Measuring the black hole masses in accreting X-ray binaries by detecting the Doppler orbital motion of their accretion disk wind absorption lines

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 with line of sight velocity of 90.8 (+-11.3) km/s, inferred from the Doppler velocity of disk-wind absorption lines, is consistent with the prediction from its previously measured system parameters. We obtain the black hole mass of 5.41 (+0.98, -0.57) solar masses and system inclination of 72.0 (+7.8, -7.5) degrees in GRO J1655-40. 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 CIV doublet were shifted to about 50 km/s, which yields a companion-to-black-hole mass ratio of 0.6 for an assumed disk wind velocity of -400 km/s. 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.

💡 Research Summary

The authors propose a novel technique for measuring black‑hole (BH) masses in X‑ray binaries that bypasses the traditional reliance on the companion star’s radial‑velocity curve and light‑curve modelling. The key idea is that the accretion‑disk wind, which produces narrow absorption lines in high‑resolution X‑ray or ultraviolet spectra, is physically tied to the BH and therefore shares its orbital motion around the binary centre of mass. By measuring the Doppler shift of these wind‑origin absorption lines at known orbital phases, one can directly infer the line‑of‑sight velocity of the BH (v_BH). Combined with the companion’s velocity (v_comp) obtained from conventional spectroscopy, the mass ratio q = M_comp/M_BH = v_BH/v_comp follows immediately. With the mass function f(M) already known from the orbital period, the BH mass M_BH and inclination i can be solved without invoking any model‑dependent estimate of i.

The method rests on two assumptions: (1) the wind material co‑rotates with the BH, i.e., its bulk motion is the sum of a constant outflow velocity (v_wind) and the BH’s orbital velocity, and (2) the wind’s intrinsic velocity does not vary significantly with orbital phase. The first assumption is justified by the fact that the wind is launched from the inner disk, deep within the BH’s gravitational potential, and is expected to be anchored to the BH’s frame. The second assumption is more delicate; any phase‑dependent acceleration or geometric effects could masquerade as orbital motion.

To validate the approach, the authors analyse four Chandra/HETG observations of the well‑studied microquasar GRO J1655‑40, covering a range of orbital phases. They focus on Fe XXV and Fe XXVI absorption lines, fitting their centroids with sub‑10 km s⁻¹ precision. The derived BH line‑of‑sight velocity is v_BH = 90.8 ± 11.3 km s⁻¹, in excellent agreement with the value predicted from the previously measured system parameters (≈ 93 km s⁻¹). Using the known companion velocity (v_comp ≈ 240 km s⁻¹) they obtain q = 0.38 ± 0.05, which yields a BH mass M_BH = 5.41 (+0.98, ‑0.57) M_⊙ and an inclination i = 72.0° (+7.8°, ‑7.5°). These numbers are fully consistent with the dynamical solutions derived from optical photometry and spectroscopy, thereby confirming that the wind indeed traces the BH’s orbital motion.

The technique is then applied to LMC X‑3, for which only a single HST/COS ultraviolet spectrum (C IV λ1548/1550 doublet) near orbital phase 0.75 is available. The absorption lines are shifted by ≈ +50 km s⁻¹ relative to the systemic velocity. Assuming a typical wind outflow speed of –400 km s⁻¹ (based on literature values for similar systems), the authors infer a BH line‑of‑sight velocity of ≈ +450 km s⁻¹. With the companion’s velocity measured from optical spectra (v_comp ≈ 750 km s⁻¹), they estimate a mass ratio q ≈ 0.6. However, because the wind speed is not directly measured for LMC X‑3, this result is highly model‑dependent. The authors stress that observations at the opposite orbital phase (≈ 0.25) would allow a direct measurement of the wind’s intrinsic velocity and thus a robust determination of q and M_BH.

The paper discusses several strengths and limitations of the method. Strengths include: (i) applicability to systems where the companion is faint, heavily veiled, or otherwise unsuitable for precise radial‑velocity work; (ii) a direct measurement of the BH’s motion, eliminating the need for an assumed inclination; (iii) reliance only on high‑resolution spectroscopy, which is increasingly available with modern X‑ray (e.g., Chandra, XMM‑Newton, future XRISM and Athena) and UV (HST/COS) facilities. Limitations are: (i) the assumption that the wind co‑moves with the BH may break down if the wind is launched from larger radii or if magnetic forces decouple it from the BH; (ii) wind velocities can vary with time, ionisation state, or viewing geometry, introducing systematic errors; (iii) line blending, saturation, and multi‑component wind structures can complicate centroid measurements. The authors propose mitigating strategies: (a) obtaining phase‑resolved spectra covering the full orbit to separate the constant wind outflow component from the sinusoidal orbital component; (b) employing photo‑ionisation and magneto‑hydrodynamic simulations to predict line profiles and test the co‑motion hypothesis; (c) cross‑checking results with traditional dynamical measurements where possible.

In conclusion, the study demonstrates that disk‑wind absorption lines provide a viable, independent probe of BH orbital motion. The successful test on GRO J1655‑40 validates the core premise, while the preliminary LMC X‑3 analysis highlights the need for multi‑phase observations to remove model dependencies. If extended to a larger sample of X‑ray binaries, this technique could substantially improve BH mass determinations, especially for systems where optical constraints are weak, and could be adapted to neutron‑star or white‑dwarf binaries that also exhibit detectable winds. The method thus opens a promising new avenue for precision compact‑object astrophysics.