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NASA NTRS2016

Astrophysical Implications of the Binary Black Hole Merger GW150914

The discovery of the gravitational-wave (GW) source GW150914 with the Advanced LIGO detectors provides the first observational evidence for the existence of binary black hole (BH) systems that in spiral and merge within the age of the universe. Such BH mergers have been predicted in two main types of formation models, involving isolated binaries in galactic fields or dynamical interactions in young and old dense stellar environments. The measured masses robustly demonstrate that relatively heavy BHs (> or approx. 25 Stellar Mass) can form in nature. This discovery implies relatively weak massive-star winds and thus the formation of GW150914 in an environment with a metallicity lower than about 12 of the solar value. The rate of binary-BH (BBH) mergers inferred from the observation of GW150914 is consistent with the higher end of rate predictions (> or approx. 1/cu Gpc/yr) from both types of formation models. The low measured redshift (z approx. = 0.1) of GW150914 and the low inferred metallicity of the stellar progenitor imply either BBH formation in a low-mass galaxy in the local universe and a prompt merger, or formation at high redshift with a time delay between formation and merger of several Gyr. This discovery motivates further studies of binary-BH formation astrophysics. It also has implications for future detections and studies by Advanced LIGO and Advanced Virgo, and GW detectors in space.

stars↗
NASA NTRS2020

Dynamic Scheduling: Target of Opportunity Observations of Gravitational Wave Events

The simultaneous detection of electromagnetic and gravitational waves from the coalescence of two neutron stars (GW170817 and GRB170817A) has ushered in a new era of ‘multimessenger’ astronomy, with electromagnetic detections spanning from gamma to radio. This great opportunity for new scientific investigations raises the issue of how the available multimessenger tools can best be integrated to constitute a powerful method to study the transient Universe in particular. To facilitate the classification of possible optical counterparts to gravitational wave events, it is important to optimize the scheduling of observations and the filtering of transients, both key elements of the follow-up process. In this work, we describe the existing workflow whereby telescope networks such as GRANDMA and GROWTH are currently scheduled; we then present modifications we have developed for the scheduling process specifically, so as to face the relevant challenges that have appeared during the latest observing run of Advanced LIGO and Advanced Virgo. We address issues with scheduling more than one epoch for multiple fields within a skymap, especially for large and disjointed localizations. This is done in two ways: by optimizing the maximum number of fields that can be scheduled and by splitting up the lobes within the skymap by right ascension to be scheduled individually. In addition, we implement the ability to take previously observed fields into consideration when rescheduling. We show the improvements that these modifications produce in making the search for optical counterparts more efficient, and we point to areas needing further improvement.

Gravitational waves↗
NASA NTRS2019

GROWTH on S190510g: DECam Observation Planning and Follow-up of a Distant Binary Neutron Star Merger Candidate

The first two months of the third Advanced LIGO and Virgo observing run (2019 April–May) showed that distant gravitational-wave (GW) events can now be readily detected. Three candidate mergers containing neutron stars (NS) were reported in a span of 15 days, all likely located more than 100 Mpc away. However, distant events such as the three new NS mergers are likely to be coarsely localized, which highlights the importance of facilities and scheduling systems that enable deep observations over hundreds to thousands of square degrees to detect the electromagnetic counterparts. On 2019 May 10 02:59:39.292 UT the GW candidate S190510g was discovered and initially classified as a binary neutron star (BNS) merger with 98% probability. The GW event was localized within an area of 3462 deg2, later refined to 1166 deg2 (90%) at a distance of 227 ± 92 Mpc. We triggered Target-of-Opportunity observations with the Dark Energy Camera (DECam), a wide-field optical imager mounted at the prime focus of the 4 m Blanco Telescope at Cerro Tololo Inter-American Observatory in Chile. This Letter describes our DECam observations and our real-time analysis results, focusing in particular on the design and implementation of the observing strategy. Within 24 hr of the merger time, we observed 65% of the total enclosed probability of the final skymap with an observing efficiency of 94%. We identified and publicly announced 13 candidate counterparts. S190510g was reclassified 1.7 days after the merger, after our observations were completed, with a "BNS merger" probability reduced from 98% to 42% in favor of a "terrestrial classification.

Igor Andreoni↗
NASA NTRS2019

A Year in the Life of GW 170817: The Rise and Fall of a Structured Jet from a Binary Neutron Star Merger

We present the results of our year-long afterglow monitoring of GW 170817, the first binary neutron star merger detected by Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo. New observations with the Australian Telescope Compact Array and the Chandra X-ray Telescope were used to constrain its late-time behaviour. The broad-band emission, from radio to X-rays, is well-described by a simple power-law spectrum with index β ∼ 0.585 at all epochs. After an initial shallow rise ∝t0.9, the afterglow displayed a smooth turnover, reaching a peak X-ray luminosity of LX ≈ 5 × 1039 erg s−1 at 160 d, and has now entered a phase of rapid decline, approximately ∝t−2. The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ≈22◦ from its axis. Within such model, the properties of the explosion (such as its blast wave energy EK ≈ 2 × 1050 erg, jet width θc ≈ 4◦, and ambient density n ≈ 3 × 10−3 cm−3) fit well within the range of properties of cosmological short gamma-ray bursts.

Acceleration of particles↗
NASA NTRS2020

GROWTH on S190814bv: Deep Synoptic Limits on the Optical/Near-infrared Counterpart to a Neutron Star–Black Hole Merger

On 2019 August 14, the Advanced LIGO and Virgo interferometers detected the high-significance gravitational wave (GW) signal S190814bv. The GW data indicated that the event resulted from a neutron star–black hole (NSBH) merger, or potentially a low-mass binary BH merger. Due to the low false-alarm rate and the precise localization (23 deg^(2) at 90%), S190814bv presented the community with the best opportunity yet to directly observe an optical/near-infrared counterpart to an NSBH merger. To search for potential counterparts, the GROWTH Collaboration performed real-time image subtraction on six nights of public Dark Energy Camera images acquired in the 3 weeks following the merger, covering >98% of the localization probability. Using a worldwide network of follow-up facilities, we systematically undertook spectroscopy and imaging of optical counterpart candidates. Combining these data with a photometric redshift catalog, we ruled out each candidate as the counterpart to S190814bv and placed deep, uniform limits on the optical emission associated with S190814bv. For the nearest consistent GW distance, radiative transfer simulations of NSBH mergers constrain the ejecta mass of S190814bv to be M(ej) < 0.04 Mꙩ at polar viewing angles, or M(ej) < 0.03 Mꙩ if the opacity is κ < 2 sq.cm/g. Assuming a tidal deformability for the NS at the high end of the range compatible with GW170817 results, our limits would constrain the BH spin component aligned with the orbital momentum to be χ < 0.7 for mass ratios Q < 6, with weaker constraints for more compact NSs.

Igor Andreoni↗
NASA NTRS2020

Gravitational-Wave Constraints on the Equatorial Ellipticity of Millisecond Pulsars

We present a search for continuous gravitational waves from five radio pulsars, comprising three recycled pulsars (PSR J0437−4715, PSR J0711−6830, and PSR J0737−3039A) and two young pulsars: the Crab pulsar (J0534+2200) and the Vela pulsar (J0835−4510). We use data from the third observing run of Advanced LIGO and Virgo combined with data from their first and second observing runs. For the first time, we are able to match (for PSR J0437−4715) or surpass (for PSR J0711−6830) the indirect limits on gravitational-wave emission from recycled pulsars inferred from their observed spin-downs, and constrain their equatorial ellipticities to be less than 10−8. For each of the five pulsars, we perform targeted searches that assume a tight coupling between the gravitational-wave and electromagnetic signal phase evolution. We also present constraints on PSR J0711−6830, the Crab pulsar, and the Vela pulsar from a search that relaxes this assumption, allowing the gravitational-wave signal to vary from the electromagnetic expectation within a narrow band of frequencies and frequency derivatives.

R Abbott↗
NASA NTRS2020

GW190521: A Binary Black Hole Merger with a Total Mass of 150 Mꙩ

On May 21, 2019 at 03:02:29 UTC Advanced LIGO and Advanced Virgo observed a short duration gravitational-wave signal, GW190521, with a three-detector network signal-to-noise ratio of 14.7, and an estimated false-alarm rate of 1 in 4900 yr using a search sensitive to generic transients. If GW190521 is from a quasicircular binary inspiral, then the detected signal is consistent with the merger of two black holes with masses of 85 (+21,−14) Mꙩ and 66 (+17,−18) Mꙩ (90% credible intervals). We infer that the primary black hole mass lies within the gap produced by (pulsational) pair-instability supernova processes, with only a 0.32% probability of being below 65 M⊙. We calculate the mass of the remnant to be 142 (+28,−16) Mꙩ, which can be considered an intermediate mass black hole (IMBH). The luminosity distance of the source is 5.3 (+2.4,−2.6) Gpc, corresponding to a redshift of 0.82 (+0.28,−0.34) . The inferred rate of mergers similar to GW190521 is 0.13 (+0.30,−0.11) Gpc^(−3) per yr.

R. Abbott↗
NASA NTRS2021

DDOTI Observations of Gravitational-Wave Sources Discovered in O3

We present optical follow-up observations with the Deca-Degree Optical Transient Imager (DDOTI) telescope of gravitational-wave (GW) events detected during the Advanced LIGO and Advanced Virgo O3 observing run. DDOTI is capable of responding to an alert in a few minutes, has an instantaneous field of about 69 deg2, and obtains 10σ upper limits of wlim = 18.5–20.5 AB mag in 1000 s of exposure, depending on the conditions. We observed 54 per cent (26 out of 48) of the unretracted GW alerts and did not find any electromagnetic counterparts. We compare our upper limits to various possible counterparts: the kilonova AT 2017gfo, models of radioactive- and magnetar-powered kilonovae, short gamma-ray burst afterglows, and active galactic nucleus (AGN) flares. Although the large positional uncertainties of GW sources do not allow us to place strong constraints during O3, DDOTI observations of well-localized GW events in O4 and beyond could meaningfully constrain models of compact binary mergers. We show that DDOTI is able to detect kilonovae similar to AT 2017gfo up to about 200 Mpc and magnetar-powered kilonovae up to 1 Gpc. We calculate that nearby (≲200 Mpc) afterglows have a high chance (≈70 per cent) to be detected by rapid (≲3 h) DDOTI observations if observed on-axis, whereas off-axis afterglows are unlikely to be seen. Finally, we suggest that long-term monitoring of massive BBH events with DDOTI could confirm or rule out late AGN flares associated with these events.

gravitational waves↗
NASA NTRS2021

First Demonstration of Early Warning Gravitational-wave Alerts

Gravitational-wave observations became commonplace in Advanced LIGO-Virgo's recently concluded third observing run. 56 nonretracted candidates were identified and publicly announced in near real time. Gravitational waves from binary neutron star mergers, however, remain of special interest since they can be precursors to high-energy astrophysical phenomena like γ-ray bursts and kilonovae. While late-time electromagnetic emissions provide important information about the astrophysical processes within, the prompt emission along with gravitational waves uniquely reveals the extreme matter and gravity during—and in the seconds following—merger. Rapid communication of source location and properties from the gravitational-wave data is crucial to facilitate multimessenger follow-up of such sources. This is especially enabled if the partner facilities are forewarned via an early warning (pre-merger) alert. Here we describe the commissioning and performance of such a low-latency infrastructure within LIGO-Virgo. We present results from an end-to-end mock data challenge that detects binary neutron star mergers and alerts partner facilities before merger. We set expectations for these alerts in future observing runs.

Ryan Magee↗
DOE OSTI2023

AI ensemble for signal detection of higher order gravitational wave modes of quasi-circular, spinning, non-precessing binary black hole mergers

We introduce spatiotemporal-graph models that concurrently process data from the twin advanced LIGO detectors and the advanced Virgo detector. We trained these AI classifiers with 2.4 million IMRPhenomXPHM waveforms that describe quasi-circular, spinning, non-precessing binary black hole mergers with component masses m{1,2}∈[3M⊙,50M⊙], and individual spins sz{1,2}∈[−0.9,0.9]; and which include the (ℓ,|m|)={(2,2),(2,1),(3,3),(3,2),(4,4)} modes, and mode mixing effects in the ℓ=3,|m|=2 harmonics. We trained these AI classifiers within 22 hours using distributed training over 96 NVIDIA V100 GPUs in the Summit supercomputer. We then used transfer learning to create AI predictors that estimate the total mass of potential binary black holes identified by all AI classifiers in the ensemble. We used this ensemble, 3 classifiers for signal detection and 2 total mass predictors, to process a year-long test set in which we injected 300,000 signals. This year-long test set was processed within 5.19 minutes using 1024 NVIDIA A100 GPUs in the Polaris supercomputer (for AI inference) and 128 CPU nodes in the ThetaKNL supercomputer (for post-processing of noise triggers), housed at the Argonne Leadership Computing Facility. These studies indicate that our AI ensemble provides state-of-the-art signal detection accuracy, and reports 2 misclassifications for every year of searched data. This is the first AI ensemble designed to search for and find higher order gravitational wave mode signals.

Tian, Minyang↗
NASA NTRS2021

Gravitational-Wave Physics and Astronomy in the 2020s and 2030s

The 100 years since the publication of Albert Einstein’s theory of General Relativity saw significant development of the understanding of the theory, the identification of potential astrophysical sources of sufficiently strong gravitational waves, and development of key technologies for gravitational-wave detectors. In 2015, the first gravitational wave signals were detected by the two US Advanced LIGO instruments. In 2017, Advanced LIGO and the European Advanced Virgo detectors pinpointed a binary neutron star coalescence that was also seen across the electromagnetic spectrum. The field of gravitational wave astronomy is just starting, and this Roadmap of future developments surveys the potential for growth in bandwidth and sensitivity of future gravitational-wave detectors and discusses the science results anticipated to come from upcoming instruments.

Compact astrophysical objects↗
NASA NTRS2016

Going the Distance: Mapping Host Galaxies of LIGO and VIRGO Sources in Three Dimensions using Local Cosmography and Targeted Follow-Up

The Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) discovered gravitational waves (GWs) from a binary black hole merger in 2015 September and may soon observe signals from neutron star mergers. There is considerable interest in searching for their faint and rapidly fading electromagnetic (EM) counterparts, though GW position uncertainties are as coarse as hundreds of square degrees. Because LIGO's sensitivity to binary neutron stars is limited to the local universe, the area on the sky that must be searched could be reduced by weighting positions by mass, luminosity, or star formation in nearby galaxies. Since GW observations provide information about luminosity distance, combining the reconstructed volume with positions and redshifts of galaxies could reduce the area even more dramatically. A key missing ingredient has been a rapid GW parameter estimation algorithm that reconstructs the full distribution of sky location and distance. We demonstrate the first such algorithm, which takes under a minute, fast enough to enable immediate EM follow-up. By combining the three-dimensional posterior with a galaxy catalog, we can reduce the number of galaxies that could conceivably host the event by a factor of 1.4, the total exposure time for the Swift X-ray Telescope by a factor of 2, the total exposure time for a synoptic optical survey by a factor of 2, and the total exposure time for a narrow-field optical telescope by a factor of 3. This encourages us to suggest a new role for small field of view optical instruments in performing targeted searches of the most massive galaxies within the reconstructed volumes.

catalogs – galaxies: distances and redshifts –↗
NASA NTRS2014

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by the Interplanetary Network

We present the results of a search for gravitational waves associated with 223 gamma ray bursts (GRBs) detected by the InterPlanetary Network (IPN) in 2005-2010 during LIGO's fifth and sixth science runs and Virgo's first, second, and third science runs. The IPN satellites provide accurate times of the bursts and sky localizations that vary significantly from degree scale to hundreds of square degrees. We search for both a well-modeled binary coalescence signal, the favored progenitor model for short GRBs, and for generic, unmodeled gravitational wave bursts. Both searches use the event time and sky localization to improve the gravitational wave search sensitivity as compared to corresponding all-time, all-sky searches. We find no evidence of a gravitational wave signal associated with any of the IPN GRBs in the sample, nor do we find evidence for a population of weak gravitational wave signals associated with the GRBs. For all IPN-detected GRBs, for which a sufficient duration of quality gravitational wave data are available, we place lower bounds on the distance to the source in accordance with an optimistic assumption of gravitational wave emission energy of 10(exp−2) solar mass c(exp 2) at 150 Hz, and find a median of 13 Mpc. For the 27 short-hard GRBs we place 90% confidence exclusion distances to two source models: a binary neutron star coalescence, with a median distance of 12 Mpc, or the coalescence of a neutron star and black hole, with a median distance of 22 Mpc. Finally, we combine this search with previously published results to provide a population statement for GRB searches in first-generation LIGO and Virgo gravitational wave detectors and a resulting examination of prospects for the advanced gravitational wave detectors.

gravitational wave detectors↗
DOE OSTI2026

Lunar accelerometer network gravitational observatory (LANGO)

With ground-based interferometers detecting hundreds of gravitational-wave (GW) events, GW astronomy has continued to blossom. U.S. and European scientists are developing plans to construct third-generation ground-based interferometers. ESA has proceeded through the mission formulation phase of space-based interferometer in a lower-frequency band, 10 –4 –0.1 Hz. Despite all these exciting developments, there is still a missing frequency band, 0.1–10 Hz. This mid-frequency band is rich with interesting astrophysical events. Coalescence and merger of intermediate-mass black holes (IMBHs) will occur in this frequency band. Coalescing stellar-mass BHs will pass through this frequency band days before they reach the frequency band of LIGO and Virgo. Detection of such signals would enable a mid-frequency detector to issue an advance notice to the high-frequency GW detectors, as well as to optical, x-ray and γ-ray telescopes. We propose Lunar Accelerometer Network Gravitational Observatory (LANGO) to detect GWs in this frequency band. In the first phase (LANGO 1), we propose to deploy four ambient-temperature (250 K) accelerometers in the tetrahedral or in a square configuration on the hemisphere facing the Earth. After successful operation at 250 K, LANGO would be upgraded to a cryogenic (4 K) version with over two orders of magnitude increased sensitivity (LANGO 2), with coherent rejection of seismic noise implemented. LANGO is a full-tensor detector, capable of determining the source direction and wave polarization. Each test mass (TM) is suspended as a pendulum with resonance frequency ∼ 0.01 Hz, thus is only weakly coupled to the lunar surface horizontally. LANGO is designed to detect the relative motion of globally separated, nearly free, TMs by using the Moon as a large quiet platform. LANGO 1 and 2 accelerometers aim at sensitivities ⩽ 10 –11 m s –2 Hz –1/2 and ⩽ 10 –13 m s –2 Hz –1/2 in the horizontal axes over the frequency band of 1 mHz–10 Hz, which yield GW sensitivities 1.1 x 10 -21 Hz -1/2 and 3.8 x 10 -24 Hz -1/2 at 1 Hz, respectively. The LANGO accelerometers will be 10 3 –10 5 times more sensitive than Apollo seismometers. With such sensitivity, LANGO will also make great contribution to the advancement of lunar geophysics.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2019

GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observedby LIGO and Virgo During the First and Second Observing Runs

We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above1M during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run (O1), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run (O2), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star in spiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between18.6þ3.2−0.7M and 84.4þ15.8−11.1M and range in distance between 320þ120−110 and 2840þ1400−1360Mpc. No neutron star–black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of 110−3840Gpc−3y−1 for binary neutron stars and 9.7−101Gpc−3y−1 for binary black holes assuming fixed population distributions and determine a neutron star–black hole merger rate 90% upper limit of 610Gpc−3y−1.

Astrophysics↗
NASA NTRS2016

Galaxy Strategy for Ligo-Virgo Gravitational Wave Counterpart Searches

In this work we continue a line of inquiry begun in Kanner et al. which detailed a strategy for utilizing telescopes with narrow fields of view, such as the Swift X-Ray Telescope (XRT), to localize gravity wave (GW) triggers from LIGO (Laser Interferometer Gravitational-Wave Observatory) / Virgo. If one considers the brightest galaxies that produce 50 percent of the light, then the number of galaxies inside typical GW error boxes will be several tens. We have found that this result applies both in the early years of Advanced LIGO when the range is small and the error boxes large, and in the later years when the error boxes will be small and the range large. This strategy has the beneficial property of reducing the number of telescope pointings by a factor 10 to 100 compared with tiling the entire error box. Additional galaxy count reduction will come from a GW rapid distance estimate which will restrict the radial slice in search volume. Combining the bright galaxy strategy with a convolution based on anticipated GW localizations, we find that the searches can be restricted to about 18 plus or minus 5 galaxies for 2015, about 23 plus or minus 4 for 2017, and about 11 plus or minus for 2020. This assumes a distance localization at the putative neutron star-neutron star (NS-NS) merger range mu for each target year, and these totals are integrated out to the range. Integrating out to the horizon would roughly double the totals. For localizations with r (rotation) greatly less than mu the totals would decrease. The galaxy strategy we present in this work will enable numerous sensitive optical and X-ray telescopes with small fields of view to participate meaningfully in searches wherein the prospects for rapidly fading afterglow place a premium on a fast response time.

galaxies: statistics aEuro" gamma-ray burst: gener↗
NASA NTRS2016

A Dark Energy Camera Search for Missing Supergiants in the LMC After the Advanced LIGO Gravitational-Wave Event GW150914

The collapse of a stellar core is expected to produce gravitational waves (GWs), neutrinos, and in most cases a luminous supernova. Sometimes, however, the optical event could be significantly less luminous than a supernova and a direct collapse to a black hole, where the star just disappears, is possible. The GW event GW150914 was detected by the LIGO Virgo Collaboration via a burst analysis that gave localization contours enclosing the Large Magellanic Cloud (LMC). Shortly thereafter, we used DECam to observe 102 deg(exp.2) of the localization area,including 38 deg(exp. 2) on the LMC for a missing supergiant search. We construct a complete catalog of LMC luminous red supergiants, the best candidates to undergo invisible core collapse, and collected catalogs of other candidates:less luminous red supergiants, yellow supergiants, blue supergiants, luminous blue variable stars, and Wolf-Rayet stars. Of the objects in the imaging region, all are recovered in the images. The timescale for stellar disappearance is set by the free-fall time, which is a function of the stellar radius. Our observations at 4 and 13 days after the event result in a search sensitive to objects of up to about 200 solar radii. We conclude that it is unlikely that GW150914 was caused by the core collapse of a relatively compact supergiant in the LMC, consistent with the LIGO Collaboration analyses of the gravitational waveform as best interpreted as a high mass binary black hole merger. We discuss how to generalize this search for future very nearby core-collapse candidates.

galaxies: individual (LMC) – gravitational waves↗
DOE OSTI2025

Assessing the impact of uniform rotation on the structure of neutron stars

Driven by recent laboratory experiments and astronomical observations, significant advances have deepened our understanding of neutron-star physics. NICER's Pulse Profile Modeling has refined our knowledge of neutron star masses and radii, while gravitational-wave detections have revealed key insights into the structure of neutron stars. Particularly relevant is the extraction of the tidal deformability by the LIGO-Virgo collaboration and the most recent determination of stellar radii by NICER, both suggesting a relatively soft equation of state (EOS) at intermediate densities. Additionally, measurements from the PREX collaboration and from pulsar timing suggest instead that the EOS is stiff in the vicinity of saturation density and at the highest densities accessible to date. But how stiff can the EOS be at these very high densities? Recent events featuring compact objects near the “lower mass gap” have raised questions about the existence of very massive neutron stars. Motivated by this finding and in light of new refinements to theoretical models, we explore the possibility that these massive objects may indeed be rapidly rotating neutron stars. Here, we explore how rotation affects both the maximum neutron star mass and their associated radii, and discuss the implications they may have on the equation of state.

Equations of state of nuclear matter↗