Gravitational Waves from Massive Black Hole Mergers in ASTRID: Predictions for LISA

Abstract

We use the ASTRID cosmological simulation to forecast massive black hole (MBH) mergers detectable by Laser Interferometer Space Antenna (LISA) down to $z=0$. ASTRID directly models MBH dynamical friction, allowing a realistic tracking of their trajectory. It also incorporates relatively low-mass MBH seeds down to $5\times10^{4} M_{\odot}$, providing a more complete picture of LISA MBH mergers. We find that LISA MBH mergers initially have high eccentricities, peaking around $e_0 = 0.8$ across all redshifts. Accounting for this boosts the event rate from 5.6 yr$^{-1}$ (if circular orbits are assumed) to 10.5 yr$^{-1}$. This enhancement is largely due to additional inspiral sources that will coalesce after LISA's observation, which constitute $46\%$ of detected events.This underscores the importance of LISA's sensitivity to the early inspiral phase, especially for eccentric binaries that emit gravitational waves across a wider frequency band. Most LISA events in ASTRID arise from $M_{\mathrm{BH}}\sim10^{5-6}\ M_\odot$, low-redshift ($z<2$) and low mass-ratio ($q\sim0.01$-$0.1$) mergers. Accounting for eccentricity broadens the detectable MBH mass range up to $10^{9} M_\odot$ and shifts the peak of detectable mergers to a lower redshift $z_{\rm peak}=0.8$. This implies that the most massive LISA events may also be PTA sources. We predict LISA events to be in various galaxy environments, including many low-mass satellite galaxies. The electromagnetic (EM) counterparts of most LISA sources have active galactic nuclei (AGN) luminosities $L_{\rm bol}>10^{42}$ erg s$^{-1}$, albeit only $1\%$ with $>10^{44}$ erg s$^{-1}$. The brightest AGN are those associated with the rare LISA/PTA events with $M_{\rm BH}>10^{8} M_\odot$.

Figures (12)

• Figure 1: Examples of MBH mergers with a circular orbit ($e = 0.09$; upper panel) and a highly eccentric orbit ($e = 0.95$; lower panel) in ASTRID at $z=0.8$. The plots on the left display the separation $\Delta r$ between the two merging black holes as a function of time, with pink and blue crosses marking the last three pairs of $r_{\text{apo}}$ and $r_{\text{peri}}$ used to calculate the eccentricity values. The plots on the right show the corresponding orbital trajectories of the secondary black hole relative to the primary black hole's position. The black and red dots mark the locations of the primary black hole (BH1) and the secondary black hole (BH2) before the merger.
• Figure 2: Waveforms for three binaries of different mass and orbital eccentricity $e_0$ during the 4 years before the coalescence. The strain is calculated for $z=1$, and the mass and the initial $e_0$ are labeled on the upper right corner. In each panel, the black dotted line is the LISA instrument sensitivity curve with the galactic binary background. The thick black curve shows the strain assuming initial $e_0=0$. The thin blue curves track the strain at different evolution times. The lines of constant time are shaded from light to dark for early to late evolution. On each blue curve, the circle, square, triangle, and diamond markers represent the evolution of individual harmonics: n=2, 10, 50, and 100, respectively. The thick green curve plots the frequency having the highest strain $f_{\mathrm{peak}}$ for the eccentric waveforms during the evolution.
• Figure 3: The MBH population in ASTRID at different redshifts. $Upper:$ The black hole mass function in terms of comoving number density ($\mathrm{dex}^{-1} h^3 \mathrm{Mpc}^{-3}$). $Lower:$ The ratio between the number of the MBH involved in mergers and the total MBH.
• Figure 4: Illustration of ASTRID at $z=0.8$. The upper panel shows the large-scale structure in a slice of $100 \times 60 \times 10\ \mathrm{Mpc}^{3}\,h^{-3}$, with gas temperature represented by color: hotter regions appear in red, while cooler regions are shown in blue. Yellow circles mark the locations of detectable mergers (i.e., with SNR $>10$) occurring within the 670 Myr around $z=0.8$. Five merging systems are selected as examples, whose positions are marked in the plot. The middle panels show the stellar density field within $600\ \mathrm{kpc}/h$ around the merging MBH binaries, color-coded by the stellar age, where blue regions represent young stars. The red crosses show the position of the primary MBH (or the remnant MBH), the green crosses show the secondary MBH. The bottom panels show the host galaxy of the merging MBHs, with the RGB channels representing the flux in the rest-frame $grz$ color bands.
• Figure 5: Probability density function (PDF) of merger orbit eccentricities $e_0$ measured based on Eq. \ref{['eq:ecc_cal']}. Left: PDF for mergers at different redshifts. Solid curves represent the distribution from ASTRID merger population, and dotted curves show the fitted $\beta$ distribution (Equ. \ref{['equ:fitted_ecc_pdf']}) for the redshifts with the corresponding color. Right: PDF for mergers with different total MBH masses.