On Estimating the Masses of Star Clusters Embedded in Clouds of Interstellar Gas and Dust

Abstract

In the article, a method is developed for estimating the dynamic masses of the stellar and gas components of cluster-cloud systems under conditions of non-isolation and significant non-stationarity of stellar and gas subsystems in a regular field. A number of estimates of the dynamic masses of the stellar and gas components of the system are made without using the virial theorem for zero and positive values of the total energies \(E\) of the system as a whole and \(E_{2}\) of its gaseous subsystem. The well-known estimates of the free-fall time \(\tau_{\textrm{ff}}\) for fragments in the force field of a sphere of uniform and inhomogeneous density sphere simulating a system of gas and stars are refined. The estimates of the \(\tau_{\textrm{ff}}\) quantities are supplemented by estimates of the radial velocities \(v_{r}\) of the fragments in such systems. A number of relations between the parameters of the stellar and gas subsystems in the considered models of embedded clusters are obtained. It is shown that instead of one virial coefficient to describe the system, it is necessary to use three coefficients, the formulas for which are given. The relations make it possible to estimate the dynamic masses of non-isolated and non-stationary subsystems from data on the structural-dynamic characteristics of an embedded cluster. It is shown that the ratio \({\overline{v}}_{c,1}^{2}/\sigma_{1,v}^{2}>4\), where \(\sigma_{1,v}^{2}\) is the mean square of the velocities of the stellar subsystem in the case of its virial equilibrium, and \({\overline{v}}_{c,1}^{2}\) is the mean square of the critical velocities of the stars in this subsystem. It is shown that embedded clusters with parameters \(x=R_{1}/R_{2}\) and \(\mu=M_{1}/M_{2}\) have maximum values \({\overline{v}}_{c,1}^{2}/\sigma_{1,v}^{2}\) along some curve in the \((x,\mu)\) space (\(M_{i}\) and \(R_{i}\) are the mass and radius of the \(i\)th subsystem). The embedded clusters with parameters \((x,\mu)\) close to this curve are the least susceptible to destruction space relaxation processes. It is shown that, depending on the initial energies \(E\) and \(E_{2}\), the masses of a subsystem of stars in an embedded cluster can be much smaller than the virial masses of this subsystem. This result is also of particular interest for estimating the dynamic masses of galaxy clusters. It is noted that an increase in the degree of non-stationarity of the considered models of embedded clusters leads to a decrease in the periods of oscillations of the stellar subsystem.