Measuring the Masses of Stars:

# Measuring the Masses of Stars:

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## Measuring the Masses of Stars:

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1. 0 Binary Stars Measuring the Masses of Stars: Please press “1” to test your transmitter.

2. 0 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.

3. 0 The Center of Mass center of mass = balance point of the system. Both masses equal => center of mass is in the middle, rA = rB. The more unequal the masses are, the more it shifts toward the more massive star.

4. Remember: What is Kepler’s 3rd law?(Py = orbital period in years; aAU = average distance in AU) • Py = aAU • Py2 = aAU • Py = aAU2 • Py2 = aAU3 • Py3 = aAU2

5. Estimating Stellar Masses RewriteKepler’s 3. Law as 1 = aAU3 / Py2 Valid for theSolar system: star with1 solar massin the center. We findalmost the same lawfor binary starswith massesMA and MBdifferent from 1 solar mass: aAU3 ____ MA + MB = Py2 (MA and MB in units of solar masses)

6. Examples: a) Binary system with period of P = 32 years and separation of a = 16 AU: 163 ____ MA + MB = = 4 solar masses. 322 b) Any binary system with a combination of period P and separation a that obeys Kepler’s 3. Law must have a total mass of 1 solar mass.

7. If we know that two stars are orbiting each other once every 5 years, at an average separation of 5 AU, and we know that one of the stars has a mass of 3 solar masses, what is the mass of the second star? • 1 solar mass. • 2 solar masses. • 3 solar masses. • 4 solar masses. • 5 solar masses. MA + MB = 53/52 = 5 MA + MB = 5 and MA = 3 => MB = 2

8. Spectroscopic Binaries Usually, binary separation a can not be measured directly because the stars are too close to each other. But a lower limit (i.e. smallest possible value) onthe masses can still be estimated in the most common case: Spectroscopic Binaries:

9. Spectroscopic Binaries Approaching Center of Mass A B Receding Assume the two stars A and B have the same absorption line in their spectra. They are so close to one another that we can only see them as one star, and we can only measure their combined spectrum. What will we see in the combined spectrum at the instant illustrated above? Flux l0 Wavelength l

10. What will we see in the spectrum? Approaching • We will see one line exactly at wavelength l0. • We will see a blue shifted line from star A and a red shifted line from star B. • We will see a red shifted line from star A and a blue shifted line from star B. • We will see no absorption line. • We will see an emission line at wavelength l0. Center of Mass A B Receding

11. 0 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

12. Masses of Stars in the Hertzsprung-Russell Diagram Masses in units of solar masses 40 18 High masses 6 The higher a star’s mass, the more luminous it is. 3 1.7 1.0 High-mass stars have much shorter lives than low-mass stars Mass 0.8 0.5 Sun: ~ 10 billion yr. Low masses 10 Msun: ~ 30 million yr. 0.1 Msun: ~ 3 trillion yr.

13. Masses of Stars in the Hertzsprung-Russell Diagram 40 18 What is the typical mass of the type of stars that show the strongest Balmer lines in their spectra? High masses 6 3 1.7 1.0 Mass 0.8 • 0.5 solar masses. • 1 solar mass. • 3 solar masses. • 10 solar masses. • 40 solar masses. 0.5 Low masses

14. Maximum Masses of Main-Sequence Stars Mmax ~ 100 solar masses a) More massive clouds fragment into smaller pieces during star formation. b) Very massive stars lose mass in strong stellar winds h Carinae Example: h Carinae: Binary system of a 60 Msun and 70 Msun star. Dramatic mass loss; major eruption in 1843 created double lobes.

15. Minimum Mass of Main-Sequence Stars: Mmin = 0.08 Msun At masses below 0.08 Msun, stellar progenitors do not get hot enouth to ignite thermonuclear fusion. Gliese 229B → Brown Dwarfs

16. Considering that brown dwarfs are much colder than main-sequence stars, in which wavelength band do you think they could be most easily observed? • Infrared. • Optical • Ultraviolet. • X-rays. • Gamma-rays.

17. Brown Dwarfs Hard to find because they are veryfaint and cool; emit mostly in theinfrared. Many have been detected instar forming regionslike theOrion Nebula.