Lines of Hydrogen. Most prominent lines in many astronomical objects: Balmer lines of hydrogen

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1

2 The Family of Stars

3 Lines of Hydrogen Most prominent lines in many astronomical objects: Balmer lines of hydrogen

4 The Balmer Thermometer Balmer line strength is sensitive to temperature: Most hydrogen atoms are ionized => weak Balmer lines Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n = 2 => weak Balmer lines

5 Measuring the Temperatures of Stars Comparing line strengths, we can measure a star s surface temperature!

6 Spectral Classification of Stars Different types of stars show different characteristic sets of absorption lines. Temperature

7 Spectral Classification of Stars Mnemonics to remember the spectral sequence: Oh Oh Only Be Boy, Bad A An Astronomers Fine F Forget Girl/Guy Grade Generally Kiss Kills Known Me Me Mnemonics

8 Surface temperature Stellar Spectra O B A F G K M

9 The Composition of Stars From the relative strength of absorption lines (carefully accounting for their temperature dependence), one can infer the composition of stars.

10 Infrared Spectra of Stars Major differences appear in the infrared spectra of cool stars (M stars T, L dwarfs)

11 The Size (Radius) of a Star We already know flux increases with surface temperature (~T 4 ); hotter stars are brighter. But brightness also increases with size: A B Star B will be brighter than star A. Absolute brightness is proportional to the surface area of the star, and thus its radius squared, L ~ R 2. Quantitatively: L = 4 R 2 T 4 Surface area of the star Surface flux due to a blackbody spectrum

12 Example: Polaris has just about the same spectral type (and thus surface temperature) as our Sun, but it is 10,000 times brighter than our Sun. Thus, Polaris is 100 times larger than the Sun. This causes its luminosity to be = 10,000 times more than our Sun s.

13 Organizing the Family of Stars: The Hertzsprung-Russell Diagram Absolute mag. or Luminosity We know: That 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: Luminosity versus Temperature (or spectral type) Hertzsprung-Russell Diagram Temperature Spectral type: O B A F G K M

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

15 The Hertzsprung-Russell Diagram Same temperature, but much brighter than MS stars Must be much larger Giant stars

16 Radii of Stars in the Hertzsprung-Russell Diagram Rigel Betelgeuse Polaris Sun 100 times smaller than the sun

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

18 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

19 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.

20 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 the center of mass shifts toward the more massive star.

21

22 Estimating Stellar Masses Recall Kepler s 3rd Law: P y2 = 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 P 2 y (M A and M B in units of solar masses)

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

24 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

25 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

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

27 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!

28 Eclipsing Binaries Example: Algol in the constellation of Perseus 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.

29

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

31 Masses of Stars in the Hertzsprung-Russell Diagram The higher a star s mass, the more luminous (brighter) it is: Masses in units of solar masses L ~ M 3.5 High-mass stars have much shorter lives than low-mass stars: t life ~ M -2.5 Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr.

32 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.

33

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

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