Saturation of the curve -- diagnostics of the continuum and H$\beta$ emission in Population B active galaxy NGC 5548

NGC 5548 has been hailed as an archetypical type-1 active galactic nuclei (AGN) and serves as a valuable laboratory to study the long-term variation of its broad-line region (BLR). In this work, we re-affirm our finding on the connection between the continuum variability in the optical regime and the corresponding H$\beta$ response to it, in order to realize the increase, albeit with a gradual saturation, in the H$\beta$ emitting luminosity with increasing AGN continuum. This effect is also known as the Pronik-Chuvaev effect after the authors who first demonstrated this effect using long-term monitoring of another well-studied Type-1 AGN - Mrk 6. We employ a homogeneous, multi-component spectral fitting procedure over a broad range of spectral epochs that is then used to create the continuum and H$\beta$ light curves. We focus on the epoch range 48636-49686 MJD, different from our previous analysis. We again notice a clear signature of shallowing in the trend between the H$\beta$ and the continuum luminosities. We attempt to recover this H$\beta$ emission trend as a response to a significant continuum flux increase using CLOUDY photoionization simulations and employ a suitable broad-band spectral energy distribution for this source. We explore the wide range in the physical parameters space for modelling the H$\beta$ emission from the BLR appropriate for this source. We employ a constant density, single cloud model approach in this study and successfully recover the observed shallowing of the H$\beta$ emission with respect to the rising AGN continuum and provide constraints on the local BLR densities and the location of the H$\beta$ emitting BLR which agrees with the H$\beta$ time-lags reported from the long-term reverberation mapping monitoring. On the contrary, we do not find a significant breathing effect in the location of the H$\beta$ line-emitting BLR for this epoch in NGC 5548.