Probing the disc-jet coupling in S4 0954+65, PKS 0903-57, & 4C +01.02 with $\gamma$-rays

We present a comprehensive variability study on three blazars, S4 0954+65, PKS 0903-57, and 4C +01.02 covering a mass range of log(M/M$_{\odot}$) = 8--9, by using $\sim$15 years-long $\gamma$-ray light curves from \textit{Fermi}-LAT. The variability level is characterized by the fractional variability amplitude which is higher for $\gamma$-rays compared to optical/UV and X-rays emissions. A power spectral density (PSD) study and damped random walk (DRW) modeling are done to probe the characteristic timescale. The PSD is fitted with a single power-law (PL) and bending power-law models and the corresponding success fraction was estimated. In the case of PKS 0903-57, We observed a break in the $\gamma$-ray PSD at 256 days which is comparable to the viscous timescale in the accretion disc suggesting a possible disk-jet coupling. The non-thermal damping timescale from the DRW modeling is compared with the thermal damping timescale for AGNs including our three sources. Our sources lie on the best-fit of the $\mathrm{\tau^{rest}_{damping}} - M_{BH}$ plot derived for AGN suggesting a possible accretion disc-jet connection. If the jet's variability is linked to the disc's variability, we expect a log-normal flux distribution, often connected to the accretion disc's multiplicative processes. Our study observed a double log-normal flux distribution, possibly linked to long and short-term variability from the accretion disk and the jet. In summary, PSD and DRW modeling results for these three sources combined with blazars and AGNs studied in literature favor a disc-jet coupling scenario. However, more such studies are needed to refine this understanding.