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100 M
mass
400 R
10-6 g/cm3
density
radius
0.01R
106 g/cm3
0.07M
uses ~20,000
stars
Mass - Luminosity Relation
Stellar Evolution
Models
Radius
Mass
Observations
H-R Diagram
L
[B-V, Mv]
T
Stars pile up where
times are long
Pressure
Density
Composition
Evolution always
faster for larger mass
Basic Stellar Structure Equations:
1) Eqtn of State: PT P1/V~ PT so
P=(k/H)T where 1/ = 2X + (3/4)Y + (1/2)Z with
radiative P: P = (k/H)T + (a/3)T4
2) Hydrostatic Equilibrium: P(r)/r = -GM(r)(r)/r2
3) Mass continuity: M(r)/r = 4r2(r)
4) Luminosity gradient (in thermal equilibrium):
L(r)/r = 4r2(r)(,T, comp) where T
5) T gradient: T(r)/r = -3(r)L(r)/16acr2T(r)3
where  T-3.5 (opacity is bound-free, free-free, e- scattering)
0.1R
T=15x106
=100g/cm3
0.5R
T=3x106
=1
R
T=6000K
=3x10-8 g/cm3
Stellar Life Cycle
1. Birth [Molecular Clouds, T Tauri stars]
2. Middle Age [Main sequence, H>He fusion]
3. Giant-Supergiant [Shell burning, high z fusion]
4. Death [low mass-planetary nebula>white dwarf]
[high mass- Supernova>pulsar, black hole]
Theory
Observation
Giant Molecular Clouds
10-100pc, 100,000M
Radio
T<100K
Collapse trigger:
SN
cloud-cloud collisions
density wave
O and B stars form
IR
winds
smaller mass stars
Herbig-Haro,
T Tauri
Star Cluster NGC 2264
Minimum mass for collapse (Jean’s Mass)
MJ ~ (5kT/GmH)3/2 (3/4o)1/2
or MJ ~ 3kTR/GmH
Minimum radius:
RJ ~ (15kT/4GmH o)1/2
or RJ ~ GmHM/3kT
Cloud fragments & collapses if M>MJ, R>RJ
Free-fall time = (3/32Go)1/2
for T~150K, n~108/cm3, ~2x10-16 g/cm3
tff ~ 4700 yr
Dense, cold regions can support only small masses (so collapse),
while warm, diffuse regions can support larger masses (stable)
Unfortunately, no good quantitative theory to predict star
formation rate or stellar mass distribution !
IMF = Initial Mass Function
 (log m) = dN/d log m  m-
N is number of stars in logarithmic mass
range log m + d log m
= 1.35 Salpeter slope (logarithmic)
in linear units (m)= dN/dm  m- 
where  =  + 1 (= 2.35 Salpeter)
Big question: Is it universal?
Birth Sequence
• trigger [SN, cloud-cloud, density wave]
• cloud fragments and collapses [Jeans mass and radius]
• early collapse isothermal - E radiated away
• interior becomes adiabatic[no heat transfer] - E trapped so T rises
• protostellar core forms [~ 5 AU] with free-falling gas above
• dust vaporizes as T increases
• convective period
• radiative period
• nuclear fusion begins [starts zero-age main sequence]
Pre–Main-Sequence Evolutionary
Tracks
Hiyashi
tracks
105 yrs
106 yrs
radiative
107 yrs
convective
Middle Age - stable stars
Gravity balance pressure
Main sequence [stage of hydrostatic equilibrium]
• Mass >1.5 Msun [CNO cycle, convective core, radiative envelope]
• Mass = 0. 4 - 1.5Msun[p-p cycle, radiative core, convective envelope]
• Mass = 0. 08 - 0. 4Msun[p-p cycle, all convective interior]
Lifetime on Main Sequence = 1010 M/L
• Mass = 10 - 80 MJup [0. 01 - 0. 08Msun][brown dwarf]
• Mass < 10MJup[< 0.01Msun][planets]
Energy in sun (stars)
L = 4 x 1033 ergs/s
solar constant
Age = 4.6 billion yrs (1.4 x 1017 secs
Total E = 6 x 1050 ergs
fusion is only source capable of this energy
mass with T > 10 million
E=1. 3 x 1051 ergs
lifetime = E available = 1. 3 x 1051 ergs ~ 3 x 1017s ~ 10 billion yrs
E loss rate
4 x 1033 ergs/s
test with neutrinos
37Cl + 
37Ar + e- for E > 0.81 MeV
71Ga + 
71Ge + e- for E > 0.23 MeV
1)
p + p  np + e+ + 
2)
np + p  npp + 
3)
npp + npp  npnp + p + p
4H  1 He + energy
4.0132  4.0026 (m=0.05 x 10-24g
E = mc2 = 0.05 x 10-24g (9 x 1020cm2/s2) = 4 x 10-5 ergs
0.43 MeV
1H
+ 1H  2H + e+ + 
1H
99.8%
+ 1H  2H + e+ + 
1.44
MeV
0.25%
2H
+ 1H  3He + 
91%
ppI
3He
+ 3He 4He + 2 1H
3He
9%
+ 3He 7Be + 
0.1%
7Be
7Li
+ e-  7Li + 
+ 1H  4He + 4He
ppII
7Be
+ 1H  8 B + 
8B
 8Be + e+ + 
8Be
 4He + 4He
ppIII
High vs Low mass stars have different fusion
reactions and different physical structure
M > 1.5 M CNO cycle; convective core and radiative envelope
M < 1.5 M p-p cycle; radiative core and convective envelope
M < 0.4 M p-p cycle; entire star is convective
M < 0.7 M H fusion never begins
Giant-Supergiant Stage
• H fusion stops - core contracts and heats up
• H shell burning starts - outer layers expand
• core T reaches 100 million K - He flash, He fusion starts
• high mass - multiple shell and fusion stages
• C to O, O to Ne, Ne to Si, Si to Fe
• Fusion stops at Fe
Post–Main-Sequence Evolution
He-C fusion : Triple Alpha
4He
+ 4He  8Be + 
8Be
+ 4He  12C + 
3He  1C
energy = 1.17 x 10-5 ergs
H-R Diagram of a Globular Cluster
Clusters of Different Ages
Main-sequence fitting for cluster distances
1. Use CCD to get b, v images of cluster stars
2. Plot color-mag diagram of v vs b-v
3. Find main sequence turnoff & lower MS stars
4. For the SAME B-V on lower MS, read mv from
cluster and Mv from H-R diagram
5. Use distance modulus m-M to calculate d
Stellar Death
Low mass
He or C,O core
Planetary nebula
Remnant < 1.4 Msun
White Dwarf
Size
~ Earth
High mass
Fe core
Supernova
Remant < 3Msun
Neutron star
> 3Msun
Black Hole
~15 km
Density(g/cm3) 106
1014
MagField(G) 104-108
1012
Rotation
minutes
<sec
Pressure
e- degeneracy
neutron degeneracy
0
infinity
?
<<sec
none
Low Mass Death - a White Dwarf
degeneracy
Pauli exclusion principle: no 2 electrons can be in the same
state (position & momentum)
as T increases, more states available P  T
at high density, collisions restricted P  
if all states full, gas is degenerate
as star contracts,  increases so becomes degenerate
as T increases, degeneracy is lifted
when He - C fusion starts, core is degenerate
He flash removes degeneracy
WDs are totally degenerate
up to 1. 4 M degeneracy pressure stops the collapse
White Dwarf M-R Relation
P  5/3
  M/R3
hydro-equil
P  M2/R4
M2/R4  M5/3/ R5
M1/3  1/R
R  1/M1/3
1175 WDs from SDSS
WDs from SDSS
a (WD binary, b,c massive
single stars)
massive single
stars
Type I - no H, found in all galaxies
Type II - H, only in spiral arms (massive stars)
Famous Supernovae
Naked eye in Milky Way:
1054 Crab
1572 Tycho
1604 Kepler
In LMC
SN 1987a Feb 1987 neutrino burst seen
We are overdue ~ 1/20 yrs/galaxy
Neutron stars=pulsars
found in radio 1967
density=1014g/cm3
mass < 3M
R ~ 10 km
B ~ 1012G
pulse 1-1000/sec
LGM
pulsting neutron star
rotating neutron star
Black Body = thermal (Planck Function)
Synchrotron = non-thermal (relativistic)
c = eB/2me
Flux
Wavelength
Black Holes (R=0,  = )
for object in orbit around mass M at distance R:
escape velocity = (2GM/R)1/2
for light, v = c
c= (2GM/R)1/2
c2 = 2GM/R
Rs = 2GM/c2 Schwarzschild radius
Rs is event horizon
1M Rs = 3km, 10M Rs = 30km, 150kg Rs = 10-23cm
Earth has Newtonian Physics; BHs have Relativistic Physics
if you ride into a BH  you go in
if you watch someone ride in  they stay at Rs
Proof of Black Hole:
1) Single-lined spectroscopic binary
Kepler’s Law M1+M2=P(K1+K2) 3/4Gsin3i ~ 20M
spectral type M1 shows M1 ~ 10M
M2 ~ 10M but invisible
2) strong X-ray emission
1036-38 ergs/s