Systematic NICER study of the low-ionized Fe K$\alpha$ line on RS Canum Venaticorum type stars

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 NICER (0.2$-$12 keV) archive data for the Fe K$\alpha$ line of RS Canum Venaticorum type stars. Among our analyzed 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$-$6.54 keV with its equivalent width of 44.3$-$578.4 eV: 18 observations during flares, 6 observations during unconfirmed possible flare candidates and one at a quiescent phase. These observations indicate a positive correlation between the Fe K$\alpha$ line intensity and the 7.11$-$20 keV thermal plasma luminosity with its powerlaw index of $0.86 \pm 0.46$. 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 has a negative correlation with the 7.11$-$20 keV thermal plasma luminosity with its powerlaw index of $-0.27 \pm 0.10$. This anti-correlation 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.