Probing Broadband Spectral Energy Distribution and Variability of Mrk\,501 in the low flux state

We conducted a multi-wavelength analysis of the blazar Mrk\,501, utilizing observations from \emph{Astro}Sat (SXT, LAXPC), \emph{Swift-UVOT}, and \emph{Fermi-LAT} during the period August 15, 2016 to March 27, 2022. The resulting multi-wavelength light curve revealed relatively low activity of the source across the electromagnetic spectrum. Notably, logparabola and broken power-law models provided a better fit to the joint X-ray spectra from \emph{Astro}Sat-SXT/LAXPC instruments compared to the power-law model. During the low activity state, the source showed the characteristic harder when brighter trend at the X-ray energies. To gain insights into underlying physical processes responsible for the broadband emission, we performed a detailed broadband spectral analysis using the convolved one-zone leptonic model with different forms of particle distributions such as logparabola (LP), broken power-law (BPL), power-law model with maximum energy ($\xi_{max}$), and energy-dependent acceleration (EDA) models. Our analysis revealed similar reduced-$\chi^2$ values for the four particle distributions. The LP and EDA models exhibited the lowest jet powers. The correlation analyses conducted for the LP and BPL models revealed that there is a positive correlation between jet power and bulk Lorentz factor. Specifically, in the LP model, jet power proved independent of $\gamma_{min}$, whereas in the broken power-law model, jet power decreased with an increase in $\gamma_{min}$. The jet power in the LP/EDA particle distribution is nearly 10 percent of the Eddington luminosity of a $10^7$ M$_\odot$ black hole. This result suggests that the jet could potentially be fueled by accretion processes.