Realistic consecutive galaxy mergers form eccentric PTA sources

TL;DR

The paper investigates how consecutive major galaxy mergers can generate eccentric supermassive black hole binaries that fall into the pulsar timing array (PTA) frequency band. It combines high-resolution Griffin N-body resimulations with a semi-analytical model to evolve binary black holes from initial galactic encounters through to coalescence, incorporating dynamical friction, stellar hardening, and gravitational wave emission, and calibrating three SAM parameters with an MCMC fit. The authors find that all binaries entering the PTA band have eccentricities $e_{\rm PTA}>0.85$, with coalescence times shorter at higher resolution due to larger binary eccentricities $e_{\rm b}$, and that triple black hole systems form in several cases. These results highlight the importance of eccentricity and multi-body dynamics in shaping the PTA gravitational-wave background and imply that PTA data analyses should incorporate realistic eccentricity evolution from successive galaxy mergers.

Abstract

Results from pulsar timing arrays (PTAs) show evidence of a gravitational wave background (GWB) consistent with a population of unresolved supermassive black hole binaries (BHBs). The observed spectrum shows a flattening at lower frequencies that can be explained by a population of eccentric BHBs. This study aims to determine the dynamical evolution and merger timescales of the most massive BHBs, which are potential sources of the GWB. We select successive galactic major mergers from the IllustrisTNG100-1 cosmological simulation and re-simulate them at high resolution with the N-body code Griffin, down to binary separations of the order of a parsec. Coalescence timescales are estimated using a semi-analytical model that incorporates gravitational wave emission and stellar hardening. Throughout our investigation, we consider the impact of prior mergers on the remnant galaxy in the form of core scouring and anisotropy, which can influence the subsequent formation and evolution of BHBs. We find that all the binaries in our sample enter the PTA band with an eccentricity e>0.85: such a large eccentricity can impact the shape of the PTA observed GWB spectrum, and it highlights the importance of including the eccentricity of binaries when interpreting the PTA signal. Furthermore, we find that: (i) starting from initial separations of a few tens of kpcs, the dynamical friction phase lasts for a few hundred Myrs; (ii) the binary formation time is not resolution dependent; (iii) the scatter on the eccentricity at binary formation decreases with increasing resolution; (iv) triple systems form whenever a third galaxy interacts with a binary which hasn't yet reached coalescence.

Figures (16)

• Figure 1: Merger tree 197109 - HR. We show the time evolution of the BHs separation in Griffin simulations. The horizontal dashed black line indicates the softening length $e_{0,\rm{BH}}=1$pc. Red vertical lines represent binary formation times; yellow vertical lines represent initial times chosen for the SAM; green vertical lines are the predicted coalescence times, with the corresponding uncertainties drawn as green shaded areas. Note that for the second BHB the predicted time of coalescence almost overlaps with $t_{0,\rm{SAM}}$. This is because the eccentricity at binary formation is so extreme that the system merges immediately due to GW emission. As a consequence, this particular system does not form a triplet.
• Figure 2: For each BHB formed, we plot the dynamical friction time scale ($\Delta t_{\rm{DF}}=t_{\rm{b}}-t_0$, top panels), and the total coalescence time ($\Delta t_{\rm{coal}}=t_{\rm{coal}}-t_0$, bottom panels) as a function of the initial distance between the progenitor galaxies ($d_0$). Data are colour coded according to the initial eccentricity of the galactic merger. Note that we chose to use log$_{10} (1-e_0)$ to make the colour gradient clearer, so the colour bar goes from high (yellow) to low (blue) eccentricity values. Panels on the left refer to LR runs, while panels on the right show data from their HR counterparts. Empty circles, squares and diamonds represent the first, second and third binary in each tree, respectively.
• Figure 3: Evolution of the orbital eccentricity of the first (top panel), second (middle panel) and third (bottom panel) BHB formed in Tree 197109-HR. We highlight with coloured vertical lines the key times in the binary's evolution: initial time of the galactic merger ($t_0$, cyan), time of binary formation ($t_{\rm{b}}$, red), time where we start the SAM ($t_{\rm{SAM}}$, orange), time when the binary enters the PTA band ($t_{\rm{PTA}}$, blue) and time of coalescence ($t_{\rm{coal}}$, green). For each time, we also report the corresponding eccentricity value, plotted as a point, following the same colour scheme. The horizontal orange line denotes the MCMC best-fit value of the initial eccentricity used for the semi-analytical evolution.
• Figure 4: Histogram of the eccentricity upon entry in the PTA band of all binaries for which we can compute the peak gravitational wave frequency ($f_{\rm{GW,p}}$).
• Figure 5: Difference between the eccentricity at binary formation ($e_{\rm{b}}$) and the initial eccentricity of the merger ($e_0$) as a function of the initial galactic merger orbital eccentricity ($e_0$). The dashed horizontal line at $(e_{\rm{b}} - e_0)=0$ highlights where the points should be if the was 1:1 correlation. Empty and filled dots represent data from the LR and HR runs, respectively. The faint red shaded area highlights the region where $e_0>0.9$, while the darker red shaded area defines the region where $e_0>0.98$