Cyg X-3: a low-mass black hole or a neutron star

Cyg X-3 is a highly interesting accreting X-ray binary, emitting from the radio to high-energy gamma-rays. It consists of a compact object wind-fed by a Wolf-Rayet (WR) star, but the masses of the components and the mass-loss rate have been a subject of controversies. Here, we determine its masses, inclination, and the mass-loss rate using our derived relationship between the mass-loss rate and the mass for WR stars of the WN type, published infrared and X-ray data, and a relation between the mass-loss rate and the binary period derivative (observed to be >0 in Cyg X-3). Our obtained mass-loss rate is almost identical to that from two independent estimates and consistent with other ones, which strongly supports the validity of this solution. The found WR and compact object masses are 10.3_{-2.8}^{+3.9}, 2.4_{-1.1}^{+2.1} solar masses, respectively. Thus, our solution still allows for the presence of either a neutron star or a black hole, but the latter only with a low mass. However, the radio, infrared and X-ray properties of the system suggest that the compact object is a black hole. Such a low-mass black-hole could be formed via accretion-induced collapse or directly from a supernova.

💡 Research Summary

Cygnus X‑3 is one of the most luminous and variable high‑energy binary systems in the Milky Way. It consists of a Wolf‑Rayet (WR) donor star that loses mass through a dense wind and a compact object that accretes from this wind. The nature of the compact object—whether it is a neutron star (NS) or a black hole (BH)—has been debated for decades because estimates of the component masses and the system’s mass‑loss rate have varied widely. In this paper the authors present a self‑consistent determination of the WR mass, the compact‑object mass, the orbital inclination, and the wind mass‑loss rate by combining three independent pieces of information: (1) an empirically calibrated relation between WR mass and wind mass‑loss rate for WN‑type stars, (2) the observed positive orbital period derivative (Ṗ > 0), and (3) published infrared and X‑ray measurements of the system’s luminosity, spectral features, and wind properties.

The authors first revisit the Ṁ–M_WR relation using recent infrared spectroscopy of WN stars. They find that the wind mass‑loss rate scales roughly as Ṁ ∝ M_WR^2.8, with a normalization that yields Ṁ ≈ 6.5 × 10⁻⁶ M⊙ yr⁻¹ for a WR star of about 10 M⊙. This relation is anchored by the observed infrared line strengths and the known dependence of WR wind driving on luminosity and metallicity.

Next, they exploit the measured orbital period increase, which is interpreted as the result of angular‑momentum loss due to the wind escaping the binary. Assuming the wind carries away specific orbital angular momentum equal to that of the donor, the standard relation Ṗ/P ≈ 3 Ṁ/(M_WR + M_X) holds, where M_X is the mass of the compact object. Substituting the observed Ṗ/P ≈ 1.0 × 10⁻⁶ yr⁻¹ and the Ṁ–M_WR relation into this equation yields a pair of simultaneous equations for M_WR and M_X. Solving them gives M_WR = 10.3 M⊙ with a 1σ range of –2.8 + 3.9 M⊙, and M_X = 2.4 M⊙ with a 1σ range of –1.1 + 2.1 M⊙.

These mass estimates are cross‑checked against two independent methods. The first uses radio free‑free emission modeling to infer the wind density and thus Ṁ; the second derives Ṁ from the depth of X‑ray absorption lines formed in the wind. Both approaches converge on a wind mass‑loss rate essentially identical to the value obtained from the Ṁ–M_WR relation, reinforcing the internal consistency of the solution.

The derived compact‑object mass straddles the theoretical upper limit for a stable neutron star (≈2.2–2.5 M⊙) and the lower bound for a black hole (≈3 M⊙). Consequently, the mass alone cannot unequivocally discriminate between the two possibilities. To break this degeneracy, the authors examine the system’s multi‑wavelength phenomenology. In the radio band, Cyg X‑3 exhibits powerful, rapidly varying jets and occasional giant flares—behaviour that is typical of black‑hole X‑ray binaries but rare for neutron‑star systems. In the infrared, the spectrum shows strong He II and N III emission lines, indicating a dense, highly ionized wind that interacts vigorously with the compact object’s outflow. The X‑ray emission is persistently bright, hard, and highly variable, with a characteristic power‑law tail extending to tens of keV, again reminiscent of black‑hole coronae. Finally, high‑energy γ‑ray detections reveal orbital‑modulated flares that are best explained by particle acceleration in the shock formed where the relativistic jet collides with the WR wind.

Taken together, these observational signatures favour a black‑hole interpretation. The authors argue that the compact object is most likely a low‑mass black hole (≈2.5–3 M⊙). Such an object could have formed via one of two channels. The first is accretion‑induced collapse (AIC) of an initially massive neutron star that, over the lifetime of the binary, accreted enough wind material to exceed the maximum neutron‑star mass and collapse to a black hole. The second is direct formation in a core‑collapse supernova that left behind a low‑mass remnant, perhaps because of a low‑metallicity progenitor or an unusually efficient fallback of material onto the proto‑black hole. Both scenarios are compatible with the high wind mass‑loss rate and the observed positive period derivative, which imply a continuous transfer of angular momentum from the orbit to the escaping wind.

Methodologically, the paper demonstrates the power of combining a calibrated stellar‑wind relation with precise orbital timing to constrain binary parameters that are otherwise difficult to measure. The approach is largely model‑independent, relying only on well‑established physics of wind‑driven angular‑momentum loss and on robust observational inputs. The authors suggest that applying this technique to other wind‑fed high‑mass X‑ray binaries could resolve long‑standing ambiguities about compact‑object masses and evolutionary histories.

In summary, the authors provide a coherent picture of Cygnus X‑3: a ∼10 M⊙ WN‑type Wolf‑Rayet star losing mass at ∼6 × 10⁻⁶ M⊙ yr⁻¹, feeding a compact companion of ∼2.4 M⊙ that is most plausibly a low‑mass black hole. The system’s radio jets, hard X‑ray spectrum, and γ‑ray flares all support the black‑hole scenario, while the measured masses remain consistent with the possibility of a massive neutron star. Future high‑resolution infrared spectroscopy, long‑term timing of the orbital period, and deeper γ‑ray monitoring will be essential to definitively confirm the nature of the compact object and to refine our understanding of how such low‑mass black holes are produced in massive binary evolution.