The large columns of dusty gas enshrouding and fuelling star-formation in young , massive stellar clusters may render such systems optically thick to radiation well into the infrared .
This raises the prospect that both ‘ ‘ direct ’ ’ radiation pressure produced by absorption of photons leaving stellar surfaces and ‘ ‘ indirect ’ ’ radiation pressure from photons absorbed and then re-emitted by dust grains may be important sources of feedback in such systems .
Here we evaluate this possibility by deriving the conditions under which a spheroidal , self-gravitating , mixed gas-star cloud can avoid catastrophic disruption by the combined effects of direct and indirect radiation pressure .
We show that radiation pressure sets a maximum star cluster formation efficiency of \epsilon _ { max } \sim 0.9 at a ( very large ) gas surface density of \sim 10 ^ { 5 } M _ { \odot } pc ^ { -2 } ( { Z _ { \odot } } / Z ) \simeq 20 g cm ^ { -2 } ( { Z _ { \odot } } / Z ) , but that gas clouds above this limit undergo significant radiation-driven expansion during star formation , leading to a maximum stellar surface density very near this value for all star clusters .
Data on the central surface mass density of compact stellar systems , while sparse and partly confused by dynamical effects , are broadly consistent with the existence of a metallicity-dependent upper-limit comparable to this value .
Our results imply that this limit may preclude the formation of the progenitors of intermediate-mass black holes for systems with Z \hbox to 0.0 pt { \raise 1.505 pt \hbox { $ > $ } } { \lower 3.01 pt \hbox { $ \sim$ } } 0.2 { % Z _ { \odot } } .