Zooming in on the GeV $\gamma$-ray flare of the blazar PKS 1725+123 with a multimessenger lens
Blazars are promising sources of extragalactic high-energy astrophysical neutrinos, detected at energies $\gtrsim 10$ TeV by the IceCube neutrino observatory. Here, we report the first-ever broadband timing and spectral study of the flat-spectrum radio quasar PKS 1725+123, which has recently emerged as a compelling multimessenger target following its spatial association with the IceCube event IC-201021A. This triggered extensive follow-up observations from radio to VHE $\gamma$-rays, and a multi-episode flare was identified at a later time. During this period, the source exhibited high flux variability across all wavelengths. The {\it Fermi}-LAT analysis suggests rapid variability on timescales of less than 6 hours, implying a compact emission region with a radius of $\sim10^{16}$ cm. Our one-zone leptohadronic model shows that the high-energy $\gamma$-ray flux is produced by a combination of inverse-Compton scattering of external photons from the hot accretion disk and the broad-line region, while the X-ray emission is dominated by synchrotron self-Compton radiation from relativistic electrons. The secondary radiation from the hadronic cascade is found to be sub-dominant in the $\gamma$-ray regime, and the X-ray data constrain the maximum proton energy to $\sim 20$ PeV in the observer frame. Photopion production occurs predominantly with accretion-disk photons, resulting in an estimated muon-neutrino event rate of $\approx 0.3~\mathrm{yr}^{-1}$ during the flaring state with the flux peaking at $\sim1$ PeV. Future observations of TeV $\gamma$-rays by CTA and LHAASO will further constrain cosmic-ray production in this source.