Electromagnetic signatures from accreting massive black hole binaries in time domain photometric surveys

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We study spectral and time variability of accreting massive black hole binaries (MBHBs) at milli-parsec separations surrounded by a geometrically thin circumbinary disc. To this end, we present the first computation of the expected spectral energy distribution (SED) and light curves (LCs) from 3D hyper-Lagrangian resolution hydrodynamic simulations of these systems. We modelled binaries with a total mass of $10^6$ M$_ eccentricities of $e=0,\, 0.9$, and a mass ratio of $q=0.1,\, 1$. The circumbinary disc has an initial aspect ratio of 0.1, features an adiabatic equation of state, and evolves under the effect of viscous heating, black-body cooling, and self gravity. To construct the SED, we considered black-body emission from each element of the disc and we added a posteriori an X-ray corona with a luminosity proportional to that of the mini-discs that form around each individual black hole. We find significant variability of the SED, especially at high energies, which translates into LCs displaying distinctive modulations of a factor of $ 2$ in the optical and of $ 10$ in UV and X-rays. We analysed in detail the flux variability in the optical band that will be probed by the Vera Rubin Observatory (VRO). We find clear modulations on the orbital period and half of the orbital period in all systems. Only in equal-mass binaries, we find an additional, longer-timescale modulation, associated with an over-density forming at the inner edge of the circumbinary disc (commonly referred to as a lump). When considering the VRO flux limit and nominal survey duration, we find that equal-mass, circular binaries are unlikely to be identified, due to the lack of prominent peaks in their Fourier spectra. Conversely, unequal-mass and/or eccentric binaries can be singled out up to $z 0.5$ (for systems with bol $ erg s$^ $) and $z 2$ (for systems with bol $ erg s$^ $). Identifying electromagnetic signatures of MBHBs at separations of $ $ pc is of paramount importance to understand the physics of the gravitational wave (GW) sources of the future Laser Interferometer Space Antenna, and to pin down the origin of the GW background (GWB) observed in pulsar timing arrays.