Caught in the act: detections of recoiling supermassive black holes from simulations

TL;DR

This study investigates whether gravitational-wave recoil can displace supermassive black holes (SMBHs) from massive early-type galaxies and whether the bound stellar clusters that accompany recoiling SMBHs (BRCs) are detectable. Using PN-corrected, self-consistent Ketju/GADGET-4 simulations of gas-free major mergers, it characterizes BRC properties (masses ~$10^6$–$10^7\,M_\odot$, sizes of tens of parsecs, high velocity dispersions) and explores photometric and kinematic signatures with mock Euclid-like images and IFU/SL observations (MUSE, HARMONI, MICADO, ERIS, JWST). The results show BRCs detectable up to $z\sim1$ for kicks up to ~$0.6\,v_{esc}$, with an overall detectability of about 20% when projection effects are included, and suggest a potential population of up to ~8000 detectable BRCs below $z\lesssim0.6$ in upcoming surveys. A practical workflow combining photometric preselection and kinematic follow-up is proposed to identify BRCs, leveraging elevated $\sigma_{\star}$ and characteristic LOSVD features, supported by prospects from Euclid and ELT-era facilities. The findings offer a direct observational avenue to probe the most massive SMBH mergers and advance our understanding of SMBH-galaxy co-evolution.

Abstract

We study the detectability of supermassive black holes (SMBHs) with masses of $M_{\bullet}\gtrsim 10^{9}\,\mathrm{M}_\odot$ displaced by gravitational wave recoil kicks $(v_{\rm kick}=0\mathrm{-}2000\,\mathrm{km\,s}^{-1})$ in simulations of merging massive $(M_{\star}>10^{11}\,\mathrm{M}_\odot)$ early-type galaxies. The used KETJU code combines the GADGET-4 fast multiple gravity solver with accurate regularised integration and post-Newtonian corrections (up to PN3.5) around SMBHs. The ejected SMBHs carry clusters of bound stellar material (black hole recoil clusters, BRCs) with masses in the range of $10^6 \lesssim M_{\text{BRC}} \lesssim 10^7\,\mathrm{M}_\odot$ and sizes of several $10\,\mathrm{pc}$. For recoil velocities up to $60\%$ of the galaxy escape velocity, the BRCs are detectable in mock photometric images at a Euclid-like resolution up to redshift $z \sim 1.0$. By Monte Carlo sampling the observability for different recoil directions and magnitudes, we predict that in $\sim20\%$ of instances the BRCs are photometrically detectable, most likely for kicks with SMBH apocentres less than the galaxy effective radius. BRCs occupy distinct regions in the stellar mass/velocity dispersion vs. size relations of known star clusters and galaxies. An enhanced velocity dispersion in excess of $σ\sim 600\,\mathrm{km\,s}^{-1}$ coinciding with the SMBH position provides the best evidence for an SMBH-hosting stellar system, effectively distinguishing BRCs from other faint stellar systems. BRCs are promising candidates to observe the aftermath of the yet-undetected mergers of the most massive SMBHs and we estimate that up to 8000 BRCs might be observable below $z\lesssim 0.6$ with large-scale photometric surveys such as Euclid and upcoming high-resolution imaging and spectroscopy with the Extremely Large Telescope.

Figures (8)

• Figure 1: The intrinsic BRC mass $M_\mathrm{BRC}$ at apocentre (circles) and pericentre (squares) as a function of kick velocity. Points are coloured by the radial displacement of the SMBH from the galaxy centre. For $v_\mathrm{kick} \gtrsim 540\,\mathrm{km}\,\mathrm{s}^{-1}$, $M_\mathrm{BRC}$ decreases exponentially. The grey-shaded region indicates recoil velocities less than the velocity dispersion of the SMBH binary-scoured core $\sigma_{\star,0}$.
• Figure 2: Black hole recoil cluster mock detections assuming different observation redshifts ($z=\{0.2,0.6,1.0\}$, each row respectively). Left column: projected stellar mass density at a time $t\simeq0.03\,\mathrm{Gyr}$ after $t_\mathrm{coal}$, with the remnant SMBH and BRC moving along the positive $x$-axis with velocity $v_\mathrm{kick}=540\,\mathrm{km}\,\mathrm{s}^{-1}$. Centre column: a mock image of the remnant galaxy, in Euclid VIS band apparent magnitude. Right column: the prominence from the apparent magnitude mock image. For each redshift, the BRC is seen to have a prominence of $\hat{K}\gtrsim 4.0$, and is thus detectable.
• Figure 3: Top left: Modelled relation between $v_\mathrm{kick}$ (for recoil $\geq \sigma_{\star,0}$) and apocentre, with blue regions indicating Bayesian highest density intervals (HDIs), and the dash-dotted line the detection threshold $r_\mathrm{d}(v_\mathrm{kick})$, of which 33% samples exceed. Top right: Marginal cumulative distribution of apocentre distances. The CDF is segemented at the median. Centre left: Transform sampled cumulative distribution of time to apocentre, with the CDF segmented at the median. Centre right: Minimum angular offset from the LOS axis $\theta_\mathrm{min}$ that allows $r_\mathrm{apo,proj}$ to exceed $r_\mathrm{d}(v_\mathrm{kick})$, colored by HDI. The space above the blue contours (including the region around $v_\mathrm{kick}\sim 350\,\mathrm{km}\,\mathrm{s}^{-1}$) indicates angular offsets for which the BRC would be detectable. Bottom left: Recoil velocity distribution binned in $100\,\mathrm{km}\,\mathrm{s}^{-1}$ bins (orange), and weighted by the corresponding posterior draw of observational probability $\cos\theta_\mathrm{min}$ (blue) The $y$-axis depicts the frequency of a particular bin relative to the total number of posterior draws. Bottom right: Corresponding cumulative distribution to the bottom left panel.
• Figure 4: Mock MUSE IFU observations for three recoil velocities: $0\,\mathrm{km}\,\mathrm{s}^{-1}$ (top row), $540\,\mathrm{km}\,\mathrm{s}^{-1}$ (middle row), and $720\,\mathrm{km}\,\mathrm{s}^{-1}$ (bottom row). Arrows indicate the instantaneous velocity vector of the SMBH (black circle), and the dotted circle the radius beyond which the BRC has a projected density above that of the galaxy. In the case of no SMBH recoil, there are symmetric 'lobes' of increased $\sigma$, whereas for non-zero recoil velocity, asymmetry in the lobes are present, with the absence of a lobe indicating the approximate position of the SMBH. In the middle left and bottom right panels we show an inset mock HARMONI IFU map centred on the SMBH position in a $1.5\,\mathrm{kpc}$ aperture, highlighting the locally-enhanced velocity dispersion of the BRC.
• Figure 5: Top row: Velocity dispersion profile (centred on the BRC at apocentre for the $v_\mathrm{kick}=540\,\mathrm{km}\,\mathrm{s}^{-1}$ simulation) for three long-slit spectroscopy instruments: MICADO (a first-generation ELT instrument), ERIS, and JWST, with each column corresponding to a different observation redshift of the BRC. MICADO offers the best chance of detection at higher redshifts than either ERIS or JWST. Centre row: Mock IFU maps for ERIS at different redshifts consistent with the top row. Bottom row: Mock IFU maps for JWST at different redshifts consistent with the top row. For both rows, the IFU maps are centred on the SMBH. Consistent with long-slit spectroscopy observations, the BRC is visible in velocity dispersion only at the lowest redshift.