High-resolution Giant Metrewave Radio Telescope H{\sc i} 21\,cm imaging of the host galaxy of FRB\,20250316A

We report Giant Metrewave Radio Telescope (GMRT) H{\sc i} 21,cm imaging of NGC,4141, the host galaxy of FRB,20250316A at $z=0.0063$. Our GMRT H{\sc i} 21,cm images have spatial resolutions, at $z\approx 0.0063$, of $\approx 0.48-8.0$~kpc, and find evidence for (i)~a companion galaxy, LEDA,2582852, to the south-west, (ii)~a nearby (27-kpc distant) H{\sc{i}} cloud to the south-west, (iii)~disturbances in the H{\sc{i}} distributions of both NGC,4141 and LEDA,2582852, and (iv)~high H{\sc{i}} column densities in the south-western outskirts of NGC,4141. A Sloan Digital Sky Survey spectrum shows evidence for a low metallicity and a high star-formation rate (SFR) surface density activity in the south-western disk of NGC,4141, while H$\alpha$-based SFR estimates over the last 10~Myr are higher than radio-based SFRs over the last 100~Myr. The above evidence indicates that NGC,4141 has recently acquired metal-poor gas, via either a merger or accretion, that resulted in the south-western starburst and that may have also triggered large-scale star-formation activity in NGC,4141, resulting in the formation of the stellar progenitor of FRB,20250316A and the other transients. Our highest-resolution (480~pc) GMRT H{\sc{i}} 21,cm image finds no H{\sc{i}} 21,cm emission from the location of FRB,20250316A or the nearby star-forming region, suggesting that most of the H{\sc{i}} here has been either ionized or converted into the molecular phase. Our non-detection of continuum emission at the location of FRB,20250316A yields the $3\sigma$ upper limit $<3.2\times {10}^{25}$~erg~s${}^{-1}$~Hz${}^{-1}$, on the 1.4~GHz specific luminosity of a putative persistent radio source associated with FRB,20250316A, one of the strongest constraints on the radio luminosity of such an associated persistent radio source.