The Family of Stars Chapter 8:

Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of: LuminosityversusTemperature (or spectral type) Luminosity Temperature Spectral type: O B A F G K M Hertzsprung-Russell Diagram or Absolute mag.

The Hertzsprung Russell Diagram Most stars are found along the Main Sequence

The Hertzsprung-Russell Diagram Stars spend most of their active life time on the Main Sequence. Same temperature, but much brighter than MS stars → Must be much larger → Giant Stars Same temp., but fainter → Dwarfs

Radii of Stars in the Hertzsprung- Russell Diagram 10,000 times the sun’s radius 100 times the sun’s radius As large as the sun 100 times smaller than the sun Rigel Betelgeuze Sun Polaris

Luminosity Classes Ia Bright Supergiants Ib: Supergiants II: Bright Giants III: Giants IV: Subgiants V: Main- Sequence Stars Ia Ib II III IV V

Luminosity effects on the width of spectral lines Same spectral type, but different luminosity Lower gravity near the surfaces of giants  smaller pressure  smaller effect of pressure broadening  narrower lines

Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass If we can measure and understand their orbital motion, we can estimate the stellar masses.

The Center of Mass center of mass = balance point of the system Both masses equal => center of mass is in the middle, r A = r B. The more unequal the masses are, the more it shifts toward the more massive star.

Estimating Stellar Masses Recall Kepler’s 3. Law: P y 2 = a AU 3 Valid for the Solar system: star with 1 solar mass in the center We find almost the same law for binary stars with masses M A and M B different from 1 solar mass: M A + M B = a AU 3 ____ Py2Py2 (M A and M B in units of solar masses)

Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.

Spectroscopic Binaries Usually, the binary separation a can not be measured directly because the stars are too close to each other. A limit on the separation and thus the masses can be inferred in the most common case: Spectroscopic Binaries

Spectroscopic Binaries The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum. Doppler shift → Measurement of radial velocities → Estimate of separation a → Estimate of masses

Spectroscopic Binaries Time Typical sequence of spectra from a spectroscopic binary system

Eclipsing Binaries Usually, the inclination angle of binary systems is unknown → uncertainty in mass estimates. Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on!

Eclipsing Binaries Peculiar “double-dip” light curve Example: VW Cephei

Eclipsing Binaries From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane. Example: Algol in the constellation of Perseus

The Mass-Luminosity Relation More massive stars are more luminous. L ~ M 3.5

Masses of Stars in the Hertzsprung- Russell Diagram Masses in units of solar masses Low masses High masses Mass The higher a star’s mass, the more luminous (brighter) it is: High-mass stars have much shorter lives than low-mass stars: Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr. L ~ M 3.5 t life ~ M -2.5

Surveys of Stars Ideal situation: Determine properties of all stars within a certain volume Problem: Fainter stars are hard to observe; we might be biased towards the more luminous stars.

A Census of the Stars Faint, red dwarfs (low mass) are the most common stars. Giants and supergiants are extremely rare. Bright, hot, blue main- sequence stars (high- mass) are very rare.