The nanohertz gravitational wave background (GWB) is believed to be dominated by GW emission from supermassive black hole binaries (SMBHBs). Observations of several dualactive galactic nuclei (AGN) strongly suggest a link between AGN and SMBHBs, given that these dualAGN systems will eventually form bound binary pairs. Here we develop an exploratory SMBHB population model based on empirically constrained quasar populations, allowing us to decompose the GWB amplitude into an underlying distribution of SMBH masses, SMBHB number density, and volume enclosing the GWB. Our approach also allows us to selfconsistently predict the number of local SMBHB systems from the GWB amplitude. Interestingly, we find the local number density of SMBHBs implied by the commonprocess signal in the NANOGrav 12.5yr data set to be roughly five times larger than previously predicted by other models. We also find that at most ∼25% of SMBHBs can be associated with quasars. Furthermore, our quasarbased approach predicts ≳95% of the GWB signal comes from
This content will become publicly available on August 1, 2024
 NSFPAR ID:
 10447212
 Author(s) / Creator(s):
 ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
 Date Published:
 Journal Name:
 The Astrophysical Journal Letters
 Volume:
 952
 Issue:
 2
 ISSN:
 20418205
 Page Range / eLocation ID:
 L37
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract z ≲ 2.5, and that SMBHBs contributing to the GWB have masses ≳10^{8}M _{⊙}. We also explore how different empirical galaxy–black hole scaling relations affect the local number density of GW sources, and find that relations predicting more massive black holes decrease the local number density of SMBHBs. Overall, our results point to the important role that a measurement of the GWB will play in directly constraining the cosmic population of SMBHBs, as well as their connections to quasars and galaxy mergers. 
Abstract We report multiple lines of evidence for a stochastic signal that is correlated among 67 pulsars from the 15 yr 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 gravitationalwave background. The presence of such a gravitationalwave background with a powerlaw 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 powerlaw spectrum model with Bayes factors of 200–1000, depending on spectral modeling choices. We have built a statistical background distribution for the latter Bayes factors using a method that removes interpulsar correlations from our data set, finding p = 10 −3 (≈3 σ ) for the observed Bayes factors in the null nocorrelation scenario. A frequentist test statistic built directly as a weighted sum of interpulsar correlations yields p = 5 × 10 −5 to 1.9 × 10 −4 (≈3.5 σ –4 σ ). 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 − 0.6 + 0.7 × 10 − 15 (median + 90% credible interval) at a reference frequency of 1 yr −1 . The inferred gravitationalwave 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 gravitationalwave origin of this signal.more » « less

MCMC chains for the GWB analyses performed in the paper "The NANOGrav 15 yr Data Set: Search for Signals from New Physics".
The data is provided in pickle format. Each file contains a NumPy array with the MCMC chain (with burnin already removed), and a dictionary with the model parameters' names as keys and their priors as values. You can load them as
with open ('path/to/file.pkl', 'rb') as pick: temp = pickle.load(pick) params = temp[0] chain = temp[1]
The naming convention for the files is the following:
 igw: inflationary Gravitational Waves (GWs)
 sigw: scalarinduced GWs
 sigw_box: assumes a boxlike feature in the primordial power spectrum.
 sigw_delta: assumes a deltalike feature in the primordial power spectrum.
 sigw_gauss: assumes a Gaussian peak feature in the primordial power spectrum.
 pt: cosmological phase transitions
 pt_bubble: assumes that the dominant contribution to the GW productions comes from bubble collisions.
 pt_sound: assumes that the dominant contribution to the GW productions comes from sound waves.
 stable: stable cosmic strings
 stablec: stable strings emitting GWs only in the form of GW bursts from cusps on closed loops.
 stablek: stable strings emitting GWs only in the form of GW bursts from kinks on closed loops.
 stablem: stable strings emitting monochromatic GW at the fundamental frequency.
 stablen: stable strings described by numerical simulations including GWs from cusps and kinks.
 meta: metastable cosmic strings
 metal: metastable strings with GW emission from loops only.
 metals metastable strings with GW emission from loops and segments.
 super: cosmic superstrings.
 dw: domain walls
 dwsm: domain walls decaying into Standard Model particles.
 dwdr: domain walls decaying into dark radiation.
For each model, we provide four files. One for the run where the newphysics signal is assumed to be the only GWB source. One for the run where the newphysics signal is superimposed to the signal from Supermassive Black Hole Binaries (SMBHB), for these files "_bhb" will be appended to the model name. Then, for both these scenarios, in the "compare" folder we provide the files for the hypermodel runs that were used to derive the Bayes' factors.
In addition to chains for the stochastic models, we also provide data for the two deterministic models considered in the paper (ULDM and DM substructures). For the ULDM model, the naming convention of the files is the following (all the ULDM signals are superimposed to the SMBHB signal, see the discussion in the paper for more details)
 uldm_e: ULDM Earth signal.
 uldm_p: ULDM pulsar signal
 uldm_p_cor: correlated limit
 uldm_p_unc: uncorrelated limit
 uldm_c: ULDM combined Earth + pulsar signal direct coupling
 uldm_c_cor: correlated limit
 uldm_c_unc: uncorrelated limit
 uldm_vecB: vector ULDM coupled to the baryon number
 uldm_vecB_cor: correlated limit
 uldm_vecB_unc: uncorrelated limit
 uldm_vecBL: vector ULDM coupled to BL
 uldm_vecBL_cor: correlated limit
 uldm_vecBL_unc: uncorrelated limit
 uldm_c_grav: ULDM combined Earth + pulsar signal for gravitationalonly coupling
 uldm_c_grav_cor: correlated limit
 uldm_c_cor_grav_low: low mass region
 uldm_c_cor_grav_mon: monopole region
 uldm_c_cor_grav_low: high mass region
 uldm_c_unc: uncorrelated limit
 uldm_c_unc_grav_low: low mass region
 uldm_c_unc_grav_mon: monopole region
 uldm_c_unc_grav_low: high mass region
 uldm_c_grav_cor: correlated limit
For the substructure (static) model, we provide the chain for the marginalized distribution (as for the ULDM signal, the substructure signal is always superimposed to the SMBHB signal)

Abstract Supermassive black holes (SMBHs) reside at the center of every massive galaxy in the local universe with masses that closely correlate with observations of their host galaxy, implying a connected evolutionary history. The population of binary SMBHs, which form following galaxy mergers, is expected to produce a gravitationalwave background (GWB) detectable by pulsar timing arrays (PTAs). PTAs are starting to see hints of what may be a GWB, and the amplitude of the emerging signal is toward the higher end of model predictions. Simulated populations of binary SMBHs can be constructed from observations of galaxies and are used to make predictions about the nature of the GWB. The greatest source of uncertainty in these observationbased models comes from the inference of the SMBH mass function, which is derived from observed host galaxy properties. In this paper, I undertake a new approach for inferring the SMBH mass function, starting from a velocity dispersion function rather than a galaxy stellar mass function. I argue that this method allows for a more direct inference by relying on a larger suite of individual galaxy observations as well as relying on a more “fundamental” SMBH mass relation. I find that the resulting binary SMBH population contains more massive systems at higher redshifts than previous models. Additionally, I explore the implications for the detection of individually resolvable sources in PTA data.

Abstract Evidence for a lowfrequency stochastic gravitationalwave 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 data sets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15 yr data set. 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 gravitationalwave frequency of ∼4 nHz, and another at ∼170 nHz. The significance of the lowfrequency candidate was greatly diminished when Hellings–Downs correlations were included in the background model. The highfrequency 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. At our most sensitive frequency of 6 nHz, we place a skyaveraged 95% upper limit of 8 × 10 −15 on the strain amplitude. We also calculate an exclusion volume and a corresponding effective radius, within which we can rule out the presence of black hole binaries emitting at a given frequency.more » « less