radius density 0.01R  400 R  g/cm g/cm 3 mass 100 M  0.07M 

Location depend on: Mass Age Composition

uses ~20,000 stars

Mass - Luminosity Relation

Stellar Evolution Models Observations Radius Mass L T Pressure Density Composition H-R Diagram [B-V, M v ] Evolution always faster for larger mass Stars pile up where times are long

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)T 4 R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

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)T 4 2) Hydrostatic Equilibrium:  P(r)/  r = -GM(r)  (r)/r 2 R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

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)T 4 2) Hydrostatic Equilibrium:  P(r)/  r = -GM(r)  (r)/r 2 3) Mass continuity:  M(r)/  r = 4  r 2  (r) R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

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)T 4 2) Hydrostatic Equilibrium:  P(r)/  r = -GM(r)  (r)/r 2 3) Mass continuity:  M(r)/  r = 4  r 2  (r) 4) Luminosity gradient (in thermal equilibrium):  L(r)/  r = 4  r 2  (r)  ( ,T, comp) where  T R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

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)T 4 2) Hydrostatic Equilibrium:  P(r)/  r = -GM(r)  (r)/r 2 3) Mass continuity:  M(r)/  r = 4  r 2  (r) 4) Luminosity gradient (in thermal equilibrium):  L(r)/  r = 4  r 2  (r)  ( ,T, comp) where  T 5) T gradient:  T(r)/  r = -3  (r)L(r)/16  acr 2 T(r) 3 where   T -3.5 ( opacity is bound-free, free-free, e - scattering ) R T=6000K  =3x10 -8 g/cm 3 0.5R T=3x10 6  =1 0.1R T=15x10 6  =100g/cm 3

Theory Observation Giant Molecular Clouds pc, 100,000M  T<100K Radio Collapse trigger: SN cloud-cloud collisions density wave O and B stars form winds smaller mass stars IR 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: U gas = -1/2 Ω (internal energy vs g potential E

Minimum mass for collapse (Jean’s Mass) M J ~ (5kT/G  m H ) 3/2 (3/4  o ) 1/2 or M J ~ 3kTR/G  m H Minimum radius: R J ~ (15kT/4  G  m H  o ) 1/2 or R J ~ G  m H M/3kT Cloud fragments & collapses if M>M J, R>R J Free-fall time = (3  /32G  o ) 1/2 for T~150K, n~10 8 /cm 3,  ~2x g/cm 3 t ff ~ 4700 yr Dense, cold regions can support only small masses (so collapse), while warm, diffuse regions can support larger masses (stable)

Star Formation The central gases are heating as they fall into the newly forming protostar. The dark region has just developed a Jeans instability.

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

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 10 5 yrs 10 7 yrs 10 6 yrs

outflow gives P Cyg profiles

XZ Tau binary HH-30 edge-on

no magnetic field Disk accretes at ~10 -7 M  /yr, disk ejects 1-10% in high velocity wind

strong magnetic field

Main sequence [stage of hydrostatic equilibrium] Mass >1.5 M sun [CNO cycle, convective core, radiative envelope] Mass = M sun [p-p cycle, radiative core, convective envelope] Mass = M sun [p-p cycle, all convective interior] Mass = M Jup [ M sun ][brown dwarf] Mass < 10M Jup [< 0.01M sun ][planets] Lifetime on Main Sequence = M/L Gravity balances pressure Middle Age - stable stars

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 ergs/s solar constant Age = 4.6 billion yrs (1.4 x secs) Total E = 6 x ergs fusion is only source capable of this energy mass with T > 10 million E=1. 3 x ergs lifetime = E available = 1. 3 x ergs ~ 3 x s ~ 10 billion yrs E loss rate 4 x ergs/s test with neutrinos 37 Cl + 37 Ar + e - for E > 0.81 MeV 71 Ga + 71 Ge + 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  (  m=0.05 x g) E = mc 2 = 0.05 x g (9 x cm 2 /s 2 ) = 4 x ergs

1 H + 1 H  2 H + e H + 1 H  3 He +  3 He + 3 He  4 He H 3 He + 3 He  7 Be +  7 Be + e -  7 Li + 7 Be + 1 H  8 B +  7 Li + 1 H  4 He + 4 He 8 B  8 Be + e Be  4 He + 4 He 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 < 0.07 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 4 He + 4 He  8 Be +  8 Be + 4 He  12 C +  3He  1C energy = 1.17 x ergs

He flash

Open Clusters: <1000 stars, < 10 pc diameter

A Globular Cluster M10 Globular Clusters: stars, 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 m v from cluster and M v 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 M sun White Dwarf High mass Fe core Supernova Remnant 3M sun Neutron star Black Hole Size ~ Earth ~15 km 0 Density (g/cm 3 ) infinity MagField (G) ? Rotation minutes <sec <<sec Pressure e - degeneracy neutron degeneracy none

tracks from MS to WDs for different masses R high mass low mass WDs have no fusion; cool at constant 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 hydro-equil P  M 2 /R 4   M/R 3 M 2 /R 4  M 5/3 / R 5 M 1/3  1/R R  1/M 1/3

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 M sun White Dwarf High mass Fe core Supernova Remnant 3M sun Neutron star Black Hole Size ~ Earth ~15 km 0 Density (g/cm 3 ) infinity MagField (G) ? Rotation minutes <sec <<sec Pressure e - degeneracy neutron degeneracy none

Supernovae

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)

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 M sun White Dwarf High mass Fe core Supernova Remnant 3M sun Neutron star Black Hole Size ~ Earth ~15 km 0 Density (g/cm 3 ) infinity MagField (G) ? Rotation minutes <sec <<sec Pressure e - degeneracy neutron degeneracy none

Neutron stars=pulsars density=10 14 g/cm 3 mass < 3M  R ~ 10 km B ~ G pulse /sec found in radio 1967 LGM pulsating neutron star rotating neutron star

Black Body = thermal (Planck Function) Synchrotron = non-thermal (relativistic) c = eB/2  m e Wavelength Flux

Black Holes (R=0,  =  ) escape velocity = (2GM/R) 1/2 for light, v = c c = (2GM/R) 1/2 c 2 = 2GM/R for object in orbit around mass M at distance R: R s = 2GM/c 2 Schwarzschild radius R s is event horizon 1M   R s = 3km, 10M   R s = 30km, 150kg  R s = cm

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 R s Proof of Black Hole: 1) Single-lined spectroscopic binary 2) strong X-ray emission Kepler’s Law M 1 +M 2 =P(K 1 +K 2 ) 3 /2  Gsin 3 i ~ 20M  spectral type M 1 shows M 1 ~ 10M  M 2 ~ 10M  but invisible ergs/s

Her X-1 in opt & X-ray

X-ray sources

Massive X-ray Binaries (MXRBs) Name P (days) Sp q M x Vela X-1 9 B0Ia Cen X O7III 17 1 Cyg X O9.7I 3 6 Low Mass X-ray Binaries (LMXRBs) Name P(hrs) Sec M x WD Cyg X IR Her X B-F 1

E >10 51 ergs long short

Binary Evolution: Roche equipotential surfaces r c /A = log q [0.3 < q < 2] r c /A = 0.46 (M 1 /M 2 + M 1 ) 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

common envelope Possible evolution for first phase novae common envelope phases

Variable Stars clues: timescale, amplitude, light curve shape, spectrum Eclipsing: Algol ß Lyr W UMa B8-M (hrs-days) B8-G3 F0-K0 (hrs) Eruptive: single binary SNII mag (yrs) flare 1-6 mag (<hr) K-M WD: SNI -20mag (yrs) N -10mag (1000s yrs) DN mag (weeks) NL - erratic Symbiotic: 3mag (erratic) XRB: HMXRB, LMXRB  -ray Bursters RS CVn: F,G+KIV, spots Pulsating: short P long P odd Cepheids:F-K, 1-50d, 1.5mag RR Lyr: A-F, 0.5 day, 1 mag  Scuti: A-F, hrs, 0.02 mag Mira:M, yrs, 1-5mag S-R: K, M 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 min

Disk Polar Intermediate Polar

DISK ACCRETION MAGNETIC High MLow M.. X-rays 10 8 K K ACCRETION BL For slowly rotating WD: L disk = L BL = 1/2GMM wd /R wd. Hard X-rays Soft X-rays Cyclotron

Outburst cycle of the Dwarf Nova SS Cyg Cannizzo & Mattei, 1998, ApJ 505, 344 Outbursts are DISK instabilities Typical DN

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 Cepheids: F-G SG, P-L relation, HeII ionization zone pulsation mechanism RR Lyrae: A giants, M v = 0.5, P<1 day

P-L relation 1) measure m v with CCD 2) find P from light curve 3) use P-L to get M v 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) T eff = 11000K P ~ 1000s T eff = 12000K P ~ 200s cool Larger amp, more modes, unstable amps hot 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 ~ 10 7 K, radio is non-thermal Between flares, spectrum is K-M with CaII, H emission