2025MNRAS.541.1403I

The Fe K$\alpha$ fluorescence line ($\sim 6.4$ keV) has been observed during solar and stellar flares. Two emission mechanisms of the Fe K$\alpha$ line, photoionization, and collisional ionization, have been discussed, and the aim of this work is to collect evidences for each mechanism employing a statistical correlation approach between the Fe K$\alpha$ line flux and rough flare properties. Here, we systematically searched the Neutron Star Interior Composition ExploreR (0.2-12 keV) archive data for the Fe K$\alpha$ line of RS Canum Venaticorum-type stars. Among our analysed 255 observation IDs with a total exposure of $\sim 700$ ks, we found 25 data sets (total $\sim 40$ ks) exhibiting the Fe K$\alpha$ emission line at 6.37-6.54 keV with its equivalent width of 44.3-578.4 eV: 18 observations during flares, six observations during unconfirmed possible flare candidates, and one at a quiescent phase. These observations indicate a positive correlation between the Fe K$\alpha$ line intensity ($L_{\rm{K \alpha }}$) and the 7.11-20 keV thermal plasma luminosity ($L_{\mathrm{HXR}}$) with its power-law index of $0.86 \pm 0.46$ (i.e. $L_{\mathrm{K \alpha }} \propto L_{\mathrm{HXR}}^{0.86\pm 0.46}$). This correlation in the range of the thermal plasma luminosity $10^{29-33}$ erg s$^{-1}$ is consistent with the photoionization origin of the line. On the other hand, the equivalent width of the Fe K$\alpha$ line ($\mathrm{EW}_{\mathrm{K \alpha }}$) has a negative correlation with the 7.11-20 keV thermal plasma luminosity with its power-law index of $-0.27 \pm 0.10$ (i.e. $\mathrm{EW}_{\mathrm{K \alpha }} \propto L_{\mathrm{HXR}}^{-0.27\pm 0.10}$). This anticorrelation is consistent with the decline of the fluorescence efficiency with increasing the stellar flare loop height. Furthermore, we found a signature of an absorption line at $6.38^{+0.03}_{-0.04}$ keV during a superflare of $\sigma$ Gem. The equivalent width of the line was $-34.7^{+2.03}_{-1.58}$ eV. We discuss the density of the Fe ions from the equivalent width using the curve of growth analysis.