  We present results from a Chandra study of ultraluminous X-ray sources (ULXs)
in a sample of 17 nearby (D_L<60 Mpc) luminous infrared galaxies (LIRGs),
selected to have star formation rates (SFRs) in excess of 7 M_sun yr^-1 and low
foreground Galactic column densities (N_H < 5*10^20 cm^-2). A total of 53 ULXs
were detected and we confirm that this is a complete catalogue of ULXs for the
LIRG sample. We examine the evolution of ULX spectra with luminosity by
stacking the spectra of individual objects in three luminosity bins, finding a
distinct change in spectral index at luminosity ~2 *10^39 erg s^-1. This may be
a change in spectrum as 10 M_sun black holes transit from a ~Eddington to a
super-Eddington accretion regime, and is supported by a plausible detection of
partially-ionised absorption imprinted on the spectrum of the luminous ULX (L_X
~5*10^39 erg s^-1) CXOU J024238.9-000055 in NGC 1068, consistent with the
highly ionised massive wind that we would expect to see driven by a
super-Eddington accretion flow. This sample shows a large deficit in the number
of ULXs detected per unit SFR (0.2 ULXs M_sun^-1 yr^-1). This deficit also
manifests itself as a lower differential X-ray luminosity function
normalisation for the LIRG sample than for samples of other star forming
galaxies. We show that it is unlikely that this deficit is a purely
observational effect. Part of this deficit might be attributable to the high
metallicity of the LIRGs impeding the production efficiency of ULXs and/or a
lag between the star formation starting and the production of ULXs; however, we
argue that the evidence -- including very low N_ULX/L_FIR, and an even lower
ULX incidence in the central regions of the LIRGs -- shows that the main
culprit for this deficit is likely to be the high column of gas and dust in
these galaxies, that fuels the high SFR but also acts to obscure many ULXs from
our view.
