Intermediate Mass Ratio Research Articles

Examining the effects of dark matter spikes on eccentric intermediate-mass ratio inspirals using N-body simulations

ABSTRACT Recent studies suggest that dark matter (DM) spikes around intermediate-mass black holes could cause observable dephasing in gravitational wave (GW) signals from intermediate-mass ratio inspirals (IMRIs). Previous research primarily used non-self-consistent analytic methods to estimate the impact of DM spikes on eccentric IMRIs. Our study provides the first self-consistent treatment of this phenomenon using N-body simulations, incorporating post-Newtonian effects up to the 2.5 order for accurate and robust results. Contrary to prior works, which posited that the cumulative effect of two-body encounters (dynamical friction; DF) is the primary mechanism for energy dissipation, we reveal that a three-body effect (slingshot mechanism) plays a more significant role in driving the binary system’s energy loss and consequent orbital shrinkage. We find that binaries counter-rotating with respect to the DM spike merge faster, while corotating binaries merge slower, contrary to expectations from the DF theory. Using Fokker–Planck methods, we also assess the presence and detectability of spikes in realistic environments. When interacting with surrounding materials, DM spikes can have shallower slopes and lower densities than previously considered, leading to smaller signals and lower detection prospects via dephasing. Our results suggest that ‘deshifting’ rather than dephasing might be a more optimistic signature, as it is more robust even in low-density environments.

A vast population of wandering and merging IMBHs at cosmic noon

ABSTRACT Massive black holes in the centres of galaxies today must have grown by several orders of magnitude from seed black holes formed at early times. Detecting a population of intermediate mass black holes (IMBHs) can provide constraints on these elusive BH seeds. Here, we use the large volume cosmological hydrodynamical simulation Astrid, which includes IMBH seeds and dynamical friction to investigate the population of IMBH seeds. Dynamical friction is largely inefficient at sinking and merging seed IMBHs at high-z. This leads to an extensive population (several hundred per galaxy) of wandering IMBHs in large haloes at $z\sim 2$. A small fraction of these IMBHs are detectable as HLXs, Hyper Luminous X-ray sources. Importantly, at $z\sim 2$, IMBHs mergers produce the peak of GW events. We find close to a million GW events in Astrid between $z=\rm{2\!-\!3}$ involving seed IMBH mergers. These GW events (almost all detectable by LISA) at cosmic noon should provide strong constraints on IMBH seed models and their formation mechanisms. At the centre of massive galaxies, where the number of IMBHs can be as high as 10–100, SMBH-IMBH pairs can form. These Intermediate mass ratio inspirals (IMRIs) and extreme mass ratio inspirals (EMRIs), will require the next generation of milli-$\mu$Hz space-based GW interferometers to be detected. Large populations of IMBHs around massive black holes will probe their environments and MBH causal structure.

Survey of gravitational wave memory in intermediate mass ratio binaries

Survey of gravitational wave memory in intermediate mass ratio binaries

On the formation of GW190521-like binary black hole merger systems

ABSTRACT GW190521 is the most massive merging binary black hole (BBH) system detected so far. At least one of the component BHs was measured to lie within the pair-instability supernova (PISN) mass gap (∼50–135 M⊙), making its formation a mystery. However, the transient observed signal allows alternative posterior distributions. There was suggestion that GW190521 could be an intermediate-mass ratio inspiral, with the component masses m1 ∼ 170 M⊙ and m2 ∼ 16 M⊙, happening to straddle the PISN mass gap. Under this framework, we perform binary population synthesis to explore the formation of GW190521-like systems via isolated binary evolution. We numerically calculate the binding energy parameter for massive stars at different metallicities, and employ them in our calculation for common envelope evolution. Our results prefer that the progenitor binaries formed in metal-poor environment with $\rm Z\le 0.0016$. The predicted merger rate density within redshift z = 1.1 is ${\sim} 4\times 10^{-5}{\text {--}}5\times 10^{-2} \, \rm Gpc^{-3}yr^{-1}$. We expect that such events are potentially observable by upcoming both space and ground-based gravitational wave detectors.

Comparing accretion disks and dark matter spikes in intermediate mass ratio inspirals

Intermediate mass ratio inspirals (IMRIs) will be observable with space-based gravitational wave detectors such as the Llaser interferometer space antenna. To this end, the environmental effects in such systems have to be modeled and understood. These effects can include (baryonic) accretion disks and dark matter (DM) overdensities, so-called spikes. For the first time, we model an IMRI system with both an accretion disk and a DM spike present and compare their effects on the inspiral and the emitted gravitational wave signal. We study the eccentricity evolution, employ the braking index and derive the dephasing index, which turn out to be complementary observational signatures. They allow us to disentangle the accretion disk and DM spike effects in the IMRI system and can be utilized to study environmental effects in general.

Study of the intermediate mass ratio black hole binary merger up to 1000:1 with numerical relativity

We explicitly demonstrate that current numerical relativity techniques are able to accurately evolve black hole binaries with mass ratios of the order of 1000:1. This proof of principle is relevant for future third generation gravitational wave detectors and space mission LISA, as by purely numerical methods we would be able to accurately compute gravitational waves from the last stages of black hole mergers, as directly predicted by general relativity. We perform a sequence of simulations in the intermediate to small mass ratio regime, , with the small hole starting from rest at a proper distance . We compare these headon full numerical evolutions with the corresponding semianalytic point particle perturbative results finding an impressive agreement for the total gravitational radiated energy and linear momentum as well as for the waveform spectra. We display numerical convergence of the results and identify the minimal numerical resolutions required to accurately solve for these very low amplitude gravitational waves. This work represents a first step towards the considerable challenge of applying numerical-relativity waveforms to interpreting gravitational-wave observations by LISA and next-generation ground-based gravitational-wave detectors.

Intermediate-mass ratio inspirals in merging elliptical galaxies

ABSTRACT Close encounters between two initially unbound objects can result in a binary system if enough energy is released as gravitational waves (GWs). We address the scenario in which such encounters occur in merging elliptical galaxies. There is evidence that elliptical galaxies can harbour intermediate-mass black holes (IMBHs). Therefore, these systems are potentially the breeding grounds of sources of GWs corresponding to inspiraling compact objects onto a massive black hole due to the dynamics, the large densities, and the number of compact remnants they contain. We show that this process is efficient for IMBHs with masses ranging from M ∈ (103, 105) M⊙ and results in the formation of intermediate-mass ratio inspirals (IMRIs). We consider a set of IMBHs and smaller black holes with masses m2 ∈ (10, 103) M⊙ to estimate the IMRI formation rate. We find rates ranging between 10−8 and 10−5 yr−1, and the IMRI formation rate per comoving volume in merging galaxies as a function of the redshift. The peak frequencies of the gravitational radiation emitted when these IMRIs are formed are within the detection band of space-borne detectors such as the Laser Interferometer Space Antenna (LISA) and TianQin; taking into account the observable volume of these detectors, the total amount of IMRI detections per year is significant.

Comparing second-order gravitational self-force, numerical relativity, and effective one body waveforms from inspiralling, quasicircular, and nonspinning black hole binaries

We present the first systematic comparison between gravitational waveforms emitted by inspiralling, quasi-circular and nonspinning black hole binaries computed with three different approaches: second-order gravitational self-force (2GSF) theory, as implemented in the 1PAT1 model; numerical relativity (NR), as implemented by the SXS collaboration; and the effective one body (EOB) formalism, as implemented in the TEOBResumS waveform model. To compare the models we use both a standard, time-domain waveform alignment and a gauge-invariant analysis based on the dimensionless function $Q_\omega(\omega)\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. We analyse the domain of validity of the 1PAT1 model, deriving error estimates and showing that the effects of the final transition to plunge, which the model neglects, extend over a significantly larger frequency interval than one might expect. Restricting to the inspiral regime, we find that, while for mass ratios $q = m_1/m_2\le 10$ TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing $\gtrsim 1$rad; conversely, for $q\gtrsim 100$, 1PAT1 is estimated to have phase errors $<0.1$rad on a large frequency interval, while TEOBResumS develops phase differences $\gtrsim1$rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime $15\lesssim q\lesssim 64$, with $<0.5$rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for $q\gtrsim 30$, reducing the dephasing to $\approx0.27$rad even at $q=128$. Our results pave the way for the construction of GSF-informed EOB models for both intermediate and extreme mass ratio inspirals for the next generation of gravitational wave detectors.

Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case

We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function $Q_\omega\equiv \omega^2/\dot{\omega}$, where $\omega$ is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1~rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to $5\times 10^4$, the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectors

Toward a gravitational self-force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals

Building upon several recent advances in the development of effective-one-body models for spin-aligned eccentric binaries with individual masses $(m_1,m_2)$ we introduce a new EOB waveform model that aims at describing inspiralling binaries in the large mass-ratio regime, $m_1\gg m_2$. The model exploits the current state-of-the-art TEOBResumS-Dali model for eccentric binaries, but the standard EOB potentials $(A,\bar{D},Q)$, informed by Numerical Relativity (NR) simulations, are replaced with the corresponding functions that are linear in the symmetric mass ratio $\nu\equiv m_1 m_2/(m_1+m_2)^2$ taken at 8.5PN accuracy. To improve their strong-field behavior, these functions are: (i) suitably factorized and resummed using Pad\'e approximants and (ii) additionally effectively informed to state-of-the-art numerical results obtained by gravitational self-force theory (GSF). For simplicity, the spin-sector of the model is taken to be the one of TEOBResumS-Dali, though removing the NR-informed spin-orbit effective corrections. We propose the current GSF-informed EOB framework as a conceptually complete analytical tool to generate waveforms for eccentric Extreme (and Intermediate) Mass Ratio Inspirals for future gravitational wave detectors.

Numerical-relativity validation of effective-one-body waveforms in the intermediate-mass-ratio regime

One of the open problems in developing binary black hole (BBH) waveforms for gravitational wave astronomy is to model the intermediate mass ratio regime and connect it to the extreme mass ratio regime. A natural approach is to employ the effective one body (EOB) approach to the two-body dynamics that, by design, can cover the entire mass ratio range and naturally incorporates the extreme mass ratio limit. Here we use recently obtained numerical relativity (NR) data with mass ratios $m_1/m_2=(7,15,\,32,\,64,\,128)$ to test the accuracy of the state-of-the-art EOB model TEOBResumS in the intermediate mass ratio regime. We generally find an excellent EOB/NR consistency around merger and ringdown for all mass ratios and for all available subdominant multipoles, except for the $\ell=m=5$ one. This mode can be crucially improved using the new large-mass ratio NR data of this paper. The EOB/NR inspirals are also consistent with the estimated NR uncertainties. We also use several NR datasets taken by different public catalogs to probe the universal behavior of the multipolar hierarchy of waveform amplitudes at merger, that smoothly connects the equal-mass BBH to the test-mass result. Interestingly, the universal behavior is strengthened if the nonoscillatory memory contribution is included in the NR waveform. Future NR simulations with improved accuracy will be necessary to further probe, and possibly quantitatively refine, the TEOBResumS transition from late inspiral to plunge in the intermediate mass ratio regime.

The Formation of Intermediate-mass Black Holes in Galactic Nuclei

Most stellar evolution models predict that black holes (BHs) should not exist above approximately 50–70 M ⊙, the lower limit of the pair-instability mass gap. However, recent LIGO/Virgo detections indicate the existence of BHs with masses at and above this threshold. We suggest that massive BHs, including intermediate-mass BHs (IMBHs), can form in galactic nuclei through collisions between stellar-mass BHs and the surrounding main-sequence stars. Considering dynamical processes such as collisions, mass segregation, and relaxation, we find that this channel can be quite efficient, forming IMBHs as massive as 104 M ⊙. This upper limit assumes that (1) the BHs accrete a substantial fraction of the stellar mass captured during each collision and (2) that the rate at which new stars are introduced into the region near the SMBH is high enough to offset depletion by stellar disruptions and star–star collisions. We discuss deviations from these key assumptions in the text. Our results suggest that BHs in the pair-instability mass gap and IMBHs may be ubiquitous in galactic centers. This formation channel has implications for observations. Collisions between stars and BHs can produce electromagnetic signatures, for example, from X-ray binaries and tidal disruption events. Additionally, formed through this channel, both BHs in the mass gap and IMBHs can merge with the SMBHs at the center of a galactic nucleus through gravitational waves. These gravitational-wave events are extreme- and intermediate-mass ratio inspirals.

Circularization versus eccentrification in intermediate mass ratio inspirals inside dark matter spikes

Inspirals of an intermediate mass black hole (IMBH) and a solar mass type object will be observable by space based gravitational wave detectors such as the Laser Interferometer Space Antenna. A dark matter overdensity around an IMBH---a dark matter spike---can affect the orbital evolution of the system. We consider here such intermediate mass ratio inspirals on eccentric orbits, experiencing dynamical friction of the dark matter spike. We find that by including the relative velocities of the dark matter particles, the dynamical friction tends to circularize the orbit, in contrast to previous inquiries. We derive a general condition for circularization or eccentrification for any given dissipative force. In addition to the dephasing, we suggest using the circularization rate as another probe of the dark matter spike. Observing these effects would be an indicator for the particle nature of dark matter.

Dirty waveforms: multiband harmonic content of gas-embedded gravitational wave sources

ABSTRACTWe analyse the effect of stochastic torque fluctuations on the orbital evolution and the gravitational wave (GW) emission of gas-embedded sources with intermediate and extreme mass ratios. We show that gas-driven fluctuations imprint additional harmonic content in the GWs of the binary system, which we dub dirty waveforms (DWs). We find three interesting observational prospects for DWs, provided that torque fluctuations do indeed persist beyond the resolution limit of current hydrodynamical simulations. First, DWs can produce a significant stochastic GW background, comparable to other GW noise sources. Secondly, the energy flux implied by the additional harmonics can cause a detectable secular phase shift in Laser Interferometer Space Antenna (LISA) sources, even if the net torque fluctuations vanish when averaged over orbital time-scales. Lastly, the DWs of moderate-redshift nHz supermassive binaries detectable by pulsar timing arrays (PTAs) could be detectable in the mHz range, producing a new type of PTA–LISA multiband gravitational source. Our results suggest that searching for DWs and their effects can potentially be a novel way to probe the heaviest of black holes and the physics of the accretion discs surrounding them. We find these results to be a further confirmation of the many exciting prospects of actively searching for environmental effects within the data stream of future GW detectors.

High precision source characterization of intermediate mass-ratio black hole coalescences with gravitational waves: The importance of higher order multipoles

Intermediate mass ratio inspiral (IMRI) binaries -- containing stellar-mass black holes coalescing into intermediate-mass black holes ($M>100M_{\odot}$) -- are a highly anticipated source of gravitational waves (GWs) for Advanced LIGO/Virgo. Their detection and source characterization would provide a unique probe of strong-field gravity and stellar evolution. Due to the asymmetric component masses and the large primary, these systems generically excite subdominant modes while reducing the importance of the dominant quadrupole mode. Including higher order harmonics can also result in a $10\%-25\%$ increase in signal-to-noise ratio for IMRIs, which may help to detect these systems. We show that by including subdominant GW modes into the analysis we can achieve a precise characterization of IMRI source properties. For example, we find that the source properties for IMRIs can be measured to within $2\%-15\%$ accuracy at a fiducial signal-to-noise ratio of 25 if subdominant modes are included. When subdominant modes are neglected, the accuracy degrades to $9\%-44\%$ and significant biases are seen in chirp mass, mass ratio, primary spin and luminosity distances. We further demonstrate that including subdominant modes in the waveform model can enable an informative measurement of both individual spin components and improve the source localization by a factor of $\sim$10. We discuss some important astrophysical implications of high-precision source characterization enabled by subdominant modes such as constraining the mass gap and probing formation channels.

TOI–1278 B: SPIRou Unveils a Rare Brown Dwarf Companion in Close-in Orbit around an M Dwarf

Abstract We present the discovery of an 18.5 ± 0.5 M Jup brown dwarf (BD) companion to the M0V star TOI–1278. The system was first identified through a percent-deep transit in Transiting Exoplanet Survey Satellite photometry; further analysis showed it to be a grazing transit of a Jupiter-sized object. Radial velocity (RV) follow-up with the SPIRou near-infrared high-resolution velocimeter and spectropolarimeter in the framework of the 300-night SPIRou Legacy Survey carried out at the Canada–France–Hawaii Telescope led to the detection of a Keplerian RV signal with a semi-amplitude of 2306 ± 10 m s−1 in phase with the 14.5 day transit period, with a slight but nonzero eccentricity. The intermediate-mass ratio (M ⋆/M comp ∼ 31) is unique for having such a short separation (0.095 ± 0.001 au) among known M-dwarf systems. Interestingly, M-dwarf–BD systems with similar mass ratios exist with separations of tens to thousands of astronomical unit.

Merging stellar and intermediate-mass black holes in dense clusters: implications for LIGO, LISA, and the next generation of gravitational wave detectors

Context.The next generation of gravitational wave (GW) observatories would enable the detection of intermediate-mass black holes (IMBHs), an elusive type of BH expected to reside in the centres of massive clusters, dwarf galaxies, and possibly the accretion discs of active galactic nuclei. Intermediate-mass ratio inspirals (IMRIs), which are composed of an IMBH and a compact stellar object, constitute one promising source of GWs detectable by this new generation of instruments.Aims.We study the formation and evolution of IMRIs triggered by interactions between two stellar BHs and an IMBH inhabiting the centre of a dense star cluster, with the aim of placing constraints on the formation rate and detectability of IMRIs.Methods.We exploit directN-body models varying the IMBH mass, the stellar BH mass spectrum, and the star cluster properties. Our simulations take into account the host cluster gravitational field and general relativistic effects via post-Newtonian terms up to order 2.5. These simulations are coupled with a semi-analytic procedure to characterise the evolution of the remnant IMBH after the IMRI phase.Results.Generally, the IMRI formation probability attains values of ∼5−50%, with larger values corresponding to larger IMBH masses. Merging IMRIs tend to map out the stellar BH mass spectrum, suggesting that IMRIs could be used to unravel the role of dynamics in shaping BH populations in star clusters harbouring an IMBH. After the IMRI phase, an initially almost maximal(almost non-rotating) IMBH tends to significantly decrease(increase) its spin. Under the assumption that IMBHs grow mostly via repeated IMRIs, we show that only sufficiently massive (Mseed &gt; 300 M⊙) IMBH seeds can grow up toMIMBH &gt; 103 M⊙in dense globular clusters (GCs). Assuming that these seeds form at a redshift ofz ∼ 2−6, we find that around 1−5% of them would reach typical masses of ∼500−1500 M⊙at redshiftz = 0 and would exhibit low spins, generallySIMBH &lt; 0.2. Measuring the mass and spin of IMBHs involved in IMRIs could help to unravel their formation mechanism. We show that LISA can detect IMBHs in Milky Way GCs with a signal-to-noise ratioS/N = 10−100, or in the Large Magellanic Cloud, for which we get aS/N = 8−40. More generally, we provide the IMRI merger rate for different detectors, namely LIGO (ΓLIGO = 0.003−1.6 yr−1), LISA (ΓLISA = 0.02−60 yr−1), ET (ΓET = 1−600 yr−1), and DECIGO (ΓDECIGO = 6−3000 yr−1).Conclusions.Our simulations explore one possible channel for IMBH growth, namely via merging with stellar BHs in dense clusters. We find that the mass and spin of the IMRI components and the merger remnant encode crucial information about the mechanisms that regulate IMBH formation. Our analysis suggests that the future synergy among GW detectors will enable us to fully unravel IMBH formation and evolution.

Poking Holes: Looking for Gaps in LIGO/Virgo’s Black Hole Population

Abstract Stellar evolution models predict the existence of a gap in the black hole mass spectrum from ∼55 M ⊙–120 M ⊙ due to pair-instability supernovae (PISNe). We investigate the possible existence of such an “upper” mass gap in the second gravitational-wave transient catalog (GWTC-2) by hierarchically modeling the astrophysical distribution of black hole masses. We extend the Truncated and Powerlaw+Peak mass distribution families to allow for an explicit gap in the mass distribution, and apply the extended models to GWTC-2. We find that with the Truncated model there is mild evidence favoring an upper mass gap with log Bayes Factor , inferring the lower and upper bounds at and respectively. When using the Powerlaw+Peak model, we find no preference for the gap. When imposing tighter priors on the gap bounds centered on the expected PISNe gap bounds, the log Bayes factors in favor of a gap mildly increase. These results are however contingent on the parameter inference for the most massive binary, GW190521, for which follow-up analyses showed the source may be an intermediate mass ratio merger that has component masses straddling the gap. Using the GW190521 posterior samples from the analysis in Nitz &amp; Capano (2021), we find an increase in Bayes factors in favor of the gap. However, the overall conclusions are unchanged: there is no preference for a gap when using the Powerlaw+Peak model. This work paves the way for constraining the physics of pair-instability and pulsational pair-instability supernovae and high-mass black hole formation.

LION: laser interferometer on the moon

Gravitational wave astronomy has now left its infancy and has become an important tool for probing the most violent phenomena in our Universe. The LIGO/Virgo-KAGRA collaboration operates ground based detectors which cover the frequency band from 10 Hz to the kHz regime. Meanwhile, the pulsar timing array and the soon to launch LISA mission will cover frequencies below 0.1 Hz, leaving a gap in detectable gravitational wave frequencies. Here we show how a laser interferometer on the moon (LION) gravitational wave detector would be sensitive to frequencies from sub Hz to kHz. We find that the sensitivity curve is such that LION can measure compact binaries with masses between 10 and 100M ⊙ at cosmological distances, with redshifts as high as z = 100 and beyond, depending on the spin and the mass ratio of the binaries. LION can detect binaries of compact objects with higher-masses, with very large signal-to-noise ratios (SNRs), help us to understand how supermassive black holes got their colossal masses on the cosmological landscape, and it can observe in detail intermediate-mass ratio inspirals at distances as large as at least 100 Gpc. Compact binaries that never reach the LIGO/Virgo sensitivity band can spend significant amounts of time in the LION band, while sources present in the LISA band can be picked up by the detector and observed until their final merger. Since LION covers the deci-Hertz regime with such large SNRs, it truly achieves the dream of multi messenger astronomy.

Hierarchical black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties

ABSTRACTWe explore hierarchical black hole (BH) mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs), accounting for both original and dynamically assembled binary BHs (BBHs). We find that the median mass of both first- and nth-generation dynamical mergers is larger in GCs and YSCs with respect to NSCs because the lighter BHs are ejected by supernova kicks from the lower mass clusters. Also, first- and nth-generation BH masses are strongly affected by the metallicity of the progenitor stars: the median mass of the primary BH of a nth-generation merger is ∼24–38 M⊙ (∼9–15 M⊙) in metal-poor (metal-rich) NSCs. The maximum BH mass mainly depends on the escape velocity: BHs with mass up to several thousand M⊙ form in NSCs, while YSCs and GCs host BHs with mass up to several hundred M⊙. Furthermore, we calculate the fraction of mergers with at least one component in the pair-instability mass gap (fPI) and in the intermediate-mass BH regime (fIMBH). In the fiducial model for dynamical BBHs with metallicity Z = 0.002, we find fPI ≈ 0.05, 0.02 and 0.007 (fIMBH ≈ 0.01, 0.002 and 0.001) in NSCs, GCs and YSCs, respectively. Both fPI and fIMBH drop by at least one order of magnitude at solar metallicity. Finally, we investigate the formation of GW190521 by assuming that it is either a nearly equal-mass BBH or an intermediate-mass ratio inspiral.