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The Astonishing Slowness of Star Formation Mordecai-Mark Mac Low Dept. of Astrophysics American Museum of Natural History Collaborators • • • • • • • • • Miguel A. de Avillez (U. Evora, Portugal) Javier Ballesteros-Paredes (UNAM Morelia, Mexico) Dinshaw Balsara (Notre Dame) Andreas Burkert (MPI für Astronomie, Germany) Fabian Heitsch (U. Colorado/Boulder) Jongsoo Kim (Korea Astronomy Observatory) Ralf Klessen (Astrophys. Inst. Potsdam, Germany) Volker Ossenkopf (ESTEC, Netherlands) Michael D. Smith (Armagh Observatory, N. Ireland) The Oddness of Solid Rock • • • • • Rock is dense: 2500 kg m-3 Even water is dense: 1000 kg m-3: Stars are denser: 105 kg m-3 at center The average density of the Universe is 10-27 kg m-3 Even within galaxies, interstellar gas has a density of 10-21 kg m-3, or 1 atom cm-3. • How did galaxies, stars and planets ever form? Gravitational Stability • Criterion for stability of gas against gravitational collapse found by Jeans (1902). • Pressure opposes collapse: sound waves with speed cs must cross region to communicate pressure changes before collapse cs J ; t ff λJ density ρ J cs ; MJ J3 Galaxy Formation • Gas and dark matter uniform to 20 ppm when cosmic microwave background emitted. • Denser regions collapse until pressure supports • Further collapse depends on cooling (atomic collisions excite radiation, which escapes). Virgo Consortium What is a star? • Gas collapses under its own gravity • Densities build up until fusion starts in the center. pressure •Resulting thermal pressure opposes gravity •Star is in hydrostatic equilibrium, with pressure balancing gravity gravity fusion Star Formation Rate • What determines the rate of star formation in galaxies? 1/ 2 n 6 t 10 yr 3 -3 • Free-fall time ff 10 cm • Galaxy lifetimes greater than 109 yr. • Yet star formation continues today. • How are starbursts, low surface brightness galaxies different? Observations • Young stars can be identified by surrounding infalling material, models of stellar evolution. • Youngest stars only observed in dense clouds of interstellar gas and dust. • Densities are high enough to shield interior from hard UV radiation from stars, allowing molecules (primarily H2, but also CO, NH3, H2O) to form. Molecular Cloud Lifetimes • Cloud lifetimes estimated by Blitz & Shu (1980) to be around 30 Myr in Milky Way – Locations downstream from spiral arms – Stellar ages associated with clouds • Much shorter lifetimes of 5-10 Myr proposed by Ballesteros-Paredes et al. (1999), Fukui et al. (1998). – stars >10 Myr old not tied with clouds – Cluster ages vs. associated molecular gas • Individual cloud lifetimes vs. ensemble lifetimes Molecular Cloud Kinematics • Molecular spectral line ratioes show cloud temperatures to be of order 10 K, with sound speeds ~0.2 km/s • Line widths are much broader than thermal, corresponding to random motions of order 1-10 km/s, or Mach numbers 5-50. • Strong shocks should be produced, quickly dissipating the kinetic energy. Magnetic Fields • In standard scenario, magnetic fields: – Convert shocks into Alfvén waves (transverse MHD waves), which acts as a lossless spring that stores and returns kinetic energy, allowing observed supersonic motions to persist – Provide magnetohydrostatic support against collapse—ambipolar diffusion (neutral drift through ions) determines time scale for star formation (Mouschovias, Shu, Nakano) • We find magnetic fields either insufficient or unnecessary for these purposes. Decaying Turbulence • Computations with two methods – ZEUS hydro and MHD (Stone & Norman 1992, ApJ Suppl.). Available from the URL zeus.ncsa.uiuc.edu:lca_home_page.html – Smoothed particle hydrodynamics (SPH), using sink particles (Bate et al.) when G0, on a GRAPE 3 special-purpose computer (ancestor of our GRAPE 6 machines) • Periodic, uniform-density, isothermal cube • Gaussian initial velocity perturbations ML 1999 2563 time time 1283 Kinetic Energy Decay 2563 323 ZEUS hydro weak MHD 193 strong MHD SPH hydro 703 Decay Rate • Quantify loss of energy from turbulent, supersonic flow • Measure kinetic energy of boxes driven with constant energy input • Use constant Gaussian driving pattern with narrow range of wavelengths • Vary energy input rate, wavelength, magnetic field strength E 1 E 10 k=2 k=4 k=8 ML 1999 ML 1999 Ekin 0.21 3 rms mkv m = mass v = rms velocity k = wavenumber = 2/d How fast does turbulence decay? compare decay time Ek td (dEk dt ) • Mrms >> in molec. clouds • d/J < 1 needed for support Jeans length to free-fall time t ff J cs driving length = 2/k to find: td 1.2 t ff d J M rms • Turbulence decays in less than a free-fall time in molecular clouds •Observed motions cannot 1 come from initial conditions. Mach number Can Turbulence Support Against Gravitational Collapse? • Analytic work (Bonazzola et al., Léorat et al.) suggests that d < J needed for support • Test by adding self-gravity to ZEUS and SPH turbulence models • Zero or decaying turbulence models both collapse efficiently (Klessen & Burkert) • Resolution of cores difficult as collapse continues, so bracket reality with grid, SPH computations Numerical Considerations • Cannot capture core behavior correctly • Bracket with different techniques – Sink particles in SPH: indestructible once formed – Uniform grid: cores can’t collapse, destroyed easily by passing shocks • Magnetic fields diffuse through grid – Minimum number of zones in a Jeans wavelength required to prevent spurious collapse (Heitsch, Mac Low & Klessen 2001) Klessen, Heitsch, ML (2000) Heitsch, ML, Klessen (2000) Rose Center for Earth & Space Images showing star formation and the formation of an HII region from the new Space Show “Are we Alone: The Search For Life” M = 1 Mbox box = 1 Klessen, Heitsch, ML (2000) d J / M rms Magnetic fields reduce the fraction of mass in collapsed objects, but do not prevent local collapse. Heitsch, ML, Klessen (2001) Local collapse • Collapse occurs if m mJ ,T v3 / D J cs / • When increases, smaller regions collapse • Isothermal shocks give M 2 • Unless compressed regions are turbulently supported, they collapse locally despite global support Driven vs. Decaying Projected positions of sink particles from SPH models Klessen, Heitsch, Mac Low (2000) Modes of Star Formation • Slow, scattered star formation occurs in regions supported by turbulence due to low densities or high turbulent velocities. Observed in regions like Taurus. • Fast, clustered star formation occurs in regions that are not supported by turbulence, either due to density enhancements or decay of turbulence. Resembles regions like Orion, or starburst knots. What’s driving the turbulence? • Gravitational collapse fails due to fast decay • Protostellar jets and outflows – Most energy deposited outside clouds • Rotational shear of galaxies via magnetic coupling to gas (Sellwood & Balbus 1999) – Probably gives background value (~6 km/s) – Dominant for low surface brightness galaxies, outer regions of normal galaxies? Supernova Driving • In active star-forming galaxies, SN driving dominates other mechanisms • Strength of driving depends on star-formation rate, allowing self-regulation • 3D models (ML, Balsara, Avillez, Kim, 2001, on astro-ph): – Hydro adaptive grid (Avillez 2000) on 3000 x 3000 x 60,000 light year box with galactic disk, clustered, random SNe, and SN rates 1, 6, 10x Galactic value – RIEMANN MHD framework (Balsara 2000) on 600 light year periodic box with SN rate 12x Galactic value Explosions as Bright as Galaxies, • (Type II) supernovae occur when massive star fuses all available elements and gravitationally collapses. • Core forms a neutron star or black hole, while outer layers bounce explosively, releasing 1051 ergs of energy Cassiopeia A supernova remnant 3 light years Chandra X-ray Observatory Simulations of SN-Driving • Avillez (2000) AMR parallel code – – – – vertical stratification, equilibrium ionization radiative cooling isolated and clustered SNe (twice galactic rate) No self-gravity, molecule formation • Show cut through plane of 3D simulation – – – – 0.625 pc resolution in plane (800 x 800 equiv. resol.) Log of density 70 Myr 1 x 1 kpc shown • RIEMANN MHD framework (Balsara 2000) on 200 pc periodic box (1283) with SN rate 12x Galactic value Show disk movie from Avillez Magnetic Pressure Thermal Pressue ML, Balsara, Avillez, Kim Temperature Density Next Steps • Understanding molecular cloud formation – Turbulent compression vs gravitational contraction, including chemistry – Multi-scale computations including both cloud and core formation to capture entire star formation sequence • Modeling the driving of turbulence – Supernova driving vs. shear flows – Are large-scale star formation rates predictable? (empirical answer is yes: Schmidt laws) Overcooling in Galaxy Formation • Far too many dwarf galaxies cool and collapse around galaxies the size of the Milky Way in numerical simulations neglecting star formation, compared to observations (White & Rees 1978, Klypin et al. 1999, Moore et al. 1999). • Ionization by hard UV radiation (λ < 91.2 nm) alone may (Chiu, Gnedin, & Ostriker 2001), or may not (Navarro & Steinmetz 1997) provide enough heating. • Dwarf galaxy wind disruption could be solution (or contribute to it, Scannapieco et al. 2000, 2001ab). Starburst galaxies • When regulation mechanisms fail, star formation rates can be 100x Milky Way’s • The most massive of the newly formed young stars explode as supernovae in only a few Myr. • In starburst galaxies, these supernovae can drive a wind completely out of the galaxy into the surrounding intergalactic gas. Parameter Space Dwarf galaxies • Typical haloes in LCDM with values form first. h 0.7, 0 0.37, 0.63, b 0.05, 8 0.8 photoevaporation (Barkana & Loeb) H2 cooling (Ciardi & Ferrara 00, Tegmark 97) Log Mhalo Lyacooling redshift Blowouts From Isolated Dwarfs •2D, axisymmetric models •Log density shown in color scale •Box sizes of 90,000 x 45,000 light years ML & Ferrara 1999 Goals for Study of Cosmological Blowouts • Better understand feedback from early galaxies – Kinetic and thermal energy ejection into intergalactic medium (IGM) – Stop further infall of gas in own halo – Pollution of IGM by ejected heavy elements – Escape of ionizing radiation through bubbles • Calibrate sub-gridscale models for cosmological feedback in large-scale codes t=initial t=50 Myr t=collapse t=90 Myr t=initial t=collapse t=50 Myr t=90 Myr Mechanical Feedback Results • Accreting gas haloes can suppress ejection • With large enough starburst they can themselves be swept away. • Kinetic energy feedback primarily in form of ejected accreting material, not hot gas Star Formation in the Universe • Efficiency and speed of star formation in galaxies determined by the supersonic turbulent motions in the interstellar gas • Turbulence likely driven by combination of supernova explosions and galactic shear • Efficient star formation in young galaxies drives winds that can retard further growth of that galaxy and probably also nearby galaxies. Local Dwarf Models • Mac Low & Ferrara (1999) models: – dwarf disks with constant surface density in hydrostatic equilibrium – Radii from Ferrara & Tolstoy (2000) – potential of DM dominates (softened isotherm. sph.) – Persic, Salucci, Stel (1996) scaling of DM to visible mass • Starburst energy injected at galaxy centers – Excess cooling of hot gas prevented with tracer field – Conduction approximated with mass injection at center – 50 Myr of SN energy input (instantaneous burst) • Low-density IGM for low-z, isolated dwarfs Numerical Methods • ZEUS-3D (Stone & Norman 1992), second-order, Eulerian, artificial viscosity • Ionization equilibrium cooling of ambient gas, with strength dependent on metallicity Z (semiimplicit energy equation) • Density-dependent heating for thermodynamical balance • Tracer field using Yabe & Xiao (1993) transform • Turn off cooling in hot regions to avoid poisoning Isolated Dwarfs • Metals in SN ejecta escape easily – Hot, shocked ejecta have sound speed greater than escape velocity in galaxies up to LMC size • Mass much harder to strip. – In most galaxies, shock “blows out” to IGM before reaching most of ISM – Mass ejected efficiently only from galaxies with baryonic mass < 106 M (“blowaway”) More Realistic Blowouts • Higher pressures and galactic haloes confine blowouts (Silich & Tenorio-Tagle 1998, 2001) • Blowouts in galactic clusters with highpressure IGM (Murakami & Babul 1999) – Pressure confines blowout – But ram pressure from orbital motion important • Inclusion of Type I SNe (Recchi et al. 2001) • Cosmological blowouts: infall also can limit mass ejection Changes for cosmological case • Infalling halo • Dark matter solution taken from spherical collapse model of Gaussian perturbation (Meiksin 1994) • Gas cooling and collapse solved for directly • Starburst size determined from cooled mass and star formation efficiency (SFE). • Galaxy sizes as function of redshift (Mo, Mao & White) • Disk potentials included • Metalfree curve from Sutherland & Dopita, with log (erg cm3 s-1) Cooling cutoff at 103.5 K (no molecules) • Compton cooling at low, high T 4 log T (K) for ionized 36 3 -1 4 (5.4 10 erg cm s )(1 z ) T / ne gas. comp 8 t=initial t=50 Myr t=collapse t=90 Myr t=initial t=50 Myr t=collapse t=90 Myr Future work •What drives the turbulence? •Supernovae? •Young stellar jets? •Rotation of the galaxy? •How do star-forming molecular clouds form? •What quantitatively determines the star formation rate? Conclusions • Galactic winds couple inefficiently to the ISM, so ISM ejection (‘blowaway’) is hard. • Metal ejection much easier. • Accretion can substantially alter behavior of starburst blowouts • Observations only show the tip of the iceberg • Reasonable assumptions about star formation efficiency can still result in metal and mass ejection • Quantitative benchmarks being defined for use in large-scale simulations • Ionization can escape efficiently if shell fragments early (when most photons come out) Conclusions • Accretion can substantially alter behavior of starburst blowouts • Reasonable assumptions about SFE can still result in metal and mass ejection • Quantitative boundaries being defined for use in large-scale simulations • Ionization escapes efficiently, but only at early times (when most photons come out) Conclusions • Supernova feedback can drive winds, allow ionizing radiation to escape. • Metals escape efficiently, mass less so. • Effects of winds The IGM • Metal-enriched to Z 103 Z at z ~ 3 • Ly a forest linewidths 10 km s-1 broader than predicted by ionization alone (Theuns et al. 1998, Bryan et al. 1999) • Universe reionized at z < 5 (Becker et al 2001, Djorgovski et al. 2001) • Dwarf galaxies with masses 106.5-109 M condense early, producing ionizing radiation and SN-driven winds Galaxy Formation Delay • Dwarf galaxy winds also will affect nearby objects. • Mechanical energy input sufficient to sweep away gas in still linear overdense regions (Scannapieco et al. 2000, 2001) Scannapieco, Ferrara, & Broadhurst 2000 Numerical Feedback SF only outflows SF only outflows Scannapieco, Thacker, & Davis 2001 Supernova Rate Pressure Galactic 6x ML, Balsara, Avillez, Kim 10 x Log-Normal Fits •Hydro model at Galactic SN rate cool gas •Theory of Passot & Vazquez-Semadeni (PRD, 1998) from vrms log normal tilted log normal Distribution of gas pressures By volume By mass Large mass of cold gas at high pressures: pressureconfined atomic and molecular clouds? Summary • Driven turbulence can account for: – supersonic motions in molecular clouds – Very different rates of star formation in starbursts, normal galaxies, LSB • Driving most likely from SNe and MRI • SN driving can explain normal ISM. Regions of intense star formation probably unsupported and collapsing. • Pressure distribution in ISM not power-law due to shocks alone but log-normal due to shocks and rarefactions together. Length and Time Scales 1 atom cm-3, but a whole lot of cm3! The volume of the Galaxy is roughly 4 R 2 z 12 (45,000 l.y.) 2 (200 l.y.) 10 25 (104 )2 2 102 102108102 1012 l.y.3 1 light year = 9.5 1017 cm, so 1 l.y.3 (1018 )3 1054 cm3 volume=1012 1054 1066 cm3 ! 90 000 light years M100, by WFPC2 team, with Hubble Space Telescope Gravitational Collapse • Gravity acts everywhere. If nothing resists it, indefinite collapse occurs. • From primordial gas to interstellar densities takes a 100 million years • From interstellar densities to stellar densities takes another 30 million years Oh, the Pressure! • What stops gravitational collapse? • Angular momentum: forms disk •Conservation of angular momentum •Gas dissipation pressure gravity angular momentum gravity • Thermal pressure: forms star •Optical thickness •Fusion (first D, then H) The First Stars, and their Gifts • Cooling only due to molecular hydrogen • Stars likely very massive -- hundreds of solar masses. • Massive stars are short-lived (1-10 million years), exploding as supernovae, and producing all elements heavier than hydrogen, helium and lithium. Our Ingredients • Sun and other modern stars – Hydrogen & helium: from the big bang – Trace elements (everything else): from earlier stars and supernovae • Earth and other rocky planets – Carbon, nitrogen, oxygen: from dying lowmass stars – Everything heavier (Si, Fe, Al, Mg, …, U): from supernova explosions – Traces of hydrogen and helium in much reduced quantities But why are stars still forming? • Gravity should cause gas to collapse to stellar densities in tens of millions of years • Yet galaxies have been around for a thousand times as long—10 billion years • How can star formation still be occurring? • Two major explanations proposed Delay of Star Formation • “Standard model” • Magnetic fields thread ionized interstellar gas • Once and future theory • Supersonic turbulence maintains support Magnetic fields • Star formation occurs when neutral gas is dragged by gravity through ions tied to magnetic field. Turbulence • Supersonic motions prevent collapse in bulk of gas. • But, shock waves compress some of gas, causing local collapse despite global support Observations (a polemical summary) Magnetic Support • Strong magnetic fields observed, but not quite strong enough • Too many young stars in dense molecular cloud cores • Too little age spread between nearby stars Turbulence • Supersonic motions observed • Cloud shapes appear correct • Both isolated and clustered star formation occurs The Oddness of Liquid Water • Terrestrial life in all its many forms depends on liquid water. Other life could be different, but we don’t know how. • Liquid water on surface seen only on Earth • Subsurface water maybe on Mars, probably on Jovian moons (Europa, Ganymede, Callisto) • Extrasolar planets all gas giants, but moons and terrestrial planets of unknown properties could accompany them.