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radius
density
0.01R
400 R
10-6 g/cm3
106 g/cm3
mass
100 M
0.07M
uses ~20,000 stars
Mass - Luminosity Relation
Stellar Evolution
Models ObservationsRadius
Mass
L
T
Pressure
Density
Composition
H-R Diagram
[B-V, Mv]
Evolution always faster for larger mass
Stars pile up where times are long
Basic Stellar Structure Equations:
1) Eqtn of State: PT P1/V~ PT 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 = 4r2(r)
4) Luminosity gradient (in thermal equilibrium): L(r)/r = 4r2(r)(,T, comp) where T
5) T gradient: T(r)/r = -3(r)L(r)/16acr2T(r)3 where T-3.5 (opacity is bound-free, free-free, e- scattering)
R
T=6000K
=3x10-8 g/cm3
0.5R
T=3x106
=10.1R
T=15x106
=100g/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 ObservationGiant Molecular Clouds
10-100pc, 100,000M
T<100K
Radio
Collapse trigger:
SNcloud-cloud collisionsdensity wave
O and B stars form
winds
smaller mass stars
IR
Herbig-Haro,
T Tauri
Star Cluster NGC 2264
Minimum mass for collapse (Jean’s Mass)
MJ ~ (5kT/GmH)3/2 (3/4o)1/2
or MJ ~ 3kTR/GmH
Minimum radius:
RJ ~ (15kT/4GmH o)1/2
or RJ ~ GmHM/3kT
Cloud fragments & collapses if M>MJ, R>RJ
Free-fall time = (3/32Go)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
Big question: Is it universal?
(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)
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
convective
radiative
105 yrs
107 yrs
106 yrs
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]
• Mass = 10 - 80 MJup [0. 01 - 0. 08Msun][brown dwarf]
• Mass < 10MJup[< 0.01Msun][planets]
Lifetime on Main Sequence = 1010 M/L
Gravity balance pressure
Middle Age - stable stars
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 yrsE loss rate 4 x 1033 ergs/s
test with neutrinos37Cl + 37Ar + e- for E > 0.81 MeV71Ga + 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 + energy4.0132 4.0026 (m=0.05 x 10-24g
E = mc2 = 0.05 x 10-24g (9 x 1020cm2/s2) = 4 x 10-5 ergs
1H + 1H 2H + e+ + 1H + 1H 2H + e+ +
2H + 1H 3He +
3He + 3He 4He + 2 1H
3He + 3He 7Be +
7Be + e- 7Li + 7Be + 1H 8B +
7Li + 1H 4He + 4He 8B 8Be + e+ +
8Be 4He + 4He
99.8% 0.25%
91%
9%ppI
ppII
ppIII
0.43 MeV 1.44 MeV
0.1%
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 massHe or C,O corePlanetary nebulaRemnant < 1.4 Msun
White Dwarf
High massFe coreSupernovaRemant < 3Msun > 3Msun
Neutron star Black Hole
Size ~ Earth ~15 km 0
Density(g/cm3) 106 1014 infinity
MagField(G) 104-108 1012 ?
Rotation minutes <sec <<sec
Pressure e- degeneracy neutron degeneracy none
Low Mass Death - a White Dwarf
degeneracyPauli 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 liftedwhen 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
hydro-equil
P M2/R4
M/R3
M2/R4 M5/3/ R5
M1/3 1/R
R 1/M1/3
1175 WDs from SDSS
WDs from SDSS
massive single stars
a (WD binary, b,c 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
density=1014g/cm3
mass < 3M
R ~ 10 km
B ~ 1012G
pulse 1-1000/sec
found in radio 1967
LGM
pulsting neutron star
rotating neutron star
Black Body = thermal (Planck Function)
Synchrotron = non-thermal (relativistic)
c = eB/2me
Wavelength
Flux
Black Holes (R=0, = )
escape velocity = (2GM/R)1/2
for light, v = c
c= (2GM/R)1/2
c2 = 2GM/R
for object in orbit around mass M at distance 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
2) strong X-ray emission
Kepler’s Law M1+M2=P(K1+K2) 3/4Gsin3i ~ 20M
spectral type M1 shows M1 ~ 10M
M2 ~ 10M but invisible
1036-38 ergs/s
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