An empirical relation to estimate host galaxy stellar light from AGN spectra

Measurement of black hole mass for low-$z$ ($z\leq 0.8$) Active Galactic Nuclei (AGNs) is difficult due to the strong contribution from host galaxy stellar light necessitating detailed spectral decomposition to estimate the AGN luminosity. Here, we present an empirical relation to estimate host galaxy stellar luminosity from the optical spectra of AGNs at $z\leq 0.8$. The spectral data were selected from the fourteenth data release of the Sloan Digital Sky Survey (SDSS-DR14) quasar catalog having a signal-to-noise ratio at 5100 \AA (SNR$_{5100}$) $>$10 containing 11415 quasars. The median total luminosity (log ($L_\text{total}$/[erg s$^{-1}$])), stellar luminosity (log ($L_\text{star}$/[erg s$^{-1}$])), and AGN continuum luminosity (log ($L_\text{cont}$/[erg s$^{-1}$])) in our sample are 44.52, 44.06, and 44.30, respectively. We fit the AGN power-law continuum, host galaxy, and iron blend contribution, simultaneously over the entire available spectrum. We found the host galaxy fraction to anti-correlate with continuum luminosity and can be well-represented by a polynomial function, which can be used to correct the stellar light contribution from AGN spectra. We also found anti-correlation between host galaxy fraction and iron strength, Eddington ratio, and redshift. The empirical relation gives comparable results of host-fraction with the image decomposition method.