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Abstract The NANOGrav 15 yr data provide 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 of a simple power-law fit involving two parameters: an amplitudeAand a spectral indexγ. In this Letter, we consider the next logical step beyond this minimal spectral model, allowing for arunning(i.e., logarithmic frequency dependence) of the spectral index, ${\gamma }_{\mathrm{run}}\left(f\right)=\gamma +\beta \ln \left(f/f_{\mathrm{ref}}\right)$. We fit this running-power-law (RPL) model to the NANOGrav 15 yr data and perform a Bayesian model comparison with the minimal constant-power-law (CPL) model, which results in a 95% credible interval for the parameterβconsistent with no running, $\beta \in \left(-0.80,2.96\right)$, and an inconclusive Bayes factor, $B\left(\mathrm{RPL}\mathrm{versus}\mathrm{CPL}\right)=0.69\pm 0.01$. 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 nonzeroβ. 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. 

Abstract 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 (PTAs) 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 semianalytic SMBHB population model, fit to North American Nanohertz Observatory for Gravitational Waves (NANOGrav’s) 15 yr GWB amplitude, and with 1000 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 nHz, is below our GWB realizations with ap-value significancep= 0.05–0.06 (≈1.8σ–1.9σ). The second, at 16 nHz, is above our GWB realizations withp= 0.04–0.15 (≈1.4σ–2.1σ). We explore the properties of a loud SMBHB that could cause such an excursion. Our simulations also show that the expected number of SMBHBs decreases by 3 orders of magnitude, from ∼10⁶to ∼10³, between 2 and 20 nHz. This causes a break in the strain spectrum as the stochasticity of the background breaks down at ${26}_{-19}^{+28}\mathrm{nHz}$, 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. 

Abstract The 15 yr 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. 

Abstract We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index ofγ= 5 and a reference frequency off_yr= 1 yr⁻¹. Among the upper limits for eight general families of metric theories of gravity, we find the values of $A_{\mathrm{TT}}^{95\%}=(9.7\pm 0.4)\times {10}^{-16}$and $A_{\mathrm{ST}}^{95\%}=(1.4\pm 0.03)\times {10}^{-15}$for the family of metric spacetime theories that contain both TT and ST modes. 

Abstract 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 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 gravitational-wave frequency of ∼4 nHz, and another at ∼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. At our most sensitive frequency of 6 nHz, we place a sky-averaged 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. 

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 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 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 no-correlation 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 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. 

{"Abstract":["MCMC chains for the GWB analyses performed in the paper "The NANOGrav 15 yr Data Set: Search for Signals from New Physics<\/em>". <\/p>\n\nThe data is provided in pickle format. Each file contains a NumPy array with the MCMC chain (with burn-in already removed), and a dictionary with the model parameters' names as keys and their priors as values. You can load them as<\/p>\n\nwith open ('path/to/file.pkl', 'rb') as pick:\n temp = pickle.load(pick)\n\n params = temp[0]\n chain = temp[1]<\/code>\n\nThe naming convention for the files is the following:<\/p>\n\nigw<\/strong>: inflationary Gravitational Waves (GWs)<\/li>sigw: scalar-induced GWs\n\tsigw_box<\/strong>: assumes a box-like feature in the primordial power spectrum.<\/li>sigw_delta<\/strong>: assumes a delta-like feature in the primordial power spectrum.<\/li>sigw_gauss<\/strong>: assumes a Gaussian peak feature in the primordial power spectrum.<\/li><\/ul>\n\t<\/li>pt: cosmological phase transitions\n\tpt_bubble<\/strong>: assumes that the dominant contribution to the GW productions comes from bubble collisions.<\/li>pt_sound<\/strong>: assumes that the dominant contribution to the GW productions comes from sound waves.<\/li><\/ul>\n\t<\/li>stable: stable cosmic strings\n\tstable-c<\/strong>: stable strings emitting GWs only in the form of GW bursts from cusps on closed loops.<\/li>stable-k<\/strong>: stable strings emitting GWs only in the form of GW bursts from kinks on closed loops.<\/li>stable<\/strong>-m<\/strong>: stable strings emitting monochromatic GW at the fundamental frequency.<\/li>stable-n<\/strong>: stable strings described by numerical simulations including GWs from cusps and kinks.<\/li><\/ul>\n\t<\/li>meta: metastable cosmic strings\n\tmeta<\/strong>-l<\/strong>: metastable strings with GW emission from loops only.<\/li>meta-ls<\/strong> metastable strings with GW emission from loops and segments.<\/li><\/ul>\n\t<\/li>super<\/strong>: cosmic superstrings.<\/li>dw: domain walls\n\tdw-sm<\/strong>: domain walls decaying into Standard Model particles.<\/li>dw-dr<\/strong>: domain walls decaying into dark radiation.<\/li><\/ul>\n\t<\/li><\/ul>\n\nFor each model, we provide four files. One for the run where the new-physics signal is assumed to be the only GWB source. One for the run where the new-physics 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.<\/p>\n\nIn 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)<\/p>\n\nuldm_e<\/strong>: ULDM Earth signal.<\/li>uldm_p: ULDM pulsar signal\n\tuldm_p_cor<\/strong>: correlated limit<\/li>uldm_p_unc<\/strong>: uncorrelated limit<\/li><\/ul>\n\t<\/li>uldm_c: ULDM combined Earth + pulsar signal direct coupling \n\tuldm_c_cor<\/strong>: correlated limit<\/li>uldm_c_unc<\/strong>: uncorrelated limit<\/li><\/ul>\n\t<\/li>uldm_vecB: vector ULDM coupled to the baryon number\n\tuldm_vecB_cor:<\/strong> correlated limit<\/li>uldm_vecB_unc<\/strong>: uncorrelated limit <\/li><\/ul>\n\t<\/li>uldm_vecBL: vector ULDM coupled to B-L\n\tuldm_vecBL_cor:<\/strong> correlated limit<\/li>uldm_vecBL_unc<\/strong>: uncorrelated limit<\/li><\/ul>\n\t<\/li>uldm_c_grav: ULDM combined Earth + pulsar signal for gravitational-only coupling\n\tuldm_c_grav_cor: correlated limit\n\t\tuldm_c_cor_grav_low<\/strong>: low mass region  <\/li>uldm_c_cor_grav_mon<\/strong>: monopole region<\/li>uldm_c_cor_grav_low<\/strong>: high mass region<\/li><\/ul>\n\t\t<\/li>uldm_c_unc<\/strong>: uncorrelated limit\n\t\tuldm_c_unc_grav_low<\/strong>: low mass region  <\/li>uldm_c_unc_grav_mon<\/strong>: monopole region<\/li>uldm_c_unc_grav_low<\/strong>: high mass region<\/li><\/ul>\n\t\t<\/li><\/ul>\n\t<\/li><\/ul>\n\nFor 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)<\/p>"]}