Search

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 \gamma. 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, \gamma_run(f) = \gamma + \beta \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 \beta consistent with no running, \beta \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 \beta. 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., Comment: 17 pages, 4 figures, 2 tables

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. Those 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 are idealizations that 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, and use them to assess whether the optimal-statistic significance, inter-pulsar correlations, and spectral coefficients assume extreme values for the real data when compared to the replications. We confirm that the NANOGrav 15 yr data set is consistent with power-law and Hellings--Downs assumptions. 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\ $\sigma$ and 3\ $\sigma$ 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 as reported by NANOGrav., Comment: 20 pages, 14 Figures

We construct the $z=0$ galaxy stellar mass function (GSMF) by combining the GSMF at stellar masses $M_* \lesssim 10^{11.3} M_\odot$ from the census study of Leja et al. (2020) and the GSMF of massive galaxies at $M_* \gtrsim 10^{11.5} M_\odot$ from the volume-limited MASSIVE galaxy survey. To obtain a robust estimate of $M_*$ for local massive galaxies, we use MASSIVE galaxies with $M_*$ measured from detailed dynamical modeling or stellar population synthesis modeling (incorporating a bottom-heavy initial mass function) with high-quality spatially-resolved spectroscopy. These two independent sets of $M_*$ agree to within ${\sim}7$%. Our new $z=0$ GSMF has a higher amplitude at $M_* \gtrsim 10^{11.5} M_\odot$ than previous studies, alleviating prior concerns of a lack of mass growth in massive galaxies between $z\sim 1$ and 0. We derive a local black hole mass function (BHMF) from this GSMF and the scaling relation of SMBH and galaxy masses. The inferred abundance of local SMBHs above $\sim 10^{10}M_\odot$ is consistent with the number of currently known systems. The predicted amplitude of the nanohertz stochastic gravitational wave background is also consistent with the levels reported by Pulsar Timing Array teams. Our $z = 0$ GSMF therefore leads to concordant results in the high-mass regime of the local galaxy and SMBH populations and the gravitational wave amplitude from merging SMBHs. An exception is our BHMF yields a $z=0$ SMBH mass density that is notably higher than the value estimated from quasars at higher redshifts., Comment: Accepted for publication in ApJL. 17 pages, 6 figures

We present the Black Hole Explorer (BHEX), a mission that will produce the sharpest images in the history of astronomy by extending submillimeter Very-Long-Baseline Interferometry (VLBI) to space. BHEX will discover and measure the bright and narrow "photon ring" that is predicted to exist in images of black holes, produced from light that has orbited the black hole before escaping. This discovery will expose universal features of a black hole's spacetime that are distinct from the complex astrophysics of the emitting plasma, allowing the first direct measurements of a supermassive black hole's spin. In addition to studying the properties of the nearby supermassive black holes M87* and Sgr A*, BHEX will measure the properties of dozens of additional supermassive black holes, providing crucial insights into the processes that drive their creation and growth. BHEX will also connect these supermassive black holes to their relativistic jets, elucidating the power source for the brightest and most efficient engines in the universe. BHEX will address fundamental open questions in the physics and astrophysics of black holes that cannot be answered without submillimeter space VLBI. The mission is enabled by recent technological breakthroughs, including the development of ultra-high-speed downlink using laser communications, and it leverages billions of dollars of existing ground infrastructure. We present the motivation for BHEX, its science goals and associated requirements, and the pathway to launch within the next decade., Comment: Proceedings for SPIE Astronomical Telescopes and Instrumentation

Supermassive black hole binaries (SMBHBs) present us with exciting opportunities for multi-messenger science. These systems are thought to form naturally in galaxy mergers and therefore have the potential to produce electromagnetic (EM) radiation as well as gravitational waves (GWs) detectable with pulsar timing arrays (PTAs). Once GWs from individually resolved SMBHBs are detected, the identification of the host galaxy will be a major challenge due to the ambiguity in possible EM signatures and the poor localization capability of PTAs. In order to aid EM observations in choosing which sources to follow up, we attempt to quantify the number of plausible hosts in both realistic and idealistic scenarios. We outline a host galaxy identification pipeline that injects a single-source GW signal into a simulated PTA dataset, uses production-level techniques to recover the signal, quantifies the localization region and number of galaxies contained therein, and finally imposes cuts on the galaxies using the binary parameters estimated from the GW search. In an ideal case, we find that the 90% credible areas span 29 deg^2 to 241 deg^2, containing about 14 to 341 galaxies. After cuts, the number of galaxies remaining ranges from 22 at worst to 1 (the true host) at best. In a more realistic case, if the signal is sufficiently localized, the sky areas range from 287 deg^2 to 530 deg^2 and enclose about 285 to 1238 galaxies. After cuts, the number of galaxies is 397 at worst and 27 at best. While the signal-to-noise ratio is the primary determinant of the localization area of a given source, we find that the size of the area is also influenced by the proximity of nearby pulsars on the sky and the chirp mass of the source., Comment: Submitted to ApJ

The cosmic merger history of supermassive black hole binaries (SMBHBs) is expected to produce a low-frequency gravitational wave background (GWB). Here we investigate how signs of the discrete nature of this GWB can manifest in pulsar timing arrays through excursions from, and breaks in, the expected $f_{\mathrm{GW}}^{-2/3}$ power-law of the GWB strain spectrum. To do this, we create a semi-analytic SMBHB population model, fit to NANOGrav's 15 yr GWB amplitude, and with 1,000 realizations we study the populations' characteristic strain and residual spectra. Comparing our models to the NANOGrav 15 yr spectrum, we find two interesting excursions from the power-law. The first, at $2 \; \mathrm{nHz}$, is below our GWB realizations with $p$-value significance $p = 0.05$ to $0.06$ ($\approx 1.8 \sigma - 1.9 \sigma$). The second, at $16 \; \mathrm{nHz}$, is above our GWB realizations with $p = 0.04$ to $0.15$ ($\approx 1.4 \sigma - 2.1 \sigma$). We explore the properties of a loud SMBHB which could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by three orders of magnitude, from $\sim 10^6$ to $\sim 10^3$, between $2\; \mathrm{nHz}$ and $20 \; \mathrm{nHz}$. This causes a break in the strain spectrum as the stochasticity of the background breaks down at $26^{+28}_{-19} \; \mathrm{nHz}$, consistent with predictions pre-dating GWB measurements. The diminished GWB signal from SMBHBs at frequencies above the $26$~nHz break opens a window for PTAs to detect continuous GWs from individual SMBHBs or GWs from the early universe., Comment: 10 pages, 8 figures, 1 appendix, submitted to ApJ

Evidence for the majority of the supermassive black holes in the local universe has been obtained dynamically from stellar motions with the Schwarzschild orbit superposition method. However, there have been only a handful of studies using simulated data to examine the ability of this method to reliably recover known input black hole masses $M_{BH}$ and other galaxy parameters. Here we conduct a comprehensive assessment of the reliability of the triaxial Schwarzschild method at $\textit{simultaneously}$ determining $M_{BH}$, stellar mass-to-light ratio $M^{*}/L$, dark matter mass, and three intrinsic triaxial shape parameters of simulated galaxies. For each of 25 rounds of mock observations using simulated stellar kinematics and the $\texttt{TriOS}$ code, we derive best-fitting parameters and confidence intervals after a full search in the 6D parameter space with our likelihood-based model inference scheme. The two key mass parameters, $M_{BH}$ and $M^{*}/L$, are recovered within the 68% confidence interval, and other parameters are recovered between 68% and 95% confidence intervals. The spatially varying velocity anisotropy of the stellar orbits is also well recovered. We explore whether the goodness-of-fit measure used for galaxy model selection in our pipeline is biased by variable complexity across the 6D parameter space. In our tests, adding a penalty term to the likelihood measure either makes little difference, or worsens the recovery in some cases., Comment: 11 pages, 4 figures, 1 table, submitted to ApJ 01/24

Supermassive black hole (SMBH) masses can be measured by observing their dynamical effects on tracers, such as molecular gas. We present high angular resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations of the $^{12}$CO(2-1) line emission of the early-type galaxies (ETGs) NGC 1684 and NGC 0997, obtained as part of the MASSIVE survey, a volume-limited integral-field spectroscopic study of the most massive local ETGs. NGC 1684 has a regularly-rotating central molecular gas disc, with a spatial extent of $\approx 6 "$ ($\approx1.8$ kpc) in radius and a central hole slightly larger than the expected SMBH sphere of influence. We forward model the data cube in a Bayesian framework with the Kinematic Molecular Simulation (KinMS) code and infer a SMBH mass of $1.40^{+0.44}_{-0.39}\times10^9$ M$_\odot$ ($3\sigma$ confidence interval) and a F110W-filter stellar mass-to-light ratio of $(2.50\pm0.05)$ M$_\odot/\text{L}_{\odot,\text{F110W}}$. NGC 0997 has a regularly-rotating central molecular gas disc, with a spatial extent of $\approx5 "$ ($\approx2.2$ kpc) in radius and a partially-filled central hole much larger than the expected SMBH sphere of influence, thus preventing a robust SMBH mass determination. With the same modelling method, we nevertheless constrain the SMBH mass to be in the range $4.0\times10^7$ to $1.8\times10^9$ M$_\odot$ and the F160W-filter stellar mass-to-light ratio to be $(1.52\pm0.11)$ M$_\odot/\text{L}_{\odot,\text{F160W}}$. Both SMBH masses are consistent with the SMBH mass -- stellar velocity dispersion ($M_{\text{BH}}$ -- $\sigma_\text{e}$) relation, suggesting that the over-massive SMBHs present in other very massive ETGs are fairly uncommon., Comment: Main text: 17 pages, 13 figures. Appendix: 3 pages, 3 figures. Accepted for publication in MNRAS

Recently we found compelling evidence for a gravitational wave background with Hellings and Downs (HD) correlations in our 15-year data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes which produce different interpulsar correlations. In this work we search the NANOGrav 15-year data set for evidence of a gravitational wave background with quadrupolar Hellings and Downs (HD) and Scalar Transverse (ST) correlations. We find that HD correlations are the best fit to the data, and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors $\sim 2$ when comparing HD to ST correlations, and $\sim 1$ for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise-ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise-ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise-ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis., Comment: 11 pages, 5 figures

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05-year period and low redshift ($\sim0.02$) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using Pulsar Timing Array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it on simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5-year data set employing PTA signal models containing Earth term-only as well as Earth+Pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity $e_0<0.5$ and the symmetric mass ratio $\eta>0.1$. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of $88.1\pm3.7$ ns for the Earth term-only and $81.74\pm0.86$ ns for the Earth+Pulsar term searches for $e_0<0.5$ and $\eta>0.1$. Similar 95% upper limits on the chirp mass are $(1.98 \pm 0.05) \times 10^9\,M_{\odot}$ and $(1.81 \pm 0.01) \times 10^9\,M_{\odot}$. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5-year data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations., Comment: 27 Pages, 10 Figures, 1 Table, Accepted for publication in ApJ

Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a background and assess its significance make several simplifying assumptions, namely: i) Gaussianity; ii) isotropy; and most often iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated datasets, despite their fundamental assumptions not being strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them., Comment: 14 pages, 8 figures, version matching published paper

We present the results of a Bayesian search for gravitational wave (GW) memory in the NANOGrav 12.5-yr data set. We find no convincing evidence for any gravitational wave memory signals in this data set (Bayes factor = 2.8). As such, we go on to place upper limits on the strain amplitude of GW memory events as a function of sky location and event epoch. These upper limits are computed using a signal model that assumes the existence of a common, spatially uncorrelated red noise in addition to a GW memory signal. The median strain upper limit as a function of sky position is approximately $3.3 \times 10^{-14}$. We also find that there are some differences in the upper limits as a function of sky position centered around PSR J0613$-$0200. This suggests that this pulsar has some excess noise which can be confounded with GW memory. Finally, the upper limits as a function of burst epoch continue to improve at later epochs. This improvement is attributable to the continued growth of the pulsar timing array., Comment: 29 pages, 5 figures

We present Hubble Space Telescope photometry in optical (F475X) and near-infrared (F110W) bands of the globular cluster (GC) systems of the inner halos of a sample of 15 massive elliptical galaxies. The targets are selected from the volume-limited MASSIVE survey, and chosen to sample a range of environments from sparsely populated groups to BCGs in dense clusters. We also present a quantitative model of the relation between (F475X - F110W) colour and cluster metallicity [M/H], using simulated GCs. Because much of the GC population in such galaxies is built up through accretion, the metallicity distribution of the GC systems might be expected to vary with galaxy environment. The photometry is used to create a completeness-corrected metallicity distribution for each galaxy in the sample, and to fit a double Gaussian curve to each histogram in order to model the two standard red and blue subpopulations. Finally, the properties of the GC metallicity distribution are correlated against galaxy environment. We find that almost no GCS properties and host galaxy environmental properties are correlated, with the exception of a weak but consistent correlation between blue fraction and nth-nearest neighbour surface density. The results suggest that the systemic properties of the GCS, at least in the inner to mid-halo regions, are influenced more strongly by the local environment at early times, rather than by the environmental properties we see today., Comment: 21 pages, 18 figures. Accepted for publication in ApJ

This paper presents rigorous tests of pulsar timing array methods and software, examining their consistency across a wide range of injected parameters and signal strength. 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 \texttt{Enterprise} and \texttt{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 when the white noise parameters remain fixed. We perform stringent tests of consistency and correctness of the Bayesian and frequentist analysis software. For the Bayesian analysis, we test prior recovery, injection recovery, and Bayes factors. For the frequentist analysis, we test that the cross-correlation-based 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 and future analyses of PTA data., Comment: 30 pages, 10 figures, 1 table; Companion paper to "The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background"; For questions or comments, please email comments@nanograv.org

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems., Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data., Comment: 19 pages, 11 figures; submitted to Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The NANOGrav 15-year data set shows evidence for the presence of a low-frequency gravitational-wave background (GWB). While many physical processes can source such low-frequency gravitational waves, here we analyze the signal as coming from a population of supermassive black hole (SMBH) binaries distributed throughout the Universe. We show that astrophysically motivated models of SMBH binary populations are able to reproduce both the amplitude and shape of the observed low-frequency gravitational-wave spectrum. While multiple model variations are able to reproduce the GWB spectrum at our current measurement precision, our results highlight the importance of accurately modeling binary evolution for producing realistic GWB spectra. Additionally, while reasonable parameters are able to reproduce the 15-year observations, the implied GWB amplitude necessitates either a large number of parameters to be at the edges of expected values, or a small number of parameters to be notably different from standard expectations. While we are not yet able to definitively establish the origin of the inferred GWB signal, the consistency of the signal with astrophysical expectations offers a tantalizing prospect for confirming that SMBH binaries are able to form, reach sub-parsec separations, and eventually coalesce. As the significance grows over time, higher-order features of the GWB spectrum will definitively determine the nature of the GWB and allow for novel constraints on SMBH populations., Comment: Accepted by Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org. Edited to fix two equation typos (Eq.13 & 21), and minor text typos

The 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons., Comment: 74 pages, 31 figures, 4 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals., Comment: 67 pages, 73 figures, 3 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We present observations and timing analyses of 68 millisecond pulsars (MSPs) comprising the 15-year data set of the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). NANOGrav is a pulsar timing array (PTA) experiment that is sensitive to low-frequency gravitational waves. This is NANOGrav's fifth public data release, including both "narrowband" and "wideband" time-of-arrival (TOA) measurements and corresponding pulsar timing models. We have added 21 MSPs and extended our timing baselines by three years, now spanning nearly 16 years for some of our sources. The data were collected using the Arecibo Observatory, the Green Bank Telescope, and the Very Large Array between frequencies of 327 MHz and 3 GHz, with most sources observed approximately monthly. A number of notable methodological and procedural changes were made compared to our previous data sets. These improve the overall quality of the TOA data set and are part of the transition to new pulsar timing and PTA analysis software packages. For the first time, our data products are accompanied by a full suite of software to reproduce data reduction, analysis, and results. Our timing models include a variety of newly detected astrometric and binary pulsar parameters, including several significant improvements to pulsar mass constraints. We find that the time series of 23 pulsars contain detectable levels of red noise, 10 of which are new measurements. In this data set, we find evidence for a stochastic gravitational-wave background., Comment: 90 pages, 74 figures, 6 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15-year pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. The correlations follow the Hellings-Downs pattern expected for a stochastic gravitational-wave background. The presence of such a gravitational-wave background with a power-law-spectrum is favored over a model with only independent pulsar noises with a Bayes factor in excess of $10^{14}$, and this same model is favored over an uncorrelated common power-law-spectrum model with Bayes factors of 200-1000, depending on spectral modeling choices. We have built a statistical background distribution for these latter Bayes factors using a method that removes inter-pulsar correlations from our data set, finding $p = 10^{-3}$ (approx. $3\sigma$) for the observed Bayes factors in the null no-correlation scenario. A frequentist test statistic built directly as a weighted sum of inter-pulsar correlations yields $p = 5 \times 10^{-5} - 1.9 \times 10^{-4}$ (approx. $3.5 - 4\sigma$). Assuming a fiducial $f^{-2/3}$ characteristic-strain spectrum, as appropriate for an ensemble of binary supermassive black-hole inspirals, the strain amplitude is $2.4^{+0.7}_{-0.6} \times 10^{-15}$ (median + 90% credible interval) at a reference frequency of 1/(1 yr). The inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from a population of supermassive black-hole binaries, although more exotic cosmological and astrophysical sources cannot be excluded. The observation of Hellings-Downs correlations points to the gravitational-wave origin of this signal., Comment: 30 pages, 18 figures. Published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email comments@nanograv.org

The three-dimensional intrinsic shape of a galaxy and the mass of the central supermassive black hole provide key insight into the galaxy's growth history over cosmic time. Standard assumptions of a spherical or axisymmetric shape can be simplistic and can bias the black hole mass inferred from the motions of stars within a galaxy. Here we present spatially-resolved stellar kinematics of M87 over a two-dimensional $250\mbox{$^{\prime\prime}$} \times 300\mbox{$^{\prime\prime}$}$ contiguous field covering a radial range of 50 pc-12 kpc from integral-field spectroscopic observations at the Keck II Telescope. From about 5 kpc and outward, we detect a prominent 25 $\mathrm{km~s}^{-1}$ rotational pattern, in which the kinematic axis (connecting the maximal receding and approaching velocities) is $40^\circ$ misaligned with the photometric major axis of M87. The rotational amplitude and misalignment angle both decrease in the inner 5 kpc. Such misaligned and twisted velocity fields are a hallmark of triaxiality, indicating that M87 is not an axisymmetrically shaped galaxy. Triaxial Schwarzschild orbit modeling with more than 4000 observational constraints enabled us to determine simultaneously the shape and mass parameters. The models incorporate a radially declining profile for the stellar mass-to-light ratio suggested by stellar population studies. We find that M87 is strongly triaxial, with ratios of $p=0.845$ for the middle-to-long principal axes and $q=0.722$ for the short-to-long principal axes, and determine the black hole mass to be $(5.37^{+0.37}_{-0.25}\pm 0.22)\times 10^9 M_\odot$, where the second error indicates the systematic uncertainty associated with the distance to M87., Comment: Published in ApJL. 15 pages, 8 figures

We present wide-field, deep $K$-band photometry of 98 luminous early-type galaxies (ETGs) from the MASSIVE survey based on observations taken with the WIRCam instrument on the Canada-France-Hawaii Telescope. Using these images, we extract accurate total $K$-band luminosities ($L_K$) and half-light radii ($R_e$) for this sample of galaxies. We use these new values to explore the size-luminosity and Faber-Jackson relations for massive ETGs. Within this volume-limited sample, we find clear evidence for curvature in both relations, indicating that the most luminous galaxies tend to have larger sizes and smaller velocity dispersions than expected from a simple power-law fit to less luminous galaxies. Our measured relations are qualitatively consistent with the most massive elliptical galaxies forming largely through dissipationless mergers. When the sample is separated into fast and slow rotators, we find the slow rotators to exhibit similar changes in slope with increasing $L_K$, suggesting that low-mass and high-mass slow rotators have different formation histories. The curvatures in the $R_e-L_K$ and $\sigma-L_K$ relations cancel, leading to a relation between dynamical mass and luminosity that is well described by a single power-law: $R_e\sigma^2 \propto {L_K}^b$ with $b \approx 1.2$. This is consistent with the tilt of the fundamental plane observed in lower mass elliptical galaxies., Comment: 17 pages, 7 figures, accepted for publication in MNRAS

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

We have used Hubble Space Telescope (HST) images, SAURON Integral Field Spectroscopy (IFS) and adaptative optics assisted Gemini NIFS near-infrared K-band IFS to map the stellar and gas distribution, excitation and kinematics of the inner few kpc of the nearby edge-on S0 galaxy NGC 4111. The HST images map its $\approx$ 450 pc diameter dusty polar ring, with an estimated gas mass $\ge10^7$ M$_\odot$. The NIFS datacube maps the inner 110 pc radius at $\approx$ 7 pc spatial resolution revealing a $\approx$ 220 pc diameter polar ring in hot ($2267\pm166$ K) molecular H$_2$ 1-0 S(1) gas embedded in the polar ring. The stellar velocity field shows disk-dominated kinematics along the galaxy plane both in the SAURON large-scale and in the NIFS nuclear-scale data. The large-scale [O III] $\lambda5007$ \AA velocity field shows a superposition of two disk kinematics: one similar to that of the stars and another along the polar ring, showing non-circular motions that seem to connect with the velocity field of the nuclear H$_2$ ring, whose kinematics indicate accelerated inflow to the nucleus. The estimated mass inflow rate is enough not only to feed an Active Galactic Nucleus (AGN) but also to trigger circumnuclear star formation in the near future. We propose a scenario in which gas from the polar ring, which probably originated from the capture of a dwarf galaxy, is moving inwards and triggering an AGN, as supported by the local X-ray emission, which seems to be the source of the H$_2$ 1-0 S(1) excitation. The fact that we see neither near-UV nor Br$\gamma$ emission suggests that the nascent AGN is still deeply buried under the optically thick dust of the polar ring., Comment: 18 pages, 21 figures

We present a stellar dynamical mass measurement of a newly detected supermassive black hole (SMBH) at the center of the fast-rotating, massive elliptical galaxy NGC 2693 as part of the MASSIVE survey. We combine high signal-to-noise integral field spectroscopy (IFS) from the Gemini Multi-Object Spectrograph (GMOS) with wide-field data from the Mitchell Spectrograph at McDonald Observatory to extract and model stellar kinematics of NGC 2693 from the central $\sim 150$ pc out to $\sim2.5$ effective radii. Observations from Hubble Space Telescope (HST) WFC3 are used to determine the stellar light distribution. We perform fully triaxial Schwarzschild orbit modeling using the latest TriOS code and a Bayesian search in 6-D galaxy model parameter space to determine NGC 2693's SMBH mass ($M_\text{BH}$), stellar mass-to-light ratio, dark matter content, and intrinsic shape. We find $M_\text{BH} = \left(1.7\pm 0.4\right)\times 10^{9}\ M_\odot$ and a triaxial intrinsic shape with axis ratios $p=b/a=0.902 \pm 0.009$ and $q=c/a=0.721^{+0.011}_{-0.010}$, triaxiality parameter $T = 0.39 \pm 0.04$. In comparison, the best-fit orbit model in the axisymmetric limit and (cylindrical) Jeans anisotropic model of NGC 2693 prefer $M_\text{BH} = \left(2.4\pm 0.6\right)\times 10^{9}\ M_\odot$ and $M_\text{BH} = \left(2.9\pm 0.3\right)\times 10^{9}\ M_\odot$, respectively. Neither model can account for the non-axisymmetric stellar velocity features present in the IFS data., Comment: 18 pages, 9 figures, 2 tables, accepted to ApJ 2022/02/24

Most stellar-dynamical determinations of the masses of nearby supermassive black holes (SMBHs) have been obtained with the orbit superposition technique under the assumption of axisymmetry. However, few galaxies -- in particular massive early-type galaxies -- obey exact axisymmetry. Here we present a revised orbit superposition code and a new approach for dynamically determining the intrinsic shapes and mass parameters of triaxial galaxies based on spatially-resolved stellar kinematic data. The triaxial TriOS code described here corrects an error in the original van den Bosch et al. (2008) code that gives rise to incorrect projections for most orbits in triaxial models and can significantly impact parameter search results. The revised code also contains significant improvements in orbit sampling, mass constraints, and run time. Furthermore, we introduce two new parameter searching strategies -- a new set of triaxial shape parameters and a novel grid-free sampling technique -- that together lead to a remarkable gain in efficiency in locating the best-fit model. We apply the updated code and search method to NGC 1453, a fast-rotating massive elliptical galaxy. A full 6D parameter search finds $p=b/a=0.933^{+0.014}_{-0.015}$ and $q=c/a=0.779\pm0.012$ for the intrinsic axis ratios and $T=0.33\pm0.06$ for the triaxiality parameter. Despite the deviations from axisymmetry, the best-fit SMBH mass, stellar mass-to-light ratio, and dark matter enclosed mass for NGC 1453 are consistent with the axisymmetric results. More comparisons between axisymmetric and triaxial modeling are needed before drawing general conclusions., Comment: 19 pages, 8 figures, accepted to ApJ. In press

The stellar initial mass function (IMF) is a fundamental property in the measurement of stellar masses and galaxy star formation histories. In this work we focus on the most massive galaxies in the nearby universe $\log(M_{\star}/M_{\odot})>11.2$. We obtain high quality Magellan/LDSS-3 long slit spectroscopy with a wide wavelength coverage of $0.4\mu{\rm m}-1.01\mu{\rm m}$ for 41 early-type galaxies (ETGs) in the MASSIVE survey, and derive high S/N spectra within an aperture of $R_{\rm e}/8$. Using detailed stellar synthesis models, we constrain the elemental abundances and stellar IMF of each galaxy through full spectral modeling. All the ETGs in our sample have an IMF that is steeper than a Milky Way (Kroupa) IMF. The best-fit IMF mismatch parameter, $\alpha_{\rm IMF}=(M/L)/(M/L)_{\rm MW}$, ranges from 1.12 to 3.05, with an average of $\langle \alpha_{\rm IMF} \rangle=1.84$, suggesting that on average, the IMF is more bottom-heavy than Salpeter. Comparing the estimated stellar mass with the dynamical mass, we find that most galaxies have stellar masses smaller than their dynamical masses within the $1\sigma$ uncertainty. We complement our sample with lower-mass galaxies from the literature, and confirm that $\log(\alpha_{\rm IMF})$ is positively correlated with $\log(\sigma)$, $\log(M_{\star})$, and $\log(M_{\rm dyn})$. The IMF in the centers of more massive ETGs is more bottom-heavy. In addition, we find that $\log(\alpha_{\rm IMF})$ is positively correlated with both [Mg/Fe] and the estimated total metallicity [Z/H]. We find suggestive evidence that the effective stellar surface density $\Sigma_{\rm Kroupa}$ might be responsible for the variation of $\alpha_{\rm IMF}$. We conclude that $\sigma$, [Mg/Fe] and [Z/H] are the primary drivers of the global stellar IMF variation., Comment: 23 pages, 11 figures, submitted to ApJ

The binding energy liberated by the coalescence of supermassive black hole (SMBH) binaries during galaxy mergers is thought to be responsible for the low density cores often found in bright elliptical galaxies. We use high-resolution $N$-body and Monte Carlo techniques to perform single and multi-stage galaxy merger simulations and systematically study the dependence of the central galaxy properties on the binary mass ratio, the slope of the initial density cusps, and the number of mergers experienced. We study both the amount of depleted stellar mass (or ``mass deficit'), $M_{\rm def}$, and the radial extent of the depleted region, $r_{\rm b}$. We find that $r_{\rm b}\simeq r_{\rm SOI}$ and that $M_{\rm def}$ varies in the range $0.5$ to $4M_{\bullet}$, with $r_{\rm SOI}$ the influence radius of the remnant SMBH and $M_{\bullet}$ its mass. The coefficients in these relations depend weakly on the binary mass ratio and remain remarkably constant through subsequent mergers. We conclude that the core size and mass deficit do not scale linearly with the number of mergers, making it hard to infer merger histories from observations. On the other hand, we show that both $M_{\rm def}$ and $r_{\rm b}$ are sensitive to the morphology of the galaxy merger remnant, and that adopting spherical initial conditions, as done in early work, leads to misleading results. Our models reproduce the range of values for $M_{\rm def}$ found in most observational work, but span nearly an order of magnitude range around the true ejected stellar mass., Comment: 19 pages, 9 figures, 4 tables. Accepted for publication to ApJ, comments are welcome

We present estimates for the number of shadow-resolved supermassive black hole (SMBH) systems that can be detected using radio interferometers, as a function of angular resolution, flux density sensitivity, and observing frequency. Accounting for the distribution of SMBHs across mass, redshift, and accretion rate, we use a new semi-analytic spectral energy distribution model to derive the number of SMBHs with detectable and optically thin horizon-scale emission. We demonstrate that (sub)millimeter interferometric observations with ${\sim}0.1$ $\mu$as resolution and ${\sim}1$ $\mu$Jy sensitivity could access ${>}10^6$ SMBH shadows. We then further decompose the shadow source counts into the number of black holes for which we could expect to observe the first- and second-order lensed photon rings. Accessing the bulk population of first-order photon rings requires ${\lesssim}2$ $\mu$as resolution and ${\lesssim}0.5$ mJy sensitivity, while doing the same for second-order photon rings requires ${\lesssim}0.1$ $\mu$as resolution and ${\lesssim}5$ $\mu$Jy sensitivity. Our model predicts that with modest improvements to sensitivity, as many as $\sim$5 additional horizon-resolved sources should become accessible to the current Event Horizon Telescope (EHT), while a next-generation EHT observing at 345 GHz should have access to ${\sim}$3 times as many sources. More generally, our results can help guide enhancements of current arrays and specifications for future interferometric experiments that aim to spatially resolve a large population of SMBH shadows or higher-order photon rings., Comment: 37 pages, 18 figures, published in ApJ

We measured high-quality surface brightness fluctuation (SBF) distances for a sample of 63 massive early-type galaxies using the WFC3/IR camera on the Hubble Space Telescope. The median uncertainty on the SBF distance measurements is 0.085 mag, or 3.9% in distance. Achieving this precision at distances of 50 to 100 Mpc required significant improvements to the SBF calibration and data analysis procedures for WFC3/IR data. Forty-two of the galaxies are from the MASSIVE Galaxy Survey, a complete sample of massive galaxies within ~100 Mpc; the SBF distances for these will be used to improve the estimates of the stellar and central supermassive black hole masses in these galaxies. Twenty-four of the galaxies are Type Ia supernova hosts, useful for calibrating SN Ia distances for early-type galaxies and exploring possible systematic trends in the peak luminosities. Our results demonstrate that the SBF method is a powerful and versatile technique for measuring distances to galaxies with evolved stellar populations out to 100 Mpc and constraining the local value of the Hubble constant., Comment: Accepted for publication in Astrophysical Journal Supplement Series; 22 pages, 7 figures, with 61 additional figures to be published as an online figure set

Supermassive black hole binaries (SMBHBs) should form frequently in galactic nuclei as a result of galaxy mergers. At sub-parsec separations, binaries become strong sources of low-frequency gravitational waves (GWs), targeted by Pulsar Timing Arrays (PTAs). We used recent upper limits on continuous GWs from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 11yr dataset to place constraints on putative SMBHBs in nearby massive galaxies. We compiled a comprehensive catalog of ~44,000 galaxies in the local universe (up to redshift ~0.05) and populated them with hypothetical binaries, assuming that the total mass of the binary is equal to the SMBH mass derived from global scaling relations. Assuming circular equal-mass binaries emitting at NANOGrav's most sensitive frequency of 8nHz, we found that 216 galaxies are within NANOGrav's sensitivity volume. We ranked the potential SMBHBs based on GW detectability by calculating the total signal-to-noise ratio (S/N) such binaries would induce within the NANOGrav array. We placed constraints on the chirp mass and mass ratio of the 216 hypothetical binaries. For 19 galaxies, only very unequal-mass binaries are allowed, with the mass of the secondary less than 10 percent that of the primary, roughly comparable to constraints on a SMBHB in the Milky Way. Additionally, we were able to exclude binaries delivered by major mergers (mass ratio of at least 1/4) for several of these galaxies. We also derived the first limit on the density of binaries delivered by major mergers purely based on GW data., Comment: Submitted to ApJ. Send comments to Maria Charisi (maria.charisi@nanograv.org)

We present a measurement of the Hubble constant $H_0$ from surface brightness fluctuation (SBF) distances for 63 bright, mainly early-type galaxies out to 100 Mpc observed with the Wide Field Camera 3 Infrared Channel (WFC3/IR) on the Hubble Space Telescope (HST). The sample is drawn from several independent HST imaging programs using the F110W bandpass of WFC3/IR. The majority of galaxies are in the 50 to 80 Mpc range and come from the MASSIVE galaxy survey. The median statistical uncertainty on individual distance measurements is 4%. We construct the Hubble diagram with these IR SBF distances and constrain $H_0$ using {four} different treatments of the galaxy velocities. For the SBF zero point calibration, we use both the existing tie to Cepheid variables, updated for consistency with the latest determination of the distance to the Large Magellanic Cloud from detached eclipsing binaries, and a new tie to the tip of the red giant branch (TRGB) calibrated from the maser distance to NGC4258. These two SBF calibrations are consistent with each other and with theoretical predictions from stellar population models. From a weighted average of the Cepheid and TRGB calibrations, we derive $H_0=73.3{\,\pm\,}0.7{\,\pm\,}2.4$ km/s/Mpc, where the error bars reflect the statistical and systematic uncertainties. This result accords well with recent measurements of $H_0$ from Type~Ia supernovae, time delays in multiply lensed quasars, and water masers. The systematic uncertainty could be reduced to below 2% by calibrating the SBF method with precision TRGB distances for a statistical sample of massive early-type galaxies out to the Virgo cluster measured with the James Webb Space Telescope., Comment: Replaced with version accepted to ApJ. 17 pages, including detailed Appendix on the Tip of the Red Giant Branch calibration; have added an additional peculiar velocity model to the analysis

We are building an image slicer integral field unit (IFU) to go on the IMACS wide-field imaging spectrograph on the Magellan Baade Telescope at Las Campanas Observatory, the Reformatting Optically-Sensitive IMACS Enhancement IFU, or ROSIE IFU. The 50.4" x 53.5" field of view will be pre-sliced into four 12.6" x 53.5" subfields, and then each subfield will be divided into 21 0.6" x 53.5" slices. The four main image slicers will produce four pseudo-slits spaced six arcminutes apart across the IMACS f/2 camera field of view, providing a wavelength coverage of 1800 Angstroms at a spectral resolution of 2000. Optics are in-hand, the first image slicer is being aluminized, mounts are being designed and fabricated, and software is being written. This IFU will enable the efficient mapping of extended objects such as nebulae, galaxies, or outflows, making it a powerful addition to IMACS., Comment: 12 pages, 9 figures, 2 tables, submitted to SPIE

We present a detailed analysis of the behavior of the triaxial Schwarzschild orbit superposition method near the axisymmetric limit. Orbit superposition modeling is the primary method used to determine dynamical masses of supermassive black holes ($M_\mathrm{BH}$) in nearby galaxies; however, prior studies have reported conflicting results when comparing the outcome from axisymmetric orbit codes with that from a triaxial orbit code in the axisymmetric limit. We show that in order to achieve (oblate) axisymmetry in a triaxial code, care needs to be taken to axisymmetrize the short-axis tube orbits and to exclude both the long-axis tube and box orbits from the orbit library. Using up to 12 Gauss-Hermite moments of the line-of-sight velocity distributions as constraints, we demonstrate the effects of orbit types on the best-fit $M_\mathrm{BH}$ in orbit modeling of the massive elliptical galaxy NGC 1453 reported in Liepold et al. 2020. In addition, we verify the efficacy of our updated code on a mock galaxy dataset. We identify a subset of slowly precessing quasi-planar orbits for which the typical integration times can be insufficient to fully capture the equilibrium orbital behavior in both axisymmetric and triaxial systems with central black holes. Further investigation is needed for a more reliable treatment of these orbits., Comment: 19 pages, 7 figures. Accepted for publication in ApJ

We use high spatial resolution stellar velocity maps from the Gemini GMOS integral-field spectrograph (IFS) and wide-field velocity maps from the McDonald Mitchell IFS to study the stellar velocity profiles and kinematic misalignments from $\sim 200$ pc to $\sim 20$ kpc in 20 early-type galaxies with stellar mass $M_* > 10^{11.7} M_\odot$ in the MASSIVE survey. While 80% of the galaxies have low spins ($\lambda < 0.1$) and low rotational velocities ($< 50$ km/s) in both the central region and the main body, we find a diverse range of velocity features and misalignment angles. For the 18 galaxies with measurable central kinematic axes, 10 have well aligned kinematic axis and photometric major axis, and the other 8 galaxies have misalignment angles that are distributed quite evenly from $15^\circ$ to the maximal value of $90^\circ$. There is a strong correlation between central kinematic misalignment and galaxy spin, where all 4 galaxies with significant spins have well aligned kinematic and photometric axes, but only 43% of the low-spin galaxies are well aligned. The central and main-body kinematic axes within a galaxy are not always aligned. When the two kinematic axes are aligned ($\sim 60$% of the cases), they are either also aligned with the photometric major axis or orthogonal to it. We find 13 galaxies to also exhibit noticeable local kinematic twists, and one galaxy to have a counter-rotating core. A diverse assembly history consisting of multiple gas-poor mergers of a variety of progenitor mass ratios and orbits is likely to be needed to account for the predominance of low spins and the wide range of central and main-body velocity features reported here for local massive ETGs., Comment: Accepted for publication in The Astrophysical Journal. 15 pages, 7 figures

We present a new stellar dynamical mass measurement ($M_\mathrm{BH}$) of the supermassive black hole (SMBH) in NGC 1453, a fast-rotating massive elliptical galaxy in the MASSIVE survey. We measure stellar kinematics in 135 spatial bins in the central 1.5 kpc by 2 kpc region of the galaxy using high signal-to-noise ($S/N \sim 130$) spectra from the Gemini-North GMOS integral-field spectrograph (IFS). Combining with wide-field IFS kinematics out to $\sim 3$ effective radii and stellar light distributions from Hubble Space Telescope (HST) WFC3 images, we perform Schwarzschild orbit-based mass modeling in the axisymmetric limit to constrain the mass components in NGC 1453. The best-fit black hole mass is $M_\mathrm{BH} =(2.9 \pm 0.4) 10^9 M_\odot$; the mass models without a central black hole are excluded at the $8.7\sigma$ level. The NGC 1453 black hole lies within the intrinsic scatter of the SMBH and galaxy scaling relations, unlike three other galaxies hosting $\gtrsim 10^{10} M_\odot$ SMBHs in the MASSIVE sample. The high-$S/N$ GMOS spectra enable us to determine 8 moments of the Gauss-Hermite expansion of the line-of-sight velocity distributions (LOSVDs), which are used as constraints in the orbit modeling. The stellar orbits in the mass models are further constrained to produce negligible $h_9$ through $h_{12}$ to minimize spurious behavior in the LOSVDs. We show that truncating the series at $h_4$, as was often done in prior work, leads to a much weaker constraint on the inferred $M_\mathrm{BH}$ for NGC 1453. Furthermore, we discuss precautions and modifications that are needed to achieve axisymmetry in triaxial orbit codes that use the Schwarzschild method to sample the start space of stellar orbits in triaxial gravitational potentials., Comment: Accepted for publication in The Astrophysical Journal. 22 pages, 12 figures; References updated

We study black hole - host galaxy correlations, and the relation between the over-massiveness (the distance from the average $M_{BH}-\sigma$ relation) of super-massive black holes (SMBHs) and star formation histories of their host galaxies in the Illustris and TNG100 simulations. We find that both simulations are able to produce black hole scaling relations in general agreement with observations at $z=0$, but with noticeable discrepancies. Both simulations show an offset from the observations for the $M_{BH}-\sigma$ relation, and the relation between $M_{BH}$ and the Sersic index. The relation between $M_{BH}$ and stellar mass $M_*$ is tighter than the observations, especially for TNG100. For massive galaxies in both simulations, the hosts of over-massive SMBHs (those above the mean $M_{BH}-\sigma$ relation) tend to have larger Sersic indices and lower baryon conversion efficiency, suggesting a multidimensional link between SMBHs and properties of their hosts. In Illustris, the hosts of over-massive SMBHs have formed earlier and have lower present-day star formation rates, in qualitative agreement with the observations for massive galaxies with $\sigma>100 \rm km/s$. For low-mass galaxies, such a correlation still holds in Illustris but does not exist in the observed data. For TNG100, the correlation between SMBH over-massiveness and star formation history is much weaker. The hosts of over-massive SMBHs generally have consistently larger star formation rates throughout history. These galaxies have higher stellar mass as well, due to the strong $M_{BH}-M_*$ correlation. Our findings show that simulated SMBH scaling relations and correlations are sensitive to features in the modeling of SMBHs., Comment: 18 pages, 11 figures, submitted to ApJ

We use observations from the GEMINI-N/GMOS integral-field spectrograph (IFS) to obtain spatially resolved stellar kinematics of the central $\sim 1$ kpc of 20 early-type galaxies (ETGs) with stellar masses greater than $10^{11.7} M_\odot$ in the MASSIVE survey. Together with observations from the wide-field Mitchell IFS at McDonald Observatory in our earlier work, we obtain unprecedentedly detailed kinematic maps of local massive ETGs, covering a scale of $\sim 0.1-30$ kpc. The high ($\sim 120$) signal-to-noise of the GMOS spectra enable us to obtain two-dimensional maps of the line-of-sight velocity, velocity dispersion $\sigma$, as well as the skewness $h_3$ and kurtosis $h_4$ of the stellar velocity distributions. All but one galaxy in the sample have $\sigma(R)$ profiles that increase towards the center, whereas the slope of $\sigma(R)$ at one effective radius ($R_e$) can be of either sign. The $h_4$ is generally positive, with 14 of the 20 galaxies having positive $h_4$ within the GMOS aperture and 18 having positive $h_4$ within $1 R_e$. The positive $h_4$ and rising $\sigma(R)$ towards small radii are indicative of a central black hole and velocity anisotropy. We demonstrate the constraining power of the data on the mass distributions in ETGs by applying Jeans anisotropic modeling (JAM) to NGC~1453, the most regular fast rotator in the sample. Despite the limitations of JAM, we obtain a clear $\chi^2$ minimum in black hole mass, stellar mass-to-light ratio, velocity anisotropy parameters, and the circular velocity of the dark matter halo., Comment: Accepted to ApJ

Supermassive black holes are located at the center of most, if not all, massive galaxies. They follow close correlations with global properties of their host galaxies (scaling relations), and are thought to play a crucial role in galaxy evolution. Yet, we lack a complete understanding of fundamental aspects of their growth across cosmic time. In particular, we still do not understand: (1) whether black holes or their host galaxies grow faster and (2) what is the maximum mass that black holes can reach. The high angular resolution capability and sensitivity of 30-m class telescopes will revolutionize our understanding of the extreme end of the black hole and galaxy mass scale. With such facilities, we will be able to dynamically measure masses of the largest black holes and characterize galaxy properties out to redshift $z \sim 1.5$. Together with the evolution of black hole-galaxy scaling relations since $z \sim 1.5$, the maximum mass black hole will shed light on the main channels of black hole growth., Comment: Astro2020 white paper, 7 pages, 1 figure

In this paper we study the molecular gas content of a representative sample of 67 of the most massive early-type galaxies in the local universe, drawn uniformly from the MASSIVE survey. We present new IRAM-30m telescope observations of 30 of these galaxies, allowing us to probe the molecular gas content of the entire sample to a fixed molecular-to-stellar mass fraction of 0.1%. The total detection rate in this representative sample is 25$^{+5.9}_{-4.4}$%, and by combining the MASSIVE and ATLAS$^{\rm 3D}$ molecular gas surveys we find a joint detection rate of 22.4$^{+2.4}_{-2.1}$%. This detection rate seems to be independent of galaxy mass, size, position on the fundamental plane, and local environment. We show here for the first time that true slow rotators can host molecular gas reservoirs, but the rate at which they do so is significantly lower than for fast-rotators. Objects with a higher velocity dispersion at fixed mass (a higher kinematic bulge fraction) are less likely to have detectable molecular gas, and where gas does exist, have lower molecular gas fractions. In addition, satellite galaxies in dense environments have $\approx$0.6 dex lower molecular gas-to-stellar mass ratios than isolated objects. In order to interpret these results we created a toy model, which we use to constrain the origin of the gas in these systems. We are able to derive an independent estimate of the gas-rich merger rate in the low-redshift universe. These gas rich mergers appear to dominate the supply of gas to ETGs, but stellar mass loss, hot halo cooling and transformation of spiral galaxies also play a secondary role., Comment: 19 pages, 12 figures, accepted by MNRAS

Pulsar timing arrays (PTAs) are on the verge of detecting low-frequency gravitational waves (GWs) from supermassive black hole binaries (SMBHBs). With continued observations of a large sample of millisecond pulsars, PTAs will reach this major milestone within the next decade. Already, SMBHB candidates are being identified by electromagnetic surveys in ever-increasing numbers; upcoming surveys will enhance our ability to detect and verify candidates, and will be instrumental in identifying the host galaxies of GW sources. Multi-messenger (GW and electromagnetic) observations of SMBHBs will revolutionize our understanding of the co-evolution of SMBHs with their host galaxies, the dynamical interactions between binaries and their galactic environments, and the fundamental physics of accretion. Multi-messenger observations can also make SMBHBs 'standard sirens' for cosmological distance measurements out to $z\simeq0.5$. LIGO has already ushered in breakthrough insights in our knowledge of black holes. The multi-messenger detection of SMBHBs with PTAs will be a breakthrough in the years $2020-2030$ and beyond, and prepare us for LISA to help complete our views of black hole demographics and evolution at higher redshifts., Comment: Submitted to the Astro2020 decadal review. This is one of five core white papers written by members of the NANOGrav Collaboration, see also: J.Cordes et al., S.R.Taylor et al., X.Siemens et al., and E.Fonseca et al

We measure the stellar populations as a function of radius for 90 early-type galaxies (ETGs) in the MASSIVE survey, a volume-limited integral-field spectroscopic (IFS) galaxy survey targeting all northern-sky ETGs with absolute K-band magnitude M_K < -25.3 mag, or stellar mass M* 4x10^11 M_sun, within 108 Mpc. We are able to measure reliable stellar population parameters for individual galaxies out to 10-20 kpc (1-3 R_e) depending on the galaxy. Focusing on ~R_e (~10 kpc), we find significant correlations between the abundance ratios, sigma, and M* at large radius, but we also find that the abundance ratios saturate in the highest-mass bin. We see a strong correlation between the kurtosis of the line of sight velocity distribution (h4) and the stellar population parameters beyond R_e. Galaxies with higher radial anisotropy appear to be older, with metal-poorer stars and enhanced [alpha/Fe]. We suggest that the higher radial anisotropy may derive from more accretion of small satellites. Finally, we see some evidence for correlations between environmental metrics (measured locally and on >5 Mpc scales) and the stellar populations, as expected if satellites are quenched earlier in denser environments., Comment: 17 pages, 7 figures, Appendix not included here due to size constraints. Posted after responding to referee's comments

Most galaxies are hosted by massive, invisible dark matter haloes, yet little is known about the scatter in the stellar mass--halo mass relation for galaxies with host halo masses $M_{h}\le 10^{11}M_{\odot}$. Using mock catalogues based on dark matter simulations, we find that two observable signatures are sensitive to scatter in the stellar mass--halo mass relation even at these mass scales; i.e., conditional stellar mass functions and velocity distribution functions for neighbouring galaxies. We compute these observables for 179,373 galaxies in the Sloan Digital Sky Survey (SDSS) with stellar masses $M_{\ast} > 10^9 M_{\odot}$ and redshifts 0.01 $< z <$ 0.307. We then compare to mock observations generated from the $\textit{Bolshoi-Planck}$ dark matter simulation for stellar mass--halo mass scatters ranging from 0 to 0.6 dex. The observed results are consistent with simulated results for most values of scatter ($<$0.6 dex), and SDSS statistics are insufficient to provide firm constraints. However, this method could provide much tighter constraints on stellar mass--halo mass scatter in the future if applied to larger data sets, especially the anticipated Dark Energy Spectroscopic Instrument Bright Galaxy Survey. Constraining the value of scatter could have important implications for galaxy formation and evolution., Comment: 11 pages, 1 table, 9 main body figures, 9 appendix figures

We use spatially resolved two-dimensional stellar velocity maps over a $107"\times 107"$ field of view to investigate the kinematic features of 90 early-type galaxies above stellar mass $10^{11.5}M_\odot$ in the MASSIVE survey. We measure the misalignment angle $\Psi$ between the kinematic and photometric axes and identify local features such as velocity twists and kinematically distinct components. We find 46% of the sample to be well aligned ($\Psi < 15^{\circ}$), 33% misaligned, and 21% without detectable rotation (non-rotators). Only 24% of the sample are fast rotators, the majority of which (91%) are aligned, whereas 57% of the slow rotators are misaligned with a nearly flat distribution of $\Psi$ from $15^{\circ}$ to $90^{\circ}$. 11 galaxies have $\Psi \gtrsim 60^{\circ}$ and thus exhibit minor-axis ("prolate") rotation in which the rotation is preferentially around the photometric major axis. Kinematic misalignments occur more frequently for lower galaxy spin or denser galaxy environments. Using the observed misalignment and ellipticity distributions, we infer the intrinsic shape distribution of our sample and find that MASSIVE slow rotators are consistent with being mildly triaxial, with mean axis ratios of $b/a=0.88$ and $c/a=0.65$. In terms of local kinematic features, 51% of the sample exhibit kinematic twists of larger than $20^{\circ}$, and 2 galaxies have kinematically distinct components. The frequency of misalignment and the broad distribution of $\Psi$ reported here suggest that the most massive early-type galaxies are mildly triaxial, and that formation processes resulting in kinematically misaligned slow rotators such as gas-poor mergers occur frequently in this mass range., Comment: Accepted to MNRAS

We present near-infrared observations of 35 of the most massive early-type galaxies in the local universe. The observations were made using the infrared channel of the Hubble Space Telescope Wide Field Camera 3 in the F110W (1.1 $\mu$m) filter. We measured surface brightness profiles and elliptical isophotal fit parameters from the nuclear regions out to a radius of ~10 kpc in most cases. We find that 37% (13) of the galaxies in our sample have isophotal position angle rotations greater than 20 degrees over the radial range imaged by WFC3/IR, which is often due to the presence of neighbors or multiple nuclei. Most galaxies in our sample are significantly rounder near the center than in the outer regions. This sample contains six fast rotators and 28 slow rotators. We find that all fast rotators are either disky or show no measurable deviation from purely elliptical isophotes. Among slow rotators, significantly disky and boxy galaxies occur with nearly equal frequency. The galaxies in our sample often exhibit changing isophotal shapes, sometimes showing both significantly disky and boxy isophotes at different radii. The fact that parameters vary widely between galaxies and within individual galaxies is evidence that these massive galaxies have complicated formation histories, and some of them have experienced recent mergers and have not fully relaxed. These data demonstrate the value of high spatial resolution IR imaging of galaxies and provide measurements necessary for determining stellar masses, dynamics, and black hole masses in high mass galaxies., Comment: 31 pages, 39 figures, accepted for publication in the Astrophysical Journal