  The masses of compact objects in X-ray binaries are best constrained through
dynamical measurements, relying on radial velocity curves of the companion
star. In anticipation of upcoming high X-ray spectral resolution telescopes, we
explore their potential to constrain the mass function of the compact object.
Fe K line fluorescence is a common feature in the spectra of luminous X-ray
binaries, with a Doppler-broadened component from the inner accretion disc
extensively studied. If a corresponding narrow line from the X-ray irradiated
companion can be isolated, this provides am opportunity to further constrain
the binary system properties. Here, we model binary geometry to determine the
companion star's solid angle, and deduce the iron line's equivalent width. We
find that for systems with a mass ratio $q > 0.1$, the expected K${\alpha}$
equivalent width is 2-40 eV. Simulations using XSPEC indicate that new
microcalorimeters will have sufficient resolution to be able to produce
K${\alpha}$ emission line radial velocity measurements with precision of 5-40
km s$^{-1}$, for source continuum fluxes exceeding $10^{-12}$ erg cm$^{-2}$
s$^{-1}$. Several caveats need to be considered; this method is dependent on
successful isolation of the narrow line from the broad component, and the
observation of clear changes in velocity independent of scatter arising from
complex wind and disc behaviour. These issues remain to be proven with
microcalorimeters, but this method has the potential to constrain binary
parameters where optical measurements are not viable.
