Binary Hardening Research Articles

Signatures of circumbinary disc dynamics in multimessenger population studies of massive black hole binaries

ABSTRACT We investigate the effect of the cutting-edge circumbinary disc (CBD) evolution models on massive black hole binary (MBHB) populations and the gravitational wave background (GWB). We show that CBD-driven evolution leaves a tell-tale signature in MBHB populations, by driving binaries towards an equilibrium eccentricity that depends on the binary mass ratio. We find high orbital eccentricities ($e_{\rm b} \sim 0.5$) as MBHBs enter multimessenger observable frequency bands. The CBD-induced eccentricity distribution of MBHB populations in observable bands is independent of the initial eccentricity distribution at binary formation, erasing any memory of eccentricities induced in the large-scale dynamics of merging galaxies. Our results suggest that eccentric MBHBs are the rule rather than the exception in upcoming transient surveys, provided that CBDs regularly form in MBHB systems. We show that the GWB amplitude is sensitive to CBD-driven preferential accretion onto the secondary, resulting in an increase in GWB amplitude $A_{\rm yr^{-1}}$ by over 100 per cent with just 10 per cent Eddington accretion. As we self-consistently allow for binary hardening and softening, we show that CBD-driven orbital expansion does not diminish the GWB amplitude, and instead increases the amplitude by a small amount. We further present detection rates and population statistics of MBHBs with $M_{\rm b} \gtrsim 10^6 \, {\rm M}_{\odot }$ in Laser Interferometer Space Antenna, showing that most binaries have equal mass ratios and can retain residual eccentricities up to $e_{\rm b} \sim 10^{-3}$ due to CBD-driven evolution.

Core Formation by Binary Scouring and Gravitational Wave Recoil in Massive Elliptical Galaxies

Scouring by supermassive black hole (SMBH) binaries is the most accepted mechanism for the formation of the cores seen in giant elliptical galaxies. However, an additional mechanism is required to explain the largest observed cores. Gravitational-wave (GW) recoil is expected to trigger further growth of the core, as subsequent heating from dynamical friction of the merged SMBH removes stars from the central regions. We model core formation in massive elliptical galaxies from both binary scouring and heating by GW recoil and examine their unique signatures. We aim to determine whether the nature of cores in 3D space density can be attributed uniquely to either process and whether the magnitude of the kick can be inferred. We perform N-body simulations of galactic mergers of multicomponent galaxies, based on the observed parameters of four massive elliptical galaxies with cores >0.5 kpc. After binary scouring and hardening, the merged SMBH remnant is given a range of GW recoil kicks with 0.5–0.9 of the escape speed of the galaxy. We find that binary scouring alone can form the cores of NGC 1600 and A2147-BCG, which are <1.3 kpc in size. However, the >2 kpc cores in NGC 6166 and A2261-BCG require heating from GW recoil kicks of <0.5 of the galaxy escape speed. A unique feature of GW recoil heating is flatter cores in surface brightness, corresponding to truly flat cores in 3D space density. It also preferentially removes stars on low angular momentum orbits from the galactic nucleus.

Gaia uncovers difference in B and Be star binarity at small scales: evidence for mass transfer causing the Be phenomenon

ABSTRACT Be stars make up almost 20 per cent of the B star population, and are rapidly rotating stars surrounded by a disc; however the origin of this rotation remains unclear. Mass transfer within close binaries provides the leading hypothesis, with previous detections of stripped companions to Be stars supporting this. Here, we exploit the exquisite astrometric precision of Gaia to carry out the largest to date comparative study into the binarity of matched samples of nearby B and Be stars from the Bright Star Catalogue. By utilizing new ‘proper motion anomaly’ values, derived from Gaia DR2 and DR3 astrometric data alongside previous values calculated using Hipparcos and Gaia data, and the Gaia-provided RUWE, we demonstrate that we can identify unresolved binaries down to separations of 0.02 arcsec. Using these measures, we find that the binary fractions of B and Be stars are similar between 0.04 and 10 arcsec, but the Be binary fraction is significantly lower than that of the B stars for separations below 0.04 arcsec. As the separation range of these ‘missing’ binaries is too large for mass transfer, and stripped companions are not retrieved by these measures, we suggest the companions migrate inwards via binary hardening within a triple system. This confirms statistically for the first time the hypothesis that binary interaction causes the Be phenomenon, with migration causing the dearth of Be binaries between 0.02 and 0.04 arcsec. Furthermore, we suggest that triplicity plays a vital role in this migration, and thus in the formation of Be stars as a whole.

Ketju – resolving small-scale supermassive black hole dynamics in gadget-4

ABSTRACT We present the new public version of the ketju supermassive black hole (SMBH) dynamics module, as implemented into gadget-4. ketju adds a small region around each SMBH where the dynamics of the SMBHs and stellar particles are integrated using an algorithmically regularized integrator instead of the leapfrog integrator with gravitational softening used by gadget-4. This enables modelling SMBHs as point particles even during close interactions with stellar particles or other SMBHs, effectively removing the spatial resolution limitation caused by gravitational softening. ketju also includes post-Newtonian (PN) corrections, which allows following the dynamics of SMBH binaries to sub-parsec scales and down to tens of Schwarzschild radii. Systems with multiple SMBHs are also supported, with the code also including the leading non-linear cross terms that appear in the PN equations for such systems. We present tests of the code showing that it correctly captures, at sufficient mass resolution, the sinking driven by dynamical friction and binary hardening driven by stellar scattering. We also present an example application demonstrating how the code can be applied to study the dynamics of SMBHs in mergers of multiple galaxies and the effect they have on the properties of the surrounding galaxy. We expect that the presented ketju SMBH dynamics module can also be straightforwardly incorporated into other codes similar to gadget-4, which would allow coupling small-scale SMBH dynamics to the rich variety of galactic physics models that exist in the literature.

Massive black hole mergers with orbital information: predictions from the ASTRID simulation

ABSTRACT We examine massive black hole (MBH) mergers and their associated gravitational wave signals from the large-volume cosmological simulation Astrid . Astrid includes galaxy formation and black hole models recently updated with an MBH seed population between 3 × 104h−1M⊙ and 3 × 105h−1M⊙ and a sub-grid dynamical friction (DF) model to follow the MBH dynamics down to 1.5 ckpc h−1. We calculate the initial eccentricities of MBH orbits directly from the simulation at kpc-scales, and find orbital eccentricities above 0.7 for most MBH pairs before the numerical merger. After approximating unresolved evolution on scales below ${\sim 200\, \text{pc}}$, we find that the in-simulation DF on large scales accounts for more than half of the total orbital decay time ($\sim 500\, \text{Myr}$) due to DF. The binary hardening time is an order of magnitude longer than the DF time, especially for the seed-mass binaries (MBH &amp;lt; 2Mseed). As a result, only $\lesssim 20{{\rm per \,cent}}$ of seed MBH pairs merge at z &amp;gt; 3 after considering both unresolved DF evolution and binary hardening. These z &amp;gt; 3 seed-mass mergers are hosted in a biased population of galaxies with the highest stellar masses of $\gt 10^9\, {\rm M}_\odot$. With the higher initial eccentricity prediction from Astrid , we estimate an expected merger rate of 0.3−0.7 per year from the z &amp;gt; 3 MBH population. This is a factor of ∼7 higher than the prediction using the circular orbit assumption. The Laser Interferometer Space Antenna events are expected at a similar rate, and comprise $\gtrsim 60\,{\rm{per\,cent}}$ seed-seed mergers, $\sim 30\,{\rm{per\,cent}}$ involving only one seed-mass MBH, and $\sim 10\,{\rm{per\,cent}}$ mergers of non-seed MBHs.

Massive black hole evolution models confronting the n-Hz amplitude of the stochastic gravitational wave background

ABSTRACT We estimate the amplitude of the nano-Hz stochastic gravitational wave background (GWB) resulting from an unresolved population of inspiralling massive black hole binaries (MBHBs). To this aim, we use the L-Galaxies semi-analytical model applied on top of the Millennium merger trees. The dynamical evolution of MBHBs includes dynamical friction, stellar and gas binary hardening, and gravitational wave (GW) feedback. At the frequencies proved by the Pulsar Timing Array experiments, our model predicts an amplitude of ${\sim }1.2 \times 10^{-15}$ at ${\sim }3 \times 10^{-8}\, \rm Hz$ in agreement with current estimations. The contribution to the background comes primarily from equal-mass binaries with chirp masses above $\rm 10^{8}\, M_{\odot }$. We then consider the recently detected common red noise in NANOGrav, PPTA, and EPTA data, working under the hypothesis that it is indeed a stochastic GWB coming from MBHBs. By boosting the massive black hole growth via gas accretion, we show that our model can produce a signal with an amplitude $A\approx (2\!-\!3) \times 10^{-15}$. There are, however, difficulties in predicting this background level without mismatching key observational constraints such as the quasar bolometric luminosity functions or the local black hole mass function. This highlights how current and forthcoming GW observations can, for the first time, confront galaxy and black hole evolution models.

Stellar hardening of massive black hole binaries: the impact of the host rotation

ABSTRACT Massive black hole binaries (MBHBs) with masses of ∼104 to $\sim 10^{10} \, \mathrm{M}_{\odot {}}$ are one of the main targets for currently operating and forthcoming space-borne gravitational wave observatories. In this paper, we explore the effect of the stellar host rotation on the bound binary hardening efficiency, driven by three-body stellar interactions. As seen in previous studies, we find that the centre of mass (CoM) of a prograde MBHB embedded in a rotating environment starts moving on a nearly circular orbit about the centre of the system shortly after the MBHB binding. In our runs, the oscillation radius is ≈ 0.25 (≈ 0.1) times the binary influence radius for equal mass MBHBs (MBHBs with mass ratio 1:4). Conversely, retrograde binaries remain anchored about the centre of the host. The binary shrinking rate is twice as fast when the binary CoM exhibits a net orbital motion, owing to a more efficient loss cone repopulation even in our spherical stellar systems. We develop a model that captures the CoM oscillations of prograde binaries; we argue that the CoM angular momentum gain per time unit scales with the internal binary angular momentum, so that most of the displacement is induced by stellar interactions occurring around the time of MBHB binding, while the subsequent angular momentum enhancement gets eventually quashed by the effect of dynamical friction. The effect of the background rotation on the MBHB evolution may be relevant for LISA sources, that are expected to form in significantly rotating stellar systems.

Binaries are softer than they seem: effects of an external potential on the scattering dynamics of binaries

ABSTRACT Binary evolution is influenced by dynamical scattering with other stars in dense environments. Heggie’s law states that, due to their environments, hard binaries (whose orbital energy surpasses the typical energy of single stars) tend to harden (increase their orbital energy), while soft binaries typically soften. Here, we show that Heggie’s law sometimes needs to be revised, by accounting for an external potential, for example, for binaries in nuclear stellar discs or active galactic nucleus discs, that are affected by the central massive black hole, or binary planetesimals in protoplanetary discs, affected by the host star. We find that in such environments, where the Hill radius is finite, binary-single scattering can have different outcomes. In particular, a three-body encounter could be cut short due to stars being ejected beyond the Hill radius, thereby ceasing to participate in further close interactions. This leads to a systematic difference in the energy changes brought about by the encounter, and in particular slows binary hardening, and even causes some hard binaries to soften, on average, rather than harden. We use our previously derived analytical, statistical solution to the bound chaotic three-body problem to quantitatively characterise the revision of the hardening-softening phase transition and evolution of binaries. We also provide an analytical calculation of the mean hardening rate of binaries in any environment (also reproducing the results of detailed N-body simulations). We show that the latter exhibits a non-trivial dependence on the Hill radius induced by the environment.

Properties of loss cone stars in a cosmological galaxy merger remnant

Aims.We investigate the orbital and phase space properties of loss cone stars that interact strongly with a hard, high-redshift binary supermassive black hole (SMBH) system formed in a cosmological scenario.Methods.We use a novel hybrid integration approach that combines the directN-body codeφ-GRAPE with ETICS, a collisionless code that employs the self-consistent field method for force calculation. The hybrid approach shows considerable speed-up over direct summation for particle numbers &gt; 106, while retaining accuracy of directN-body for a subset of particles. During the SMBH binary evolution we monitor individual stellar interactions with the binary in order to identify stars that noticeably contribute to the SMBH binary hardening.Results.We successfully identify and analyze in detail the properties of stars that extract energy from the binary. We find that the summed energy changes seen in these stars match very well with the overall binary energy change, demonstrating that stellar interactions are the primary drivers of SMBH binary hardening in triaxial, gas-poor systems. We find that 76% of these stars originate from centrophilic orbits, only possible in a triaxial system. As a result, even the slight triaxiality of our system results in efficient refilling of the loss cone, avoiding the final parsec problem. We distinguish three different populations of interactions based on their apocenter. We find a clear prevalence of interactions co-rotating with the binary. Nevertheless, retrograde interactions are the most energetic, contributing only slightly less than the prograde population to the overall energy exchange. The most energetic interactions are also likely to result in a change of sign in the angular momentum of the star. We estimate the merger timescale of the binary to be ≈20 Myr, a value larger by a factor of two than the timescale reported in a previous study.

Formation of counter-rotating and highly eccentric massive black hole binaries in galaxy mergers

ABSTRACT Supermassive black hole (SMBH) binaries represent the main target for missions such as the Laser Interferometer Space Antenna and Pulsar Timing Arrays. The understanding of their dynamical evolution prior to coalescence is therefore crucial to improving detection strategies and for the astrophysical interpretation of the gravitational wave data. In this paper, we use high-resolution N-body simulations to model the merger of two equal-mass galaxies hosting a central SMBH. In our models, all binaries are initially prograde with respect to the galaxy sense of rotation. But, binaries that form with a high eccentricity, e ≳ 0.7, quickly reverse their sense of rotation and become almost perfectly retrograde at the moment of binary formation. The evolution of these binaries proceeds towards larger eccentricities, as expected for a binary hardening in a counter-rotating stellar distribution. Binaries that form with lower eccentricities remain prograde and at comparatively low eccentricities. We study the origin of the orbital flip by using an analytical model that describes the early stages of binary evolution. This model indicates that the orbital plane flip is due to the torque from the triaxial background mass distribution that naturally arises from the galactic merger process. Our results imply the existence of a population of SMBH binaries with a high eccentricity and could have significant implications for the detection of the gravitational wave signal emitted by these systems.

UnderTracker: Generating Robust Binaries Using Execution Flow Traces

Programs are developed in a manner so that they execute and fulfill their intended purpose. In doing so, programmers trust the language to help them achieve their goals. Binary hardening is one such concept that prevents program behavior deviation and conveys the programmer’s intention. Therefore, to maintain the integrity of the program, measures need to be taken to avoid code-tampering. The proposed approach enforces code verification from instruction-to-instruction by using the programmer’s intended control flow. UnderTracker implements execution flow at the instruction cache by utilizing the read-only data-cache available in the program. The key idea is to place a control transfer code in data-cache and call it from instruction cache via labels. UnderTracker injects labels into the binary without affecting the semantics of the program. After the code execution starts, it verifies every control point’s legality before passing the control to the next instruction, by passively monitoring the execution flow. We proposed a cache-based monitoring method to verify code integrity. In this, we used side-channel information to monitor the program’s execution state. This monitoring system uses a sliding window scheme to detect the violation of code integrity with high reliability. This paper proposes an efficient technique, called UnderTracker to strengthen the binary integrity of an I/O intensive running program, with the nominal overhead of only 5-6% on top of the normal execution.

A relation between the radial velocity dispersion of young clusters and their age

The majority of massive stars (&gt; 8M⊙) in OB associations are found in close binary systems. Nonetheless, the formation mechanism of these close massive binaries is not understood yet. Using literature data, we measured the radial-velocity dispersion (σ1D) as a proxy for the close binary fraction in ten OB associations in the Galaxy and the Large Magellanic Cloud, spanning an age range from 1 to 6 Myr. We find a positive trend of this dispersion with the cluster’s age, which is consistent with binary hardening. Assuming a universal binary fraction offbin= 0.7, we converted theσ1Dbehavior to an evolution of the minimum orbital periodPcutofffrom ∼9.5 years at 1 Myr to ∼1.4 days for the oldest clusters in our sample at ∼6 Myr. Our results suggest that binaries are formed at larger separations, and they harden in around 1 to 2 Myr to produce the period distribution observed in few million year-old OB binaries. Such an inward migration may either be driven by an interaction with a remnant accretion disk or with other young stellar objects present in the system. Our findings constitute the first empirical evidence in favor of migration as a scenario for the formation of massive close binaries.

Exploring the Mass Segregation Effect of X-Ray Sources in Globular Clusters. IV. Evidence of Black Hole Burning in ω Centauri

Abstract Using X-ray sources as sensitive probes of stellar dynamical interactions in globular clusters (GCs), we study the mass segregation and binary burning processes in ω Cen. We show that the mass segregation of X-ray sources is quenched in ω Cen, while the X-ray source abundance of ω Cen is much smaller than other GCs, and the binary hardness ratio (defined as , with f b being the binary fraction, and L K being the cumulative X-ray and K-band luminosity of GCs, respectively) of ω Cen is located far below the correlation line of the dynamically normal GCs. This evidence suggests that the binary burning processes are highly suppressed in ω Cen, and other heating mechanisms, very likely a black hole subsystem (BHS), are essential in the dynamical evolution of ω Cen. Through the black hole burning processes (i.e., dynamical hardening of the BH binaries), the BHS is dominating the energy production of ω Cen, which also makes ω Cen a promising factory of gravitational-wave sources in the Galaxy.

The Population III Origin of GW190521

Abstract We explore the possibility that the recently detected black hole binary (BHB) merger event GW190521 originates from the first generation of massive, metal-free, so-called Population III (Pop III) stars. Based on improved binary statistics derived from N-body simulations of Pop III star clusters, we calculate the merger rate densities of Pop III BHBs similar to GW190521, in two evolution channels: classical binary stellar evolution and dynamical hardening in high-redshift nuclear star clusters. Both channels can explain the observed rate density. However, the latter is favored by better agreement with observation and less restrictions on uncertain parameters. Our analysis also indicates that given the distinct features of the two channels, future observation of BHB mergers similar to GW190521 with third-generation gravitational wave detectors will greatly improve our knowledge of the evolution of Pop III BHBs, especially for their dynamics during cosmic structure formation.

Accelerated orbital decay of supermassive black hole binaries in merging nuclear star clusters

ABSTRACT The coalescence of supermassive black holes (SMBHs) should generate the strongest sources of gravitational waves (GWs) in the Universe. However, the dynamics of their coalescence is the subject of much debate. In this study, we use a suite of N-body simulations to follow the merger of two nuclear star clusters (NSCs), each hosting an SMBH in their centre. We find that the presence of distinct star clusters around each SMBH has important consequences for the dynamical evolution of the SMBH binary: (i) The separation between the SMBHs decreases by a few orders of magnitude in the first few Myrs by the combined effects of dynamical friction and a drag force caused by tidally stripped stars. In fact, this is a significant speedup for equal mass ratio binaries, and becomes extreme for unequal mass ratios, e.g. 1:10 or 1:100, which traditional dynamical friction alone would not permit to bind. (ii) The subsequent binary hardening is driven by the gravitational slingshots between the SMBH binary and stars, and also depends on the mass ratio between the SMBHs. Thus, with this additional drag force, we find that all SMBHs in our suite coalesce within a Hubble time. Given that about 50 per cent of Milky Way-sized galaxies host NSCs, our results are encouraging for upcoming GW observations with the Laser Interferometer Space Antenna – LISA – which will detect SMBH coalescence in the 104–107 M⊙ mass range.

Gravitational Waves from the Inspiral of Supermassive Black Holes in Galactic-scale Simulations

Abstract We study the orbital evolution and gravitational wave (GW) emission of supermassive black hole (SMBH) binaries formed in gas-free mergers of massive early-type galaxies using the hybrid tree-regularized N-body code Ketju. The evolution of the SMBHs and the surrounding galaxies is followed self-consistently from the large-scale merger down to the final few orbits before the black holes coalesce. Post-Newtonian corrections are included up to PN3.5 level for the binary dynamics, and the GW calculations include the corresponding corrections up to PN1.0-level. We analyze the significance of the stellar environment on the evolution of the binary and the emitted GW signal during the final GW emission dominated phase of the binary hardening and inspiral. Our simulations are compared to semi-analytic models that have often been used for making predictions for the stochastic GW background emitted by SMBHs. We find that the commonly used semi-analytic parameter values produce large differences in merger timescales and eccentricity evolution, but result in only differences in the GW spectrum emitted by a single binary at frequencies , which are accessible by current pulsar timing arrays. These differences are in part caused by the strong effects of the SMBH binaries on the surrounding stellar population, which are not included in the semi-analytic models.

Resilience to combined attacks

Threats to critical infrastructure are rapidly changing. It is important to anticipate how adversaries can combine various types of attacks for more devastating effects. Executives and those in leadership need a plan to prevent or mitigate these combined attacks. This paper reviews cyber, physical and electromagnetic threats and provides a guide to incrementally protect critical infrastructure. By reviewing this information, readers should be able to understand the emerging threats, ways adversaries can combine attacks and practical steps that can be taken to reduce the likelihood of an attack. The concepts discussed in this paper apply to both existing and new infrastructure. Readers will learn about cyber defence technologies including binary hardening, contextual access control, artificial intelligence (AI), re-imaging and automated orchestration. For physical defence, readers will gain an understanding of the threats posed by snipers and weaponised drones and how to prevent or minimise their impact. To protect against electromagnetic threats, readers will learn about solar storms, directed energy weapons and electromagnetic pulses. They will learn how to use new shielding materials and devices to protect the power, cooling, telecommunication and computing systems. The information in this paper should enable readers to take immediate actions to reduce their own vulnerabilities and empower them to affect policies, design codes and laws. By influencing decision makers, readers should be able to reduce risks and lessen the likelihood and severity of an attack.

Evolution of supermassive black hole binaries and tidal disruption rates in non-spherical galactic nuclei

Binary supermassive black holes (SMBH) are expected to form naturally during galaxy mergers. After the dynamical friction phase, when the two SMBHs become gravitationally bound to each other, and a brief stage of initial rapid hardening, the orbit gradually continues to shrink due to three-body interactions with stars that enter the loss cone of the binary. Using the stellar-dynamical Monte Carlo code Raga, we explore the co-evolution of the binary SMBH and the nuclear star cluster in this slow stage, for various combinations of parameters (geometry of the star cluster, primary/secondary SMBH mass, initial eccentricity, inclusion of stellar captures/tidal disruptions). We compare the rates of stellar captures in galactic nuclei containing a binary to those of galaxies with a single SMBH. At early times, the rates are substantially higher in the case of a binary SMBH, but subsequently they drop to lower levels. Only in triaxial systems both the binary hardening rates and the capture rates remain sufficiently high during the entire evolution. We find that the hardening rate is not influenced by star captures, nor does it depend on eccentricity; however, it is higher when the difference between the black hole masses is greater. We confirm that the eccentricity of the binary tends to grow, which may significantly shorten the coalescence time due to earlier onset of gravitational-wave emission. We also explore the properties of the orbits entering the loss cone, and demonstrate that it remains partially full throughout the evolution in the triaxial case, but significantly depleted in the axisymmetric case. Finally, we study the distribution of ejected hypervelocity stars and the corresponding mass deficits in the central parts of the galaxies hosting a binary, and argue that the missing mass is difficult to quantify observationally.

A Chandra Survey of Milky Way Globular Clusters. II. Testing the Hills–Heggie Law

Abstract Binary–single and binary–binary encounters play a pivotal role in the evolution of star clusters, as they may lead to the disruption or hardening of binaries, a novel prediction of the Hills–Heggie law. Based on our recent Chandra survey of Galactic globular clusters (GCs), we revisit the role of stellar dynamical interactions in GCs, focusing on main-sequence (MS) binary encounters as a potential formation channel of the observed X-ray sources in GCs. We show that the cumulative X-ray luminosity (L X), a proxy of the total number of X-ray-emitting binaries (primarily cataclysmic variables and coronally active binaries) in a given GC, is highly correlated with the MS binary encounter rate (Γ b ), as . We further test the Hills–Heggie law against the binary hardness ratio, defined as the relative number of X-ray-emitting hard binaries to MS binaries and approximated by , with L K being the GC K-band luminosity and f b the MS binary fraction. We demonstrate that the binary hardness ratio of most GCs is larger than that of the solar neighborbood stars, and exhibits a positive correlation with the cluster specific encounter rate (γ), as . We also find a strong correlation between the binary hardness ratio and cluster velocity dispersion (σ), with , which is consistent with the Hills–Heggie law. We discuss the role of binary encounters in the context of the Nuclear Star Cluster, arguing that the X-ray-emitting, close binaries detected therein could have been predominantly formed in GCs that later inspiralled to the Galactic center.

Dynamical Evolution and Merger Timescales of LISA Massive Black Hole Binaries in Disk Galaxy Mergers

Abstract The Laser Interferometer Space Antenna (LISA) will detect gravitational-wave (GW) signals from merging supermassive black holes (BHs) with masses below 107 M ⊙. It is thus of paramount importance to understand the orbital dynamics of these relatively light central BHs, which typically reside in disk-dominated galaxies, in order to produce reliable forecasts of merger rates. To this aim, realistic simulations probing BH dynamics in unequal-mass disk galaxy mergers, into and beyond the binary hardening stage, are performed by combining smooth particle hydrodynamics and direct N-body codes. The structural properties and orbits of the galaxies are chosen to be consistent with the results of galaxy formation simulations. Stellar and dark matter distributions are triaxial down to the central 100 pc of the merger remnant. In all cases, a BH binary forms and hardens on timescales of at most 100 Myr, coalescing on another few-hundred-megayear timescale, depending on the characteristic density and orbital eccentricity. Overall, the sinking of the BH binary takes no more than ∼0.5 Gyr after the merger of the two galaxies is completed, but it can be much faster for very plunging orbits. Comparing with previous numerical simulations following the decay of BHs in massive early-type galaxies at z ∼ 3, we confirm that the characteristic density is the most crucial parameter determining the overall BH merging timescale, despite the structural diversity of the host galaxies. Our results lay down the basis for robust forecasts of LISA event rates in the case of merging BHs.