Stars + Galaxies: Back of the Envelope Properties. David Spergel

Transcription

1 Stars + Galaxies: Back of the Envelope Properties David Spergel

2 Free-fall time (1) r = GM r 2 (2) r t = GM 2 r 2 (3) t free fall r3 GM 1 Gρ Free-fall time for neutron star is milliseconds (characteristic timescale for gravitational waves) Free-fall time for the Sun is 10 3 s (characteristic timescale for gravitational waves) Characteristic time for universe = Hubble Time

3 Cosmology (ȧ a ) 2 = 8π 3 Gρ t 2 Gρ

4 Kelvin-Helmholtz Time Time scale to radiate gravitational energy U = GM 2 /R t = GM 2 /RL 30 million years for the Sun Timescale for proto-star evolution

5 Einstein Time Time scale to radiate gravitational energy U = Mc 2 t = Mc 2 /L years for the Sun

6 Nuclear Energy U = Mc 2 t = Mc 2 /L Helium burning is 7 MeV nucleon Sun doesn t use all of the available fuel Lifetime ~ 1010 years Timescale

7 Nuclear Burning R = f(v)σ(v)dv v 2 exp ( m nv 2 ) S(E) 2kT E exp ( Z1 Z 2 e 2 ) hv

8 Stellar Structure Hydrostatic Equilibrium: Mass Conservation: Thermal Conduction: Equation of State: Energy Production:

9 Hydrostatic Equilibrium dp dr = GM(r) ρ R 2 Using ρ M /R 3, this implies p R = GM R 2 M R 3 = GM 2 R 5 Using ideal gas law, p = ρkt/µ, kt = GMµ R

10 Mass-Luminosity Relation dt dr = l(r) 3 κρ 4πr 2 16 σ B T 3 Using ρ M /R 3, this implies L = R 2T 3 ρ T R L M 3

11 Mass Luminosity Relation

12 Stellar Lifetimes t = ɛmc2 L t M 2 Massive Stars live short brilliant lives!

13 Stellar Populations Mass function: dn dm M 2.35 The lowest mass stars dominate the mass of a stellar population L(t) = Mmax (t) 0 M 2.35 L(M)dM = M 2.15 max(t) t 1.07 The most massive stars dominate the luminosity of a population

14 Radii and Temperature R M 0.9 L T 4 R 2 T L M R0.5

15 Spiral Arms

16 Later Stages of Stellar Evolution Red Giant Branch (RGB) Degenerate Core of Helium Envelope burning Hydrogen Helium Flash Horizontal Branch Core burning of Helium to Carbon Asymptotic Giant Branch (AGB) Degenerate Core of Carbon Envelope burning Helium

17 Fuel Consumption Thereom The contribution by any Post Main Sequence evolutionary phase to the total luminosity of a simple stellar population is proportional to the amount of nuclear fuel burned in that phase t HB t MS = L MS L HB U HB U MS L MS L HB E He C E H He

18 Degeneracy Pressure As a star burns H -> He, it leaves behind a degenerate gas supported by electron degeneracy pressure Nuclear burning cycles are alternated by period of rapid gravitational collapse Chandrasekhar Mass (maximum mass supported by degeneracy pressure) (followed by flashes)

19 Chandrasekhar Mass E G = GM 2 R When the electrons become relativistic, their total Fermi energy is approximately, ( ) E F = Ncp F = Nc = N 4/3 c x R = M 4/3 c m 4/3 p R Equating the two: ( ) 3/2 c 1 M ch = = M Pl 3 G m 2 p m 2 p

20 HR Diagram

21 Globular Cluster HR Diagram

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23 Stellar Models MESA (Paxton et al. 2011, ApJS, 192, 3) mesa.sourceforge.net Can stably evolve stars through Helium flash, RGB and HB to White Dwarf

24 Dust and Gas Stars form in Molecular Clouds These clouds contain copious amounts of dust that absorb starlight (in the optical, UV and near IR) and reemit in the IR Dust grains are micron size and composed primarily of carbon and silicates

25 Dust Emission Electric Dipole Limit (Size << λ) σ abs λ 2 F ν ν 2 B ν (T ) ν 4

26 Galaxy Spectrum

27 Other Emission Processes Radio: Free-free emission Synchrotron emission Radio emission scales with synchrotron

28 X-ray UV VIS Near IR Mid IR Far IR Radio M81 D=3 Mpc

29 Galaxy Properties David Spergel

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31 Tinker et al. 2008

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33 Blanton et al Gyr burst

34 4000 Angstrom Break

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36 Kauffmann et al. 2003

37 Galaxy Morphology

38 Spiral Galaxies Two parameter family: Luminosity and Surface Brightness Exponential distribution of stars Tully-Fisher Sanders and Verheijen 1998

39 Spiral Galaxy Formation Tidal torque generates solid body rotation in gas Gas cools and collapses to form a disk conserving angular momentum

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41 Elliptical Galaxies R e effective radius I e mean surface brightness within eff. radius σ0 velocity dispersion log Dn = log Re log Ie

42 Black Hole Scaling Relation Gultekin et al. 2009