Refining the mass estimate for the intermediate-mass black hole candidate in NGC 3319

Recent X-ray observations by Jiang et al. have identified an active galactic nucleus (AGN) in the bulgeless spiral galaxy NGC 3319, located just $14.3\pm1.1\,$Mpc away, and suggest the presence of an intermediate-mass black hole (IMBH; $10^2\leq M_\bullet/\mathrm{M_{\odot}}\leq10^5$) if the Eddington ratios are as high as 3 to $3\times10^{-3}$. In an effort to refine the black hole mass for this (currently) rare class of object, we have explored multiple black hole mass scaling relations, such as those involving the (not previously used) velocity dispersion, logarithmic spiral-arm pitch angle, total galaxy stellar mass, nuclear star cluster mass, rotational velocity, and colour of NGC 3319, to obtain ten mass estimates, of differing accuracy. We have calculated a mass of $3.14_{-2.20}^{+7.02}\times10^4\,\mathrm{M_\odot}$, with a confidence of 84% that it is $\leq$$10^5\,\mathrm{M_\odot}$, based on the combined probability density function from seven of these individual estimates. Our conservative approach excluded two black hole mass estimates (via the nuclear star cluster mass, and the fundamental plane of black hole activity $\unicode{x2014}$ which only applies to black holes with low accretion rates) that were upper limits of $\sim$$10^5\,{\rm M}_{\odot}$, and it did not use the $M_\bullet\unicode{x2013}L_{\rm 2-10\,keV}$ relation's prediction of $\sim$$10^5\,{\rm M}_{\odot}$. This target provides an exceptional opportunity to study an IMBH in AGN mode and advance our demographic knowledge of black holes. Furthermore, we introduce our novel method of meta-analysis as a beneficial technique for identifying new IMBH candidates by quantifying the probability that a galaxy possesses an IMBH.