New possible way to determine stellar wind terminal velocity from analysis of Lyman-$α$ absorption spectra

Abstract: Stellar winds interact with the partially ionized interstellar medium (ISM), forming astrospheres. A key feature of this interaction is the hydrogen wall - secondary interstellar atoms produced via charge exchange near the tangential discontinuity separating the stellar wind from the ionized ISM component. This secondary component is decelerated and heated compared to primary interstellar hydrogen, making the hydrogen wall detectable through Lyman-$α$ absorption spectra toward nearby stars. Such structures have been observed by the Hubble Space Telescope around the Sun and other stars. In this paper, we propose that another feature of the stellar wind/partially ionized ISM interaction may also be detectable in Lyman-$α$ spectra: the neutral stellar wind. It forms via charge exchange between supersonic stellar wind protons and interstellar atoms penetrating deep into the astrosphere due to their long mean free paths. We present a parametric numerical analysis of astrospheric structures and their synthetic Lyman-$α$ absorption spectra. Using a 2D kinetic-hydrodynamic model, we vary the terminal wind velocity while maintaining constant dynamic pressure to keep the astrosphere size consistent. For winds slower than the solar wind (terminal velocities $V_0 \lesssim 200$ km/s), charge exchange efficiency in the supersonic region increases dramatically, producing a distinct and observable absorption feature from the neutral wind. This signature is negligible for solar-like winds ($V_0 \approx 400$ km/s) but emerges as a direct spectroscopic diagnostic for winds up to $\sim 200$ km/s. Detecting this neutral wind absorption offers a novel method to directly constrain stellar wind velocities.