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Laura Blecha

Publications and source records attributed to Laura Blecha.

At least 37 records · Page 2Linked to original sources

Inferring Mbh-Mbulge Evolution from the Gravitational Wave Background

We test the impact of an evolving supermassive black hole (SMBH) mass scaling relation (Mbh-Mbulge) on the predictions for the gravitational wave background (GWB). The observed GWB amplitude is 2-3 times higher than predicted by astrophysically informed models which suggests the need to revise the assumptions in those models. We compare a semi-analytic model's ability to reproduce the observed GWB spectrum with a static versus evolving-amplitude Mbh-Mbulge relation. We additionally consider the influence of the choice of galaxy stellar mass function on the modeled GWB spectra. Our models are able to reproduce the GWB amplitude with either a large number density of massive galaxies or a positively evolving Mbh-Mbulge amplitude (i.e., the Mbh / Mbulge ratio was higher in the past). If we assume that the Mbh-Mbulge amplitude does not evolve, our models require a galaxy stellar mass function that implies an undetected population of massive galaxies (Mstellar > 10^11 Msun at z > 1). When the Mbh-Mbulge amplitude is allowed to evolve, we can model the GWB spectrum with all fiducial values and an Mbh-Mbulge amplitude that evolves as alpha(z) = alpha_0 (1 + z)^(1.04 +/- 0.5).

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Toward Complete Merger Identification at Cosmic Noon with Deep Learning

As we enter the era of large imaging surveys such as $\textit{Roman}$, Rubin, and $\textit{Euclid}$, a deeper understanding of potential biases and selection effects in optical astronomical catalogs created with the use of ML-based methods is paramount. This work focuses on a deeper understanding of the performance and limitations of deep learning-based classifiers as tools for galaxy merger identification. We train a ResNet18 model on mock Hubble Space Telescope CANDELS images from the IllustrisTNG50 simulation. Our focus is on a more challenging classification of galaxy mergers and nonmergers at higher redshifts $1<z<1.5$, including minor mergers and lower mass galaxies down to the stellar mass of $10^8 M_\odot$. We demonstrate, for the first time, that a deep learning model, such as the one developed in this work, can successfully identify even minor and low mass mergers even at these redshifts. Our model achieves overall accuracy, purity, and completeness of 73%. We show that some galaxy mergers can only be identified from certain observation angles, leading to a potential upper limit in overall accuracy. Using Grad-CAMs and UMAPs, we more deeply examine the performance and observe a visible gradient in the latent space with stellar mass and specific star formation rate, but no visible gradient with merger mass ratio or merger stage.

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AGN feedback in merging galaxies with a SMUGGLE multiphase ISM

We study fast nuclear winds driven by Active Galactic Nucleus (AGN) feedback in merging galaxies using high-resolution hydrodynamics simulations. We use Stars and MUltiphase Gas in GaLaxiEs (SMUGGLE) to explicitly model the multiphase interstellar medium (ISM) and employ sub-grid dynamical friction for massive black holes (BHs). Furthermore, we use a super-Lagrangian refinement scheme to resolve AGN feedback coupling to the ISM at $\sim10-100\,$pc scales. By comparison between merging and isolated galaxies, with and without AGN feedback, we identify trends in the complex interplay between dynamics, BH fueling and feedback, and star formation and feedback. We consider three galaxy types: Milky Way analogs, Sbc-type galaxies, and Small Magellanic Cloud (SMC) analogs. The synergy between AGN feedback and merger dynamics is strongest in the Milky Way-like mergers, where the AGN winds are energetically dominant and entrain more gas when the initially thin disks become thick and amorphous during the merger. In contrast, the merger of thicker, vigorously star-forming Sbc galaxies is not strongly impacted by AGN feedback until star formation declines in the post-merger phase. Finally, while the sub-grid dynamical friction prescription effectively retains BHs in galactic nuclei during more massive mergers, the clumpy multiphase ISM induces significant wandering of low-mass BHs $\mathrm{(<10^5M_\odot)}$ in the shallow potentials of the SMC-like galaxies. These low-mass BHs wander at distances $\gtrsim 2$ kpc from the galactic center, yielding negligible BH accretion and feedback. This has implications for LISA event rates and present a further challenge to understanding the rapid growth of $z\sim7-10$ quasars discovered by JWST.

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Molecular Gas in Major Mergers Hosting Dual and Single AGN at <10 kpc Nuclear Separations

We present high-resolution ($\sim$50$-$100 pc) Atacama Large Millimeter Array (ALMA) observations of $^{12}$CO(2-1) or $^{12}$CO(1-0) emission in seven local ($z$ $\lesssim$ 0.05) major mergers -- five of which are dual active galactic nuclei (AGN) systems, and two of which are single AGN systems. We model the molecular gas kinematics through rotating disk profiles using a Bayesian Markov chain Monte Carlo approach. The residuals were then used to isolate non-rotating components of the molecular gas -- the most likely contributor to future SMBH growth. We find that more massive SMBHs have higher surface densities of non-rotating molecular gas within their sphere of influence. This potential molecular gas supply, however, does not correlate with the current accretion efficiency of the SMBHs, suggesting that only a fraction of the observed non-rotating gas is currently reaching the SMBH. Finally, we tentatively find no significant differences in the nuclear molecular gas masses of single AGN and dual AGN hosts, both within the SMBH sphere of influence and within the central kiloparsec. Our results indicate that the probability of occurrence of the dual AGN phenomenon is likely dependent on AGN variability and/or obscuration rather than the availability of molecular gas in the nuclear regions.

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BEES: Quasar lifetime measurements from extended rest-optical emission line nebulae at $z\sim6$

Measurements of quasar lifetimes at high redshift indicate that the earliest billion-solar-mass supermassive black holes (SMBHs) have only been active as luminous quasars for less than a million years. Recently, extended Ly$α$ nebulae around $z\sim6$ quasars have revealed that these short observed lifetimes are unlikely a sightline-dependent effect. However, the interpretation of Ly$α$ emission is not straightforward due to its resonant nature. In this work, we use rest-frame optical emission lines, which more directly trace photoionization by the quasar, to unambiguously validate the short line-of-sight quasar lifetimes observed at early cosmic epochs. We use deep James Webb Space Telescope/NIRSpec IFU observations of five $z\sim 6$ quasars with small proximity zones to search for their extended emission line nebulae in H$α$ and [O III]$5007$, and detect extended emission in both emission lines around four quasars in our sample. We then use the light-crossing time of these nebulae to measure quasar lifetimes along transverse sightlines. Using their H$α$ nebulae, we also confirm that recombination is likely the dominant emission mechanism behind their previously detected Ly$α$ nebulae. Our results confirm the existence of high-redshift quasars with extremely short lifetimes, $t_{\rm Q} \lesssim 10^{5}\ {\rm yr}$, hosting billion-solar-mass black holes, indicating that rapid accretion is likely responsible for the assembly of SMBHs in the early Universe.

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Heavy seeds and the first black holes: Insights from the BRAHMA simulations

From the luminous quasars at $z \sim 6$ to the recent $z \sim 9-11$ AGNs revealed by JWST, observations of the earliest black hole (BH) populations can provide unique constraints on BH formation and growth models. We use the BRAHMA simulations with constrained initial conditions to investigate BH assembly in extreme overdense regions. The simulations implement heavy seeds ($\sim 10^4-10^5 M_{\odot})$ forming in dense, metal-poor gas exposed to sufficient Lyman-Werner flux. With gas accretion modeled via Bondi-Hoyle formalism and BH dynamics and mergers using a subgrid dynamical friction scheme, we isolate the impact of seeding, dynamics, accretion, and feedback on early BH growth. With fiducial stellar and AGN feedback inherited from IllustrisTNG, accretion is strongly suppressed at $z \gtrsim 9$, leaving mergers as the dominant growth channel. Gas accretion dominates at $z \lesssim 9$, where permissive models (super-Eddington or low radiative efficiency) build $\sim 10^9\ M_{\odot}$ BHs powering quasars by $z \sim 6$, while stricter IllustrisTNG-based prescriptions yield much lower BH masses ($\sim 10^6-10^8\ M_{\odot}$). Our seed models strongly affect merger-driven growth at $z \gtrsim 9$: only the most lenient models (with $\sim 10^5\ M_{\odot}$ seeds) produce enough BH mergers to reach $\gtrsim 10^6\ M_{\odot}$ by $z \sim 10$, consistent with current estimates for GN-z11. Our dynamical friction model gives low merger efficiencies, hindering the buildup of $\gtrsim 10^7\ M_{\odot}$ BHs by $z \sim 9-10$, as currently inferred for GHZ9, UHZ1, and CAPERS-LRD-z9. If the BH-to-stellar mass ratios of these sources are indeed as extreme as currently inferred, they would require either very short BH merger timescales or reduced AGN thermal feedback. Weaker stellar feedback boosts both star formation and BH accretion and cannot raise these ratios.

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Accretion onto supermassive and intermediate mass black holes in cosmological simulations

Accretion is the dominant contribution to the cosmic massive black hole density in the Universe today. Yet, modelling it in cosmological simulations is challenging due to the dynamic range involved, as well as the theoretical uncertainties of the underlying mechanisms driving accretion from galactic to black hole horizon scales. We present a simple, flexible parametrization for gas inflows onto massive black holes in order to manage this uncertainty in large-volume cosmological simulations. This is done as part of the "Learning the Universe'' collaboration, which aims to jointly infer the initial conditions and physical processes governing the evolution of the Universe using a Bayesian forward-modelling approach. To allow such a forward-modelling, we update the prescription for accretion with a two-parameter free-fall based inflow estimate that allows for a radius-dependent inflow rate and add a simple model for unresolved accretion disks. We use uniform resolution cosmological hydrodynamical simulations and the IllustrisTNG framework to study the massive black hole population and its dependence on the introduced model parameters. Once the parameters of the accretion formula are chosen to result in a roughly similar redshift zero black hole mass density, the differences caused by the details in the accretion formula are moderate in the supermassive black hole regime, indicating that it is difficult to distinguish between accretion mechanisms based on luminous active galactic nuclei powered by supermassive black holes. Applying the same models to intermediate mass black holes at high redshift, however, reveals significantly different accretion rates in high redshift, moderate luminosity active galactic nuclei and different frequencies and mass distributions of intermediate mass black hole mergers for the same black hole formation model.

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A 13-Billion-Year View of Galaxy Growth: Metallicity Gradient Evolution from the Local Universe to $z=9$ with JWST and Archival Surveys

The galaxy gas-phase metallicity gradients have been extensively studied over the past four decades, both in the local and high-redshift universe, as they trace the baryon cycle and growth of galaxies. With the unprecedented spatial resolution and sensitivity of JWST, it is now possible to measure metallicity and its radial gradients out to redshifts as high as $z = 9$. Here, we present a sample of 455 spectroscopically confirmed galaxies from redshifts $1.7 \lesssim z \lesssim 9$ that are spatially resolved on sub-kiloparsec (kpc) scales by deep JWST NIRCam or NIRISS Wide Field Slitless Spectroscopy (WFSS). Synthesizing these new JWST observations with legacy observations from the literature, we observe that at redshift $z > 5$, galaxy centers are more metal-rich, exhibiting negative metallicity gradients of $\sim-0.4$ dex kpc$^{-1}$. These gradients flatten over time, reaching near-zero around $z \approx 2$, coinciding with the peak of the cosmic star formation rate. Beyond this point, the gradients become negative again at lower redshifts approaching $z=0$. This evolution likely reflects transitions in galaxy formation modes: an inside-out growth phase dominated by intense central star formation with inefficient feedback and limited gas mixing during ``cosmic dawn", enhanced gas mixing due to feedback-driven wind and gas accretion at ``cosmic noon", and a later phase of slow evolution and reduced feedback toward the present day. These physical processes, including gas accretion and feedback, not only regulate star and galaxy formation on a cosmic scale but also shape the evolutionary pathways of individual galaxies over cosmic time.

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Central Cluster Galaxies: A Hotspot for Detectable Gravitational Waves from Black Hole Mergers

After Pulsar Timing Arrays (PTAs) have announced the evidence for a low-frequency gravitational wave background (GWB), the continuous waves (CWs) are the next anticipated gravitational wave (GW) signals. In this work, we model CW sources detectable by PTAs based on the massive black hole (MBH) merger population in the ASTRID cosmological simulation. We evolve MBH binaries, simulate their GW emissions, and calculate their detection probability (DP) for PTAs. The most detectable CW sources are produced by MBH mergers with masses M_BH > 10^10 solarmass in the lowest frequency bins with f<10 nHz. Remarkably, these mergers occur within massive galaxies with the stellar mass larger than 10^12 solarmass located at the center of galaxy clusters. Particularly striking in ASTRID is a triple merger event, wherein two consecutive mergers occur within 500 Myr interval in the same cluster core, generating high-DP CW signals at ~ 2nHz and ~ 10nHz. We also investigate the electromagnetic (EM) signatures associated with these events: either single or dual active galactic nuclei (AGN) in the massive host galaxies that are undergoing star formation. This research provides new insights into the low-frequency GW sky and informs future multi-messenger searches for PTA CW sources.

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Signatures of BH seeding on the $\mathrm{M_{\displaystyle \bullet}}-σ$ relation: Predictions from the BRAHMA simulations

The James Webb Space Telescope (JWST) has identified a large population of supermassive ($10^6$-$10^8~\mathrm{M}_\odot$) black holes (BHs) in the early universe ($z \sim 4$-$7$). Current measurements suggest that many of these BHs exhibit higher BH-to-stellar mass ratios than local populations, opening a new window into the earliest stages of BH-galaxy coevolution and offering the potential to place tight constraints on BH seeding and growth in the early universe. In this work, we use the BRAHMA simulations to investigate the impact of BH seeding on the $\mathrm{M_{\bullet}}-σ$ relation. These simulations adopt heavy $\sim10^5~\mathrm{M}_{\odot}$ seeds and systematically varied BH seeding models, resulting in distinct predictions for seed abundances. We find that different seed models lead to different normalizations of the $\mathrm{M_{\bullet}}-σ$ relation at higher redshifts ($z > 2$) across all $σ$, and at low redshift for systems with low $σ$ ($50~\mathrm{km\ s^{-1}} \lesssim σ\lesssim 80~\mathrm{km\ s^{-1}}$). The most lenient seed model also shows negligible evolution in the $\mathrm{M_{\bullet}}-σ$ relation across redshift, while more restrictive models have substantially lower normalization on the $\mathrm{M_{\bullet}}-σ$ relation for high $σ$ ($\sim 100~\mathrm{km\ s^{-1}}$) at high redshifts, and evolve upward toward the local relation. We demonstrate that the $\mathrm{M_{\bullet}}-σ$ evolution is a direct consequence of merger-dominated BH growth in low mass galaxies ($\lesssim 10^9~M_{\odot}$) and accretion dominated BH growth in high mass ($\gtrsim10^9~M_{\odot}$) galaxies. Furthermore, the scatter in the $\mathrm{M_{\bullet}}-σ$ relation is larger for the more restrictive models due to the inability of many BHs to grow significantly beyond their seed mass.

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Dynamics of low-mass black hole seeds in the BRAHMA simulations using subgrid-dynamical friction: Impact on merger-driven black hole growth in the high redshift Universe

We analyze the dynamics of low-mass black hole (BH) seeds in the high-redshift ($z\gtrsim5$) Universe using a suite of $[4.5~\mathrm{Mpc}]^3$ and $[9~\mathrm{Mpc}]^3$ BRAHMA cosmological hydrodynamic simulations. The simulations form seeds with mass $M_{\mathrm{seed}}=2.2\times10^3~M_{\odot}$ in halos that exceed critical thresholds of dense & metal-poor gas mass ($5-150~M_{\mathrm{seed}}$) and the halo mass ($1000-10000~M_{\mathrm{seed}}$). While the initial BRAHMA boxes pinned the BHs to the halo centers, here we implement a sub-grid dynamical friction (DF) model. We also compare simulations where the BH is allowed to wander without the added DF. We investigate the spatial and velocity offsets of BHs in their host subhalos, as well as BH merger rates. We find that subgrid DF is crucial to ensure that a significant fraction of BHs effectively sink to halo centers by $z\sim5$, thereby enabling them to get gravitationally bound and merge with other BHs at separations close to the spatial resolution ($\sim0.2-0.4~\rm kpc$) of the simulation. For the BHs that merge, the associated merger time scales lag between $\sim100-1000~\mathrm{Myr}$ after their host halos merge. Compared to predictions using BH repositioning, the overall $z\gtrsim5$ BH merger rates under subgrid DF decrease by a factor of $\sim4-10$. Under subgrid DF, the different seed models predict merger rates between $\sim100-1000$ events per year at $z\gtrsim5$. These mergers dominate early BH growth, assembling BHs up to $\sim10^4-10^5~M_{\odot}$ by $z\sim5$, wherein $\lesssim2~\%$ of their mass is assembled via gas accretion. Our results highlight the promise for constraining seeding mechanisms using gravitational waves from future facilities such as the Laser Interferometer Space Antenna.

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Mergers and Recoil in Triple Massive Black Hole Systems from Illustris

Massive black hole binaries (MBHBs) form through galaxy mergers and are among the loudest sources of gravitational waves (GWs) in the universe. If the binary inspiral time is long, a subsequent galaxy merger can introduce a third black hole, forming a triple system. In the Illustris cosmological simulation, 6% of MBHBs form such triples at parsec scales, where strong three-body interactions are likely. We apply results from numerical simulations of triple MBHs to strong triples identified in Illustris to assess their impact on MBH mergers and recoils. We find that strong triple interactions increase the overall merger fraction by 4%. Including triple interactions raises the merger fraction of MBHs in strong triple systems from 40% to 69%, relative to modeling binary evolution in isolation. Furthermore, massive, major mergers are over three times more likely to be facilitated by strong triple interactions than mergers in general. We also compare GW recoil kicks to gravitational slingshot kicks from triple interactions. Both mechanisms can produce kicks exceeding host escape speeds, ejecting MBHs and producing wandering or offset black holes. Although slingshots yield the highest velocity kicks, GW recoils dominate the ejected population when assuming random MBH spin orientations. Under this assumption, ejections from GW recoil and slingshot kicks reduce the total number of mergers by 6%. Our results highlight the impact of strong triple dynamics and GW recoils on MBH evolution and support their inclusion in cosmological simulations.

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The NANOGrav 15 Yr Data Set: Removing Pulsars One by One from the Pulsar Timing Array

Evidence has emerged for a stochastic signal correlated among 67 pulsars within the 15-year pulsar-timing data set compiled by the NANOGrav collaboration. Similar signals have been found in data from the European, Indian, Parkes, and Chinese PTAs. This signal has been interpreted as indicative of the presence of a nanohertz stochastic gravitational wave background. To explore the internal consistency of this result we investigate how the recovered signal strength changes as we remove the pulsars one by one from the data set. We calculate the signal strength using the (noise-marginalized) optimal statistic, a frequentist metric designed to measure correlated excess power in the residuals of the arrival times of the radio pulses. We identify several features emerging from this analysis that were initially unexpected. The significance of these features, however, can only be assessed by comparing the real data to synthetic data sets. After conducting identical analyses on simulated data sets, we do not find anything inconsistent with the presence of a stochastic gravitational wave background in the NANOGrav 15-year data. The methodologies developed here can offer additional tools for application to future, more sensitive data sets. While this analysis provides an internal consistency check of the NANOGrav results, it does not eliminate the necessity for additional investigations that could identify potential systematics or uncover unmodeled physical phenomena in the data.

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The NANOGrav 15-year Gravitational-Wave Background Methods

Pulsar timing arrays (PTAs) use an array of millisecond pulsars to search for gravitational waves in the nanohertz regime in pulse time of arrival data. This paper presents rigorous tests of PTA methods, examining their consistency across the relevant parameter space. We discuss updates to the 15-year isotropic gravitational-wave background analyses and their corresponding code representations. Descriptions of the internal structure of the flagship algorithms Enterprise and PTMCMCSampler are given to facilitate understanding of the PTA likelihood structure, how models are built, and what methods are currently used in sampling the high-dimensional PTA parameter space. We introduce a novel version of the PTA likelihood that uses a two-step marginalization procedure that performs much faster in gravitational wave searches, reducing the required resources facilitating the computation of Bayes factors via thermodynamic integration and sampling a large number of realizations for computing Bayesian false-alarm probabilities. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis methods. For the Bayesian analysis, we test prior recovery, simulation recovery, and Bayes factors. For the frequentist analysis, we test that the optimal statistic, when modified to account for a non-negligible gravitational-wave background, accurately recovers the amplitude of the background. We also summarize recent advances and tests performed on the optimal statistic in the literature from both GWB detection and parameter estimation perspectives. The tests presented here validate current analyses of PTA data.

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The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays

Pulsar-timing-array experiments have reported evidence for a stochastic background of nanohertz gravitational waves consistent with the signal expected from a population of supermassive--black-hole binaries. Their analyses assume power-law spectra for intrinsic pulsar noise and for the background, as well as a Hellings--Downs cross-correlation pattern among the gravitational-wave--induced residuals across pulsars. These assumptions may not be realized in actuality. We test them in the NANOGrav 15 yr data set using Bayesian posterior predictive checks. After fitting our fiducial model to real data, we generate a population of simulated data-set replications. We use the replications to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients are extreme. We recover Hellings--Downs correlations in simulated data sets at significance levels consistent with the correlations measured in the NANOGrav 15 yr data set. A similar test on spectral coefficients shows that their values in real data are not extreme compared to their distributions across replications. We also evaluate the evidence for the stochastic background using posterior-predictive versions of the frequentist optimal statistic and of Bayesian model comparison, and find comparable significance (3.2 $σ$ and 3 $σ$ respectively) to what was previously reported for the standard statistics. We conclude with novel visualizations of the reconstructed gravitational waveforms that enter the residuals for each pulsar. Our analysis strengthens confidence in the identification and characterization of the gravitational-wave background.

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The NANOGrav 15-year Data Set: Search for Gravitational Wave Memory

We present the results of a search for nonlinear gravitational wave memory in the NANOGrav 15-year data set. We find no significant evidence for memory signals in the dataset, with a maximum Bayes factor of 3.1 in favor of a model including memory. We therefore place upper limits on the strain of potential gravitational wave memory events as a function of sky location and observing epoch. We find upper limits that are not always more constraining than previous NANOGrav results. We show that it is likely due to the increase in common red noise between the 12.5-year and 15-year NANOGrav datasets.

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The Gravitational Wave Background from Massive Black Holes in the ASTRID Simulation

Recent pulsar timing array (PTA) observations have detected nanohertz gravitational waves, likely originating from massive black hole binaries (MBHBs). The detected amplitude is unexpectedly higher than inferred from the electromagnetic measurements. We present new gravitational wave background (GWB) results from the ASTRID simulation. Its large volume and on-the-fly dynamical friction for MBHs provide new insights into the MBHB population, offering a more accurate assessment of its contribution to the observed GWB. ASTRID predicts a GWB from MBHBs of $h_c=2.8\times10^{-15}$, or $\sim45\%$ of the observed amplitude at $\sim 4\,{\rm nHz}$ and $h_c=2.5\times10^{-16}$ ($5\%$) with $h_c\propto f^{-1.6}$ at $\sim 30\,{\rm nHz}$. These predictions remain below current PTA constraints but align with previous empirical models based on the observed MBH mass functions. By comparison, TNG300 with post-processed MBH dynamics yields a range between $70-90\%$ ($20\% - 30\%$) of the observed levels at low (high) frequencies. At low frequencies, ASTRID predicts that the bulk of the GWB originates from MBHB with masses $M_{\rm tot}=1-3\times 10^9\,M_\odot$ peaking at $z\approx 0.3$, consistent with TNG300. Notably, both simulations predict significant GWB contribution from minor mergers ($q<0.2$) by up to $\sim 40\%$. By tracing the full merger trees of local MBHs in ASTRID, we show that they generate GWs at $\sim 10\%-80\%$ of the maximum signal assuming no accretion and recent equal-mass mergers. Finally, we demonstrate the importance of on-the-fly MBH dynamics, the lack of which leads to $3- 5$ times excessive mass growth by merger, and a similar boost to the GWB prediction.

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The NANOGrav 15 yr Data Set: Running of the Spectral Index

The NANOGrav 15-year data provides compelling evidence for a stochastic gravitational-wave (GW) background at nanohertz frequencies. The simplest model-independent approach to characterizing the frequency spectrum of this signal consists in a simple power-law fit involving two parameters: an amplitude A and a spectral index γ. In this paper, we consider the next logical step beyond this minimal spectral model, allowing for a running (i.e., logarithmic frequency dependence) of the spectral index, γ_run(f) = γ+ β\ln(f/f_ref). We fit this running-power-law (RPL) model to the NANOGrav 15-year data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameter βconsistent with no running, β\in [-0.80,2.96], and an inconclusive Bayes factor, B(RPL vs. CPL) = 0.69 +- 0.01. We thus conclude that, at present, the minimal CPL model still suffices to adequately describe the NANOGrav signal; however, future data sets may well lead to a measurement of nonzero β. Finally, we interpret the RPL model as a description of primordial GWs generated during cosmic inflation, which allows us to combine our results with upper limits from big-bang nucleosynthesis, the cosmic microwave background, and LIGO-Virgo-KAGRA.

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