  We present H-band spectra of the candidate counterparts of five ULXs (two in
NGC 925, two in NGC 4136, and Holmberg II X-1) obtained with Keck/MOSFIRE. The
candidate counterparts of two ULXs (J022721+333500 in NGC 925 and
J120922+295559 in NGC 4136) have spectra consistent with (M-type) red
supergiants (RSGs). We obtained two epochs of spectroscopy of the candidate
counterpart to J022721+333500, separated by 10 months, but discovered no radial
velocity variations with a 2-$\sigma$ upper limit of 40 km/s. If the RSG is the
donor star of the ULX, the most likely options are that either the system is
seen at low inclination (< 40$^\circ$), or the black hole mass is less than 100
M$_\odot$, unless the orbital period is longer than 6 years, in which case the
obtained limit is not constraining. The spectrum of the counterpart to
J120922+295559 shows emission lines on top of its stellar spectrum, and the
remaining three counterparts do not show absorption lines that can be
associated with the atmosphere of a star; their spectra are instead dominated
by emission lines. Those counterparts with RSG spectra may be used in the
future to search for radial velocity variations, and, if those are present,
determine dynamical constraints on the mass of the accretor.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics