Jonathan C. Tan

THE FORMATION OF MASSIVE STARS FROM TURBULENT CORES

Observations indicate that massive stars in the Galaxy form in regions of very high surface density, � � 1 gc m � 2 . Clusters containing massive stars and globular clusters have a column density comparable to this. The total pressure in clouds of such a column density is P=k � 10 8 10 9 Kc m � 3 , far greater than that in the diffuse interstellar medium or the average in giant molecular clouds. Observations show that massive-star– forming regions are supersonically turbulent, and we show that the molecular cores out of which individual massive stars form are as well. The protostellar accretion rate in such a core is approximately equal to the instantaneous mass of the star divided by the free-fall time of the gas that is accreting onto the star, as described by Stahler, Shu, & Taam. The star formation time in this turbulent core model for massive-star formation is several times the mean free-fall time of the core out of which the star forms but is about equal to that of the region in which the core is embedded. The high densities in regions of massive-star formation lead to typical timescales for the formation of a massive star of about 10 5 yr. The corresponding accretion rate is high enough to overcome the radiation pressure due to the luminosity of the star. For the typical case we consider, in which the cores out of which the stars form have a density structure � / r � 1:5 , the protostellar accretion rate grows with time as _ m� / t. We present a new calculation of the evolution of the radius of a protostar and determine the protostellar accretion luminosity. At the high accretion rates that are typical in regions of massive-star formation, protostars join the main sequence at about 20 M� . We apply these results to predict the properties of protostars thought to be powering several observed hot molecular cores, including the Orion hot core and W3(H2O). In the appendices we discuss the pressure in molecular clouds and argue that ‘‘ logatropic ’’ models for molecular clouds are incompatible with observation. Subject headings: hydrodynamics — ISM: clouds — stars: formation — turbulence

Slow Star Formation in Dense Gas: Evidence and Implications

It has been known for more than 30 years that star formation in giant molecular clouds (GMCs) is slow, in the sense that only ~1% of the gas forms stars every free-fall time. This result is entirely independent of any particular model of molecular cloud lifetime or evolution. Here we survey observational data on higher density objects in the interstellar medium, including infrared dark clouds and dense molecular clumps, to determine whether these objects form stars slowly like GMCs, or rapidly, converting a significant fraction of their mass into stars in one free-fall time. We find no evidence for a transition from slow to rapid star formation in structures covering 3 orders of magnitude in density. This has important implications for models of star formation, since competing models make differing predictions for the characteristic density at which star formation should transition from slow to rapid. The data are inconsistent with models that predict that star clusters form rapidly and in free-fall collapse. Magnetic- and turbulence-regulated star formation models can reproduce the observations qualitatively, and the turbulence-regulated star formation model of Krumholz & McKee quantitatively reproduces the infrared-HCN luminosity correlation recently reported by Gao & Solomon Slow star formation also implies that the process of star cluster formation cannot be one of global collapse, but must instead proceed over many free-fall times. This suggests that turbulence in star-forming clumps must be driven, and that the competitive accretion mechanism does not operate in typical cluster-forming molecular clumps.

Massive star formation in 100,000 years from turbulent and pressurized molecular clouds

Massive stars (with mass m* > 8 solar masses M[circdot]) are fundamental to the evolution of galaxies, because they produce heavy elements, inject energy into the interstellar medium, and possibly regulate the star formation rate. The individual star formation time, t*f, determines the accretion rate of the star; the value of the former quantity is currently uncertain by many orders of magnitude, leading to other astrophysical questions. For example, the variation of t*f with stellar mass dictates whether massive stars can form simultaneously with low-mass stars in clusters. Here we show that t*f is determined by the conditions in the stars natal cloud, and is typically ∼105 yr. The corresponding mass accretion rate depends on the pressure within the cloud—which we relate to the gas surface density—and on both the instantaneous and final stellar masses. Characteristic accretion rates are sufficient to overcome radiation pressure from ∼100M[circdot] protostars, while simultaneously driving intense bipolar gas outflows. The weak dependence of t*f on the final mass of the star allows high- and low-mass star formation to occur nearly simultaneously in clusters.

STAR FORMATION IN DISK GALAXIES. I. FORMATION AND EVOLUTION OF GIANT MOLECULAR CLOUDS VIA GRAVITATIONAL INSTABILITY AND CLOUD COLLISIONS

We investigate the formation and evolution of giant molecular clouds (GMCs) in a Milky-Way-like disk galaxy with a flat rotation curve. We perform a series of three-dimensional adaptive mesh refinement numerical simulations that follow both the global evolution on scales of ~20 kpc and resolve down to scales 10 pc with a multiphase atomic interstellar medium. In this first study, we omit star formation and feedback, and focus on the processes of gravitational instability and cloud collisions and interactions. We define clouds as regions with n H ≥ 100 cm-3 and track the evolution of individual clouds as they orbit through the galaxy from their birth to their eventual destruction via merger or via destructive collision with another cloud. After ~140 Myr a large fraction of the gas in the disk has fragmented into clouds with masses ~106 M ☉ and a mass spectrum similar to that of Galactic GMCs. The disk settles into a quasi-steady-state in which gravitational scattering of clouds keeps the disk near the threshold of global gravitational instability. The cloud collision time is found to be a small fraction, ~1/5, of the orbital time, and this is an efficient mechanism to inject turbulence into the clouds. This helps to keep clouds only moderately gravitationally bound, with virial parameters of order unity. Many other observed GMC properties, such as mass surface density, angular momentum, velocity dispersion, and vertical distribution, can be accounted for in this simple model with no stellar feedback.

The Formation of the First Stars. II. Radiative Feedback Processes and Implications for the Initial Mass Function

We consider the radiative feedback processes that operate during the formation of the first stars. (1) Photodissociation of H2 in the local dark matter minihalo occurs early in the growth of the protostar but does not affect subsequent accretion. (2) Lyα radiation pressure acting at the boundary of the H II region that the protostar creates in the accreting envelope reverses infall in the polar directions when the star reaches ~20-30 M☉ but cannot prevent infall from other directions. (3) Expansion of the H II region beyond the gravitational escape radius for ionized gas occurs at masses ~50-100 M☉. However, accretion from the equatorial regions can continue since the neutral accretion disk shields a substantial fraction of the accretion envelope from direct ionizing flux. (4) At higher stellar masses, ~140 M☉ in the fiducial case, photoevaporation-driven mass loss from the disk, together with declining accretion rates, halts the increase in the protostellar mass. We identify this process as the mechanism that determines the mass of Population III.1 stars (i.e., stars with primordial composition that have not been affected by prior star formation). The initial mass function of these stars is set by the distribution of entropy and angular momentum. The Appendix gives approximate solutions to a number of problems relevant to the formation of the first stars: the effect of Rayleigh scattering on line profiles in media of very large optical depth, the intensity of Lyα radiation in very opaque media, radiative acceleration in terms of the gradient of a modified radiation pressure, the flux of radiation in a shell with an arbitrary distribution of opacity, and the vertical structure of an accretion disk supported by gas pressure with constant opacity.

A 100 pc ELLIPTICAL AND TWISTED RING OF COLD AND DENSE MOLECULAR CLOUDS REVEALED BY HERSCHEL AROUND THE GALACTIC CENTER

Thermal images of cold dust in the Central Molecular Zone of the Milky Way, obtained with the far-infrared cameras on board the Herschel satellite, reveal a similar to 3 x 10(7) M-circle dot ring of dense and cold clouds orbiting the Galactic center. Using a simple toy model, an elliptical shape having semi-major axes of 100 and 60 pc is deduced. The major axis of this 100 pc ring is inclined by about 40 degrees with respect to the plane of the sky and is oriented perpendicular to the major axes of the Galactic Bar. The 100 pc ring appears to trace the system of stable x(2) orbits predicted for the barred Galactic potential. Sgr A* is displaced with respect to the geometrical center of symmetry of the ring. The ring is twisted and its morphology suggests a flattening ratio of 2 for the Galactic potential, which is in good agreement with the bulge flattening ratio derived from the 2MASS data.

The Formation of the First Stars. I. Mass Infall Rates, Accretion Disk Structure, and Protostellar Evolution

We present a theoretical model for primordial star formation. First we describe the structure of the initial gas cores as virialized, quasi-hydrostatic objects in accord with recent high-resolution numerical studies. The accretion rate can then be related to characteristic densities and temperatures that are set by the cooling properties of molecular hydrogen. We allow for rotation of the gas core, assuming angular momentum conservation inside the sonic point of the flow. In the typical case, most mass then reaches the star via an accretion disk. The structure of the inner region of this disk is described with the standard theory of viscous disks, but with allowance for the substantial energies absorbed in ionizing and dissociating the gas. The size of the protostar and its luminosity depend on the accretion rate, the energetics of the accreting gas, and the ability of the radiation to escape from the stellar accretion shock. We combine these models for the infall rate, inner disk structure, and protostellar evolution to predict the radiation field that is the basis for radiative feedback processes acting against infall (second paper in the series). For realistic initial angular momenta, the photosphere of the protostar is much smaller and hotter than in the spherical case, leading to stronger radiative feedback at earlier stages in the evolution. In particular, once the star is older than its Kelvin-Helmholtz time, contraction toward the main sequence causes a rapid increase in ionizing and far-ultraviolet luminosity at masses ~30 M? in the fiducial case. Since the cores out of which the first stars formed were much more massive than 30 M? and since feedback is dynamically unimportant at lower masses, we conclude that the first stars should have had masses 30 M?.

EQUILIBRIUM STAR CLUSTER FORMATION

We argue that rich star clusters take at least several local dynamical times to form and so are quasi-equilibrium structures during their assembly. Observations supporting this conclusion include morphologies of star-forming clumps, momentum flux of protostellar outflows from forming clusters, age spreads of stars in the Orion Nebula cluster (ONC) and other clusters, and the age of a dynamical ejection event from the ONC. We show that these long formation timescales are consistent with the expected star formation rate in turbulent gas, as recently evaluated by Krumholz & McKee. Finally, we discuss the implications of these timescales for star formation efficiencies, the disruption of gas by stellar feedback, mass segregation of stars, and the longevity of turbulence in molecular clumps.

Star Formation Rates in Disk Galaxies and Circumnuclear Starbursts from Cloud Collisions

We invoke star formation triggered by cloud-cloud collisions to explain global star formation rates of disk galaxies and circumnuclear starbursts. Previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields. Theories based on triggering by spiral density waves fail to explain star formation in systems without such waves. Furthermore, observations suggest gas and stellar disk instabilities are decoupled. Following Gammie, Ostriker, & Jog, the cloud collision rate is set by the shear velocity of encounters with initial impact parameters of a few tidal radii, due to differential rotation in the disk. This, together with the effective confinement of cloud orbits to a two-dimensional plane, enhances the collision rate above that for particles in a three-dimensional box. We predict ΣSFR(R) ∝ ΣgasΩ(1 - 0.7β). For constant circular velocity (β = 0), this is in agreement with recent observations by Kennicutt. Our estimates for the normalization of this star formation law, while uncertain, are consistent with the observed star formation in the Milky Way and starburst galaxies. We predict a B-band Tully-Fisher relation: LB ∝ v, also consistent with observations. As additional tests, we predict enhanced/reduced star formation in regions with relatively high/low shear rates, and lower star formation efficiencies in clouds of higher mass.

Supermassive Stars in Quasar Disks

We propose that supermassive stars may form in quasar accretion disks, and we discuss possible observational consequences. The structure and stability of very massive stars are reviewed. Because of high accretion rates, quasar disks are massive, and the fringes of their optically luminous parts are prone to fragmentation. Starting from a few hundred solar masses, a dominant fragment will grow to the isolation mass, which is a significant fraction of the disk mass, more quickly than the fragment contracts onto the stellar main sequence. A gap will form in the disk, and the star will migrate inward on the accretion timescale, which is comparable to the stars main-sequence lifetime. By interrupting the gas supply to the inner disk, the gap may temporarily dim and redden the quasar. The final stages of stellar migration will be a strong source of low-frequency gravitational waves.