Gravothermal oscillations in multi-component models of star clusters

In this paper, gravothermal oscillations are investigated in multi-component star clusters which have power law initial mass functions (IMF). For the power law IMFs, the minimum masses ($m_{min}$) were fixed and three different maximum stellar masses ($m_{max}$) were used along with different power-law exponents ($\alpha$) ranging from 0 to -2.35 (Salpeter). The critical number of stars at which gravothermal oscillations first appear with increasing $N$ was found using the multi-component gas code SPEDI. The total mass ($M_{tot}$) is seen to give an approximate stability condition for power law IMFs with fixed values of $m_{max}$ and $m_{min}$ independent of $\alpha$. The value $M_{tot}/m_{max} \simeq 12000$ is shown to give an approximate stability condition which is also independent of $m_{max}$, though the critical value is somewhat higher for the steepest IMF that was studied. For appropriately chosen cases, direct N-body runs were carried out in order to check the results obtained from SPEDI. Finally, evidence of the gravothermal nature of the oscillations found in the N-body runs is presented.