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David Izquierdo-Villalba

Publications and source records attributed to David Izquierdo-Villalba.

At least 19 recordsLinked to original sources

The LISA Astrophysics MBHcatalogues Project: A comparison of predictions of simulated massive black hole binaries

In the hierarchical paradigm of galaxy formation, central massive black holes (MBHs) are expected to coalesce after the merger of their host galaxies. One of the main goals of the Laser Interferometer Space Antenna (LISA) is to constrain the origin and growth of MBHs through their merger rates and mass distribution. Predicting MBH merger rates requires not only tracing their statistical population from large to small physical scales (kpc to sub-pc) but also modelling their formation, accretion, dynamics, mergers, and their galactic physical processes across cosmic time. This project is the result of a large collaborative effort undertaken by the LISA Astrophysics Working Group, bringing together its collective expertise on MBH formation, evolution, and modelling, to build a comprehensive understanding of MBH merger rates across cosmic time. The project compares various theoretical predictions of MBH merger rates, quantifies the spread, and evaluates the global astrophysical uncertainties of the LISA event rates. To build a unique and complete view, our work is based on about 20 semi-analytical models and cosmological simulations from the literature, all employing distinct approaches to modelling MBH and galaxy physics. To compute the merger rates, we also incorporate delays arising from the dynamical phase of MBH hardening to coalescence. We present the expected LISA merger rates given current galaxy formation models and discuss how the merger rate depends on model assumptions, such as the seeding model and the resolution of cosmological simulations.

astro-ph.GA

Massive Star Clusters in the Semi-Analytical Galaxy Formation Model L-Galaxies 2020

It is established that there exists a direct link between the formation history of star cluster populations and their host galaxies. However, our lack of understanding of the assembly of star cluster populations impede our ability to use them as tracers of galaxy evolution. In this work we introduce a new variation of the L-Galaxies 2020 semi-analytic galaxy formation model that includes the formation of star clusters above 10^4 MSun and probes different physical assumptions that affect their evolution over cosmic time. We use properties of different galaxy components and localised star formation to determine the bound fraction of star formation in disks. After randomly sampling masses from an environmentally-dependent star cluster initial mass function, we assign to each object a half-mass radius, metallicity, and distance from the galaxy centre. We consider up to 2000 individual star clusters per galaxy and evolve their properties over time taking into account stellar evolution, two-body relaxation, tidal shocks, dynamical friction, and a re-positioning during galaxy mergers. Our simulation successfully reproduces several observational quantities, such as the empirical relationship between the absolute V-band magnitude of the brightest young star clusters and the host galaxy star formation rate, the mass function of young star clusters, and mean metallicities of the star cluster distributions versus galaxy masses. The simulation reveals great complexity in the z=0 star cluster population resulting from differential destruction channels and origins, including in-situ populations in the disk, a major merger-induced heated component in the halo, and accreted star clusters. Model variations point out the importance of the shape of the star cluster initial mass function, the initial distribution of half-mass radii, or the relationship between the sound speed of cold gas and the SFR.

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Overmassive and Undermassive Massive Black Holes: The Role of Environment and Gravitational-Wave Recoils

Understanding the connection between galaxy properties and their central massive black holes (MBHs) is key to unveiling their co-evolution. We use the ${\tt L{-}Galaxies{-} \it BH}$ semi-analytical model and the ${\tt Millennium}$ suite of simulations to investigate the physical origin of galaxies hosting overmassive and undermassive MBHs with respect to the $M_{\rm BH}-M_*$ relation, across stellar mass and cosmic time. We find that distinct evolutionary pathways drive different offsets from the scaling relation. Overmassive MBHs are primarily associated with galaxies that experienced enhanced merger history and secular activity. At $z\,{>}\,4$, this activity often leads to early, rapid MBH growth, frequently involving super-Eddington accretion episodes. At low redshift, a minority of overmassive systems ($20\%$) instead arise from environmental effects that reduce the stellar mass of the host, shifting galaxies above the relation without requiring additional MBH growth. Undermassive MBHs originate from two main channels. In massive galaxies, gravitational recoil following MBH mergers can eject the central MBH, temporarily leaving the galaxy without a nucleus. During this phase, MBHs coming from previous galaxy mergers can become the new central MBHs, but their masses remain below the expected ones from the scaling relation, as they never co-evolved with their new host galaxy. In low-mass galaxies ($M_*<10^9 M_\odot$), undermassive MBHs are more commonly linked to a quiescent evolutionary history, with limited mergers and weak secular processes that suppress an efficient MBH growth. We therefore conclude that outliers of the $M_{\rm BH}-M_*$ do not arise from a single mechanism, but from the interplay between environmental effects, gravitational recoils, and diverse MBH fueling histories, whose relative importance varies with galaxy mass and redshift.

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Back to basics: Little Red Dots as galaxies and dust-obscured AGNs in a synthetic NIRCam sky simulated with L-GalaxiesBH

The enigmatic Little Red Dots (LRDs) discovered by the James Webb Space Telescope (JWST) exhibit properties challenging their interpretation as common galaxies or Active Galactic Nuclei (AGN). Understanding their nature is key to placing them within our picture of early galaxy and massive black hole (MBH) evolution. To this aim, we build a realistic comparison between LRD observations with photometric properties of galaxies and AGN simulated by the L-GalaxiesBH model in a NIRCam mock sky. We model stellar continua and emission lines, the MBH emission from accretion disk, infrared radiation from dusty torus, and lines from narrow and broad line regions, accounting for dust attenuation and obscuration. Using realistic photometric cuts, we select a population of LRDs including both AGN and galaxies. The LRD fraction peaks at 40% ($\sim10^{-4}\rm Mpc^{-3}$) at $z\sim4$. Our LRDs are central galaxies spanning $M_*=10^8-10^{10.5}\rm M_\odot$. A population of galaxies with $M_*<10^9\rm M_\odot$ appear as LRDs due to older stellar populations. At higher masses, LRDs dominate the halo and stellar mass functions ($M_{\rm vir} > 10^{11.5}\rm M_\odot$, $M_* > 10^{9.5}\rm M_\odot$), and the interplay between AGN and galaxy emission drives the LRD selection. AGN dominate rest-frame UV-optical emission, while dust obscuration is secondary. LRDs host lighter MBHs ($\sim 10^{6.5}\rm M_\odot$) than non-LRDs ($\sim 10^{7.5}\rm M_\odot$), with fainter emission unable to balance their hosts Balmer breaks. We find no evidence for dominant heavy-seed origin of MBHs. LRD Galaxies (97% hosting MBHs) and LRD AGNs are disk-dominated, with LRD AGNs showing larger bulges formed mainly via disk instabilities.

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Bright siren without electromagnetic counterpart by LISA-Taiji-TianQin network

Gravitational waves (GWs) with electromagnetic counterparts (EMc) offer a novel approach to measure the Hubble constant ($H_0$), known as bright sirens, enabling $H_0$ measurements by combining GW-derived distances with EM-derived redshifts. Host galaxy identification is essential for redshift determination but remains challenging due to poor GW sky localization and uncertainties in EMc models. To overcome these limitations, we exploit the ultra-high-precision localization ($ΔΩ_s \sim 10^{-4} \, \text{deg}^2$) with a space-based GW detector network (LISA-Taiji-TianQin), which permits unique host identification solely from GW signals. We integrate five massive black hole binary (MBHB) population models and two galaxy number density models to compute the redshift horizon for host galaxy identification and evaluate $H_0$ constraints. We find that (1) The network enhances localization by several orders of magnitude compared to single detectors; (2) The identification horizon reaches $z\sim 1.2$ for specific MBHBs in the most accurate localization case; (3) The population model choice critically impacts the outcomes: the most refined population models yield to independent EMc identification rate of 0.6-1 $\text{yr}^{-1}$ with $H_0$ constraints $< 1\%$ fractional uncertainty, the less refined models lead to the rate $<0.1\text{yr}^{-1}$ and $1-2\%$ uncertainty on $H_0$.

astro-ph.CO

Constraints on the early growth of massive black holes from PTA and JWST with L-GalaxiesBH

Recent Pulsar Timing Arrays (PTAs) results provided strong evidence for a stochastic gravitational wave background (sGWB), consistent with a population of merging massive black holes (MBHs) at $z<1$. Meanwhile, JWST observations at $z>5$ suggest a higher number density of accreting MBHs than previously estimated. Together with constraints from local MBHs and high-$z$ quasars, these findings offer a unique opportunity to test MBH seeding and early growth models. We explore this using ${\tt L-Galaxies}\textit{BH}$, a new extension of the galaxy formation model ${\tt L-Galaxies}$, developed to explicitly model all stages of MBH evolution, including seeding, accretion, and binary dynamics. To take advantage of both the high resolution of the ${\tt MillenniumII}$ and the large volume of the ${\tt Millennium}$ simulations, we run ${\tt L-Galaxies}\textit{BH}$ on the former and use its outputs as initial conditions for the latter, via our $\textit{grafting}$ method. We find that reproducing the number density of high-$z$ active MBHs observed by JWST requires either a heavy seed formation rate significantly higher than that predicted by current models ($\gtrsim 0.01 Mpc^{-3}$ at $z \sim 10$), or widespread formation of light seeds undergoing multiple phases of super-Eddington accretion. Furthermore, matching the amplitude of the PTA sGWB signal requires nearly all galaxies with stellar masses $M_{*}> 10^9 M_\odot$ to host central MBHs by $z\sim0$. Given the extreme heavy seed densities required to satisfy both PTA and JWST constraints, our results favor a scenario in which MBHs originate from light seeds that grow rapidly and efficiently in the early universe. This work demonstrates the power of combining multi-messenger data with physical models to probe the origins and evolution of MBHs across cosmic time.

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Off-center black hole seed formation? Implications for high and low redshift massive black holes

Recent studies show that light seeds of black holes, which grow into massive black holes (MBHs) over time, often struggle to remain at the centers of their birthplaces in high-redshift galaxies, limiting their ability to accrete gas and merge with other black holes. In this work, we investigate how off-center formation of the first seeds affects the evolution of the MBH and massive black hole binary (MBHB) populations over cosmic history. To this end, we use the $\texttt{L-Galaxies}{\it BH}$ semi-analytical model, which includes multiple seed formation mechanisms, with light Population III remnants being the most significant contributors. To incorporate off-center formation, we modify the model to track the initial seed location, the sinking timescales toward the galactic center, and any growth during this phase. The results indicate that seed formation occurring away from the galactic center has a negligible impact on the MBH population at $z<1$, but causes significant differences at higher redshifts. Particularly, the abundance of $10^5 M_{\odot}$ MBHs at $z>4$ can be up to 2-10 times smaller compared to a nuclear seed formation model. Quasar luminosity functions with $\rm L_{bol}>10^{44} \rm erg/s$ are similarly affected, although they still align with observational constraints. The off-centre formation also alters the galaxy-MBH mass relation. At $z>5$, the amplitude of the relation can be up to 2 dex smaller than in nuclear seed models. These differences fade by $z \sim 2$ for galaxies $>10^{11} M_{\odot}$, and by $z=0$ for smaller galaxies. Notably, the overmassive MBH population recently unveiled by JWST is still present in the model, suggesting they can form independently of the seed dynamics. Finally, the merging rate of MBHs within LISA sensitivity band is strongly impacted. Specifically, there is a suppression of events at high-$z$ and an enhancement at low-$z$.

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Identifying massive black hole binaries via light curve variability in optical time-domain surveys

Accreting massive black hole binaries (MBHBs) often display periodic variations in their emitted radiation, providing a distinctive signature for their identification. In this work, we explore the MBHBs identification via optical variability studies by simulating the observations of the LSST survey. To this end, we generate a population of MBHBs using the L-Galaxies semi-analytical model, focusing on systems with observed orbital periods $\leq$ 5 years. This ensures that at least two complete cycles of emission can be observed within the 10-year mission of LSST. To construct mock optical light curves, we first calculate the MBHB average magnitudes in each LSST filter by constructing a self-consistent SED that accounts for the binary accretion history and the emission from a circumbinary disc and mini-discs. We then add variability modulations by using six 3D hydrodynamic simulations of accreting MBHBs with different eccentricities and mass ratios as templates. To make the light curves realistic, we mimic the LSST observation patterns and cadence, and we include stochastic variability and LSST photometric errors. Our results show from $10^{-2}$ to $10^{-1}$ MBHBs per square degree, with light curves that are potentially detectable by LSST. These systems are mainly low-redshift ($z\lesssim1.5$), massive ($\gtrsim10^{7}\, M_{\odot}$), equal-mass (${\sim} 0.8$), relatively eccentric (${\sim}0.6$), and with modulation periods of around $3.5$ years. Using periodogram analysis, we find that LSST variability studies have a higher success rate ($>$50%) for systems with high eccentricities ($e>$0.6). Additionally, at fixed eccentricity, detections tend to favour systems with more unequal mass ratios. The false alarm probability shows similar trends. Circular binaries systematically feature high values ($\gtrsim 10^{-1}$). Eccentric systems have low-FAP tails, down to $\sim10^{-8}$.

astro-ph.HE

Dissecting the nanoHz gravitational wave sky: frequency-correlated anisotropy induced by eccentric supermassive black hole binaries

Revealing the nature of the nanoHz gravitational wave (GW) signal recently reported by Pulsar Timing Arrays (PTAs) collaborations around the world is the next goal of low-frequency GW astronomy. The signal likely originates from the incoherent superposition of GWs emitted by a cosmological population of supermassive black hole binaries (SMBHBs). Those binaries can be highly eccentric and/or strongly coupled to their nuclear environment, resulting in an attenuation of the overall GW signal at low frequencies. In this paper, we propose to use the correlation properties of the distributed GW power in the sky across the frequency spectrum as a smoking gun for eccentric SMBHBs thus allowing to break the spectral degeneracy between eccentricity and environmental effect. The simple underlying idea is that, contrary to circular binaries, eccentric ones emit a broadband spectrum thus resulting in similar sky maps at different frequencies. We first demonstrate the applicability of this simple concept on sky maps constructed directly from the theoretical sky distribution of the GWB power induced by realistic populations of SMBHBs. We then demonstrate the viability of this analysis on simulated SKA-like PTA data. By statistically comparing sky maps reconstructed from hundreds injected circular and highly eccentric SMBHB populations, we find that eccentricity can be detected at $3σ$ in more than $50\%$ of cases.

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Lighting up the nano-hertz gravitational wave sky: opportunities and challenges of multimessenger astronomy with PTA experiments

Pulsar Timing Array (PTA) experiments have the potential to unveil continuous gravitational wave (CGW) signals from individual massive black hole binaries (MBHBs). Detecting them in both gravitational waves (GW) and the electromagnetic (EM) spectrum will open a new chapter in multimessenger astronomy. We investigate the feasibility of conducting multimessenger studies by combining the CGW detections from an idealized 30-year SKA PTA and the optical data from the forthcoming LSST survey. To this end, we employed the $\texttt{L-Galaxies}$ semi-analytical model applied to the $\texttt{Millennium}$ simulation. We generated 200 different all-sky lightcones that include galaxies, massive black holes, and MBHBs whose emission is modeled based on their star formation histories and gas accretion physics. We predict an average of $\approx 33$ CGW detections, with signal-to-noise ratios $ S/N > 5$. The detected MBHBs are typically at $z < 0.5$, with masses of $ \sim 3 \times 10^{9} M_{\odot}$, mass ratios $> 0.6$ and eccentricities $\lesssim 0.2$. In terms of EM counterparts, we find less than 15% of these systems to be connected with an AGN detectable by LSST, while their host galaxies are easily detectable ($ < 23$ mag) massive ($ M_{\star} > 10^{11} M_{\odot}$) ellipticals with typical star formation rates ($10^{-15} yr^{-1} < sSRF < 10^{-10} yr^{-1}$). Although the CGW-EM counterpart association is complicated by poor sky localization (only 35% of these CGWs are localized within $\rm 100\, deg^2$), the number of galaxy host candidates can be considerably reduced (thousands to tens) by applying priors based on the galaxy-MBH correlations. However, picking the actual host among these candidates is highly non-trivial, as they occupy a similar region in any optical color-color diagram. Our findings highlight the considerable challenges entailed in opening the low-frequency multimessenger GW sky.

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High-definition imaging of a filamentary connection between a close quasar pair at z=3

Filaments connecting halos are a long-standing prediction of cold dark matter theories. We present a detection of the cosmic web emission connecting two quasar-host galaxies at redshift z ~3.22 in the MUSE Ultra Deep Field (MUDF). The very deep observations unlock a high-definition view of the filament morphology, a measure of the transition radius between the intergalactic and circumgalactic medium, and the characterization of the surface brightness profiles along the filament and in the transverse direction. Through systematic comparisons with simulations, we validate the filaments' typical density predicted in the current cold dark-matter model. Our analysis of the MUDF field, an excellent laboratory for quantitatively studying filaments in emission, opens a new avenue to constrain the physical properties of the cosmic web and to trace the distribution of dark matter on large scales.

astro-ph.CO

Stars or gas? Constraining the hardening processes of massive black-hole binaries with LISA

Massive black-hole binaries will be the loudest sources detectable by LISA. These systems are predicted to form during the hierarchical assembly of cosmic structures and coalesce by interacting with the surrounding environment. The hardening phase of their orbit is driven by either stars or gas and encodes distinctive features into the binary black holes that can potentially be reconstructed with gravitational-wave observations. We present a Bayesian framework to assess the likelihood of massive mergers being hardened by either gaseous or stellar interactions. We use state-of-the-art astrophysical models tracking the cosmological evolution of massive black-hole binaries and construct a large number of simulated catalogs of sources detectable by LISA. From these, we select a representative catalog and run both parameter estimation assuming a realistic LISA response as well model comparison capturing selection effects. Our results suggest that, at least within the context of the adopted models, future LISA observations can confidently constrain whether stars or gas are responsible for the binary hardening. We stress that accurate astrophysical modeling of the black-hole spins and the inclusion of subdominant emission modes in the adopted signal might be crucial to avoid systematic biases.

astro-ph.HE

A link to the past: characterizing wandering black holes in Milky Way-type galaxies

A population of non-stellar black holes ($\gtrsim$100 M$_{\odot}$) has been long predicted to wander the Milky Way. We aim to characterize this population by using the L-Galaxies semi-analytical model applied on top of the high resolution Millennium-II merger trees. Our results predict $\sim$10 wandering black holes with masses $\sim$2 $\times$ 10$^{3}$ M$_{\odot}$ in a typical $z$ = 0 Milky Way galaxy, accounting for $\sim$2$\%$ of the total non-stellar black hole mass budget of the galaxy. We find that the locations of these wanderers correlate with their formation scenario. While the ones concentrated at $\lesssim$1 kpc from the galactic nucleus on the disk come from past galactic mergers, the ones formed as a consequence of ejections due to gravitational recoils or the disruption of satellite galaxies are typically located at $\gtrsim$100 kpc. Such small and large distances might explain the absence of strong observational evidence for wandering black holes in the Milky Way. Our results also indicate that $\sim$67$\%$ of the wandering population is conformed by the leftovers of black hole seeds that had little to no growth since their formation. We find that wandering black holes that are leftover seeds become wanderers at an earlier time with respect to grown seeds, and also come from more metal-poor galaxies. Finally, we show that the number of wandering black holes in a Milky Way-type galaxy depends on the seeding efficiency.

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Resolving the nano-Hz gravitational wave sky: the detectability of eccentric binaries with PTA experiments

Pulsar Timing Array (PTA) collaborations reported evidence of a nano-Hz stochastic gravitational wave background (sGWB) compatible with an adiabatically inspiraling population of massive black hole binaries (MBHBs). Despite the large uncertainties, the relatively flat spectral slope of the recovered signal suggests a possible prominent role of MBHB dynamical coupling with the environment or/and the presence of an eccentric MBHB population. This work aims at studying the capabilities of future PTA experiments to detect single MBHBs under the realistic assumption that the sGWB is originated from an eccentric binary population coupled with its environment. To this end, we generalize the standard signal-to-noise ratio (SNR) and Fisher Information Matrix calculations used in PTA for circular MBHBs to the case of eccentric systems. We consider an ideal 10-year MeerKAT and 30-year SKA PTAs and apply our method over a wide number of simulated eccentric MBHB populations. We find that the number of resolvable MBHBs for the SKA (MeerKAT) PTA is ${\sim}\,30$ ($4$) at $\rm SNR\,{>}\,5$ (${>}\,3$), featuring an increasing trend for larger eccentricity values of the MBHB population. This is the result of eccentric MBHBs at ${\lesssim}\,10^{-9}\, \rm Hz$ emitting part of their power at high harmonics, thus reaching the PTA sensitivity band. Our results also indicate that resolved MBHBs do not follow the eccentricity distribution of the underlying MBHB population, but prefer low eccentricity values (${<}\,0.6$). Finally, the recovery of binary intrinsic properties and sky-localization do not depend on the system eccentricity, while orbital parameters such as eccentricity and initial orbital phase show clear trends. Although simplified, our results show that SKA will enable the detection of tens of MBHBs, projecting us into the era of precision gravitational wave astronomy at nano-Hz frequencies.

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The rise and fall of bars in disc galaxies from $z=1$ to $z=0$. The role of the environment

We investigate the influence of the environment on the evolution of barred and unbarred disc galaxies with a mass $>10^{10}\Msun$ from z=1 down to z=0, employing the TNG50 magnetic-hydrodynamical simulation. We find that 49% of z=1 disc galaxies undergoes a morphological transformation, transitioning into either a lenticular or spheroidal, while the other 51% retains the massive disc. The morphological alteration is mostly influenced by the environment. Lenticular and spheroidal galaxies tend to exist in denser environments and have more frequent mergers compared to disc galaxies. We find that over half of the barred galaxies (60.2%) retain the bar structure and have experienced fewer mergers compared to those galaxies that lose their bars (5.6%). These latter ones start with weaker and shorter bars at z=1 influenced by tidal interactions and are frequently observed in more populated areas. Additionally, our study reveals that less than 20% of unbarred galaxies will never develop a bar and exhibit the quietest merger history. Unbarred galaxies that experience bar formation after z=1 exhibit more frequent instances of merging events. Furthermore, tidal interactions with a close companion may account for bar formation in at least one-third of the cases. Our findings highlight that stable bars are prevalent in disc galaxies. Bar evolution may nonetheless be affected by the environment. Interactions with nearby companions or tidal forces caused by mergers have the capacity to disrupt the disc. This perturbance may materialise as the dissolution of the bar, the formation of a bar, or, in its most severe form, the complete destruction of the disc, resulting in morphological transformation. Bars that are weak and short at z=1 and undergo major or minor mergers may eventually dissolve, whereas unbarred galaxies that enter crowded environments or experience a merger may develop a bar.

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Connecting low-redshift LISA massive black hole mergers to the nHz stochastic gravitational wave background

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of $z<1$ MBHs above $\rm 10^8 M_{\odot}$, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs ($\rm {<} 10^7 \, M_{\odot}$) detectable by LISA. To this end, we use the $\texttt{L-Galaxies}$ semi-analytical model applied to the $\texttt{Millennium}$ suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of the model show that the global (integrated up to high-$z$) LISA detection rate is {\it not} significantly affected when compared to a fiducial model whose nHz sGWB signal is ${\sim}\,2$ times smaller. In both cases, the global rate yields ${\sim}\,12 \rm yr^{-1}$ and is dominated by systems of $\rm 10^{5-6} M_{\odot}$. The main differences are limited to low-$z$ ($z<3$), high-mass (${>}\rm 10^6\, M_{\odot}$) LISA MBHBs. The model compatible with the latest PTA results predicts up to ${\sim}\,1.6$ times more detections, with a rate of ${\sim}1\rm yr^{-1}$. We find that these LISA MBHB systems have 50\% probability of shining with bolometric luminosities $>10^{43}\rm erg/s$. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected.

astro-ph.GA

Massive Black Holes in Galactic Nuclei

Massive black holes are key inhabitants of the nuclei of galaxies. Moreover, their astrophysical relevance has gained significant traction in recent years, thanks especially to the amazing results that are being (or will be) delivered by instruments such as the James Webb Space Telescope, Pulsar Timing Array projects and LISA. In this Chapter, we aim to detail a broad set of aspects related to the astrophysical nature of massive black holes embedded in galactic nuclei, with a particular focus on recent and upcoming advances in the field. In particular, we will address questions such as: What shapes the relations connecting the mass of massive black holes with the properties of their host galaxies? How do massive black holes form in the early Universe? What mechanisms keep on feeding them so that they can attain very large masses at z = 0? How do binaries composed of two massive black holes form and coalesce into a single, larger black hole? Here we present these topics from a mainly theoretical viewpoint and discuss how present and upcoming facilities may enhance our understanding of massive black holes in the near future.

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