Preliminary census of galaxies in the LISA localisation volume: I. Searching for LISA candidate massive black hole binary merger hosts using Sloan Digital Sky Survey photometry

Abstract: With the launch of the Laser Interferometer Space Antenna (LISA), we will be able to estimate the sky position, luminosity distance (d${L}$), chirp mass, and mass ratio for detected merging massive black hole binary (MBHB) systems. LISA's uncertainties on these estimates will evolve over time, and enable electromagnetic (EM) follow-up observations as early as a month from coalescence. In this paper, we create a framework that takes simulated LISA parameter estimates for sky localisation and d${L}$ for a MBHB and performs a census of matching EM galaxies, or candidate host galaxies. We used this framework to investigate these parameter estimates for simulated MBHB systems with masses of $3\times10^{5}$, $3\times10^{6}$, and $1\times10^{7}$M$_{\odot}$ at redshifts of $0.3$ and $0.5$ and used these parameters to select matching galaxies from archival Sloan Digital Sky Survey (SDSS) photometry. We found that the number of candidate host galaxies for a simulated MBHB system at a redshjft of $0.3$ and $1$ hour from coalescence ranged from tens to thousands. After coalescence, we found that our census numbers dropped to zero for all systems when considering median constraints most likely due to survey limitations. For a MBHB with mass $3\times10^{6}$M$_{\odot}$ at $1$ hour from coalescence, increasing the redshift from $0.3$ to $0.5$ or varying the sky position within the SDSS footprint resulted in the number of EM counterparts increasing by approximately a factor of $2$.