Stellar Masses and Luminosity

1. Stellar Masses and Luminosity • If we know the Spectral type of a star (i.e. its luminosity), and its temp, then we can determine its size from Stephan’s law: • L = Area of Star x temp4 x constant • This means that small hot stars can be MUCH brighter than larger cooler stars. • Since Temp is easily measured from the peak wavelength of the spectrum, we can immediately know the size of the star. • For Example, Deneb has a luminosity of 170,000 times the luminosity of the sun. Its spectral type is A2, which means its temp is about 10,000 Kelvin (remember the sun;s temp is 5800 kelvin). • This Makes the Area of Deneb about 40000 x the area of the sun, so its radius and diameter are about 200x the diameter of the sun.l Don’t worry..you won’t have do this math.. . So, is there any way we can find the mass of a star like Deneb?

2. Masses of Stars • Mass is the single most important property of any star. • at each stage of a star’s life, mass determines… • what its luminosity will be • what its spectral type will be • The mass of a star can only be measured directly by … • observing the effect which gravity from another object has on the star • This is most easily done for two stars which orbit one another…a binary star!

3. Binary Stars(two stars which orbit one another) • Optical doubles • two unrelated stars which are in the same area of the sky • Visual binaries • a binary which is spatially resolved, i.e. two stars are seen (e.g.Sirius)

4. Binary Stars • Spectroscopic binaries • a binary which is spatially unresolved, i.e only one star is seen; the existence of the second star is inferred from the Doppler shift of lines.

5. Binary Stars • Eclipsing binaries • a binary whose orbital plane lies along our line of sight, thus causing “dips” in the light curve.

6. Binary Stars • The stars orbit each other via gravity. • So the laws of Kepler & Newton apply! • Remember Newton’s version of Kepler’s Third Law: P2 = 42 a3 / G (m1 + m2) • If you can measure the orbital period of the binary (P) and the distance between the stars (a), then you can calculate the sum of the masses of both stars (m1 + m2).

7. The Hertzsprung-Russell Diagram • A very useful diagram for understanding stars • We plot two major properties of stars: • Temperature (x) vs. Luminosity (y) • Spectral Type (x) vs. Absolute Magnitude (y) • Stars tend to group into certain areas bright MV faint Spectral type hot cool

8. Here are the Stars of Orion. Betelguese: 1000 x the diameter of the sun. Temp = 3000K (burr!) The Orion Nebula—a star forming region! Rigel: 70,000x Lsun Temp = 10,000Kelvin. Whis the most Luminious? The Largest? Which isn’t a star at all?

9. BRIGHT HOT COOL FAINT

10. The Main Sequence (MS) 90% of all stars lie on the main sequence!

11. Stellar Luminosity • Review: The luminosity of a star depends on 2 things: • surface temperature • surface area (radius) • L =  T4 4  R2 • The stars have different sizes!! • The largest stars are in the upper right corner of the H-R Diagram. • Note that Absolute Magnitude is a measure of the Luminosity of the Star • Apparent visual Magnitude is a measure of the Apparent Brightness (or Intensity) of the starlight reaching the observer.

12. Regions of the H-R Diagram

13. Stellar Luminosity Classes

14. Stellar Masses on the H-R Diagram

15. Mass-Luminosity Relation We use binary stars to measure directly the masses of stars of every type. This leads to the: L  m3.5 for main sequence stars only • As one moves to the upper-left of the main sequence: • stars become more massive • stars become more luminous • stars become fewer in number

16. Mass–Luminosity Relation • All main sequence stars fuse H into He in their cores. • Luminosity depends directly on mass because: • more mass means more weight from the star’s outer layers • nuclear fusion rates must be higher in order to maintain gravitational equilibrium

17. Lifetime on the Main Sequence How long will it be before MS stars run out of fuel? i.e. Hydrogen? How much fuel is there? M How fast is it consumed? L  M3.5 How long before it is used up? Time = Amount/(rate it is being used) M/L = M/M3.5 = M-2.5

18. Lifetime on the Main Sequence • O & B Dwarfs burn fuel like a Hummer! • M Dwarfs burn fuel like a compact Hybrid (Prius! • Our Sun will last 1010 years on the Main Sequence. Let •  = (Lifetime of Sun)/(Lifetime of Star) • MS Lifetime  = 1010 yrs / M2.5

19. Lifetime on the Main Sequence So for example: 3.2 x 107 yr B2 dwarf (10 M) lasts F0 dwarf (2 M) lasts 1.8 x 109 yr M0 dwarf (.5 M) lasts 5.6 x 1010 yr But the Universe is 1.37 x 1010 yr old! Every M dwarf that was ever created is still on the main sequence!!

20. Another Rung on the distance ladder: Cepheid Variables She studied the light curves of variable stars in the Magellenic clouds. Assumption: all stars are at the Same distance Henrietta Leavitt (1868-1921)

21. Cepheid Variables The brightness of the stars varied in a regular pattern.

22. Cepheid Variables prototype:  Cephei F - G Bright Giants (II) whose pulsation periods (1-100 days) get longer with brightness (MV = -2 to -6) Distance Indicator!!

23. Cepheid Variables

24. The Instability Strip There appears to be an almost vertical region on the H-R Diagram where all stars within it (except on the Main Sequence) are variable. They pulsate due to partial ionization!