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100 M
mass
400 R
10-6 g/cm3
density
radius
0.01R
106 g/cm3
0.07M
Location
depend on:
Mass
Age
Composition
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
0.5R
T=3x106
=1
R
T=6000K
=3x10-8 g/cm3
0.1R
T=15x106
=100g/cm3
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
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
0.1R
T=15x106
=100g/cm3
0.5R
T=3x106
=1
R
T=6000K
=3x10-8 g/cm3
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)
0.1R
T=15x106
=100g/cm3
0.5R
T=3x106
=1
R
T=6000K
=3x10-8 g/cm3
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
0.1R
T=15x106
=100g/cm3
0.5R
T=3x106
=1
R
T=6000K
=3x10-8 g/cm3
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
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
Birth Sequence
• trigger [SN, cloud-cloud, density wave]
• star formation “eats” its way into the cloud
Cone
nebula HST
Clusters dissolve into the
field in ~ 10 Myr
Star Cluster NGC 2264
Birth Sequence
•
trigger [SN, cloud-cloud, density wave]
• cloud fragments and collapses [Jeans mass and radius]
• free-fall [~4000 yr]
Jean’s instability:
Ugas = -1/2 Ω
(internal energy vs g potential E
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)
Star Formation
The dark region has
just developed a
Jeans instability.
The central gases are
heating as they fall into the
newly forming protostar.
Matthew Bate simulation of collapse and
fragmentation of 500 solar mass cloud to
produce a cluster of 183 stars and bds including
40 multiple systems
QuickTime™ and a
H.264 decompressor
are needed to see this picture.
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
outflow gives
P Cyg
profiles
XZ Tau
binary
HH-30
edge-on
Quick Time™ and a
GIF dec ompressor
are needed to s ee this pic ture.
no magnetic field
Disk accretes at ~10-7M /yr, disk ejects 1-10% in high velocity wind
strong magnetic field
Middle Age - stable stars
Gravity balances 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]
Mass - Luminosity Relation
M<0.7M; L/L=0.35(M/M)2.62
M> 0.7M; L/L=1.02 (M/M)3.92
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
+
71Ga + 
37Cl
37Ar
+ e- for E > 0.81 MeV
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 < 0.07 M H fusion never begins
CNO cycle
Mass - Luminosity Relation
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
He flash
Open Clusters: <1000
stars, < 10 pc diameter
A Globular Cluster
M10
Globular Clusters: 104-106 stars, 20-100 pc diameter
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 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]
Stellar Death
Low mass
He or C,O core
Planetary nebula
Remnant < 1.4 Msun
White Dwarf
Size
~ Earth
High mass
Fe core
Supernova
Remnant < 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
WDs have no fusion; cool at constant R
tracks from MS to WDs for different masses
high mass
low mass
R
black dwarfs
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
DB WDs
DZ WDs
Stellar Death
Low mass
He or C,O core
Planetary nebula
Remnant < 1.4 Msun
White Dwarf
Size
~ Earth
High mass
Fe core
Supernova
Remnant < 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
Supernovae
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)
Type Ia SN lc’s and spectra - obs and models
Famous Supernovae
Naked eye in Milky Way:
1054 Crab
1572 Tycho - type Ia
1604 Kepler - type Ia
In LMC
SN 1987a Feb 1987 neutrino burst seen
We are overdue ~ 1/20 yrs/galaxy
Stellar Death
Low mass
He or C,O core
Planetary nebula
Remnant < 1.4 Msun
White Dwarf
Size
~ Earth
High mass
Fe core
Supernova
Remnant < 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
Neutron stars=pulsars
found in radio 1967
density=1014g/cm3
mass < 3M
R ~ 10 km
B ~ 1012G
pulse 1-1000/sec
LGM
pulsating 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 /2Gsin3i ~ 20M
spectral type M1 shows M1 ~ 10M
M2 ~ 10M but invisible
2) strong X-ray emission
1036-38 ergs/s
Her X-1 in opt & X-ray
X-ray sources
Massive X-ray Binaries (MXRBs)
Name
P (days)
Vela X-1
9
Cen X-3
2.1
Cyg X-1
5.6
Sp
q
B0Ia 12
O7III 17
O9.7I 3
Mx
1.9
1
6
Low Mass X-ray Binaries (LMXRBs)
Name
P(hrs)
Sec
1626-67 0.7
WD
Cyg X-3 4.8
IR
Her X-1 40.8
B-F
Mx
1
long
E >1051ergs
short
Binary Evolution: Roche equipotential surfaces
rc /A = 0.38 + 0.2 log q [0.3 < q < 2]
rc /A = 0.46 (M1/M2 + M1)1/3 [0<q<0.3]
20M + 8M P=5 days
t = 1 million yrs
transfers 15M in 30,000yrs
5M + 23M P=11 days
P= 13 days t=10 million yrs
X-ray binary for 10,000 yrs
P = 4 hrs
Possible evolution for
first
common envelope
phase
novae common
envelope phases
Variable Stars
clues: timescale,
amplitude, light curve shape, spectrum
Eclipsing: Algol
B8-M
ß Lyr
W UMa
(hrs-days) B8-G3
Eruptive: single
binary
SNII 15-20 mag (yrs)
flare 1-6 mag (<hr) K-M
Pulsating: short P
Cepheids:F-K, 1-50d, 1.5mag
RR Lyr: A-F, 0.5 day, 1 mag
 Scuti: A-F, hrs, 0.02 mag
F0-K0 (hrs)
WD: SNI -20mag (yrs)
N -10mag (1000s yrs)
DN - 2-7 mag (weeks)
NL - erratic
Symbiotic: 3mag (erratic)
XRB: HMXRB, LMXRB
-ray Bursters
RS CVn: F,G+KIV, spots
long P
Mira:M, yrs, 1-5mag
S-R: K, M
odd
ß Ceph: B, 0.5d
ZZ Ceti: WD, min
Cataclysmic Variables
white dwarf primary with a low mass (G-M) secondary,
orbital periods of 67 min-2 days
Nova: TNR, high mass WD, outbursts 8-15
mag every few thousand yrs, ~20/yr in MW
Dwarf nova: disk instability, outbursts 2-7
mag every week-30 yrs
Novalike: high, low states on
timescales of months, high accretion
AM CVn: 2 white dwarfs, orbital
periods of 10-45 min
Disk
Intermediate Polar
Polar
MAGNETIC
ACCRETION
DISK ACCRETION
.
= 1/2GMM
For slowly rotating WD:
Ldisk = LBL
.
High M
wd/Rwd
.
Low M
108 K
X-rays
9000-40000 K
BL
Hard X-rays
Soft X-rays
Cyclotron
Typical DN
Outburst cycle
of the Dwarf
Nova SS Cyg
Cannizzo &
Mattei, 1998,
ApJ 505, 344
Outbursts
are DISK
instabilities
Typical CV
spectra in
DR1
CVs in EDR in
Szkody et al.
2002, AJ, 123,
430
Pulsating stars:
Asteroseismology
• Pulsations 
Only systematic
way to study
the stellar
interior
• Pulsations are
observed in stars
all over the HR
diagram
ZZ Ceti stars
Pulsations in a star
Pulsation period and amplitude depend on
the average density. P  1/2
Low density
long P, high amplitude
High density
short P, low amplitude
Density profile decides how deep the pulsations penetrate in the star.
(Deeper the penetration
more we learn about the interior)
Centrally condensed stars like our Sun have shallow pulsations
Uniform density stars like white dwarfs have deep pulsations
Cepheids and RR Lyrae
RR Lyrae: A giants, Mv = 0.5, P<1 day
Cepheids: F-G SG, P-L relation, HeII
ionization zone pulsation mechanism
P-L relation
1) measure mv with CCD
2) find P from light curve
3) use P-L to get Mv
4) m-M
d
•
White dwarfs show non-radial g-modes on account of their high gravity
Periods of 100s to 1000s
•
These modes are characterized by quantum numbers (k,l,m)
similar to atomic orbitals
Spherical gravitational potential  Spherical electrostatic potential
l determines the number of borders between hot and cool zones on the surface
m is the number of borders that pass through the pole of the rotation axis
k determines the number of times the pulsation wiggles from the center to the surface
Two flavors of ZZ Ceti stars (DAVs)
cool
Teff = 11000K
P ~ 1000s
Larger amp,
more modes,
unstable amps
hot
Teff = 12000K
P ~ 200s
Less modes,
more stability
Flare Stars
Flare <15s to 1 hr, repeats hrs - days
Amplitude up to 4 mag
Opt is thermal brem at T ~ 107K, radio is non-thermal
Between flares, spectrum is K-M with CaII, H emission