On the formation of a star.

Abstract

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the formation of a star. McVittie, G. C. Abstract The problem investigated is that of the collapse of an isolated spherical cloud of interstellar gas; the cloud has initially a diameter of some parsecs and a mean density of from 10-15 to 10-24 g/cm3, and finally becomes an object of stellar dimensions and density. The forces acting are assumed to be the pressure-gradient force and the gravitational self-attraction alone; viscosity, radiation-pressure, centrifugal force, etc., all being neglected in comparison. The equations governing the motion are the hydrodynamical equation of motion and the equation of continuity, but the motion is assumed to be non-adiabatic so that each gas element loses heat energy as it moves. This loss of energy is presumed to take place by the emission of radiation which escapes from the sphere of gas. The first law of thermodynamics provides a formula for calculating the rate of loss, "following the motion" of each unit mass of gas. The boundary and initial and final conditions are these: at the boundary the pressure and density are always zero and the gas-velocity is equal to the velocity of the boundary; initially, the gas is at rest but not in equilibrium and each of its elements has an inward acceleration; finally, the gas is at rest and also in equilibrium. This final state is assumed to be a complete polytrope. The equations of motion and of continuity can be solved exactly for the pressure and density under the assumption that the velocity q of the gas is given by the linear-wave rule, viz. I df ~=J~1r~ (I) where j is an arbitrary function of the time I and r is distance from the center. The solution, however, involves a second arbitrary function h of the variable r/f. It is proved that h can be determined in terms of the Emden function which describes the complete polytrope giving the final equilibrium state. The initial and final conditions, though they impose certain restrictions on f, do not define this function completely which means that the gas-sphere can collapse to stellar dimensions in a variety of ways. Each of these ways, however, gives rise to different ways of emission of energy. A lower limit for the time of collapse can be calculated and a specific model, having a specific expression for f as a function of 1, indicates that this time varies from I0~ to I0~ years according as the initial mean density is 10-15 to 10-24 g/cm1. The initial central temperature of the gas sphere can also be calculated and turns out to lie between 500 or 800 and I absolute, according as the mean density lies between the limits quoted and the mass of the sphere is 5 or 10 times that of the sun. Various ways of avoiding this low-temperature difficulty are discussed, one of which is that the final equilibrium state might be taken to correspond to an Emden function with a singularity at the origin. The total emission of radiation during the collapse is calculated and shown to be equivalent to a small loss of mass for the gas-sphere, smaller than occurs, for example, in a nova outburst. The final rate of emission of energy from the surface of the star is also found to be small relative to the luminosity of the sun. These two results are to be expected because radiative processes have not been taken into account in the theory. The investigation is intended to show how an interstellar gas-cloud could form a star, and not how it must do so, by tracing out the whole development of the motion from start to finish using the exact theory of gas-dynamics and gravitational theory. The work was done as part of a project sponsored by the National Science Foundation. University of Illinois Observatory, Urbana, Ill. Publication: The Astronomical Journal Pub Date: 1956 DOI: 10.1086/107393 Bibcode: 1956AJ.....61Q.185M full text sources ADS |