STAR FORMATION In honor of Yakov B. Zeldovich Moscow June 20, 2014 Chris McKee

Learning Teaching Research Committees The Zeldovich Box AGE Percent Time Spent Fortunately, Rashid is still a young man!

The Problem of Star Formation Stars form at a rate of about 1 M sun /yr in the Galaxy

The Problem of Star Formation Stars form at a rate of about 1 M sun /yr in the Galaxy Stars have masses in the range: < Msun: Brown dwarfs > 100 M sun : Stars > 8 M sun 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 ?

Characteristic timescale set by self-gravity: d2Rd2R dt 2 ~ R t2t2 ~ GM R2R2  t2 t2  R3R3 ~ 1 GG Free-fall time: t ff = (3  /32G    x 10 5 (10 5 cm -3 /n) 1/2 yr Gravitational Collapse from Dimensional Analysis--1

Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass c s 2  P/  GM/R  M ~ Rc s 2 /G Radius: R ~ c s t ff ~ c s /(G  ) 1/2  Mass ~ Rc s 2 /G ~ c s 3 t ff /G ~ c s 3 /(G 3  ) 1/2 Bonnor-Ebert mass = maximum mass of stable isothermal sphere: M BE = 1.18 c thermal 3 /(G 3  ) 1/2 Necessary condition for star formation: M > M BE Gravitational Collapse from Dimensional Analysis--2

Characteristic accretion rate: m*m* · ~ m BE / t ff ~ c s 3 /(G 3  ) 1/2  (G  ) 1/2 ~ c s 3 /G For a singular isothermal sphere (Shu 1977): m*m* · = c s 3 / G = 1.5 x (T/ 10 K) 3/2 M sun yr -1 An isothermal gas at 10 K takes 6.5 x 10 5 yr to form a 1 M sun star 6.5 x 10 7 yr to form a 100 M sun star >> age of star (~ 3 Myr) Gravitational Collapse from Dimensional Analysis--3  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 pc Isothermal gas with Mach number M=10, magnetized w. Alfven Mach # M A =1 Temperature T=10 K, density n ~ 2 x 10 4 cm -3 (P.-S. Li )

Zoom-in shows star formation in the main filament: (P.-S. Li+ 2014) T = K, n ~ 10 4 cm -3

Star cluster formation in magnetized 1000 M sun clump with outflows and radiation (A. Myers+ 14) 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. Initial conditions: Self-consistent MHD turbulence w. M sonic =11, M A = 0.8 Column density Temperature

Supersonic Turbulence and the Initial Mass Function Probability distribution function for density in isothermal turbulence is lognormal: where x = ln ( 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 (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) 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 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 (~10 4 K) –Protostellar outflows carve cavities and inject kinetic energy

THE FUNDAMENTAL PROBLEM IN MASSIVE STAR FORMATION: RADIATION PRESSURE Eddington luminosity L E : radiative force balances gravity: L E  /4  r 2 c = GM  /r 2  L E = 4  GMc/(  /  ) (where  = mass/particle) Typical infrared cross section per unit mass for dust in massive protostellar envelopes:  /   5 cm 2 g -1  L E = 4  GMc/(  /  ) = 2500 (M/M sun ) L sun Force per particle due to radiation flux F = L/4  r 2 : Force = F  /c = L  /4  r 2 c where here c = speed of light  = cross section

THE FUNDAMENTAL PROBLEM IN MASSIVE STAR FORMATION: RADIATION PRESSURE--II Predict growth of protostar stops when radiative force exceeds gravity: L = 10 (M/M sun ) 3 L sun > L E = 2500 (M/M sun ) L sun  Stars cannot grow past 16 M sun But stars are observed to exist with M > 100 M sun HOW IS THIS POSSIBLE?L = 10 (M/M sun ) 3 L sun for M ~ (7-20) M sun Massive stars are very luminous: L ~ 10 6 L sun for M = 100 M sun

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 infalling gas (Krumholz et al. 2005; Cunningham et al 2011 )

3D RADIATION HYDRODYNAMIC CALCULATIONS Radiative transfer: gray, mixed frame, flux-limited diffusion with AMR  t  +   v = 0  t  v +   vv = -  P -  + (  R /c)F  t  e +  [(  e+P)v] = -  v  -  P (4  B-cE) - (  R /c) v  F  2  = 4  G   t E +  F =  P (4  B-cE) + (  R /c) v  F F 0 = - [c (E 0 ) /  R ]  E 0 where e = 0.5 v 2 + u = gas energy density, E = radiation energy density; F 0 and E 0 in comoving frame. Accurate to lowest relevant order in v/c. (Krumholz et al. 2007) (Mass) (Momentum) (Energy) (Gravity) (Radiative energy) (Flux limit)

Radiative Rayleigh-Taylor instabilities occurred shortly after yr; at least 40% of the accretion onto the stars was due to this. Time yr yr yr 3000 AU yr Radiation pressure created large, radiation- dominated bubble shortly after t = yr. Final stellar masses in binary: M = 42 M sun, 29 M sun (Krumholz+ 09) Radiation- Hydrodynamic Simulation of Massive Star Formation Ongoing research: Does RT instability occur with more accurate treatment of stellar radiation?

Effect of bipolar outflows on massive star formation: Create channels for the escape of radiation

Herbig-Haro objects A clue: evidence for bipolar ejection of spinning jets. Bipolar outflows from low-mass protostars produced in rotating, magnetized disks C. Burrows (STScI & ESA); J. Hester (Arizona St); J. Morse (STScI); NASA 1000 AU Bipolar outflows originally discovered from low-mass protostars

(Carrasco-Gonzalez et al. 2010) 6 cm (contours) 850  m (gray scale) Observation of magnetized jet from a high-mass protostar IRAS L=17,000 L sun  M  10 M sun if dominated by one star Synchrotron emission Thermal emission

Simulations of effects of outflows on massive star formation Results on outflows at t = 0.6 t ff : Outflow reduces radiation pressure by allowing escape Results for  =2 g cm -2 without winds ~ same as  =10 g cm -2 with winds (Trapping of radiation increases with  ) m pri ~20 M sun m pri ~35 M sun  = 1 g cm -2  = 2 g cm -2  = 10 g cm -2 (no wind) Outflow makes disk gas cooler  more fragmentation (lower primary mass)) 0.01 pc 0.25 pc (Cunningham+ 2011) Column density 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 Kindly translated by Ildar Khabibullin 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

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 radiation- dominated era, avoiding diffusive damping (Silk damping) First stars formed in potential wells due to dark matter, not due to their own self gravity. A key difference between first stars and contemporary stars: (Although baryonic gravity dominates on scales < 1 pc)

Key question: What was the mass of the first stars? M > 0.8 M sun since no stars have been observed that have no heavy elements

Key question: What was the mass of the first stars? M > 0.8 M sun 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 H 2 molecule Density at which collisional and radiative de-excitation are in balance: n crit ~ 10 4 cm -3 Minimum temperature set by spacing of energy levels, ~ 200 K  Characteristic mass at which gravity balances thermal energy [Jeans mass ~ c thermal 3 /(G 3  ) 1/2 ] is ~ 500 M sun (Bromm, Coppi & Larson 2002) This physics was of interest to Zeldovich:

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 M sun 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 Magnetic energy increases much faster with density than expected for uniform collapse (ρ 4/3 ): Turbulent dynamo High-resolution cosmological simulation of gravitational collapse (Turk+ 12) Initial field very weak (~ G) and was not dynamically important at end of simulation 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!