Dynamical evolution timescales for the supermassive black hole system in the galaxy NGC 7727 (Arp 222)

TL;DR

The paper addresses how quickly a close supermassive black hole binary in a merging galaxy can coalesce, focusing on NGC 7727 with two SMBHs separated by ~480 pc. Using a direct N-body code with post-Newtonian corrections and a three-component galaxy model constrained by observations, the authors trace the evolution from dynamical friction to the final PN-dominated inspiral. They find that the BHs become bound after ~60–65 Myr, harden through stellar interactions at a rate of ~0.15 pc$^{-1}$ Myr$^{-1}$, and merge in ~120–140 Myr after PN effects become significant, yielding a total merger time of $130 \pm 10$ Myr starting from today; this is shorter than prior estimates based on dynamical friction alone. The projected GW signal lies in the LISA band in the final 10 μHz range, making NGC 7727 a potential low-frequency GW source and informing event-rate expectations in the context of galaxy mergers and LISA detections.

Abstract

Context. A dual active galactic nucleus candidate with a separation of only 500 pc was recently found in NGC 7727. According to the hierarchical merging scenario, such objects would be expected to merge on a timescale of a few hundred Myr. However, estimating the accurate merging timescales for the two nuclei is still a complex challenge. Aims. Using our numerical N-body code, we can trace the full evolution of central black holes during all phases: dynamical friction of unbound black holes, binary black hole formation, hardening of the system due to two-body scattering, and emission of gravitational waves leading to the final merger. Methods. Our model has next components: the bulge contains two dense stellar nuclei, each of which hosts a black hole. The most massive black hole in the center of the galaxy has a mass of 1.54x10^8 Msol and the least massive black hole in the offset second stripped nucleus has a mass of 6.33x10^6 Msol. We followed the dynamical evolution of the system up to a final separation of four Schwarzschild radii. The black holes were added as special relativistic particles and their equation of motion contains a full post-Newtonian approximation - 2.5 term. Results. Initially, the black holes are not gravitationally bound and, thus, the system spends more than 60 Myr in the phase of dynamical friction while tightening the orbit. The two-body scattering phase takes place from 60 Myr up to 120 Myr. In the last 10 Myr, the black hole's separation is seen to be rapidly shrinking due to the gravitational wave emission. Starting from the physical separation observed today, the total merging time in our model is 130 (10) Myr. Conclusions. These results have implications for the statistics of strong sources of gravitational waves at low frequencies, namely, systems engaged in an advanced state of are expected to be prime sources for the LISA mission to observe.

Figures (7)

• Figure 1: Visualisation of the NGC 7727. Left image is from Voggel2022. Right image is from ESO's VLT Survey Telescope.
• Figure 2: Initial density distributions at projection planes ($X$, $Y$) and ($Y$, $Z$) for numerical model B = 650k, rnd2. Black and dark blue dots represent the BHs in Nuc 1 and Nuc 2, respectively.
• Figure 3: Evolution of the total cumulative mass distribution (black lines for the initial masses), for the bound stage (blue shaded lines), for the merged stage (red shaded lines), and post-Newtonian phase (green shaded lines) for model B$_{\tt rnd2}$. The labels on the shades besides black represent the passed time in the simulation in Myrs.
• Figure 4: Evolution of the black hole binary parameters at the stage of the pre-bound and bound systems. Left panel: Separations, $\Delta R$, between SMBHB for the numerical models A, B, and C as solid lines. The dotted colour lines represent the second initial randomisation seeds for the particle distributions. Horizontal black dashed lines represent the level of the Schwarzschild radii for SMBHB with summarised mass: $M_{\rm \tt SMBHB}=M_{\rm \tt BH1}+M_{\rm \tt BH2}$. Middle pane: Evolution of the inverse semimajor axis for the same models. Black dashed lines show the simple linear fit for the 'hardening' of the orbits for A, B, and C models, respectively. Right panel: Evolution of eccentricity, e, for the SMBHB system for all numerical models.
• Figure 5: Combined evolution of the black holes' parameters for the pre-merging and merging stages (including the PN phases) of the NGC 7727 SMBHB. Left upper panel: Separation $\Delta R$ between SMBHB for the numerical model C$_{\tt rnd1}$. Horizontal black dashed lines represent 10, 100, and 1000 times the Schwarzschild radii for the SMBHBs' mass. The solid black line shows the size of the semi-major axis at the time when the binary starts to harden. Right upper panel: Evolution of the inverse semi-major axis for the same model. Left and right bottom panels: Evolution of eccentricity, e, and pericentre for the SMBHB system. Different colours represent the different phases of the SMBHB evolution, with dark blue: unbound phase, blue: pre-merging, and light blue: merging, including the PN terms.