Self-lensing flares from black hole binaries V: systematic searches in LSST

Abstract

The Vera C. Rubin Observatory has now seen first light, and over a 10 year duration, LSST is projected to catalogue tens of millions of quasars, many of which are expected to be associated with sub-parsec supermassive black hole binaries (SMBHBs). Out of these SMBHBs, up to thousands of relatively massive binary-quasars are expected to exhibit gravitational self-lensing flares (SLFs) that last for at least 20-30 days. We assess the effectiveness of the Lomb-Scargle (LS) periodogram and matched filters (MFs) as methods for systematic searches for these binaries, using toy-models of hydrodynamical, Doppler, and self-lensing variability from equal-mass, eccentric SMBHBs. We inject SLFs into random realizations of damped random walk (DRW) lightcurves, representing stochastic quasar variability, and compute the LS periodogram with and without the SLF. We find that periodograms of SLF+DRW light-curves do not have maximum peak heights that could not arise from DRW-only periodograms. On the other hand, the matched filter signal-to-noise ratio (SNR) can distinguish SLFs from noise even with LSST-like cadences and DRW noise. Furthermore, we develop a three-step procedure with matched filters, which can also recover injected binary parameters from these light-curves. We expect this method to be computationally efficient enough to be applicable to millions of quasar light-curves in LSST.

Figures (16)

• Figure 1: Left panel: Normalized accretion rates that were used to generate the two light-curves in the right panel. The dashed and dash-dotted curves indicate the accretion from the primary and the secondary, respectively. Note that in this example, the ratio of the time-averaged accretion rates $\langle \dot{M}_2(t)\rangle/\langle\dot{M}_1(t)\rangle$ is different for $e=0.15$ vs $e=0.45$, meaning that despite $M_1=M_2$ for binlite, the relative brightness of the two disks $F_{\nu,1}/F_{\nu,2}$ can be different for different eccentricities (See § \ref{['subsec: binlite']} for discussion). Right panel: Examples of binlite-simulated optical ($r$-band) light-curves from equal-mass binaries with total mass $M = 10^9\,{\rm M}_\odot$, orbital period $T_{\rm orb} = 2~\mathrm{yr}$ at redshift $z = 1$, accreting at $30\%$ of its Eddington limit and inclined at $I = 88^\circ$. We visualize the effects of varying the orbital eccentricity for two values: $e = 0.15$ and $e = 0.45$. The dashed curves indicate the light-curves assuming no self-lensing magnification or Doppler boost effects (i.e. $\mathcal{M}_1 = \mathcal{M}_2 = 1$ in Eq. \ref{['eq: total_flux']}). We also indicate the amplitude of two periodic binary signatures: self-lensing ($A_{\rm SLF}$) and accretion variability ($A_{\rm hydro}$) for reference.
• Figure 2: Histograms of the maximum peak powers in 10,000 DRW (orange) realizations and in corresponding SLF+DRW (blue, green, red) light-curves. The height of the self-lensing flare $A_{\rm SLF}$ was varied manually so that it was $1, 2.5, 5$ (blue, green, red respectively) times larger than the DRW amplitude $A_{\rm DRW}.$ The maximum peak height value among the 10,000 pure DRW cases is marked by a vertical orange line. Out of the SLF-included light-curves, none have peak heights greater than this maximum. Counterintuitvely, as $A_{\rm SLF}/A_{\rm DRW}$ is increased, the LS power decreases (see Fig. \ref{['fig:individual light curves']} for a visual explanation of this effect).
• Figure 3: light-curves and their LS periodograms representative of the trends in Fig. \ref{['fig:SLF_vs_drw_main']}. Each column varies $A_{\rm SLF}/A_{\rm DRW}$, where the first column shows pure noise, the second column shows pure SLF signal, and the final three columns show scenarios where the signal to noise ratio $A_{\rm SLF}/A_{\rm DRW}$ is increased from 1, 2.5, 5. The same DRW noise realization is kept throughout the plots. The top row shows the injected signal of each light-curve and the light-curves are shown in the middle row. The bottom row shows LS periodograms of the light-curves, where the two vertical red lines show the injected orbital frequency $f_{\rm orb}=1/T_{\rm orb}$ and $2f_{\rm orb}$ in units of 1/day. As $A_{\rm SLF}/A_{\rm DRW}$ increases, the DRW peaks decrease and the SLF peaks increase, but the SLF peaks never become the highest peaks.
• Figure 4: Fourier transform of the injected self-lensing flares in the second column of Fig. \ref{['fig:individual light curves']}. There was no noise included and the flares were sampled at a regular and dense cadence (opposed to random cadence in Fig. \ref{['fig:individual light curves']}) for this illustration.
• Figure 5: Illustration of the mock light-curve of the fiducial binary with realistic LSST data quality. The faint blue light-curve represents the binlite binary-template used to generate the signal $s(\hat{\theta})$ and the black data points $d(t)=s(\hat{\theta})+n(t)$ represent the downsampled binary-template at LSST-like observation times with LSST-like noise and a DRW added. An estimate for the flare threshold is drawn with a dashed blue line, calculated via a simple analytical approximation for the lensing duration in Eq.\ref{['eq:lensing duration']}.