Suppressed "lump" EM signature in radiation pressure dominated accreting massive black hole binaries

TL;DR

This work investigates how radiation pressure alters the electromagnetic signatures of milli-parsec MBHBs in a self-gravitating circumbinary disc using 3D hyper-Lagrangian simulations with $M_B=10^6\,M_\odot$ and varied eccentricities and mass ratios. By coupling a black-body emission model to the hydrodynamics, the authors show that radiation pressure drives the mini-discs toward UV with higher peak luminosities while cooling the circumbinary disc, shifting its emission to lower frequencies. Crucially, radiation pressure suppresses the characteristic lump modulation in equal-mass circular binaries, though eccentric systems retain orbital-period modulations, and enhanced mini-disc/stream emission increases optical detectability to higher redshifts. These results imply that radiation pressure must be incorporated to accurately predict MBHB EM counterparts and to optimize identification strategies in time-domain surveys like the Vera Rubin Observatory (LSST).

Abstract

We investigate the impact of radiation pressure on electromagnetic signatures of accreting massive black hole binaries (MBHBs) at milli-parsec separations, using 3D hyper-Lagrangian resolution hydrodynamical simulations. We model binaries embedded in a self-gravitating circumbinary disc that evolves following an adiabatic equation of state, including viscous heating and black-body cooling. Focusing on binaries with a total mass of $10^6 \, M_{\odot}$, eccentricities $e=0,0.45,0.9$ and mass ratios $q=1, 0.7$, we find that radiation pressure significantly affects both the spectral energy distributions (SEDs) and the light curves (LCs). The emission from the mini-discs shifts from the optical towards UV frequencies and with a peak luminosity orders of magnitude higher, while the circumbinary disc becomes colder and dimmer as a result of its geometrically thinner configuration. Temporal variability is affected as well: near UV and soft-X ray fluxes are higher and more variable. Crucially, radiation pressure suppresses the characteristic "lump" formation in equal-mass circular systems, while a lump is formed for higher eccentricities without imprinting any modulation on the flux. In the circular case we still find a modulation on the cavity edge timescale at a frequency $0.36 \, f_{\rm K}$, while in eccentric binaries, only robust orbital period modulations ($f=1,2 \, f_{\rm K}$) are observed, with no modulation associated with the cavity orbital motion. Moreover, the enhanced emission from the mini-discs and streams due to radiation pressure, one redshifted, results in brighter flux in the optical G band, proving detectability of MBHBs signatures even at higher redshift ($z=0.6-1.0$). Our results reveal that radiation pressure plays a crucial role in shaping MBHBs spectral and time-domain features, with implications for their identification in time-domain surveys.

Figures (6)

• Figure 1: Spectral energy distributions (SEDs) obtained by including the contribution of the radiation pressure either a posteriori (left column) or during the binary evolution (right panel) at the same accretion rate for the $e=0$$q=1$ binaries (top panel), $e=0.45$$q=0.7$ binaries (centre panel), and $e=0.9$$q=1$ binaries (bottom panel). The contribution from the different regions of the disc (e.g. mini-discs, stream, inner and outer part of the circumbinary disc and the corona) are highlighted in different colours and have been computed at the time when the accretion rate of both binaries is equal.
• Figure 2: Profiles of surface density (first row), disc aspect ratio H/R (second row), midplane temperature (third row), optical depth $\tau$ and the effective temperature (last row) for the two mini-discs around each black hole in the circular equal mass binary, at time $t=1133 \, P_{\rm B}$, the same shown in Fig. \ref{['fig:SEDs']}. Blue and orange lines correspond to the two mini-discs while the solid and dashed lines refers to the simulation without and with the implementation of the radiation pressure, respectively. We calculate the profiles of these quantities within the Roche Lobe of each black hole. We computed the midplane temperature and the effective temperature assuming that both the gas and the radiation pressure contribute to the hydrostatic equilibrium of the disc.
• Figure 3: Light curves and the corresponding Fast Fourier Transform (FFT) obtained by including the contribution of the radiation pressure either a posteriori (left column) or during the binary evolution (right panel) for the $e=0$$q=1$ binaries (top panel), $e=0.45$$q=0.7$ binaries (centre panel), and $e=0.9$$q=1$ binaries (bottom panel). In each panel, the first row shows the accretion rate (green line) and the optical G flux (blue line), while the second and last row show the flux and FFT in the UV (light blue line) and soft-X (purple line) band, respectively. The FFT is computed over 300 orbits in the window $t=1000-1300 \, P_{\rm B}$ for the circular case and over 400 orbits in the window $t=1200-1600 \, P_{\rm B}$ and $t=900-1200 \, P_{\rm B}$ for the mildly and highly eccentric cases, respectively. The FFT is normalised to unity and shown as a function of $f/f_{\rm k}$ with $f_{\rm k}$ the Keplerian frequency of the binary. The optical flux is computed considering an extra Gaussian noise component, as described in Sec. \ref{['sec:EmissionModel']}.
• Figure 4: Surface density and effective temperature maps for circular equal-mass binaries with $e=0$ (upper figure) and $e=0.9$ ($e=0.9$, $q=1$) binaries (bottom figure). For each case, the first and second row show the result of simulations without and with radiation pressure, respectively. The green circle marks the region from which the main emission modulation in the FFT originates: in gas-pressure-only cases, this corresponds to the lump ($R \sim 2.5 - 3 \,a$ for $e=0$, and $R \sim 2.9 - 4.5 \,a$ for $e=0.9$), while with radiation pressure the main emission at low frequencies in the circular binary arises from the cavity edge ($R \sim 1.81 - 2.18\,a$).
• Figure 5: Fast Fourier Transform of the optical G band flux. From the top to the last panel: circular, mildly eccentric $e=0.45$ and highly eccentric $e=0.9$ binaries. The first and second row of each case shows the FFT computed without and with the implementation of the radiation pressure, respectively. The FFT is computed over 300 orbital periods in the eccentric case and 400 orbital periods in the eccentric ones, placing the binaries at different redshifts.