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Zoltán Haiman

Publications and source records attributed to Zoltán Haiman.

At least 19 recordsLinked to original sources

A Magnetic Unification of Merging Supermassive Black Hole Binaries

The detection of an electromagnetic (EM) transient from a supermassive black hole binary (SMBHB) merging within a gaseous environment will constitute a multi-messenger milestone. Numerical simulations of these systems have mostly been performed in 2D with a constant viscosity parameter representing turbulent and magnetic stresses. These simulations predict a steep drop in accretion rate and X-ray luminosity at merger, followed by a slow recovery. However, 3D-GRMHD and 3D-MHD simulations have shown only a modest reduction in accretion rate and a fast post-merger recovery. We present a new 2D pseudo-Newtonian framework with physically motivated prescriptions for stochastic viscosity, relativistic apsidal precession, and large-scale magnetic fields. When suitably calibrated, this 2D framework accurately captures key 3D-GRMHD behavior, demonstrating that it can be used to explore binary accretion without the high computational cost of 3D-GRMHD simulations. We find that the merger signatures are most sensitive to the strength of the magnetic field, with a drop in the accretion rate at merger progressively less pronounced for stronger fields. Post-merger evolution is determined by both magnetization and relativistic precession of orbiting gas, yielding rapid recovery of accretion. For low-magnetization disks, recovery is driven by self-intersection shocks, and the dip at merger is followed by a distinct second dimming. Large-scale magnetic fields of increasing magnitude lead to magnetically arrested disk (MAD) behavior which disturbs the merging system progressively earlier before merger, and longer after. Our results unify the EM signatures of the merger of embedded coplanar SMBHBs, and provide novel observational constraints on their intrinsic magnetization.

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The effect of pressure confinement on the maximum mass of rapidly accreting supermassive stars

We derive an extension of Chandrasekhar's pulsational stability criterion for relativistic stars with a pressure boundary condition at the surface. We then apply the new criterion to hylotropes, a model describing rapidly accreting supermassive stars with a core-envelope structure. We find that confinement typically stabilises stars, delaying the onset of the general relativistic instability when the external pressure at the surface is roughly $\sim10^{-3}$ of the stars' hydrostatic pressure scale. Beyond this value, the critical mass at marginal stability increases rapidly, exceeding the value of $\sim 10^5$ M$_{\odot}$ for helium burning, isolated $n=3$ polytropes by orders of magnitude. We discuss how the required pressure boundary conditions may be produced by the combined ram and magnetic pressure supplied by the accretion flow as it assembles the supermassive star, and provide a fitting formula for the final mass before collapse. As a rough estimate assuming equipartition between magnetic and thermal pressures in a standard $α$-disk, we find that the critical mass doubles at accretion rates of order $\dot M\sim100\,{\rm M_\odot}\,{\rm yr}^{-1}$, again increasing rapidly after this value. Our results show under what conditions, potentially realized in a subset of high redshift halos, non-rotating SMS may collapse into black holes beyond the typical scale of heavy seeds.

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Statistical evidence for massive black hole recoils in active galactic nuclei

We search for a population-level signature of gravitational-wave recoiling supermassive black holes: a positive correlation between dust obscuration and the magnitude of the line-of-sight velocity offset of broad emission lines relative to the host. Using the SDSS DR16 quasar catalogue, we estimate the velocity offset, $Δv$, as the difference between the broad H$β$ redshift and a noise-weighted redshift from narrow lines ([O III] 5007, [O II] 3728, and Ca II 3934). We adopt the redshift-relative colour excess $Δ(g-i)$ as a proxy for dust column density. Analysing $\sim10^{5}$ quasars that meet basic spectral quality requirements, we find a modest but highly significant positive correlation between $|Δv|$ and $Δ(g-i)$ (Spearman $r\simeq0.12$ and Pearson $r\simeq0.13$, with $p\ll10^{-10}$ in both cases). The fraction of highly obscured quasars increases with $|Δv|$, indicating that the correlation is driven by a dust-reddened subpopulation. The result is robust to the choice of minimum $|Δv|$ threshold and to the line redshift estimator (peak vs. centroid). As expected, the correlation is largely absent when velocity offsets are computed between narrow emission lines. We find systematic differences between redshifted and blueshifted subsamples, which may point to residual velocity biases or additional physical effects (e.g. winds, inflows, orientation-dependent obscuration, or asymmetric broad-line regions). Recoiling massive black holes provide a natural explanation for the observed correlation, but alternative scenarios should be explored. If confirmed, this would enable population-level constraints on massive black hole merger rates, recoil dynamics, and active galactic nuclei disc properties.

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Preferential accretion onto eccentric and unequal binary black holes

Supermassive binary black holes (SMBBHs) are expected to be surrounded by circumbinary disks (CBDs) which affect the binary through gravitational forces and accretion. It has been reported that the binary can experience ``preferential accretion'' where one black hole (BH) out-accretes the other for hundreds of orbits, but this asymmetry has yet to be fully described or understood. In this work, we utilize a suite of 80 SMBBH hydrodynamical simulations with varying mass ratios ($q_b$) and eccentricity ($e_b$) in order to robustly delineate the behavior of preferential accretion, determine its relationship to the structure of the CBD, and study its observational consequences. We characterize the accretion-rate ratio $λ(t) \equiv \dot{M}_2(t)/\dot{M}_1(t)$ and the mass-ratio rate of change $\dot{q}_b \equiv d/dt(M_2/M_1)$ across the suite. We confirm that the secondary tends to out-accrete the primary ($λ\geq 1$), and find this preference to be strongest for low-$e_b$, low-$q_b$ binaries and increasingly time-variable toward high $e_b$. We also find that (i) the time-variability of $λ$ tracks the precession of the CBD, (ii) there can be sub- and super-Eddington accretion in a single binary, and (iii) the gas-driven approach toward equal mass becomes particularly slow for highly eccentric, high $q_b$ binaries, suggesting that some binaries may not reach $q_b=1$ within the $30\,\mathrm{Myr}$ lifetime of a quasar and therefore allowing LISA to constrain the accretion history of SMBBHs. Our findings also suggest that periodically flickering jets are a potential observable signature of many binaries.

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Hunting the first Cosmic Giants: formation and detectability of Direct Collapse Black Holes around high-redshift quasars

The rapid emergence of supermassive black holes (SMBHs) in the early Universe poses a challenge to current models of black hole growth. One promising formation pathway is the direct collapse black hole (DCBH) scenario, in which gas in pristine, low-metallicity halos forms supermassive (or quasi-) stars leading to massive black holes seeds under specific environmental conditions. In this work, we investigate the potential host environments of DCBHs by coupling a semi-analytic model tracing BH formation and galaxy co-evolution with high-resolution N-body dark matter merger trees. This allows us to trace the population of DCBHs formed during the hierarchical assembly of a $\sim 10^{12} ~\rm M_\odot$ dark matter halo hosting a bright $10^9 ~\rm M_\odot$ quasar at redshift $z \approx 7$. We find that, when accounting for local fluctuations in the UV radiation field within this early cosmic structure, massive BH seeds can form via direct collapse as early as $z \approx 22$. Even under more stringent conditions for heavy seed formation, tens of DCBHs are predicted to emerge within the simulated overdensity down to $z \sim 14$, at which point metal enrichment of the intergalactic medium inhibits further episodes of direct collapse. A significant fraction of the massive black hole population formed at $z > 14$ is expected to survive in satellite galaxies that do not merge with the central halo down to $z \approx 7$. We show that the existence of such a population of ungrown heavy BH seeds can be probed through deep JWST observations targeting regions surrounding bright high-redshift quasars, and we discuss tailored observational strategies to detect and identify these elusive systems.

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Properties of black hole mergers in disks of active galactic nuclei

Ground-based gravitational wave (GW) observatories have detected approximately 200 binary black hole (BH) mergers. The astrophysical origin of these events are debated, with evidence suggesting that at least a subset originated from dynamic environments characterized by frequent close encounters. Accretion disks in active galactic nuclei (AGNs) are of particular interest, as certain observed features could be more readily produced within such environments. In this paper, we investigate the expected properties of mergers in these environments, and their dependence on various parameters, using one-dimensional $N$-body simulations combined with a comprehensive semi-analytical model. In our fiducial model, the distributions of masses and mass ratios ($q$) are similar to those observed. However, they depend strongly on the lifetime and density of the AGN disk and on the number and accretion efficiency of BHs, with higher masses predicted as these quantities increase. The most massive mergers, such as GW231123, can be produced either by efficient gas accretion or by hierarchical mergers among $\geq 3$ generations of BHs. The observed negative correlation between $q$ and the average effective spin ($χ_{\rm eff}$), along with the positive correlation between $χ_{\rm eff}$ and the chirp mass ($M_{\rm chirp}$), can be explained by a combination of efficient gas accretion, which promotes spin alignment, and hierarchical mergers, which produce high-$|χ_{\rm eff}|$ and low-$q$ binaries. Hierarchical mergers can also explain the negative correlation between $q$ and the dispersion of $χ_{\rm eff}$, as well as the positive correlation between $|χ_{\rm eff}|$ and $M_{\rm chirp}$. We present a comprehensive study on how the expected distribution of each of these quantities depends on model parameters and assumptions, which will aid the interpretation of observed GW population properties.

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Electromagnetic Flares from Compact-Object Mergers in AGN Disks: Signatures and Predictions

Accretion disks in active galactic nuclei (AGN) are promising sites for mergers of stellar-mass black holes (BHs) detectable via gravitational waves (GWs). These environments facilitate both in-situ formation and dynamical capture of compact objects, and their subsequent mergers. The uncertain origin of GW events detected by LIGO, Virgo and KAGRA motivates searching for accompanying electromagnetic (EM) signatures. Here we investigate post-merger EM flares associated with jets launched from merger remnants, as well as from the shocked ambient gas as the jet breaks out of the disk. We find that jet breakout produces luminous gamma-ray emission, detectable with MeV-band telescopes. Cooling emission from a shocked circum-BH minidisk, winds and background AGN-disk peaks in the UV and optical, with durations ranging from about an hour to a month, and can be identified through year-long monitoring of $\sim10^3$ AGNs with luminosities ranging from $\sim 10^{44}$ to $\sim 10^{45}~{\rm erg~s^{-1}}$. With a single set of parameters, this post-merger jet model produces gamma-ray, hard X-ray and optical flares similar to those claimed to be associated with GW events. Furthermore, by incorporating a transition from a high- to low-angular-momentum accretion state after the merger, the model avoids excessive BH growth, alleviating tensions with hyper-Eddington accretion scenarios.

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Recoil-regulated extreme mass-ratio inspirals in AGN disks

Extreme mass-ratio inspirals (EMRIs) are among the primary targets of future space-based gravitational-wave observatories, such as LISA, TianQin, and Taiji. Active galactic nucleus (AGN) disks provide a gas-rich environment in which stellar-mass black holes can migrate toward central supermassive black holes and form EMRIs. Previous studies of this ``wet'' channel have largely neglected stellar interactions within the disk. Here we show that binary formation, hierarchical mergers, and recoil kicks fundamentally regulate wet EMRI formation in AGN disks. Using semi-analytical AGN disk models combined with Monte Carlo simulations across supermassive black hole masses of $10^5$--$10^7M_\odot$ and Eddington ratios of $10^{-3}$-1, we find that recoil kicks from mergers and binary--single interactions repeatedly lift stellar-mass black holes out of the disk plane, temporarily interrupting migration and strongly suppressing EMRI formation in much of parameter space. Detectable EMRIs are therefore preferentially produced in young AGNs, typically within $\sim$ 10-20Myr of disk formation, and often involve merger-grown secondary black holes. We predict LISA detection rates of $\sim$ 1-30yr$^{-1}$, with the observable population dominated by low-mass AGNs and sensitive to the poorly constrained demographics of faint active nuclei. Our results identify stellar interactions as a key ingredient in the evolution of compact objects in AGN disks and show that future EMRI observations can probe both AGN disk physics and the low-mass AGN population.

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A new sample of Little Red Dots at $z<0.45$ in DESI DR1: Broad Balmer lines, low ionization spectrum and no variability

JWST has unveiled an abundant population of compact broad-line emitters largely at $z\gtrsim4$, the Little Red Dots (LRDs), which might represent a previously unprobed supermassive black hole evolution channel predominant at high redshift. However, the LRDs have remained mostly elusive at lower redshift ($z\lesssim2$) where detailed studies are possible from ground-based observatories. We searched for low-redshift LRDs in the Dark Energy Spectroscopic Instrument (DESI) survey. Our search is primarily based on emission line properties, as opposed to earlier approaches that searched for compact sources with specific photometric spectral energy distributions. We report the discovery of eight LRDs at $z=0.2-0.45$, which show spectral features akin to the high-redshift LRDs in the rest-frame optical. The sources are characterized by broad Balmer lines, steep Balmer decrements, compact morphologies, Balmer absorption features and/or strong He I emission, but weak or absent He II, [Ne V] or other high excitation lines typical of Type I AGN. For 7 out of 8 sources, we retrieve dense-cadence light curves from time-domain surveys and for most sources we find weak to no intrinsic variability ($0.0-0.1$ mag) over $4-17$ years in the rest-frame. We also highlight the identification of a quasar with similar Balmer line profiles as LRDs, but shows differences in Balmer decrement, significant variability, and high-ionisation lines. Given the effective volume $4.9{\rm Gpc^3}$ covered by DESI DR1 at $z<0.45$, our sample corresponds to a number density of $1.6\times10^{-9}$Mpc$^{-3}$, indicating a number density $\sim$10,000 times lower than in the first billion years of cosmic time. We find a dearth of luminous and red LRDs at $z<1$ compared to higher-redshift, which could suggest lower gas feeding rates of LRD activity due to higher metallicities at later cosmic epochs.

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Connecting the Dots: UV-Bright Companions of Little Red Dots as Lyman-Werner Sources Enabling Direct Collapse Black Hole Formation

We compile a sample of 83 Little Red Dots (LRDs) with JWST imaging and find that a substantial fraction ($\sim$43%, rising to $\gtrsim$85% for the most luminous LRDs) host one or more spatially offset, UV-bright companions at projected separations of $0.5\rm \, kpc \lesssim d\lesssim 5 \rm \,kpc$, with median of $\langle d \rangle = 1.0\,\mathrm{kpc}$. This fraction is even higher when smaller spatial scales are probed at high S/N ratio: we show that the two most strongly lensed LRDs known to date, A383-LRD and the newly discovered A68-LRD, both have UV-bright companions at separations of only $d\sim0.3$ kpc, below the resolution limit of most unlensed JWST samples. We explore whether these ubiquitous red/blue configurations may be physically linked to the formation of LRDs, in analogy with the "synchronized pair" scenario originally proposed for direct-collapse black hole formation. In this picture, ultraviolet radiation from the companions, which typically have modest stellar masses ($M_\ast \sim 10^{8-9}M_\odot$), suppresses molecular hydrogen cooling in nearby gas, allowing nearly isothermal collapse and the formation of extremely compact objects, such as massive black holes or quasi-stars. Using component-resolved photometry and SED modeling, we infer Lyman-Werner radiation fields of $J_{21,LW} \sim 10^{2.5}$-$10^{5}$ at the locations of the red components, comparable to those required in direct-collapse models, suggesting that the necessary photodissociation conditions are realized in many LRD systems. This framework provides a simple and self-consistent explanation for the extreme compactness and distinctive spectral properties of LRDs, and links long-standing theoretical models for early compact object formation directly to a population now observed with JWST in the early universe.

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Probing Cosmology through Higher-Order CMB Lensing Statistics

We investigate the cosmological information in higher-order statistics of the cosmic microwave background (CMB) lensing convergence field for a near-term experiment with noise properties similar to the Simons Observatory (SO). Using a fully field-level forward-modeling pipeline based on ray-traced simulations from the MassiveNuS suite and realistic SO-like CMB lensing reconstruction, we naturally include nonlinear structure formation, post-Born effects, and higher-order reconstruction noise. We measure several non-Gaussian statistics, including Minkowski functionals, peak and minima counts, moments, and wavelet-scattering coefficients. We train Gaussian-process emulators to model each statistic's dependence on the matter density fraction $Ω_m$, the scalar power spectrum amplitude $A_s$, and the neutrino mass sum $M_ν$. We quantify the relative information gain these statistics provide beyond the lensing power spectrum and identify which are most robust to reconstruction noise. We find that morphology-based statistics, particularly Minkowski functionals and peak/minima counts, offer significant complementary constraining power: combining all non-Gaussian statistics with the power spectrum yields reductions of 40% and 38% in the marginalized uncertainties on $Ω_m$ and $A_s$, respectively, and a 70% reduction in the one-sided uncertainty on $M_ν$. These gains remain non-negligible even when the power spectrum is extended to larger scales and combined with primary CMB and BAO data, with Minkowski functionals providing an additional 11% improvement in $σ(M_ν)$ and 35% in $σ(Ω_m)$ beyond the extended power spectrum. By contrast, moments and wavelet-scattering coefficients provide more limited gains at SO noise levels. Our results highlight the potential of non-Gaussian statistics to enhance cosmological constraints from SO and future CMB surveys.

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Testing compact massive black hole binary candidates through multi-epoch spectroscopy

Emission from two massive black holes (MBHs) bound in a close binary is expected to be modulated by different processes, such as the Doppler boost due to the orbital motion, accretion rate variability generated by the interaction with a circumbinary disc, and binary gravitational self-lensing. When the binary is compact enough, the two black holes are thought to be surrounded by a common broad-line region that reprocesses the impinging periodically varying ionising flux, creating broad emission lines with variable line shapes. Therefore, the study of broad emission line variability through multi-epoch spectroscopic campaigns is of paramount importance for the unambiguous identification of a binary. In this work, we study the response of a disc-like broad-line region to the Doppler-boosted ionising flux emitted by sub-milliparsec MBH binaries on a circular orbit and compare it with the response of a broad-line region illuminated by a single MBH with a periodically but isotropically varying intrinsic luminosity. We show that in the binary case, the time lags of the blue and red wings of the broad emission lines, arising from diametrically opposite sides of the circumbinary disc, are out of phase by half of the binary's orbital period, as they each respond to the periodic "lighthouse" modulation from the binary's continuum emission. This asymmetric time lag represents a new binary signature that cannot be mimicked by a single MBH.

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First constraints on the local ionization topology in front of two quasars at z ~ 7.5

Thus far, Lyman-$α$ damping wings towards quasars have been used to probe the \textit{global} ionization state of the foreground intergalactic medium (IGM). A new parameterization has demonstrated that the damping wing signature also carries \textit{local} information about the distribution of neutral hydrogen (HI) in front of the quasar before it started shining. Leveraging a recently introduced Bayesian \texttt{JAX}-based Hamiltonian Monte Carlo (HMC) inference framework, we derive constraints on the Lorentzian-weighted HI column density $N_\mathrm{HI}^\mathrm{DW}$, the quasar's distance $r_\mathrm{patch}$ to the first neutral patch and its lifetime $t_\mathrm{Q}$ based on JWST/NIRSpec spectra of the two $z \sim 7.5$ quasars J1007+2115 and J1342+0928. After folding in model-dependent topology information, we find that J1007+2115 (and J1342+0928) is most likely to reside in a $\langle x_\mathrm{HI} \rangle = 0.32_{-0.20}^{+0.22}$ ($0.58_{-0.23}^{+0.23}$) neutral IGM while shining for a remarkably short lifetime of $\log_{10} t_\mathrm{Q} /\mathrm{yr} = 4.14_{-0.18}^{+0.74}$ (an intermediate lifetime of $5.64_{-0.43}^{+0.25}$) along a sightline with $\log_{10} N_\mathrm{HI}^\mathrm{DW} /\mathrm{cm}^{-2} = 19.70_{-0.86}^{+0.35}$ ($20.24_{-0.22}^{+0.25}$) and $r_\mathrm{patch} = 28.9_{-14.4}^{+54.0} \,\mathrm{cMpc}$ ($10.9_{-5.9}^{+5.6} \,\mathrm{cMpc}$). In light of the potential presence of local absorbers in the foreground of J1342+0928 as has been recently suggested, we also demonstrate how the Lorentzian-weighted column density $N_\mathrm{HI}^\mathrm{DW}$ provides a natural means for quantifying their contribution to the observed damping wing signal.

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Identifying Compact Chirping SMBHBs in LSST using Bayesian Analysis

The Legacy Survey of Space and Time (LSST) is expected to observe up to ${\sim}100$ million quasars in the next decade. In this work, we show that it is possible to use such data to measure the characteristic frequency evolution of a "chirp" induced by gravitational waves, which can serve as robust evidence for the presence of a compact supermassive black-hole binary. Following the LSST specifications, we generate mock lightcurves consisting of (i) a post-Newtonian chirp produced by orbital motion through, e.g., relativistic Doppler boosting, (ii) a damped random walk representing intrinsic quasar variability, and (iii) Gaussian photometric errors, while assuming non-uniform observations with extended gaps over a period of 10 yr. Through a fully-Bayesian analysis, we show that we can simultaneously measure the chirp and noise parameters with little degeneracy between the two. For chirp signals with an amplitude of $A = 0.5$ mag and a range of times to merger ($t_m = 15{-}10^4$ yr), we can typically measure a non-zero amplitude and positive frequency derivative with over $5σ$ credibility. For binaries with $t_m = 50$ yr, we achieve $3σ$ ($5σ$) confidence that the signal is chirping for $A \gtrsim 0.1$ ($A > 0.2$). Our analysis can take as little as 35 s (and typically $<$ 10 min) to run, making it scalable to a large number of lightcurves. This implies that LSST could, on its own, establish the presence of a compact supermassive black-hole binary, and thus discover gravitational wave sources detectable by LISA and by Pulsar Timing Arrays.

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The effect of intrinsic alignments on weak lensing statistics in hydrodynamical simulations

The next generation of weak gravitational lensing surveys has the potential to place stringent constraints on cosmological parameters. However, their analysis is limited by systematics such as the intrinsic alignments of galaxies, which alter weak lensing convergence and can lead to biases in cosmological parameter estimations. In this work, we investigate the impact of intrinsic alignments on non-Gaussian statistics of the weak lensing field using galaxy shapes derived from the IllustrisTNG hydrodynamical simulation. We create two catalogs of ray-traced convergence maps: one that includes the measured intrinsic shape of each galaxy and another where all galaxies are randomly rotated to eliminate intrinsic alignments. We compare an exhaustive list of weak lensing statistics between the two catalogs, including the shear-shear correlation function, the map-level angular power spectrum, one-point, peak count, minimum distribution functions, and Minkowski functionals. For each statistic, we assess the level of statistical distinguishability between catalogs for a set of future survey angular areas. Our results reveal strong small-scale correlation in the alignment of galaxies and statistically significant boosts in weak lensing convergence in both positive and negative directions for high-significance peaks and minimums, respectively. Weak lensing analyses utilizing non-Gaussian statistics must account for intrinsic alignments to avoid significantly compromised cosmological inferences.

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Thermal X-ray signatures in late-stage unequal-mass massive black hole binary mergers

The multi-messenger combination of gravitational waves (GWs) from merging massive black hole binaries (MBHBs) and the electromagnetic (EM) counterpart from the surrounding circumbinary disk (CBD) will open avenues to new scientific pursuits. In order to realize this science, we need to correctly localize the host galaxy of the merging MBHB. Multi-wavelength, time-dependent electromagnetic (EM) signatures can greatly facilitate the identification of the unique EM counterpart among many sources in LISA's localization volume. To this end, we studied merging unequal-mass MBHBs embedded in a CBD using high-resolution 2D simulations, with a $Γ$-law equation of state, incorporating viscous heating, shock heating and radiative cooling. We simulate each binary starting from before it decouples from the CBD until just after the merger. We compute EM signatures and identify distinct features before, during, and after the merger. We corroborate previous findings of a several order of magnitude drop in the thermal X-ray luminosity near the time of merger, but with delayed timing compared to an equal-mass system. The source remains X-ray dark for hours post-merger. Our main results are a potential new signature of a sharp spike in the thermal X-ray emission just before the tell-tale steep drop occurs. This feature may further help to identify EM counterparts of LISA's unequal MBHBs before merger without the need for extensive pre-merger monitoring. Additionally, we find a role-reversal, in which the primary out-accretes the secondary during late inspiral, which may diminish signatures originating from Doppler modulation.

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Can quasars, triggered by mergers, account for NANOGrav's stochastic gravitational wave background?

The stochastic gravitational wave background (GWB) recently discovered by several pulsar timing array (PTA) experiments is consistent with arising from a population of coalescing super-massive black hole binaries (SMBHBs). The amplitude of the background is somewhat higher than expected in most previous population models or from the local mass density of SMBHs. SMBHBs are expected to be produced in galaxy mergers, which are also thought to trigger bright quasar activity. Under the assumptions that (i) a fraction $f_{bin} \sim 1$ of all quasars are associated with SMBHB mergers, (ii) the typical quasar lifetime is $t_{Q} \sim 10^{8} yr$, and (iii) adopting Eddington ratios $f_{Edd} \sim 0.3$ for the luminosity of bright quasars, we compute the GWB associated directly with the empirically measured quasar luminosity function (QLF). This approach bypasses the need to model the cosmological evolution of SMBH or galaxy mergers from simulations or semi-analytical models. We find a GWB amplitude approximately matching the value measured by NANOGrav. Our results are consistent with most quasars being associated with SMBH binaries and being the sources of the GWB, and imply a joint constraint on $t_{Q}$, $f_{Edd}$ and the typical mass ratio $q \equiv M_{2}/M_{1}$. The GWB in this case would be dominated by relatively distant $\sim 10^{9} M_{\odot}$ SMBHs at $z \approx 2 - 3$, at the peak of quasar activity. Similarly to other population models, our results remain in tension with the local SMBH mass density.

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Self-regulation of high-redshift black hole accretion via jets: challenges for SMBH formation

The early growth of black holes (BHs) in atomic-cooling halos is likely influenced by feedback on the surrounding gas. While the effects of radiative feedback are well-documented, mechanical feedback, particularly from AGN jets, has been comparatively less explored. Building on our previous work that examined the growth of a 100 ${M_\odot}$ BH in a constant density environment regulated by AGN jets, we expand the initial BH mass range from 1 to $10^4$ ${M_\odot}$ and adopt a more realistic density profile for atomic-cooling halos. We reaffirm the validity of our analytic models for jet cocoon propagation and feedback regulation. We identify several critical radii-namely, the terminal radius of jet cocoon propagation, the isotropization radius of the jet cocoon, and the core radius of the atomic-cooling halo-that are crucial in determining BH growth given specific gas properties and jet feedback parameters. In a significant portion of the parameter space, our findings show that jet feedback substantially disrupts the halo's core during the initial feedback episode, preventing BH growth beyond $10^4$ ${M_\odot}$. Conversely, conditions characterized by low jet velocities and high gas densities enable sustained BH growth over extended periods. We provide a prediction for the black hole mass growth as a function of time and feedback parameters. We found that, to form a supermassive BH ($>10^6 {M_\odot}$) within 1 Gyr entirely by accreting gas from an atomic-cooling halo, the jet energy feedback efficiency must be $\lesssim 10^{-4} \dot{M}_{BH} c^2$ even if the seed BH mass is $10^4 {M_\odot}$.

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