Stars + Galaxies: Back of the Envelope Properties David Spergel - - PowerPoint PPT Presentation

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Stars + Galaxies: Back of the Envelope Properties David Spergel - - PowerPoint PPT Presentation

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Stars + Galaxies: Back of the Envelope Properties David Spergel Free-fall time r = GM (1) r 2 t 2 = GM r (2) r 2 r 3 1 (3) t free fall G GM Free-fall time for neutron star is milliseconds (char- acteristic

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SLIDE 1

Stars + Galaxies: Back of the Envelope Properties

David Spergel

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SLIDE 2

Free-fall time

(1) ¨ r = −GM r2 (2) r t2 = −GM r2 (3) tfree−fall ≃ r3 GM ≃ 1 √Gρ Free-fall time for neutron star is milliseconds (char- acteristic timescale for gravitational waves) Free-fall time for the Sun is 103s (characteristic timescale for gravitational waves)

Characteristic time for universe = Hubble Time

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Cosmology

˙ a a 2 = 8π 3 Gρ t−2 ∝ Gρ

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Kelvin-Helmholtz Time

  • Time scale to radiate gravitational energy

U = GM2/R t = GM2/RL 30 million years for the Sun Timescale for proto-star evolution

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SLIDE 5

Einstein Time

  • Time scale to radiate gravitational energy

U = Mc2 t = Mc2/L 1013 years for the Sun

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SLIDE 6

Nuclear Energy Timescale

  • Helium burning is 7 MeV

nucleon

  • Sun doesn’t use all of the

available fuel

  • Lifetime ~ 1010 years

U = εMc2 t = εMc2/L

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SLIDE 7

Nuclear Burning

R =

  • f(v)σ(v)dv

∝

  • v2 exp
  • −mnv2

2kT S(E) E exp Z1Z2e2 hv

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SLIDE 8

Stellar Structure

  • Hydrostatic Equilibrium:
  • Mass Conservation:
  • Thermal Conduction:
  • Equation of State:
  • Energy Production:
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SLIDE 9

Hydrostatic Equilibrium

dp dR = −GM(r) R2 ρ Using ¯ ρ ≃ M∗/R3

∗, this implies

p∗ R∗ = GM∗ R2

∗

M∗R3

∗ = GM 2 ∗

R5

∗

Using ideal gas law, p = ρkT/µ, kT = GMµ R

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SLIDE 10

Mass-Luminosity Relation

dT dR = − l(r) 4πr2 3 16 κρ σBT 3 Using ¯ ρ ≃ M∗/R3

∗, this implies

L = R2T 3

∗

ρ T∗ R∗ L ∝ M 3

∗

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SLIDE 11

Mass Luminosity Relation

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SLIDE 12

Stellar Lifetimes

t = ǫMc2 L t ∝ M −2 Massive Stars live short brilliant lives!

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Stellar Populations

Mass function: dn dM ∝ M −2.35 The lowest mass stars dominate the mass of a stel- lar population L(t) = Mmax(t) M −2.35L(M)dM = M 2.15

max(t) ∝ t−1.07

The most massive stars dominate the luminosity

  • f a population
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SLIDE 14

Radii and Temperature

R ∝ M 0.9 L ∝ T 4R2 T ∝ L0.25 R0.5 ∝ M 0.4

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Spiral Arms

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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
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SLIDE 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

tHB tMS = LMS LHB UHB UMS ≃ LMS LHB EHe→C EH→He

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SLIDE 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)

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SLIDE 19

Chandrasekhar Mass

EG = −GM 2 R When the electrons become relativistic, their total Fermi energy is approximately, EF = NcpF = Nc ∆x

  • = N 4/3c

R = M 4/3c m4/3

p R

Equating the two: Mch = c G 3/2 1 m2

p

= M 3

Pl

m2

p

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SLIDE 20

HR Diagram

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SLIDE 21

Globular Cluster HR Diagram

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SLIDE 22
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SLIDE 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

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SLIDE 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

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Dust Emission

  • Electric Dipole Limit (Size << λ)

σabs ∝ λ−2 Fν ∝ ν2Bν(T) ∝ ν4

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SLIDE 26

Galaxy Spectrum

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SLIDE 27

Other Emission Processes

  • Radio:
  • Free-free emission
  • Synchrotron emission
  • Radio emission scales with synchrotron
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SLIDE 28

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

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SLIDE 29

Galaxy Properties

David Spergel

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SLIDE 30
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SLIDE 31

Tinker et al. 2008

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SLIDE 32
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SLIDE 33

Blanton et al. 2002 4 Gyr burst

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4000 Angstrom Break

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SLIDE 35
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SLIDE 36

Kauffmann et al. 2003

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SLIDE 37

Galaxy Morphology

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Spiral Galaxies

Sanders and Verheijen 1998

  • Two parameter

family: Luminosity and Surface Brightness

  • Exponential

distribution of stars

  • Tully-Fisher
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SLIDE 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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SLIDE 40
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Elliptical Galaxies

  • Re effective radius
  • Ie mean surface brightness

within eff. radius

  • σ0 velocity dispersion

log Dn = log Re + 0.8 log Ie

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Black Hole Scaling Relation

Gultekin et al. 2009