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Context. Observations of blue-shifted X-ray absorption lines indicate the presence of wind from the accretion disc in X-ray binaries. Magnetohydrodynamic (MHD) driving is one possible wind-launching mechanism. Recent theoretical developments have made self-similar magnetic accretion-ejection solutions much more generalised, showing that wind can be launched at a much lower magnetisation than the equipartition value, which had previously been the only possibility. Aims. In this work, we model the transmitted spectra through MHD-driven photoionised wind models with different levels of magnetisation. We investigate the possibility of detecting absorption lines by upcoming instruments, such as XRISM and Athena. We investigate the robustness of the method of fitting asymmetric line profiles by multiple Gaussians. Methods. We used the photoionisation code XSTAR to simulate the transmitted model spectra. To cover the extensive range of velocity and density of the wind spanned over a large distance (∼105 gravitational radii), we divided the wind into slabs following a logarithmic radial grid. Fake observed spectra are finally produced by convolving model spectra with instrument responses. Since the line asymmetries are apparent in the convolved spectra as well, this can be used in future XRISM and Athena spectra as an observable diagnostic to fit for. We applied some amount of rigor in assessing the equivalent widths of the major absorption lines, including the Fe XXVI Lyα doublets, which will be clearly distinguishable thanks to the superior quality of future high-resolution spectra. Results. Disc magnetisation stands as another crucial MHD variable that can significantly alter the absorption line profiles. Pure MHD outflow models at low magnetisation are dense enough to be observed by the existing or upcoming instruments. Therefore, these models can serve as simpler alternatives to MHD-thermal models. Fitting with multiple Gaussians is a promising method for handling asymmetric line profiles, as well as the Fe XXVI Lyα doublets. [ABSTRACT FROM AUTHOR]

In our self-similar, analytical, magnetohydrodynamic (MHD) accretion–ejection solution, the density at the base of the outflow is explicitly dependent on the disc accretion rate – a unique property of this class of solutions. We had earlier found that the ejection index |$p \gt \sim 0.1 (\dot{M}_{\rm{acc}} \propto r^p)$| 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 three 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 disc, |$\rm {r_o|_{\rm{max}}} = 10^5, \, 10^6 \, \, \rm {r_G}$|⁠ , and the angle of the line of sight, i ∼ 10–25°. 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 ks 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 104–105 even for the least favourable simulated cases. [ABSTRACT FROM AUTHOR]