One hundred seven ultraluminous X-ray ( ULX ) sources with 0.3 - 10.0 keV luminosities in excess of 10 ^ { 39 } ergs s ^ { -1 } are identified in a complete sample of 127 nearby galaxies .
The sample includes all galaxies within 14.5 Mpc above the completeness limits of both the Uppsala Galaxy Catalog and the Infrared Astronomical Satellite survey .
The galaxy sample spans all Hubble types , a four decade range in mass , 7.5 < \log ( M / { M } _ { \odot } ) < 11.4 , and in star-formation rate , 0.0002 < { SFR ( M } _ { \odot } / { yr ) } \leq 3.6 .
ULXs are detected in this sample at rates of one per 3.2 \times 10 ^ { 10 } M _ { \odot } , one per \sim 0.5 M _ { \odot } yr ^ { -1 } star-formation rate , and one per 57 Mpc ^ { 3 } corresponding to a luminosity density of \sim 2 \times 10 ^ { 37 } erg s ^ { -1 } Mpc ^ { -3 } .
At these rates we estimate as many as 19 additional ULXs remain undetected in fainter dwarf galaxies within the survey volume .
An estimated 14 or 13 % , of the 107 ULX candidates are expected to be background sources .
The differential ULX luminosity function shows a power law slope \alpha \sim - 1.2 to - 2.0 with an exponential cutoff at \sim 20 \times 10 ^ { 39 } ergs s ^ { -1 } with precise values depending on the model and on whether the ULX luminosities are estimated from their observed numbers of counts or , for a subset of candidates , from their spectral shapes .
Extrapolating the observed luminosity function predicts at most one very luminous ULX , L _ { X } \sim 10 ^ { 41 } ergs s ^ { -1 } , within a distance as small as 100 Mpc .
The luminosity distribution of ULXs within the local universe can not account for the recent claims of luminosities in excess of 2 \times 10 ^ { 41 } ergs s ^ { -1 } requiring a new population class to explain these extreme objects .