So far essentially all black hole masses in X-ray binaries have been obtained by observing the companion star ’ s velocity and light curves as functions of the orbital phase .
However a major uncertainty is the estimate of the orbital inclination angle of an X-ray binary .
Here we suggest to measure the black hole mass in an X-ray binary by measuring directly the black hole ’ s orbital motion , thus obtaining the companion to black hole mass ratio .
In this method we assume that accretion disk wind moves with the black hole and thus the black hole ’ s orbital motion can be obtained from the Doppler velocity of the absorption lines produced in the accretion disk wind .
We validate this method by analyzing the Chandra/HETG observations of GRO J1655–40 , in which the black hole orbital motion ( K _ { BH } = 90.8 \pm 11.3 km s ^ { -1 } ) inferred from the Doppler velocity of disk-wind absorption lines is consistent with the prediction from its previously measured system parameters .
We thus estimate its black hole mass ( M _ { BH } = 5.41 ^ { +0.98 } _ { -0.57 } ~ { } M _ { \odot } ) and then its system inclination ( i = 72.0 ^ { +7.8 } _ { -7.5 } ~ { } ^ { \circ } ) , where M _ { BH } does not depend on i .
Additional observations of this source covering more orbital phases can improve estimates on its system parameters substantially .
We then apply the method to the black hole X-ray binary LMC X–3 observed with HST/COS near orbital phase 0.75 .
We find that the disk-wind absorption lines of C IV doublet were shifted to \sim 50 ~ { } { km~ { } s ^ { -1 } } , which yields a companion-to-black-hole mass ratio of 0.6 for an assumed disk wind velocity of -400 ~ { } { km~ { } s ^ { -1 } } .
Additional observations covering other orbital phases ( 0.25 in particular ) are crucial to ease this assumption and then to directly constrain the mass ratio .
This method in principle can also be applied to any accreting compact objects with detectable accretion disk wind absorption line features .