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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: 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 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 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: 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) 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: 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 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: 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) 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/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) 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/2me 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 /2Gsin3i ~ 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