Christopher D. Matzner

The Expulsion of Stellar Envelopes in Core-Collapse Supernovae

We examine the relation between presupernova stellar structure and the distribution of ejecta in core-collapse supernovae of Types Ib, Ic, and II, under the approximations of adiabatic, spherically symmetric flow. We develop a simple yet accurate analytical formula for the velocity of the initial forward shock that traverses the stellar envelope. For material that does not later experience a strong reverse shock, the entropy deposited by this forward shock persists into the final, freely expanding state. We demonstrate that the final density distribution can be approximated with simple models for the final pressure distribution, in a way that matches the results of simulations. Our results indicate that the distribution of density and radiation pressure in a stars ejecta depends on whether the outer envelope is radiative or convective, and if convective, on the composition structure of the star. Our models are most accurate for the high-velocity ejecta cast away from the periphery of a star. For stellar structures that limit to a common form in this region, the resulting ejecta limit to a common distribution at high velocities because the blast wave forgets its history as it approaches the stellar surface. We present formulae for the final density distribution of this material as a function of mass, for both radiative and efficiently convective envelopes. These formulae limit to the well-known planar, self-similar solutions for mass shells approaching the stellar surface. However, the assumption of adiabatic flow breaks down for shells of low optical depth, so this planar limit need not be attained. The event of shock emergence, which limits adiabatic flow, also produces a soft X-ray burst of radiation. Formulae are given for the observable properties of this burst and their dependence on the parameters of the explosion. Motivated by the relativistic expansion recently inferred by Kulkarni et al. for the synchrotron shell around SN 1998bw, we estimate the criterion for relativistic mass ejection and the rest mass of relativistic ejecta. We base our models for the entire ejecta distribution on the high-velocity solution, on our shock-velocity formula, and on realistic radiation pressure distributions. We also present simpler, but less flexible, analytical approximations for ejecta distributions. We survey the ejecta of the polytropic hydrogen envelopes of red supergiants. Our models will be useful for studies of the light curves and circumstellar or interstellar interactions of core-collapse supernovae, and of the birth of pulsar nebulae in their ejecta.

Efficiencies of Low-Mass Star and Star Cluster Formation

Using a quantitative model for bipolar outflows driven by hydromagnetic protostellar winds, we calculate the efficiency of star formation assuming that available gas is either converted into stars or ejected in outflows. We estimate the efficiency of a single star formation event in a protostellar core, finding 25%-70% for cores with various possible degrees of flattening. The core mass function and the stellar initial mass function have similar slopes because the efficiency is not sensitive to its parameters. We then consider the disruption of gas from a dense molecular clump in which a cluster of young stars is being born. In both cases, we present analytical formulae for the efficiencies that compare favorably against observations and, for clusters, against numerical simulations. We predict efficiencies in the range of 30%-50% for the regions that form clusters of low-mass stars. In our model, star formation and gas dispersal happen concurrently. We neglect the destructive effects of massive stars: our results are therefore upper limits to the efficiency in regions more massive than about 3000 M☉ .

On the Role of Massive Stars in the Support and Destruction of Giant Molecular Clouds

We argue that massive stars are the dominant sources of energy for the turbulent motions within giant molecular clouds and that the primary agent of feedback is the expansion of H II regions within the cloud volume. This conclusion is suggested by the low efficiency of star formation and corroborated by dynamical models of H II regions. We evaluate the turbulent energy input rate in clouds more massive than 3.7 × 105 M☉, for which gravity does not significantly affect the expansion of H II regions. Such clouds achieve a balance between the decay of turbulent energy and its regeneration in H II regions; summed over clouds, the implied ionizing luminosity and star formation rate are roughly consistent with the Galactic total. H II regions also photoevaporate their clouds: we derive cloud destruction times somewhat shorter than those estimated by Williams & McKee. The upper mass limit for molecular clouds in the Milky Way may derive from the fact that larger clouds would destroy themselves in less than 1 crossing time. The conditions within starburst galaxies do not permit giant molecular clouds to be supported or destroyed by H II regions, and this may explain some aspects of the starburst phenomenon.

THE DYNAMICS OF RADIATION-PRESSURE-DOMINATED H II REGIONS

We evaluate the role of radiation pressure in the dynamics of H II regions. We first determine under what conditions radiation pressure is significant in comparison to gas pressure and show that, while radiation pressure is generally unimportant for H II regions driven by a handful of massive stars, it is dominant for the larger H II regions produced by the massive star clusters found near the Galactic center and in starburst environments. We then provide a solution for the problem of how H II regions expand when radiation pressure influences their behavior. Finally, we compare radiation-dominated H II regions to other sources of stellar feedback, and argue that H II regions are probably the primary mechanism for regulating the formation of massive star clusters.

On the Role of Disks in the Formation of Stellar Systems: A Numerical Parameter Study of Rapid Accretion

We study rapidly accreting, gravitationally unstable disks with a series of idealized global, numerical experiments using the code ORION. Our numerical parameter study focuses on protostellar disks, showing that one can predict disk behavior and the multiplicity of the accreting star system as a function of two dimensionless parameters which compare the infall rate to the disk sound speed and orbital period. Although gravitational instabilities become strong, we find that fragmentation into binary or multiple systems occurs only when material falls in several times more rapidly than the canonical isothermal limit. The disk-to-star accretion rate is proportional to the infall rate and governed by gravitational torques generated by low-m spiral modes. We also confirm the existence of a maximum stable disk mass: disks that exceed ~50% of the total system mass are subject to fragmentation and the subsequent formation of binary companions.

PROTOSTELLAR DISKS: FORMATION, FRAGMENTATION, AND THE BROWN DWARF DESERT

We argue that gravitational instability of typical protostellar disks is not a viable mechanism for the fragmentation into multiple systems (binary stars, brown dwarf companions, or gas giant planets) except at periods above roughly 20,000 yr. Our conclusion is based on a comparison between prior numerical work on disk self-gravity by Gammie and our own analytical models for the dynamical and thermal state of protostellar disks. For this purpose we first develop a simple theory for the initial conditions of low-mass star formation, accounting for the effect of turbulence on the characteristic mass, accretion rate, and angular momentum of collapsing cores. We also present formulae for the probability distribution of these quantities for the case of homogeneous Gaussian turbulence. However, our conclusions are not sensitive to this parameterization. Second, we examine the criterion for fragmentation to occur during star formation, concentrating on the self-gravitational instabilities of protostellar accretion disks in their main accretion phase. Self-gravitational instabilities are strongly dependent on the thermal state of the disk, and we find that the combination of viscous heating and stellar irradiation quenches fragmentation due to Toomres local instability. Simulations by Matsumoto & Hanawa, which do not include detailed thermal evolution, predict fragmentation in an early phase of collapse. But, fragments born in this phase are on tight orbits and are likely to merge later due to disk accretion. Global instability of the disk may be required to process mass supply, but this is also unlikely to produce fragments. We conclude that numerical simulations that predict brown dwarf formation by disk fragmentation but do not account for irradiation are unrealistic. Our findings help to explain the dearth of substellar companions to stellar-type stars: the brown dwarf desert.

Supernova hosts for gamma‐ray burst jets: dynamical constraints

I constrain a possible supernova origin for gamma-ray bursts (GRBs) by modelling the dynamical interaction between a relativistic jet and a stellar envelope surrounding it. The delay in observer time introduced by the jet traversing the envelope should not be long compared with the duration of gamma-ray emission; also, the jet should not be swallowed by the spherical explosion it powers. The only stellar progenitors that comfortably satisfy these constraints, if one assumes that jets move ballistically within their host stars, are compact carbon–oxygen or helium post-Wolf–Rayet stars (type Ic or Ib supernovae); type II supernovae are ruled out. Notably, very massive stars do not appear to be capable of producing the observed bursts at any redshift unless the stellar envelope is stripped prior to collapse. The presence of a dense stellar wind places an upper limit on the Lorentz factor of the jet in the internal shock model; however, this constraint may be evaded if the wind is swept forward by a photon precursor. Shock breakout and cocoon blowout are considered individually; neither presents a likely source of precursors for cosmological GRBs. These envelope constraints could conceivably be circumvented if jets are laterally pressure-confined while traversing the outer stellar envelope. If so, jets responsible for observed GRBs must have been launched from a region several hundred kilometres wide, have been crossed by strong shocks, or have mixed with envelope material as they travel. A phase of pressure confinement and mixing would imprint correlations among jets that may explain observed GRB variability–luminosity and lag–luminosity correlations.

THE GLOBAL EVOLUTION OF GIANT MOLECULAR CLOUDS. II. THE ROLE OF ACCRETION

We present virial models for the global evolution of giant molecular clouds (GMCs). Focusing on the presence of an accretion flow and accounting for the amount of mass, momentum, and energy supplied by accretion and star formation feedback, we are able to follow the growth, evolution, and dispersal of individual GMCs. Our model clouds reproduce the scaling relations observed in both galactic and extragalactic clouds. We find that accretion and star formation contribute roughly equal amounts of turbulent kinetic energy over the lifetime of the cloud. Clouds attain virial equilibrium and grow in such a way as to maintain roughly constant surface densities, with typical surface densities of order 50-200 M ☉ pc–2, in good agreement with observations of GMCs in the Milky Way and nearby external galaxies. We find that as clouds grow, their velocity dispersion and radius must also increase, implying that the linewidth-size relation constitutes an age sequence. Lastly, we compare our models to observations of GMCs and associated young star clusters in the Large Magellanic Cloud and find good agreement between our model clouds and the observed relationship between H II regions, young star clusters, and GMCs.

Protostellar Outflow-driven Turbulence

Protostellar outflows crisscross the regions of star cluster formation, stirring turbulence and altering the evolution of the forming cluster. We model the stirring of turbulent motions by protostellar outflows, building on an observation that the scaling law of supersonic turbulence implies a momentum cascade analogous to the energy cascade in Kolmogorov turbulence. We then generalize this model to account for a diversity of outflow strengths and for outflow collimation, both of which enhance turbulence. For a single value of its coupling coefficient, the model is consistent with turbulence simulations by Li & Nakamura and, plausibly, with observations of the NGC 1333 cluster-forming region. Outflow-driven turbulence is strong enough to stall collapse in cluster-forming regions for several crossing times, relieving the mismatch between star formation and turbulent decay rates. The predicted line width-size scaling implies radial density indices between -1 and -2 for regions supported by outflow-driven turbulence, with a tendency for steeper profiles in regions that are more massive or have higher column densities.

Lithium Depletion in Fully Convective Pre-Main-Sequence Stars

We present an analytic calculation of the thermonuclear depletion of lithium in contracting, fully con- vective, preEmain-sequence stars of mass Previous numerical work relies on still uncertain M ( 0.5 M _ . physics (atmospheric opacities and convection, in particular) to calculate the e†ective temperature as a unique function of stellar mass. We assume that the starIs e†ective temperature, is -xed during T eff , Hayashi contraction and allow its actual value to be a free parameter constrained by observation. Using this approximation, we compute lithium burning analytically and explore the dependence of lithium depletion on M, and composition. Our calculations yield the radius, age, and luminosity of a preE T eff , main-sequence star as a function of lithium depletion. This allows for more direct comparisons with observations of lithium-depleted stars. Our results agree with those numerical calculations that explicitly determine stellar structure during Hayashi contraction. In agreement with Basri, Marcy, & Graham, we show that the absence of lithium in the Pleiades star HHJ 3 implies that it is older than 100 Myr. We also suggest a generalized method for dating Galactic clusters younger than 100 Myr (i.e., those with contracting stars of and for constraining the masses of lithium-depleted stars. M Z 0.08 M _ ) Subject headings: nuclear reactions, nucleosynthesis, abundances E stars: evolution E stars: interiors E stars: preEmain-sequence