arXiv subjects
Publications and source records attributed to Richard B. Larson.
This brief historical review highlights the early work of Hayashi and his associates on the thermal physics of star-forming clouds, as summarized in the temperature-density diagrams first presented by this group. Some of the more recent developments in this subject, including its application to understanding stellar masses and to understanding the formation of the first stars, are also briefly reviewed.
This contribution contains the introductory historical remarks that I presented at IAU Symposium 270 on "Computational Star Formation" held in Barcelona, Spain, May 31 - June 4, 2010. I give a personal view of some of the early histoy of the subject and I comment on some of the important things that were learned from numerical work on star formation.
The formation of compact objects like stars and black holes is strongly constrained by the requirement that nearly all of the initial angular momentum of the diffuse material from which they form must be removed or redistributed during the formation process. The mechanisms that may be involved and their implications are discussed for (1) low-mass stars, most of which probably form in binary or multiple systems; (2) massive stars, which typically form in clusters; and (3) supermassive black holes that form in galactic nuclei. It is suggested that in all cases, gravitational interactions with other stars or mass concentrations in a forming system play an important role in redistributing angular momentum and thereby enabling the formation of a compact object. If this is true, the formation of stars and black holes must be a more complex, dynamic, and chaotic process than in standard models. The gravitational interactions that redistribute angular momentum tend to couple the mass of a forming object to the mass of the system, and this may have important implications for mass ratios in binaries, the upper stellar IMF in clusters, and the masses of supermassive black holes in galaxies.
The stellar mass in disk galaxies scales approximately with the fourth power of the rotation velocity, and the masses of the central black holes in galactic nuclei scale approximately with the fourth power of the bulge velocity dispersion. It is shown here that these relations can be accounted for if, in a forming galaxy with an isothermal mass distribution, gas with a column density above about 8 Msun/pc^2 goes into stars while gas with a column density above about 2 g/cm^2 (10^4 Msun/pc^2) goes into a central black hole. The lower critical value is close to the column density of about 10 Msun/pc^2 at which atomic gas becomes molecular, and the upper value agrees approximately with the column density of about 1 g/cm^2 at which the gas becomes optically thick to its cooling radiation. These results are plausible because molecule formation is evidently necessary for star formation, and because the onset of a high optical depth in a galactic nucleus may suppress continuing star formation and favour the growth of a central black hole.
We study gravitational instabilities in disks, with special attention to the most massive clumps that form because they are expected to be the progenitors of globular-type clusters. The maximum unstable mass is set by rotation and depends only on the surface density and orbital frequency of the disk. We propose that the formation of massive clusters is related to this largest scale in galaxies not stabilized by rotation. Using data from the literature, we predict that globular-like clusters can form in nuclear starburst disks and protogalactic disks but not in typical spiral galaxies, in agreement with observations.
We study gravitational instabilities in disks, with special attention to the most massive clumps that form because they are expected to be the progenitors of globular-type clusters. The maximum unstable mass is set by rotation and depends only on the surface density and orbital frequency of the disk. We propose that the formation of massive clusters is related to this largest scale in galaxies not stabilized by rotation. Using data from the literature, we predict that globular-like clusters can form in nuclear starburst disks and protogalactic disks but not in typical spiral galaxies, in agreement with observations.
Although the basic physics of star formation is classical, numerical simulations have yielded essential insights into how stars form. They show that star formation is a highly nonuniform runaway process characterized by the emergence of nearly singular peaks in density, followed by the accretional growth of embryo stars that form at these density peaks. Circumstellar disks often form from the gas being accreted by the forming stars, and accretion from these disks may be episodic, driven by gravitational instabilities or by protostellar interactions. Star-forming clouds typically develop filamentary structures, which may, along with the thermal physics, play an important role in the origin of stellar masses because of the sensitivity of filament fragmentation to temperature variations. Simulations of the formation of star clusters show that the most massive stars form by continuing accretion in the dense cluster cores, and this again is a runaway process that couples star formation and cluster formation. Star-forming clouds also tend to develop hierarchical structures, and smaller groups of forming objects tend to merge into progressively larger ones, a generic feature of self-gravitating systems that is common to star formation and galaxy formation. Because of the large range of scales and the complex dynamics involved, analytic models cannot adequately describe many processes of star formation, and detailed numerical simulations are needed to advance our understanding of the subject.
The essential features of the stellar Initial Mass Function are, rather generally, (1) a peak at a mass of a few tenths of a solar mass, and (2) a power-law tail toward higher masses that is similar to the original Salpeter function. Recent work suggests that the IMF peak reflects a preferred scale of fragmentation associated with the transition from a cooling phase of collapse at low densities to a nearly isothermal phase at higher densities, where the gas becomes thermally coupled to the dust. The Salpeter power law is plausibly produced, at least in part, by scale-free accretion processes that build up massive stars in dense environments. The young stars at the Galactic Center appear to have unusually high masses, possibly because of a high minimum mass resulting from the high opacity of the dense star-forming gas.
We review recent advances in our understanding of the origin of the initial mass function (IMF). We emphasize the use of numerical simulations to investigate how each physical process involved in star formation affects the resulting IMF. We stress that it is insufficient to just reproduce the IMF, but that any successful model needs to account for the many observed properties of star forming regions including clustering, mass segregation and binarity. Fragmentation involving the interplay of gravity, turbulence, and thermal effects is probably responsible for setting the characteristic stellar mass. Low-mass stars and brown dwarfs can form through the fragmentation of dense filaments and disks, possibly followed by early ejection from these dense environments which truncates their growth in mass. Higher-mass stars and the Salpeter-like slope of the IMF are most likely formed through continued accretion in a clustered environment. The effects of feedback and magnetic fields on the origin of the IMF are still largely unclear. Lastly, we discuss a number of outstanding problems that need to be addressed in order to develop a complete theory for the origin of the IMF.
The thermal properties of star-forming clouds have an important influence on how they fragment into stars, and it is suggested in this paper that the low-mass stellar IMF, which appears to be almost universal, is determined largely by the thermal physics of these clouds. In particular, it is suggested that the characteristic stellar mass, a little below one solar mass, is determined by the transition from an initial cooling phase of collapse to a later phase of slowly rising temperature that occurs when the gas becomes thermally coupled to the dust. Numerical simulations support the hypothesis that the Jeans mass at this transition point plays an important role in determining the peak mass of the IMF. A filamentary geometry may also play a key role in the fragmentation process because the isothermal case is a critical one for the collapse of a cylinder: the collapse and fragmentation of a cylinder can continue freely as long as the temperature continues to decrease, but not if it begins to increase. The limited available results on the dependence of the thermal properties of clouds on metallicity do not suggest a strong dependence of the IMF on metallicity, but the far-infrared background radiation in starburst regions and in the early universe may significantly shift the peak mass to higher masses in these situations.
Identifying the processes that determine the initial mass function of stars (IMF) is a fundamental problem in star formation theory. One of the major uncertainties is the exact chemical state of the star forming gas and its influence on the dynamical evolution. Most simulations of star forming clusters use an isothermal equation of state (EOS). However, theoretical predictions and observations suggest that the effective polytropic exponent gamma in the EOS varies with density. We address these issues and study the effect of a piecewise polytropic EOS on the formation of stellar clusters in turbulent, self-gravitating molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. To approximate the results of published predictions of the thermal behavior of collapsing clouds, we increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary. The change of thermodynamic state at n_c selects a characteristic mass scale for fragmentation M_ch, which we relate to the peak of the observed IMF. Our investigation generally supports the idea that the distribution of stellar masses depends mainly on the thermodynamic state of the star-forming gas. The thermodynamic state of interstellar gas is a result of the balance between heating and cooling processes, which in turn are determined by fundamental atomic and molecular physics and by chemical abundances. Given the abundances, the derivation of a characteristic stellar mass can thus be based on universal quantities and constants.
It is suggested that the thermal physics of star-forming clouds may play a more important role than has usually been recognized in the origin of the stellar IMF and in determining a characteristic mass scale. The importance of the thermal physics has been clearly demonstrated for the formation of the first stars in the universe, where it is well understood and results in cooling to a characteristic minimum temperature at a preferred density, and hence in a characteristic scale for fragmentation. In present-day star-forming clouds, an analogous situation may exist in that at low densities the temperature is expected to decrease with increasing density, reaching a minimum when the gas becomes thermally coupled to the dust and then rising slowly at higher densities. A minimum temperature of about 5 K is predicted to occur at a density of the order of 10^(-18) g cm^(-3), and at this point the Jeans mass is about 0.3 solar masses, similar to the mass at which the IMF peaks. If most of the fragmentation in star-forming clouds occurs in filaments, as is suggested by many simulations as well as by observations, fragmentation seems likely to occur preferentially at the density where the temperature reaches a minimum, and the Jeans mass at this point may then determine a characteristic scale for fragmentation and hence a preferred stellar mass.
Using SPH numerical simulations, we investigate the effects of gas on the inspiral and merger of a massive black hole binary. This study is motivated by the very massive nuclear gas disks observed in the central regions of merging galaxies. Here we present results that expand on the treatment in a previous work (Escala, Larson, Coppi & Mardones 2004; henceforth Paper I), by studying more realistic models. We run a variety of models, ranging from simulations with a relatively smooth gas disk to cases in which the gas has a more clumpy spatial distribution. We also vary the inclination angle between the plane of the binary and the plane of the disk, and the mass ratio between the MBHs and the gaseous disk. We find that as in Paper I, in the early evolution of the system the binary separation diminishes due to gravitational drag, and in the later stages the medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis; this offset produces a torque on the binary that causes continuing loss of angular momentum and is able to reduce the separation to distances where gravitational radiation is efficient. In the simulations that we perform, we find that the coalescence timescale for the MBH binary varies between 5 10^6 yr and 2.5 10^7 yr. For MBHs that satisfy the observed `m-sigma_c' relation, we predict that in a merger of galaxies that have at least 1% of their total mass in gas, the MBHs will coalesce soon after the galaxies merge. We also predict that if the MBHs depart from the `m-sigma_c' relation, the MBH binary can create a circumbinary gap in the disk that stalls the coalescence, but this gap formation can act as a self-regulatory mechanism on MBH growth that can help to explain the existence of the `m-sigma_c' relation.
Using high-resolution SPH numerical simulations, we investigate the effects of gas on the inspiral and merger of a massive black hole binary. This study is motivated by both observational and theoretical work that indicate the presence of large amounts of gas in the central regions of merging galaxies. N-body simulations have shown that the coalescence of a massive black hole binary eventually stalls in a stellar background. However, our simulations suggest that the massive black hole binary will finally merge if it is embedded in a gaseous background. Here we present results in which the gas is assumed to be initially spherical with a relatively smooth distribution. In the early evolution of the binary, the separation dimishes due to the gravitational drag exerted by the background gas. In the later stages, when the binary dominates the gravitational potential in its vicinity, the medium responds by forming an ellipsoidal density enhancement whose axis lags behind the binary axis, and this offset produces a torque on the binary that causes continuing loss of angular momentum and is able to reduce the binary separation to distances where gravitational radiation is efficient. Assuming typical parameters from observations of Ultra Luminous Infrared Galaxies, we predict that a black hole binary will merge within $10^{7}$yrs; therefore these results imply that in a merger of gas-rich galaxies, any massive central black holes will coalescence soon after the galaxies merge. Our work thus supports scenarios of massive black hole evolution and growth where hierarchical merging plays an important role. The final coalescence of the black holes leads to gravitational radiation emission that would be detectable up to high redshift by LISA. We show that similar physical effects are important for the formation of close binary stars.
We review recent theoretical results on the formation of the first stars in the universe, and emphasize related open questions. In particular, we discuss the initial conditions for Population III star formation, as given by variants of the cold dark matter cosmology. Numerical simulations have investigated the collapse and the fragmentation of metal-free gas, showing that the first stars were predominantly very massive. The exact determination of the stellar masses, and the precise form of the primordial initial mass function, is still hampered by our limited understanding of the accretion physics and the protostellar feedback effects. We address the importance of heavy elements in bringing about the transition from an early star formation mode dominated by massive stars, to the familiar mode dominated by low mass stars, at later times. We show how complementary observations, both at high redshifts and in our local cosmic neighborhood, can be utilized to probe the first epoch of star formation.
Our current understanding of the physical processes of star formation is reviewed, with emphasis on processes occurring in molecular clouds like those observed nearby. The dense cores of these clouds are predicted to undergo gravitational collapse characterized by the runaway growth of a central density peak that evolves toward a singularity. As long as collapse can occur, rotation and magnetic fields do not change this qualitative behavior. The result is that a very small embryonic star or protostar forms and grows by accretion at a rate that is initially high but declines with time as the surrounding envelope is depleted. Rotation causes some of the remaining matter to form a disk around the protostar, but accretion from protostellar disks is not well understood and may be variable. Most, and possibly all, stars form in binary or multiple systems in which gravitational interactions can play a role in redistributing angular momentum and driving episodes of disk accretion. Variable accretion may account for some peculiarities of young stars such as flareups and jet production, and protostellar interactions in forming systems of stars will also have important implications for planet formation. The most massive stars form in the densest environments by processes that are not yet well understood but may include violent interactions and mergers. The formation of the most massive stars may have similarities to the formation and growth of massive black holes in very dense environments.
A brief review is given of the basic observed features of the stellar IMF, and also of some of the theoretical ideas and simulations that may help to explain these features. The characteristic stellar mass of order one solar mass may derive from the typical masses of the observed star-forming clumps in molecular clouds, and the typical clump mass may in turn be determined mainly by the Jeans mass, as is true in many numerical simulations of cloud collapse and fragmentation. The Salpeter power law that approximates the IMF at higher masses is less well understood, but it may result from the effects of continuing gas accretion by the more massive forming stars together with the effects of interactions and mergers in dense forming stellar systems. The mass of the most massive star that forms in a cluster is observed to increase systematically with the mass of the cluster, and the most massive clusters may form stars that are massive enough to collapse completely to black holes.
Nearly all of the initial angular momentum of the matter that goes into each forming star must somehow be removed or redistributed during the formation process. The possible transport mechanisms and the possible fates of the excess angular momentum are discussed, and it is argued that transport processes in disks are probably not sufficient by themselves to solve the angular momentum problem, while tidal interactions with other stars in forming binary or multiple systems are likely to be of very general importance in redistributing angular momentum during the star formation process. Most, if not all, stars probably form in binary or multiple systems, and tidal torques in these systems can transfer much of the angular momentum from the gas around each forming star to the orbital motions of the companion stars. Tidally generated waves in circumstellar disks may contribute to the overall redistribution of angular momentum. Stars may gain much of their mass by tidally triggered bursts of rapid accretion, and these bursts could account for some of the most energetic phenomena of the earliest stages of stellar evolution, such as jet-like outflows. If tidal interactions are indeed of general importance, planet-forming disks may often have a more chaotic and violent early evolution than in standard models, and shock heating events may be common. Interactions in a hierarchy of subgroups may play a role in building up massive stars in clusters and in determining the form of the upper IMF. Many of the processes discussed here have analogs on galactic scales, and there may be similarities between the formation of massive stars by interaction-driven accretion processes in clusters and the buildup of massive black holes in galactic nuclei.