Spectroscopic Reverberation Mapping for SARM: The Case of Mrk 1048 and Mrk 618

Robust extragalactic distance measurements are crucial for resolving the persistent discrepancy in the value of the Hubble constant (H${}_0$)). Active Galactic Nuclei (AGNs), through their compact and variable broad-line regions (BLRs), enable the determination of geometric distances when reverberation mapping (RM) is combined with spectroastrometry(SA). We report results from a spectroscopic RM campaign (October 2022 to March 2023) targeting two narrow-line Seyfert 1 galaxies, Mrk 1048 and Mrk 618, using 3.6-m DOT and 2-m HCT. High-cadence spectro-photometric monitoring was carried out using onboard instruments such as ADFOSC, HFOSC, and TANSPEC, resulting in well-sampled continuum and emission line light curves. The observed fractional variability ($F_{\mathrm{v}\mathrm{a}\mathrm{r}}$) ranged from 4% to 14% across the $g$-band, H$\beta$, and H$\alpha$ light curves. The time lags were measured using the interpolated cross-correlation function (ICCF), PyI${}^2$CCF, and $\text{textsc}JAVELIN$ methods. In the rest frame, the ICCF analysis yields H$\beta$ lags of $10.5_{-4.2}^{+2.6}$ days for Mrk 1048 and $10.2_{-2.9}^{+3.4}$ days for Mrk 618, while the corresponding H$\alpha$ lags are $18.7_{-5.4}^{+5.3}$ and $14.4_{-10.5}^{+4.6}$ days, respectively. The emission-line widths, measured from the rms spectra using ${\sigma }_{\mathrm{l}\mathrm{i}\mathrm{n}\mathrm{e}}$, give virial black hole mass estimates of $6.3_{-2.1}^{+2.0}\times {10}^7{M}_{\odot }$ for Mrk 1048 and $1.2_{-0.6}^{+0.4}\times {10}^7{M}_{\odot }$ for Mrk 618. These results will serve as a basis for absolute geometric distance calibration when combined with VLTI/GRAVITY spectro-astrometric measurements, thereby contributing to the development of AGNs as standardizable cosmological probes.