Bonnor–Ebert mass

About: Bonnor–Ebert mass is a research topic. Over the lifetime, 222 publications have been published within this topic receiving 14407 citations.

Self-similar collapse of isothermal spheres and star formation.

Abstract: We consider the problem of the gravitational collapse of isothermal spheres by applying the similarity method to the gas-dynamic flow. We argue that a previous solution obtained by Larson and Penston to describe the stages prior to core formation is physically artificial; however, we find that the flow following core formation does exhibit self-similar properties.The latter similarity solution shows that the inflow in the dense central regions proceeds virtually at free-fall before the material is arrested by a strong radiating shock upon impact with the surface of the core. Two types of similarity solutions are obtained: one is the prototype for starting states which correspond to unstable hydrostatic equilibrium; the other, for states where the mass of the cloud slightly exceeds the maximum limit allowable for hydrostatic equilibrium. In both cases, an r/sup -2/ law holds for the density distribution in the static or nearly static outer envelope, and an r/sup -3///sup 2/ law holds for the freely falling inner envelope. Rapid infall is initiated at the head of the expansion wave associated with the dropping of the central regions from beneath the envelope. A numerical example is presented which is shown to be in good agreement with the envelopemore » dynamics obtained in previous studies of star formation using hydrodynamic codes.« less

On Continued Gravitational Contraction

Abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

Photoionization-regulated Star Formation and the Structure of Molecular Clouds

Abstract: A model for the rate of low-mass star formation in Galactic molecular clouds and for the influence of this star formation on the structure and evolution of the clouds is presented. The rate of energy injection by newly formed stars is estimated, and the effect of this energy injection on the size of the cloud is determined. It is shown that the observed rate of star formation appears adequate to support the observed clouds against gravitational collapse. The rate of photoionization-regulated star formation is estimated and it is shown to be in agreement with estimates of the observed rate of star formation if the observed molecular cloud parameters are used. The mean cloud extinction and the Galactic star formation rate per unit mass of molecular gas are predicted theoretically from the condition that photionization-regulated star formation be in equilibrium. A simple model for the evolution of isolated molecular clouds is developed.

A Radiation Hydrodynamic Model for Protostellar Collapse. II. The Second Collapse and the Birth of a Protostar

Abstract: We carry out radiation hydrodynamic calculations to study physical processes in the formation of a 1 M☉ protostar. Following our previous work, calculations pursue the whole evolution from the beginning of the first collapse to the end of the main accretion phase. The adiabatic core formed after the initial collapse (i.e., the first core) experiences further gravitational collapse triggered by dissociation of molecular hydrogen, which leads to the formation of the second core, i.e., the birth of a protostar. The protostar grows in mass as accreting the infalling material from the circumstellar envelope, while the protostar keeps its radius at ~4 R☉ during the main accretion phase. These typical features in the evolution are in good agreement with previous studies. We consider two different initial conditions for the density distribution: homogeneous and hydrostatic cloud cores with the same central density of 1.415 × 10-19 g cm-3 . The homogeneous core has the total mass of 1 M☉ while the hydrostatic core has 3.852 M☉. For the initially homogeneous model, the accretion luminosity rapidly rises to the maximum value of 25 L☉ just after the birth of a protostar, and declines gradually as the mass accretion rate decreases. In contrast, the luminosity increases monotonically with time for the initially hydrostatic model. This difference arises because the mass accretion rate varies depending on the inward acceleration at the initial stage, which affects the luminosity curve. A less massive hydrostatic core would possess the similar properties in the luminosity curve to the 3.852 M☉ case, because a hydrostatic cloud core with mass lower than 3.852 M☉ can be shown to provide a smaller mass accretion rate after the birth of a protostar and a more gradual rise in the luminosity curve. Our numerical code is designed to provide the evolution of the spectral energy distribution (SED) along with the dynamical evolution in our spherically symmetric calculations. We confirm that the SED evolves from a 10 K graybody spectrum to hotter spectra typical for class I and flat spectrum sources. The SED for the class 0 sources corresponds to the age of 2 × 104 yr, which is smaller by an order of magnitude than the typical age of class I objects. Considering possible nonspherically symmetric effects, we suggest that observed class 0 sources should consist of the "genuine" class 0 objects, which are as young as 104 yr, and more evolved protostars on edge-on view ("class 0-like class I" objects). The contamination of edge-on class I objects into class 0 sources are not negligible because they are more abundant than genuine class 0 objects. Since observations indicate that the class 0 sources are typically more luminous than class I sources, the initially hydrostatic model, where the luminosity increases monotonically with time, does not match the observations. The initially homogeneous model, in contrast, shows a tendency consistent with the observations. Compiling our results and other theoretical and observational evidence, we illustrate an evolutionary picture of protostar formation. In terms of the evolutionary time and the inclination to an observer, we find that protostellar objects are clearly categorized.