STAR FORMATION In honor of Yakov B. Zeldovich June 20, 2014 Moscow Chris McKee The Zeldovich Box AGE Committees Teaching Research Learning Percent Time Spent Fortunately, Rashid is still a young man! The Problem of Star Formation Stars form at a rate of about 1 Msun/yr in the Galaxy The Problem of Star Formation Stars form at a rate of about 1 Msun/yr in the Galaxy Stars have masses in the range: < 0.075 Msun: Brown dwarfs > 100 Msun: Stars > 8 Msun explode as supernovae or collapse into black holes How can interstellar gas with a density measured in particles cm-3 collapse into stars with densities measured in g cm-3 ? Gravitational Collapse from Dimensional Analysis--1 Characteristic timescale set by self-gravity: d2R dt2 Free-fall time: ~ t2 R GM ~ t2 R2 R3 GM ~ 1 Gr tff = (3p/32Gr)1/2 = 1.4 x 105 (105 cm-3/n)1/2 yr Gravitational Collapse from Dimensional Analysis--2 Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass cs2 P/r ~ GM/R M ~ Rcs2/G Radius: R ~ cstff ~ cs/(Gr)1/2 Mass ~ Rcs2/G ~ cs3tff/G ~ cs3/(G3r)1/2 Bonnor-Ebert mass = maximum mass of stable isothermal sphere: MBE = 1.18 cthermal3 /(G3r)1/2 Necessary condition for star formation: M > MBE Gravitational Collapse from Dimensional Analysis--3 Characteristic accretion rate: · m* ~ mBE / tff ~ cs3/(G3r)1/2 (Gr)1/2 ~ cs3/G For a singular isothermal sphere (Shu 1977): · m* = 0.975 cs3 / G = 1.5 x 10-6 (T/ 10 K)3/2 Msun yr-1 An isothermal gas at 10 K takes 6.5 x 105 yr to form a 1 Msun star 6.5 x 107 yr to form a 100 Msun star >> age of star (~ 3 Myr) need better theory for formation of massive stars OUTLINE Star formation problems of interest to Zeldovich: I. Star Formation in Filaments in the Turbulent Interstellar Medium II. Radiation Hydrodynamics of Massive Star Formation III. The Formation of the First Stars I. Star Formation in Filaments in the Turbulent Interstellar Medium This paper introduced the eigenvectors of gravitational collapse The initial collapse is into a Zeldovich pancake, but these then collapse into filaments Dust emission from molecular filaments observed by the Herschel satellite Light blue lines trace filaments identified by an algorithm (Andre+ 2014) Filaments form naturally in a turbulent medium Simulation box 4.5 pc in size with finest resolution 0.002 pc Isothermal gas with Mach number M=10, magnetized w. Alfven Mach # MA=1 Temperature T=10 K, density n ~ 2 x 104 cm-3 (P.-S. Li + 2014) Zoom-in shows star formation in the main filament: T = 10 - 44 K, n ~ 104 cm-3 (P.-S. Li+ 2014) Star cluster formation in magnetized 1000 Msun clump with outflows and radiation (A. Myers+ 14) Initial conditions: Self-consistent MHD turbulence w. Msonic=11, MA= 0.8 Temperature Column density Magnetic fields reduce star formation rate and fragmentation by factor ~ 2 Strong filamentary structure in star formation Filamentary structures observed in star-forming regions arise due to gravitational instability in sheets (Miyama+ 87), a natural extension of Zeldovich’s model. Sheets are formed by strong shocks in supersonic turbulence. Supersonic Turbulence and the Initial Mass Function Probability distribution function for density in isothermal turbulence is lognormal: where x = ln ( ρ / <ρ> ), M= Mach number, and b = 1 for compressive driving, 1/3 for solenoidal driving Self-gravity leads to gravitational collapse of the densest structures, producing IMF With no gravity, density PDF is log normal After 0.42 free-fall times, self-gravity has created a high-density tail on the distribution: gas collapsing into stars (Kritsuk+ 2011) The initial mass function of stars (IMF) can be calculated theoretically from the distribution of masses in the log normal distribution that become unstable (Padoan & Nordlund, Hennebelle & Chabrier, Hopkins) Thus, a universal process—turbulence—appears to be responsible for the universal shape of the IMF (Elmegreen) II. Radiation Hydrodynamics of Massive Star Formation Stellar feedback greatly complicates star formation: –Radiation pressure drives dusty gas away –UV emission heats via photoelectric effect on dust –Ionizing luminosity creates ionized gas (~104 K) –Protostellar outflows carve cavities and inject kinetic energy THE FUNDAMENTAL PROBLEM IN MASSIVE STAR FORMATION: RADIATION PRESSURE Force per particle due to radiation flux F = L/4p r2: Force = F /c = L /4pr2c where here c = speed of light = cross section Eddington luminosity LE: radiative force balances gravity: LE /4pr2c = GM/r2 LE = 4pGMc/(/) (where = mass/particle) Typical infrared cross section per unit mass for dust in massive protostellar envelopes: / 5 cm2 g-1 LE = 4pGMc/(/) = 2500 (M/Msun) Lsun THE FUNDAMENTAL PROBLEM IN MASSIVE STAR FORMATION: RADIATION PRESSURE--II Massive stars are very luminous: L = 10 (M/Msun)3 Lsun for M ~ (7-20) Msun L ~ 106 Lsun for M = 100 Msun Predict growth of protostar stops when radiative force exceeds gravity: L = 10 (M/Msun)3 Lsun > LE = 2500 (M/Msun) Lsun Stars cannot grow past 16 Msun But stars are observed to exist with M > 100 Msun HOW IS THIS POSSIBLE? ADDRESSING THE PROBLEM OF RADIATION PRESSURE Effect of accretion disks Accreting gas has angular momentum and settles into a disk before accreting onto star Previous work has shown that disk shadow reduces the radiative force on the accreting gas (Nakano 1989; Jijina & Adams 1996; Yorke & Sonnhalter 2002) - Radiative Rayleigh-Taylor instabilities allow radiation to escape (Krumholz et al. 2009) Bipolar outflows from protostars channel radiation away from (Krumholz et al. 2005; Cunningham et al 2011) infalling gas 3D RADIATION HYDRODYNAMIC CALCULATIONS Radiative transfer: gray, mixed frame, flux-limited diffusion with AMR t r + rv = 0 (Mass) t rv + rvv = - P - r + (R/c)F (Momentum) t re + [(re+P)v] = - rv - P(4pB-cE) - (R/c) vF 2 = 4pGr (Energy) (Gravity) t E + F = P(4pB-cE) + (R/c) vF (Radiative energy) F0 = - [c(E0) / R] E0 (Flux limit) where e = 0.5 v2 + u = gas energy density, E = radiation energy density; F0 and E0 in comoving frame. Accurate to lowest relevant order in v/c. (Krumholz et al. 2007) RadiationHydrodynamic Simulation of Massive Star Formation Time 34000 yr (Krumholz+ 09) Radiation pressure created large, radiationdominated bubble shortly after t = 25000 yr. 25000 yr 41700 yr Radiative Rayleigh-Taylor instabilities occurred shortly after 34000 yr; at least 40% of the accretion onto the stars was due to this. Final stellar masses in binary: M = 42 Msun, 29 Msun 55900 yr Ongoing research: Does RT instability occur with more accurate treatment of stellar radiation? 3000 AU Effect of bipolar outflows on massive star formation: Create channels for the escape of radiation Bipolar outflows originally discovered from low-mass protostars Herbig-Haro objects • A clue: evidence for bipolar ejection of spinning jets. 1000 AU C. Burrows (STScI & ESA); J. Hester (Arizona St); J. Morse (STScI); NASA Bipolar outflows from low-mass protostars produced in rotating, magnetized disks Observation of magnetized jet from a high-mass protostar IRAS 18162-2048 L=17,000 Lsun M 10 Msun if dominated by one star 6 cm (contours) Synchrotron emission 850 m (gray scale) Thermal emission (Carrasco-Gonzalez et al. 2010) 0.25 pc 0.01 pc 0.01 pc Simulations of effects of outflows on massive star formation (Cunningham+ 2011) Results on outflows at t = 0.6 tff : Outflow reduces radiation pressure by allowing escape Outflow makes disk gas cooler more fragmentation (lower primary mass)) Results for =2 g cm-2 without winds ~ same as =10 g cm-2 with winds (Trapping of radiation increases with ) = 1 g cm-2 mpri ~20 Msun = 2 g cm-2 = 2 g cm-2 (no wind) = 10 g cm-2 Column density mpri ~20 Msun mpri ~35 Msun mpri ~35 Msun Temp. Conclusion on radiation pressure in massive star formation: Three effects—disks, radiative Rayleigh-Taylor instability and bipolar outflows—are important in overcoming radiation pressure Outflows allow radiation to escape, reducing importance of Rayleigh-Taylor instabilities III. The Formation of the First Stars JETP 16, 1395 (1963) Zeldovich’s theory before the discovery of the microwave background and inflation. Assumed fluctuations were statistical and universe cold Concluded galaxy formation possible only if stars created large-scale perturbations Kindly translated by Ildar Khabibullin Three discoveries since Zeldovich’s paper: 1) The CMB => the universe was hot, not cold, when it was much denser 2) Inflation: Quantum fluctuations magnified by inflation provided initial perturbations 3) Dark matter: Perturbations in dark matter grew during the radiationdominated era, avoiding diffusive damping (Silk damping) A key difference between first stars and contemporary stars: First stars formed in potential wells due to dark matter, not due to their own self gravity. (Although baryonic gravity dominates on scales < 1 pc) Key question: What was the mass of the first stars? M > 0.8 Msun since no stars have been observed that have no heavy elements Key question: What was the mass of the first stars? M > 0.8 Msun since no stars have been observed that have no heavy elements The mass of the star determines the nature and mass of heavy elements ejected (Heger & Woosley 2002) Initial conditions for gravitational collapse set by physics of H2 molecule This physics was of interest to Zeldovich: Density at which collisional and radiative de-excitation are in balance: ncrit ~ 104 cm-3 Minimum temperature set by spacing of energy levels, ~ 200 K Characteristic mass at which gravity balances thermal energy [Jeans mass ~ cthermal3 /(G3r)1/2] is ~ 500 Msun (Bromm, Coppi & Larson 2002) Mass of the first stars: Analytic theory (McKee & Tan 08): mass set by photoevaporation of accretion disk Isentropic collapse: entropy within factor 2 of best estimate => M* = 60 – 320 Msun Numerical simulation (Hirano+ 14): 3D cosmological simulations + 2D radiation-hydrodynamic simulations of individual stars Good general agreement between theory and simulation: First stars very massive Challenges in the Formation of the First Stars: Magnetic Fields High-resolution cosmological simulation of gravitational collapse Magnetic energy increases much faster with density than expected for uniform collapse (ρ4/3): Turbulent dynamo Initial field very weak (~10-14 G) and was not dynamically important at end of simulation (Turk+ 12) No stars formed in this simulation, and the effect of magnetic fields on the formation of the first stars is unknown Challenges in the Formation of the First Stars: Magnetic Fields But Zeldovich could have told us that magnetic fields could be important: Title: Magnetic fields in astrophysics Authors: Zeldovich, Ya. B. Publication: The Fluid Mechanics of Astrophysics and Geophysics, New York: Gordon and Breach, 1983 Keywords: ASTROPHYSICS, MAGNETIC FIELDS, DYNAMO THEORY HAPPY BIRTHDAY, YAKOV B.! AND THANK YOU, RASHID!