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Ingrid H. Stairs

Publications and source records attributed to Ingrid H. Stairs.

At least 55 records · Page 3Linked to original sources
arXiv2024

An unusual pulse shape change event in PSR J1713+0747 observed with the Green Bank Telescope and CHIME

The millisecond pulsar J1713+0747 underwent a sudden and significant pulse shape change between April 16 and 17, 2021 (MJDs 59320 and 59321). Subsequently, the pulse shape gradually recovered over the course of several months. We report the results of continued multi-frequency radio observations of the pulsar made using the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the 100-meter Green Bank Telescope (GBT) in a three-year period encompassing the shape change event, between February 2020 and February 2023. As of February 2023, the pulse shape had returned to a state similar to that seen before the event, but with measurable changes remaining. The amplitude of the shape change and the accompanying TOA residuals display a strong non-monotonic dependence on radio frequency, demonstrating that the event is neither a glitch (the effects of which should be independent of radio frequency, $ν$) nor a change in dispersion measure (DM) alone (which would produce a delay proportional to $ν^{-2}$). However, it does bear some resemblance to the two previous "chromatic timing events" observed in J1713+0747 (Demorest et al. 2013; Lam et al. 2016), as well as to a similar event observed in PSR J1643-1224 in 2015 (Shannon et al. 2016).

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arXiv2024

The NANOGrav 12.5-year data set: A computationally efficient eccentric binary search pipeline and constraints on an eccentric supermassive binary candidate in 3C 66B

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 $η>0.1$. 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 $η>0.1$. 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.

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arXiv2023

How to Detect an Astrophysical Nanohertz Gravitational-Wave Background

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.

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arXiv2023

Comprehensive Bayesian analysis of FRB-like bursts from SGR 1935+2154 observed by CHIME/FRB

The bright millisecond-duration radio burst from the Galactic magnetar SGR 1935+2154 in 2020 April was a landmark event, demonstrating that at least some fast radio burst (FRB) sources could be magnetars. The two-component burst was temporally coincident with peaks observed within a contemporaneous short X-ray burst envelope, marking the first instance where FRB-like bursts were observed to coincide with X-ray counterparts. In this study, we detail five new radio burst detections from SGR 1935+2154, observed by the CHIME/FRB instrument between October 2020 and December 2022. We develop a fast and efficient Bayesian inference pipeline that incorporates state-of-the-art Markov chain Monte Carlo techniques and use it to model the intensity data of these bursts under a flexible burst model. We revisit the 2020 April burst and corroborate that both the radio sub-components lead the corresponding peaks in their high-energy counterparts. For a burst observed in 2022 October, we find that our estimated radio pulse arrival time is contemporaneous with a short X-ray burst detected by GECAM and HEBS, and Konus-Wind and is consistent with the arrival time of a radio burst detected by GBT. We present flux and fluence estimates for all five bursts, employing an improved estimator for bursts detected in the side-lobes. We also present upper limits on radio emission for X-ray emission sources which were within CHIME/FRB's field-of-view at trigger time. Finally, we present our exposure and sensitivity analysis and estimate the Poisson rate for FRB-like events from SGR 1935+2154 to be $0.005^{+0.082}_{-0.004}$ events/day above a fluence of $10~\mathrm{kJy~ms}$ during the interval from 28 August 2018 to 1 December 2022, although we note this was measured during a time of great X-ray activity from the source.

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arXiv2023

The NANOGrav 15-year data set: Search for Transverse Polarization Modes in the Gravitational-Wave Background

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.

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arXiv2023

Proposed host galaxies of repeating fast radio burst sources detected by CHIME/FRB

We present a search for host galaxy associations for the third set of repeating fast radio burst (FRB) sources discovered by the CHIME/FRB Collaboration. Using the $\sim$ 1 arcmin CHIME/FRB baseband localizations and probabilistic methods, we identify potential host galaxies of two FRBs, 20200223B and 20190110C at redshifts of 0.06024(2) and 0.12244(6), respectively. We also discuss the properties of a third marginal candidate host galaxy association for FRB 20191106C with a host redshift of 0.10775(1). The three putative host galaxies are all relatively massive, fall on the standard mass-metallicity relationship for nearby galaxies, and show evidence of ongoing star formation. They also all show signatures of being in a transitional regime, falling in the ``green valley'' which is between the bulk of star-forming and quiescent galaxies. The plausible host galaxies identified by our analysis are consistent with the overall population of repeating and non-repeating FRB hosts while increasing the fraction of massive and bright galaxies. Coupled with these previous host associations, we identify a possible excess of FRB repeaters whose host galaxies have $M_{\mathrm{u}}-M_{\mathrm{r}}$ colors redder than the bulk of star-forming galaxies. Additional precise localizations are required to confirm this trend.

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arXiv2023

The NANOGrav 12.5-Year Data Set: Dispersion Measure Mis-Estimation with Varying Bandwidths

Noise characterization for pulsar-timing applications accounts for interstellar dispersion by assuming a known frequency-dependence of the delay it introduces in the times of arrival (TOAs). However, calculations of this delay suffer from mis-estimations due to other chromatic effects in the observations. The precision in modeling dispersion is dependent on the observed bandwidth. In this work, we calculate the offsets in infinite-frequency TOAs due to mis-estimations in the modeling of dispersion when using varying bandwidths at the Green Bank Telescope. We use a set of broadband observations of PSR J1643-1224, a pulsar with an excess of chromatic noise in its timing residuals. We artificially restricted these observations to a narrowband frequency range, then used both data sets to calculate residuals with a timing model that does not include short-scale dispersion variations. By fitting the resulting residuals to a dispersion model, and comparing the ensuing fitted parameters, we quantify the dispersion mis-estimations. Moreover, by calculating the autocovariance function of the parameters we obtained a characteristic timescale over which the dispersion mis-estimations are correlated. For PSR J1643-1224, which has one of the highest dispersion measures (DM) in the NANOGrav pulsar timing array, we find that the infinite-frequency TOAs suffer from a systematic offset of ~22 microseconds due to DM mis-estimations, with correlations over ~1 month. For lower-DM pulsars, the offset is ~7 microseconds. This error quantification can be used to provide more robust noise modeling in NANOGrav's data, thereby increasing sensitivity and improving parameter estimation in gravitational wave searches.

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arXiv2023

The NANOGrav 12.5-year Data Set: Search for Gravitational Wave Memory

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.

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arXiv2023

The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background

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.

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arXiv2023

The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background

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.

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arXiv2023

The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget

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.

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arXiv2023

The NANOGrav 15-year Data Set: Observations and Timing of 68 Millisecond Pulsars

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.

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arXiv2023

The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background

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. $3σ$) 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. $3.5 - 4σ$). 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.

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arXiv2023

The NANOGrav 12.5-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Pulsar timing array collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), are seeking to detect nanohertz gravitational waves emitted by supermassive black hole binaries formed in the aftermath of galaxy mergers. We have searched for continuous waves from individual circular supermassive black hole binaries using the NANOGrav's recent 12.5-year data set. We created new methods to accurately model the uncertainties on pulsar distances in our analysis, and we implemented new techniques to account for a common red noise process in pulsar timing array data sets while searching for deterministic gravitational wave signals, including continuous waves. As we found no evidence for continuous waves in our data, we placed 95\% upper limits on the strain amplitude of continuous waves emitted by these sources. At our most sensitive frequency of 7.65 nanohertz, we placed a sky-averaged limit of $h_0 < $ $(6.82 \pm 0.35) \times 10^{-15}$, and $h_0 <$ $(2.66 \pm 0.15) \times 10^{-15}$ in our most sensitive sky location. Finally, we placed a multi-messenger limit of $\mathcal{M} <$ $(1.41 \pm 0.02) \times 10^9 M_\odot$ on the chirp mass of the supermassive black hole binary candidate 3C~66B.

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arXiv2023

The Green Bank North Celestial Cap Survey. VIII. 21 New Pulsar Timing Solutions

We present timing solutions for 21 pulsars discovered in 350 MHz surveys using the Green Bank Telescope (GBT). All were discovered in the Green Bank North Celestial Cap pulsar survey, with the exception of PSR J0957-0619, which was found in the GBT 350 MHz Drift-scan pulsar survey. The majority of our timing observations were made with the GBT at 820 MHz. With a spin period of 37 ms and a 528-day orbit, PSR J0032+6946 joins a small group of five other mildly recycled wide binary pulsars, for which the duration of recycling through accretion is limited by the length of the companion's giant phase. PSRs J0141+6303 and J1327+3423 are new disrupted recycled pulsars. We incorporate Arecibo observations from the NANOGrav pulsar timing array into our analysis of the latter. We also observed PSR J1327+3423 with the Long Wavelength Array, and our data suggest a frequency-dependent dispersion measure. PSR J0957-0619 was discovered as a rotating radio transient, but is a nulling pulsar at 820 MHz. PSR J1239+3239 is a new millisecond pulsar (MSP) in a 4-day orbit with a low-mass companion. Four of our pulsars already have published timing solutions, which we update in this work: the recycled wide binary PSR J0214+5222, the non-eclipsing black widow PSR J0636+5128, the disrupted recycled pulsar J1434+7257, and the eclipsing binary MSP J1816+4510, which is in an 8.7 hr orbit with a redback-mass companion.

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arXiv2022

The Green Bank North Celestial Cap Survey. VII. 12 New Pulsar Timing Solutions

We present timing solutions for 12 pulsars discovered in the Green Bank North Celestial Cap (GBNCC) 350 MHz pulsar survey, including six millisecond pulsars (MSPs), a double neutron star (DNS) system, and a pulsar orbiting a massive white dwarf companion. Timing solutions presented here include 350 and 820 MHz Green Bank Telescope data from initial confirmation and follow-up as well as a dedicated timing campaign spanning one year. PSR J1122$-$3546 is an isolated MSP, PSRs J1221$-$0633 and J1317$-$0157 are MSPs in black widow systems and regularly exhibit eclipses, and PSRs J2022+2534 and J2039$-$3616 are MSPs that can be timed with high precision and have been included in pulsar timing array experiments seeking to detect low-frequency gravitational waves. PSRs J1221$-$0633 and J2039$-$3616 have Fermi Large Area Telescope $γ$-ray counterparts and also exhibit significant $γ$-ray pulsations. We measure proper motion for three of the MSPs in this sample and estimate their space velocities, which are typical compared to those of other MSPs. We have detected the advance of periastron for PSR J1018$-$1523 and therefore measure the total mass of the double neutron star system, $m_{\rm tot}=2.3\pm0.3$ M$_{\odot}$. Long-term pulsar timing with data spanning more than one year is critical for classifying recycled pulsars, carrying out detailed astrometry studies, and shedding light on the wealth of information in these systems post-discovery.

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arXiv2022

Pulse Profiles and Polarization of Terzan 5 Pulsars

Terzan 5 is a rich globular cluster within the galactic bulge that contains 39 known millisecond pulsars, the largest known population of any globular cluster. The Terzan 5 pulsars are faint, so that individual observations of most of the pulsars have too little signal-to-noise (S/N) to measure reliable flux density or polarization information. We combined over 5.2\,days of archival data, at each of 1.5\,GHz and 2.0\,GHz, taken with the Green Bank Telescope over the past 11\,years. We created high S/N profiles for 32 of the pulsars and determined precise rotation measures (RMs) for 28 of them. We used the RMs, and the known pulsar positions and dispersion measures (DMs), to map the projected parallel component of the Galactic magnetic field toward the cluster. The $\langle B_{||}\rangle$ shows a rough gradient of $\sim$6\,nG/arcsec ($\sim$160\,nG/parsec), or fractionally, a change of $\sim$20$\%$ in the right ascension direction across the cluster, implying Galactic magnetic field variability at sub-parsec scales. We also measured average flux densities $S_ν$ for the pulsars, ranging from $\sim$10\,$μ$Jy to $\sim$2\,mJy, and an average spectral index $α= -1.35$, where $S_ν\propto ν^α)$. This spectral index is flatter than most known pulsars, likely a selection effect due to the high frequencies used in pulsar searches to mitigate dispersion and scattering. The inferred pulsar luminosity function is roughly power-law, with slope $(d\log N)/(d\log L) = -1$ at the high-luminosity end. At the low-luminosity end, there are incompleteness effects implying that Terzan 5 contains many more pulsars to be found.

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arXiv2022

Snowmass 2021 Cosmic Frontier White Paper: The Dense Matter Equation of State and QCD Phase Transitions

Our limited understanding of the physical properties of matter at ultra-high density, high proton/neutron number asymmetry, and low temperature is presently one of the major outstanding problems in physics. As matter in this extreme state is known to only exist stably in the cores of neutron stars (NSs), complementary measurements from electromagnetic and gravitational wave astrophysical observations of NSs, combined with terrestrial laboratory constraints and further theoretical investigations, hold the promise to provide important insight into the properties of matter in a region of the quantum chromodynamics phase space that is otherwise inaccessible. This multidisciplinary endeavor imposes the following requirements for facilities and resources in the upcoming decade and beyond: * A next generation of gravitational wave detectors to uncover more double NS and neutron star-black hole mergers; * Sensitive radio telescopes to find the most massive and fastest spinning NSs; * Large-area, high-time-resolution and/or high angular resolution X-ray telescopes to constrain the NS mass-radius relation; * Suitable laboratory facilities for nuclear physics experiments to constrain the dense matter equation of state; * Funding resources for theoretical studies of matter in this regime; * The availability of modern large-scale high performance computing infrastructure. The same facilities and resources would also enable significant advances in other high-profile fields of inquiry in modern physics such as the nature of dark matter, alternative theories of gravity, nucleon superfluidity and superconductivity, as well as an array of astrophysics, including but not limited to stellar evolution, nucleosynthesis, and primordial black holes.

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