The line modulations of H-like Fe, Ca, Ar, and S observed with $XRISM$/Resolve in Cyg X-3
Cygnus X-3, hosting a Wolf-Rayet (WR) star whose dense wind produces various spectral lines due to photoionization by X-rays from a compact object, provides an ideal laboratory for studying wind dynamics and density structure. We measured the orbital modulations of the Fe, Ca, Ar, and S Ly$\alpha$ lines observed with the X-ray microcalorimeter (Resolve) onboard the $XRISM$, taking account of both emission and absorption lines of the Ly$\alpha$ complexes. The modulations of Doppler shifts of the Fe, Ca, Ar, and S Ly$\alpha$ lines showed amplitudes of 500 km s$^{-1}$ and phase offsets of 0.04, 0.09, 0.11, and 0.17, respectively, in units of an orbital period (4.8 hours) relative to the orbital motion of the compact object. This result indicated that H-like Fe most closely follows the compact object's motion. The line widths ranged from 400 to 1000 km s$^{-1}$. The intensities of both emission and absorption lines reached their minima around orbital phase 0.0 and their maxima around phase 0.5. The absorption peaks, however, did not align exactly with phase 0.5, suggesting the inhomogeneous structures such as an accretion wake and/or a bow shock. We compared the observed modulations with calculations based on a stellar wind model, accelerated by ultraviolet radiation from the WR star. One of the calculations qualitatively reproduced the observed trend that H-like Fe ions were concentrated near the compact object, whereas H-like S was distributed across the binary system, with H-like Ca and Ar showing intermediate spatial distributions. From this comparison, we estimated that a mass-loss rate of the stellar wind was approximately $5 \times 10^{-6}$-$1 \times 10^{-5}\ M_{\odot}\ {\rm yr}^{-1}$.