A Model for the Expansion of the Orion Nebula.

A model for the expansion of the Orion Nebula has been constructed. It is assumed that before the stars in the Trapezium began to ionize and heat the nebula, the nebula consisted of a cloud of neutral gas which was at rest relative to the cluster with a distribution of density given by the isothermal function. The plausibility of these initial conditions is discussed. The gas in the nebula was ionized and heated when the stars in the Trapezium began to radiate in the Lyman continuum. It is assumed that the onset of the ionizing radiation occurred in an interval of time which can be neglected, and on this assumption, one finds that the interval of time in which the nebula became ionized is also negligible. Finally, it is assumed that in the heated gas the gradient of the pressure was large compared with all other forces. For these initial conditions, the equations governing the isothermal expansion of the nebula have been integrated. The solution is presented as an evolutionary sequence of models in each of which the density and the velocity of expansion are given as functions of the radial distance. Each model in the sequence can be compared with published observational results concerning the distributions of density and velocity, and on the basis of these comparisons, the models which give the best representations of th present state of the nebula can be found. From the parameters characterizing the models which were selected in this way, it is estimated that the age of the Orion Nebula is of the order of 20 000 years. The effects of turbulence, a magnetic field, and the finite time scale for the onset of the ionizing radiation will be discussed briefly. This research has been supported by the Office of Naval Research.