaries.

Types of Binaries Visual Binary: Can see both stars & follow their orbits over Zme. Spectroscopic Binary: Cannot separate the two stars, but see their orbit mozons as Doppler shifs in their spectra. Eclipsing Binary: Cannot separate stars, but see the total brightness drop when they periodically eclipse each other.

Visual Binary 1890 1940 1990

Center of Mass Two stars orbit about their center of mass: a 2 a 1 M 2 M a 1 Measure semi-major axis, a, from projected orbit and the distance. Relative positions give: M 1 / M 2 = a 2 / a 1

Measuring Masses Newton s Form of Kepler s Third Law: Measure Period, P, by following the orbit. Measure semi major axis, a, and mass RaZo (M 1 /M 2 ) from projected orbit.

Problems We need to follow the orbits long enough to trace them out in detail. This can take decades. Need to work out the projeczon on the sky. Everything depends crizcally on the distance: semi major axis depends on d derived mass depends on d 3!!

Spectroscopic Binaries Most binaries are too far away to see both stars separately. But, you can detect their orbital mozons by the periodic Doppler shics of their spectral lines. Determine the orbit period & size from velocizes.

B A B A B A A B

Problems Cannot see the two stars separately: Semi major axis must be guessed from orbit Can t tell how the orbit is Zlted on the sky Everything depends crizcally on knowing the distance.

Eclipsing Binaries Two stars orbizng nearly edge on. See a periodic drop in brightness as one star eclipses the other. Combine with spectra which measure orbital speeds. With the best data, one can find the masses without having to know the distance!

Eclipsing Binary 3 4 2 1 Brightness 1 2 3 4 Time

Problems Eclipsing Binaries are very rare Orbital plane must line up just right Measurement of the eclipse light curves complicated by details: ParZal eclipses yield less accurate numbers. Atmospheres of the stars sofen edges. Close binaries can be Zdally distorted.

Stellar Masses Masses are known for only ~200 stars. Range: ~0.1 to 50 Solar Masses Stellar masses can only be measured for binary stars.

Stellar Radii Very difficult to measure because stars are so far away. Methods: Eclipsing binaries (need distance) Interferometry (single stars) Lunar OccultaZon (single stars) Radii are only measured for about 500 stars

Summary: Color of a star depends on its Temperature Red Stars are Cooler Blue Stars are HoJer Spectral ClassificaZon Classify stars by their spectral lines Spectral differences mostly due to Temperature Spectral Sequence (Temperature Sequence) O B A F G K M L T

Types of Binary Stars Visual Spectroscopic Eclipsing Summary: Only way to measure stellar masses: Only ~150 stars Radii are measured for very few stars.

QuesZons: What does the temperature of a star mean? Are there stars with temperatures higher than 50000K? Are hojer stars brighter than cooler stars? Are they more luminous? Why did it take so long to find L & T stars?

QuesZons What star do we know the mass of very precisely? Why is it so unlikely that binaries are in eclipsing systems? Most binaries are seen as spectroscopic. Why? How can we know the sizes of more stars than masses?