Absorption lines from magnetically driven winds in X-ray binaries II: high resolution observational signatures expected from future X-ray observatories

In our self-similar, analytical, magneto-hydrodynamic (MHD) accretion-ejection solution, the density at the base of the outflow is explicitly dependent on the disk accretion rate - a unique property of this class of solutions. We had earlier found that the ejection index $p >\sim 0.1 (\dot{M}_{acc} \propto r^p ) $ is a key MHD parameter that decides if the flow can cause absorption lines in the high resolution X-ray spectra of black hole binaries. Here we choose 3 dense warm solutions with $p = 0.1, 0.3, 0.45$ and carefully develop a methodology to generate spectra which are convolved with the Athena and XRISM response functions to predict what they will observe seeing through such MHD outflows. In this paper two other external parameters were varied - extent of the disk, $\rm{r_o|_{max}} = 10^5, \, 10^6 \,\, \rm{r_G}$, and the angle of the line of sight, $i \sim 10 - 25^{\circ}$. Resultant absorption lines (H and He-like Fe, Ca, Ar) change in strength and their profiles manifest varying degrees of asymmetry. We checked if a) the lines and ii) the line asymmetries are detected, in our suit of synthetic Athena and XRISM spectra. Our analysis shows that Athena should detect the lines and their asymmetries for a standard 100 ksec observation of a 100 mCrab source - lines with equivalent width as low as a few eV should be detected if the 6-8 keV counts are larger than $10^4 - 10^5$ even for the least favourable simulated cases.