2025ApJ...991...68T

We present a new spectropolarimetric method for the estimation of the inclination of X-ray binaries using the linear polarization (LP) value in black hole (BH) sources, based on the early paper by R. A. Sunyaev & L. G. Titarchuk. The X-ray LP arises from multiple scattering of initially soft photons in a hot, optically thick Compton cloud (CC) using a flat geometry. R. A. Sunyaev & L. G. Titarchuk showed that the LP degree P depends on the binary inclination i and remains independent of the photon energy. Moreover, P follows a characteristic angular distribution based on the CC optical depth τ₀; in particular, for τ₀ > 10, the LP follows the S. Chandrasekhar distribution. In light of the vast number of recent IXPE spectropolarimetric observations of BHs, testing this approach in combination with spectral analysis of these sources by other missions is desirable. In particular, the BH source, 4U 1957+115, was observed with IXPE in the high/soft state for which a P of ∼ 2% was found. To apply the new method, in addition to knowing P for a given source, it is necessary to estimate the CC optical depth τ₀ and then to calculate the best-fit photon index Γ and the plasma temperature kT_e. We present the X-ray spectral analysis of 4U 1957+115 using data from IXPE, NuSTAR, NICER, RXTE, Swift, Suzaku, and ASCA. We show that the X-ray source spectra are well described by the Comptonization model with Γ varying from 1.5 to 3. We find a monotonic increase in Γ with the mass accretion rate, $\dot{M}$, and a final saturation of the index at Γ ∼ 3 for high $\dot{M}$. We determine a BH mass by the scaling method: M₁₉₅₇ = 4.8 ± 1.8M_⊙, assuming a source distance of 22 kpc, using H 1743-322, 4U 1630-47, and GRS 1915+105 as reference sources.