Simulating radiative feedback and star cluster formation in GMCs: II. Mass dependence of cloud destruction and cluster properties

The process of radiative feedback in Giant Molecular Clouds (GMCs) is an important mechanism for limiting star cluster formation through the heating and ionization of the surrounding gas. We explore the degree to which radiative feedback affects early ($\lesssim$5 Myr) cluster formation in GMCs having masses that range from 10$^{4-6}$ M$_{\odot}$ using the FLASH code. The inclusion of radiative feedback lowers the efficiency of cluster formation by 20-50\% relative to hydrodynamic simulations. Two models in particular --- 5$\times$10$^4$ and 10$^5$ M$_{\odot}$ --- show the largest suppression of the cluster formation efficiency, corresponding to a factor of $\sim$2. For these clouds only, the internal energy, a measure of the energy injected by radiative feedback, exceeds the gravitational potential for a significant amount of time. We find a clear relation between the maximum cluster mass, M$_{cl,max}$, formed in a GMC of mass M$_{GMC}$; M$_{cl,max}\propto$ M$_{GMC}^{0.81}$. This scaling result suggests that young globular clusters at the necessary scale of $10^6 M_{\odot}$ form within host GMCs of masses near $\sim 5 \times 10^7 M_{\odot}$. We compare simulated cluster mass distributions to the observed embedded cluster mass function ($dlog(N)/dlog(M) \propto M^{\beta}$ where $\beta$ = -1) and find good agreement ($\beta$ = -0.99$\pm$0.14) only for simulations including radiative feedback, indicating this process is important in controlling the growth of young clusters. However, the high star formation efficiencies, which range from 16-21\%, and high star formation rates compared to locally observed regions suggest other feedback mechanisms are also important during the formation and growth of stellar clusters.