Black holes as telescopes: Discovering supermassive binaries through quasi-periodic lensed starlight

Abstract

Supermassive black hole (SMBH) binary systems are unavoidable outcomes of galaxy mergers. Their dynamics encode information about their formation and growth, the composition of their host galactic nuclei, the evolution of galaxies, and the nature of gravity. Many SMBH binaries with separations pc-kpc have been found, but closer (sub-parsec) binaries remain to be confirmed. Identifying these systems may elucidate how binaries evolve past the ``final parsec'' until gravitational radiation drives them to coalescence. Here we show that SMBH binaries in non-active galactic nuclei can be identified and characterized by the gravitational lensing of individual bright stars, located behind them in the host galaxy. The rotation of `caustics' -- regions where sources are hugely magnified due to the SMBH binary's orbit and inspiral -- leads to Quasi-Periodic Lensing of Starlight (QPLS). The extreme lensing magnification of individual bright stars produces a significant variation in the host galaxies' luminosity; their lightcurve traces the orbit of the SMBH binary and its evolution. QPLS probes the population of sources observable by pulsar timing arrays and space detectors (LISA, TianQin), offering advance warning triggers for merging SMBHs for coincident or follow-up GW detections. SMBH population models predict $1-50\; [190-5,000] \left({n_\star}/{\rm pc}^{-3}\right)$ QPLS binaries with period less than $10\; [40]$ yr with comparable masses and $z<0.3$, where $n_\star$ is the stellar number density. Additionally, stellar and orbital motion will lead to frequent instances of single/double flares caused by SMBHBs with longer periods. This novel signature can be searched for in a wealth of existing and upcoming time-domain photometric data: identifying quasi-periodic variability in galactic lightcurves will reveal an ensemble of binary systems and illuminate outstanding questions around them.

Figures (12)

• Figure 1: Quasi-periodic lensing of starlight: a bright star (left) is highly magnified by a binary supermassive black hole binary (center). The caustic rotates as the binary orbits, producing a bright quasi-periodic signal at the central region of the host galaxy (right). The SMBHB in the diagram has total mass of $10^{10} \mathrm{M}_{\odot}$ and an initial period of 2 years. The distance between the lens and source plane is 1 kpc, the star has a size of $10R_{\odot}$. The red dots in the lens plane mark the positions of the images. There are 5(3) images when the source is inside (outside) the caustic curves, out of which 4(2) images are near the critical curve hence highly magnified. In addition to the diamond-shaped caustic, two triangle-shaped caustics form at about 230 pc from the center of mass (not shown). Credit: NASA/ESA, SXS/AEI, ESO composite-figures.
• Figure 2: Magnification as a function of time-to-merger in QPLS by an inspiraling $10^{10} \mathrm{M}_{\odot}+10^{10} \mathrm{M}_{\odot}$ SMBH binary. The source star has a radius of $10 R_{\odot}$ and is 1 kpc from the binary, the initial binary period is 1 year producing a lensing spike every 2 months. The host galaxy is assumed to be at redshift $z=0.5$. The insets show the snapshots of the source plane with the fixed source star and the caustic curve, which rotates and shrinks during the inspiral. The source planes are plotted with the same scale shown in the last inset. Animations of the evolution of the SMBHB orbits, critical curves, images, caustic curves and the lightcurve are demonstrated in a GitHub repository https://github.com/whanxi/SMBHB-Lensing-Animations.
• Figure 3: Lensing lightcurves by SMBH binaries in the LISA mass range. The host galaxies are assumed to be at redshift $z=0.5$. The total mass, initial period, initial eccentricity, source radius, source-lens distance are labeled in the plots, where $T_{\rm day} = T/{\rm day}$. Top: a quasi-circular LISA binary $7.5\cdot10^5$ yr before merger representing the LISA binary population at an earlier stage. Middle: an eccentric binary 11 years before merging in the LISA band. Bottom: A highly eccentric LISA binary which enters the LISA band during each periastron passage represented by the grey lines. The inset shows one periastron passage, where the width of the gray line represents the few hours long time interval where the gravitational wave bursts are in the LISA band. https://github.com/whanxi/SMBHB-Lensing-Animations
• Figure 4: Prospects for multi-messenger observations of SMBHBs using QPLS in the plane of total SMBH mass and redshifted orbital period. Slanted filled regions show the systems that will merge in 10 years for different values of the eccentricity. Horizontal lines correspond to the systems shown in Figs. \ref{['fig:massive_light_curve']} (A) and \ref{['fig:lisa_light_curve']} (B,C,D - top to bottom) at $z=0.5$. LISA regions show the orbital period where the signal-to-noise-ratio above $10^{-4}$ Hz reaches $>10$ for equal-mass, non-spinning and quasi-circular SMBHBs at $z=0.5$ (dashed) and $z=5$ (solid). PTA regions correspond to IPTA 2025 (solid) and SKA 2034 (dashed) for quasi-circular q=1 SMBHs at z=0.5 Charisi:2021dwc. Horizontal arrows show the cadence-to-survey time of several transient surveys (these apply for all masses). For Rubin/LSST we distinguish the cadence of any-filter (thin, 4 days) from that of all-6-filters (thick, 24 days). A circular (eccentric) binary produces 4 (1) single-peaked or double-peaked caustic crossings during each orbital period.
• Figure 5: Dimensionless orbital separation $d=a/\xi_0$ (Eq. \ref{['eq:d_dimensionless_scale']}) of a binary lens if the source is at 1 kpc. Dashed lines represent constant physical orbital separation. The dashed line indicates the transition to GW-dominated inspiral at $a=10^3 GM/c^2$Haiman_Kocsis_Menou2009.