Accretion rates and beaming in ultraluminous X-ray sources

I show that extreme beaming factors b are not needed to explain ultraluminous X-ray sources (ULXs) as stellar-mass binaries. For neutron-star accretors, one typically requires b∼ 0.13, and for black holes almost no beaming (b∼ 0.8). The main reason for the high apparent luminosity is the logarithmic increase in the limiting luminosity for super-Eddington accretion. The required accretion rates are explicable in terms of thermal-time-scale mass transfer from donor stars of mass 6–10 M⊙, or possibly transient outbursts. Beaming factors ≲0.1 would be needed to explain luminosities significantly above 1040L40 erg s−1, but these requirements are relaxed somewhat if the accreting matter has low hydrogen content.