The Host Galaxy of the Hyperactive Repeating FRB 20240114A: Behind a Galaxy Cluster

We report on the optical spectroscopic observations of the host galaxy of the hyperactive repeating fast radio burst, FRB 20240114A. The host galaxy is a dwarf galaxy at a redshift of $z=0.1306\pm0.0002$. With a rest-frame coverage of 4300-7900 \AA, we have detected H$\rm{\alpha}$, H$\rm{\beta}$, [O III]$\lambda\lambda$4959,5007, [N II]$\lambda\lambda$6548,6583, and [S II]$\lambda$6716 emission lines. The emission line ratios suggest that the ionization in the host galaxy is dominated by star formation. The star formation rate (SFR) derived from the H$\rm{\alpha}$ emission line is $(0.06 \pm 0.01) \ \rm{M_{\odot} \ yr^{-1}}$, and the SED fitting suggests the lower limit of the SFR(UV) is $0.09 \ \rm{M_{\odot} \ yr^{-1}}$. The stellar mass is $(\rm 4.0 \pm 1.8) \times 10^8 \ M_{\odot}$, making the specific star formation rate $\rm log \ sSFR(H\rm \alpha) = -9.8 \pm 0.2 \ yr^{-1}$. The line ratios indicate an upper limit of a metallicity of $\rm 12+log_{10} ([O/H]) \sim 8.5$. As the nearest dwarf host galaxy with a repeating FRB, the activity of FRB 20240114A and the properties of this host galaxy closely resemble those of FRB 20121102A and FRB 20190520B. The H$\rm{\alpha}$-traced dispersion measure (DM) provided by the ionized gas of the host galaxy has a moderate contribution of $\sim 200 \rm \ pc \ cm^{-3}$, assuming a warm ionized gas. We found that the distributions of the stellar mass versus SFR are significantly different between repeating and one-off FRBs, as determined by the MANOVA test with $p=0.0116$.