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Multimessenger Prospects for Low-Luminosity Gamma-Ray Bursts: Joint Neutrino and X-Ray Observations

Low--luminosity gamma-ray bursts (LLGRBs) are promising candidates for high-energy neutrinos, yet no coincident neutrino events have been detected so far. Recent advances in X-ray time-domain astronomy, together with the development of next-generation neutrino telescopes, open new opportunities for joint X-ray and neutrino observations of these transients. We calculate the jet dynamical evolution and the associated neutrino production for both non-magnetized and magnetized outflows. For individual events, joint X-ray and neutrino detection is generally limited to nearby LLGRBs or sources with high luminosities. Thus, we consider a next-generation neutrino telescope with an effective area enhanced by a factor of $\sim30$ relative to IceCube. In the non-magnetized scenario, joint detection of individual events is enabled for sources with typical isotropic luminosities of $L_{\mathrm{iso}}\sim10^{47}\,\mathrm{erg\,s^{-1}}$ out to luminosity distances of $D_L\sim1.6\times10^{2}\,\mathrm{Mpc}$, corresponding to an expected detection rate of order $1$ per year. In contrast, for the magnetized scenario at the same luminosity, the accessible distance is significantly reduced, with joint observations confined to sources within $D_L\sim6.5\times10^{1}\,\mathrm{Mpc}$ and an expected detection rate of order $0.5$ per year. For stacked samples of $\sim100$ magnetized LLGRBs, stacking substantially enlarges the accessible distance range, enabling joint observations for sources with representative luminosities of $L_{\mathrm{iso}}\sim1\times10^{47}\,\mathrm{erg\,s^{-1}}$ out to $D_L\lesssim7.0\times10^{2}\,\mathrm{Mpc}$ and corresponding to an expected detection rate of order $2$ per year. These results demonstrate that joint X-ray and next-generation neutrino observations enable a practical multimessenger probe of LLGRBs.