A hot core in the group-dominant elliptical galaxy NGC 777

NGC 777 provides an example of a phenomenon observed in some group-central ellipticals, in which the temperature profile shows a central peak, despite the short central cooling time of the intra-group medium. We use deep Chandra X-ray observations of the galaxy, supported by uGMRT 400 MHz radio imaging, to investigate the origin of this hot core. We confirm the centrally-peaked temperature profile and find that entropy and cooling time both monotonically decline to low values (2.62 [+0.19, -0.18] keV cm$^2$ and 71.3 [+12.8, -13.1] Myr) in the central ~700 pc. Faint diffuse radio emission surrounds the nuclear point source, with no clear jets or lobes but extending to ~10 kpc on a northwest-southeast axis. This alignment and extent agree well with a previously identified filamentary H$α$+[NII] nebula. While cavities are not firmly detected, we see X-ray surface brightness decrements on the same axis at 10-20 kpc radius which are consistent with the intra-group medium having been pushed aside by expanding radio lobes. Any such outburst must have occurred long enough ago for lobe emission to have faded below detectability. Cavities on this scale would be capable of balancing radiative cooling for at least ~240 Myr. We consider possible causes of the centrally peaked temperature profile, including gravitational heating of gas as the halo relaxes after a period of AGN jet activity, and heating by particles leaking from the remnant relativistic plasma of the old radio jets.