We study the impact of new mass-radius information from PSR J1614-2230, PSR J2124-3358, and 47 Tuc X7 in a combined equation of state inference based on chiral effective field theory constraints at nuclear densities and using different high-density extensions, including perturbative QCD constraints. The largest impact stems from the heavy-mass PSR J1614-2230 star, which shifts heavy neutron stars to smaller radii by around 0.4 km. Moreover, the combined astrophysical NICER, LIGO/Virgo, and X-ray information drives the radius posterior to a more data-driven distribution, which is less sensitive to the high-density extension. For the equation of state, the new mass-radius information significantly tightens the pressure and speed-of-sound posterior distributions, especially around three times saturation density. Finally, we make predictions for the poorly constrained masses of PSR J2124-3358 and 47 Tuc X7 based on the combined equation of state analysis and the other astrophysical sources.

We investigate Bayesian chiral effective field theory ($χ$EFT) uncertainties, which assign a statistical interpretation to equation of state (EOS) distributions near nuclear saturation density, n$_0$, as well as constraints from perturbative quantum chromodynamics (pQCD) to Bayesian EOS inference from LIGO/Virgo, NICER and pulsar mass observations. The tails of the $χ$EFT uncertainties allow for broader pressure ranges in our priors, but large parts of these are excluded by the astrophysical observations, so that the EOS and the resulting mass-radius posteriors are still very consistent with our earlier work. Within our broad prior ranges, we observe a clear stiffening of the EOS at $n \gtrsim 3 n_0$. Moreover, the impact of the pQCD constraints on the posterior EOS and mass-radius range is negligible due to the astrophysics constraints. Exploiting the strong correlation between pure neutron matter and matter in beta equilibrium, we infer the symmetry energy slope parameter $L$ from astrophysics. For the $68\%$ credible interval, we obtain $L=42.6-52$ MeV and $L=44.2-56.7$ MeV using piecewise-polytrope and speed-of-sound high-density extensions, respectively. The $L$ posterior is mainly driven by the combination of GW170817 LIGO/Virgo and PSR J0740+6620, PSR J0437-4715, and PSR J0614-3329 NICER observations.

The pulsed X-ray emission from the neutron star surface acts as a window to study the state of matter in the neutron star interior. For accreting millisecond pulsars, the surface X-ray emission is generated from the “hotspots” formed due to the magnetically channeled accretion flow hitting the stellar surface. The emission from these hotspots is modulated by stellar rotation, giving rise to pulsations. Using global three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations of the star-disk system, we investigate the accretion hotspots and the corresponding X-ray pulse properties of accreting millisecond pulsars with dipolar magnetic fields. The accretion spot morphologies in our simulations are entirely determined by the accretion columns and vary as a function of the stellar magnetic inclination. For lower magnetic inclinations, the hotspots are shaped like crescents around the magnetic axis and are transformed into elongated bars for higher inclinations. We model the X-ray pulses resulting from the simulated hotspots using general-relativistic ray-tracing calculations and quantify the variability of the pulsed signal. The pulse amplitudes in our simulations usually range between 1% and 12% rms and are consistent with the observed values. We find that the turbulent accretion flow in the GRMHD simulations introduces significant broadband variability on a timescale similar to the stellar rotational period. We also explore the impact of electron scattering absorption and show that, along with being a key factor in determining the pulse characteristics, this also introduces significant additional variability and higher harmonics in the bolometric light curve of the accreting sources.

In this paper we present the current status of the enhanced X-ray Timing and Polarimetry mission, which has been fully approved for launch in 2030. eXTP is a space science mission designed to study fundamental physics under extreme conditions of matter density, gravity, and magnetism. The mission aims at determining the equation of state of matter at supra-nuclear density, measuring the effects of quantum electro-dynamics, and understanding the dynamics of matter in strong-field gravity. In addition to investigating fundamental physics, the eXTP mission is poised to become a leading observatory for time-domain and multi-messenger astronomy in the 2030's, as well as providing observations of unprecedented quality on a variety of galactic and extragalactic objects. After briefly introducing the history and a summary of the scientific objectives of the eXTP mission, this paper presents a comprehensive overview of: 1) the cutting-edge technology, technical specifications, and anticipated performance of the mission's scientific instruments; 2) the full mission profile, encompassing spacecraft design, operational capabilities, and ground segment infrastructure.

In the last few years, NICER data has enabled mass and radius inferences for various pulsars, and thus shed light on the equation of state for dense nuclear matter. This is achieved through a technique called pulse profile modeling. The importance of the results necessitates careful validation and testing of the robustness of the inference procedure. In this paper, we investigate the effect of sampler choice for X-PSI (X-ray Pulse Simulation and Inference), an open-source package for pulse profile modeling and Bayesian statistical inference that has been used extensively for analysis of NICER data. We focus on the specific case of the high-mass pulsar PSR J0740+6620. Using synthetic data that mimics the most recently analyzed NICER and XMM-Newton data sets of PSR J0740+6620, we evaluate the parameter recovery performance, convergence, and computational cost for MultiNest's multimodal nested sampling algorithm and UltraNest's slice nested sampling algorithm. We find that both samplers perform reliably, producing accurate and unbiased parameter estimation results when analyzing simulated data. We also investigate the consequences for inference using the real data for PSR J0740+6620, finding that both samplers produce consistent credible intervals.

It is possible for asymmetric dark matter (ADM) to accumulate in neutron star interiors and affect their global properties. Considering the effects of this accumulation, neutron star mass-radius measurements can deliver new insights into the cold dense matter equation of state (EoS). In this paper, we employ Bayesian parameter estimation using real and synthetic neutron star mass-radius data to infer constraints on the combined baryonic matter and fermionic ADM EoS, where the fermionic ADM forms a core in the neutron star interior. Using currently available mass-radius data, we find that the lower bound of the ratio between the ADM effective self-repulsion strength (g chi/m phi) and particle mass (m chi) can be constrained at the 68% (95%) credible level to 10-6.59 (10-7.77). We also find that, if neutron star mass-radius measurement uncertainties are reduced to the 2% level, the constraints on the lower bound of the ratio of g chi/m phi to m chi can be improved to 10-6.49 and 10-7.68 at the 68% and 95% credible levels, respectively. However, all other combinations, of m chi, g chi, and the ADM mass-fraction, F chi (i.e., the ratio of the gravitational ADM mass to the gravitational mass of the neutron star), are unconstrained. Furthermore, in the pressure-energy density and mass-radius planes, the inferences which include the possibility of fermionic ADM cores are nearly identical with the inferences that neglect fermionic ADM for F chi <= 1.7% and neutron star mass-radius uncertainties >= 2%. Therefore, we find that neutron star mass-radius measurements can constrain the ratio of g chi/m phi to m chi. Moreover, since the pressure-energy density and mass-radius posteriors which include fermionic ADM overlap with those that neglect fermionic ADM, we find that neutron stars with ADM are indistinguishable from purely baryonic stars. This implies that neutron stars with ADM are equally as consistent with the available mass-radius data as neutron stars without ADM.

We present an analysis of polarized X-ray pulses based on simulated data for accreting millisecond pulsars (AMPs). We used the open-source X-ray Pulse Simulation and Inference code (previously applied to NICER observations), which we upgraded to allow polarization analysis. We provide estimates of how well neutron star (NS) parameters can be constrained for the Imaging X-ray Polarimetry Explorer (IXPE) and find that strong limits on the hot region geometries can be hard to obtain if the emitting hot region is large and the number of polarized photons relatively small. However, if the star is bright enough and the hot regions are small and located so that polarization degree is higher, the observer inclination and hot spot colatitude can be constrained to a precision of within a few degrees. We also found that the shape of the hot region, whether a circle or a ring, cannot be distinguished in our most optimistic scenario. Nevertheless, future X-ray polarization missions are expected to improve the constraints, and already the recent AMP polarization detections by IXPE should help to infer the NS mass and radius when combined with modelling of X-ray pulse data sets that do not contain polarization information.

In this White Paper, we present the potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission to constrain the equation of state of dense matter in neutron stars, exploring regimes not directly accessible to terrestrial experiments. By observing a diverse population of neutron stars - including isolated objects, X-ray bursters, and accreting systems - eXTP's unique combination of timing, spectroscopy, and polarimetry enables high-precision measurements of compactness, spin, surface temperature, polarimetric signals, and timing irregularity. These multifaceted observations, combined with advances in theoretical modeling, pave the way toward a comprehensive description of the properties and phases of dense matter from the crust to the core of neutron stars. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is planned to be launched in early 2030.

Modelling the coherent pulsations observed during thermonuclear bursts offers a valuable method to probe the poorly understood equation of state of dense and cold matter. Here we apply the pulse profile modelling technique to the pulsations observed with RXTE during the 2001 superburst of 4U 1636-536. By employing a single, uniform-temperature hot spot model with varying size and temperature, along with various assumptions for background/accretion contribution, we find that each assumption leads to different inferred mass, radius, and compactness constraints. This highlights the critical need to better understand the mass accretion rate enhancement/reduction during thermonuclear bursts to accurately model burst oscillation sources using pulse profile modelling.

Pulse profile modelling using X-ray data from NICER permits the inference of mass and radius for rotation-powered millisecond pulsars. This in turn constrains the equation of state of cold dense matter. Previous studies indicate that the uncertainty in the inferred radius should reduce as neutron star spin rate increases. Here we test this using one of the pipelines currently being used for pulse profile modelling with NICER data. We synthesize a set of pulse profiles, assuming different neutron star spin frequencies, spanning the range (25-700) Hz. All of the simulated data sets are generated with the same (single) hot spot configuration, assuming a neutron star mass and radius of 1.6 M⊙ and 10 km. For this restricted set of synthetic data, we find no improvement in the radius credible interval once spin frequency exceeds a certain value (in this specific case ∼200 Hz). If this result were to apply more generally, it would have important implications for the observing strategy for current and future pulse profile modelling missions: targets can be prioritized based on properties other than their spin frequencies, as long as we are in the millisecond range.

Four neutron star radius measurements have already been obtained by modeling the X-ray pulses of rotation-powered millisecond pulsars observed by the Neutron Star Interior Composition ExploreR (NICER). We report here the radius measurement of PSR J0614-3329 employing the same method with NICER and XMM-Newton data using Bayesian Inference. For all different models tested, including one with unrestricted inclination prior, we retrieve very similar non-antipodal hot regions geometries and radii. For the preferred model, we infer an equatorial radius of R_ eq=10.29^+1.01_-0.86km for a mass of M=1.44^+0.06_-0.07 M_⊙ (median values with equal-tailed 68% credible interval), the latter being essentially constrained from radio timing priors obtained by MeerKAT. A more complex model, fitting the data equally well, resulted in a consistent inferred radius. We find that, for all different models, the pulse emission originates from two hot regions, one at the pole and the other at the equator. The resulting radius constraint is consistent with previous X-ray and gravitational wave measurements of neutron stars in the same mass range. Equation of state inferences, including previous NICER and gravitational wave results, slightly soften the equation of state with PSR J0614-3329 included and shift the allowed mass-radius region toward lower radii by ∼ 300m, which is compatible with previous analyses to within less than one standard deviation.

We investigate whether measurements of the neutron star mass and radius or the tidal deformability can provide information about the presence of hyperons inside a neutron star. This is achieved by considering two inference models, with and without hyperons, based on a field theoretical approach. While current observations do not distinguish between the two scenarios, we have shown that data simulating expected observations from future large-area X-ray timing telescopes could provide some information through Bayes' factors. Inference using simulated data generated from an equation of state containing hyperons decisively favours the hyperonic model over the nucleonic model. However, a 2 per cent uncertainty in the mass and radius determination may not be sufficient to constrain the parameters of the model when only six neutron star mass-radius measurements are considered.

Pulse profile modelling (PPM) is a technique for inferring mass, radius, and hotspot properties of millisecond pulsars. PPM is now regularly used for the analysis of rotation-powered millisecond pulsars with data from the Neutron Star Interior Composition ExploreR (NICER). Extending PPM to accreting millisecond pulsars (AMPs) is attractive, because they are a different source class featuring bright X-ray radiation from hotspots powered by accretion. In this paper, we present a modification of one of the PPM codes, x-psi, so that it can be used for AMPs. In particular, we implement a model of an accretion disc and atmosphere model appropriate for the hotspots of AMPs, and improve the overall computational efficiency. We then test parameter recovery with simulated NICER data in two scenarios with reasonable parameters for AMPs. We find in the first scenario, where the hotspot is large, that we are able to tightly and accurately constrain all parameters including mass and radius. In the second scenario, which is a high inclination system with a smaller hotspot, we find slightly widened posteriors, degeneracy between a subset of model parameters, and a slight bias in the inferred mass. This analysis of synthetic data lays the ground work for future analysis of AMPs with NICER data. Such an analysis could be complemented by future (joint) analysis of polarization data from the Imaging X-ray Polarimetry Explorer.

Pulse Profile Modeling (PPM), the technique used to infer mass, radius and geometric parameters for rotation-powered millisecond pulsars using data from the Neutron Star Interior Composition Explorer (NICER), relies on relativistic ray-tracing of thermal X-ray photons from hot spots on the neutron star surface to the observer. To verify our ray-tracing codes we have in the past conducted cross-tests for simple hot spot geometries, focusing primarily on the implementation of the space-time model. In this paper, we present verification for test problems that explore the more complex hot spot geometries that are now being employed in the NICER PPM analyses. We conclude that the accuracy of our computed waveforms is in general sufficiently high for analyses of current NICER data sets. We have however identified some extreme configurations where extra care may be needed.

In 2019 the NICER collaboration published the first mass and radius inferred for PSR J0030+0451, thanks to NICER observations, and consequent constraints on the equation of state characterizing dense matter. Two independent analyses found a mass of ∼1.3–1.4 M _⊙ and a radius of ∼13 km. They also both found that the hot spots were all located on the same hemisphere, opposite to the observer, and that at least one of them had a significantly elongated shape. Here we reanalyze, in greater detail, the same NICER data set, incorporating the effects of an updated NICER response matrix and using an upgraded analysis framework. We expand the adopted models and also jointly analyze XMM-Newton data, which enables us to better constrain the fraction of observed counts coming from PSR J0030+0451. Adopting the same models used in previous publications, we find consistent results, although with more stringent inference requirements. We also find a multimodal structure in the posterior surface. This becomes crucial when XMM-Newton data is accounted for. Including the corresponding constraints disfavors the main solutions found previously, in favor of the new and more complex models. These have inferred masses and radii of ∼[1.4 M _⊙ , 11.5 km] and ∼[1.7 M _⊙ , 14.5 km], depending on the assumed model. They display configurations that do not require the two hot spots generating the observed X-rays to be on the same hemisphere, nor to show very elongated features, and point instead to the presence of temperature gradients and the need to account for them.

Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state (EOS) of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231-1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and EOS analyses, we infer the radius to be 12.6 +/- 0.3 km and the mass to be 1.04-0.03+0.05 M circle dot, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. If using an uninformative prior but limited between 10 and 14 km, we find otherwise similar results, but Req=13.5-0.5+0.3 km for the radius. In both cases, we find a nonantipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a noncircular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile.

We give an overview of the science objectives and mission design of the "Spectroscopic Time-Resolving Observatory for Broadband Energy X-rays" observatory, which has been proposed as a NASA probe-class (similar to$1.5B) mission in response to the Astro2020 recommendation for an X-ray probe.

We report Bayesian inference of the mass, radius and hot X-ray emitting region properties - using data from the Neutron Star Interior Composition ExploreR (NICER) - for the brightest rotation-powered millisecond X-ray pulsar PSR J0437x20134715. Our modeling is conditional on informative tight priors on mass, distance and binary inclination obtained from radio pulsar timing using the Parkes Pulsar Timing Array (PPTA) (Reardon et al. 2024), and we use NICER background models to constrain the non-source background, cross-checking with data from XMM-Newton. We assume two distinct hot emitting regions, and various parameterized hot region geometries that are defined in terms of overlapping circles; while simplified, these capture many of the possibilities suggested by detailed modeling of return current heating. For the preferred model identified by our analysis we infer a mass of M = 1.418 ± 0.037 M_⊙ (largely informed by the PPTA mass prior) and an equatorial radius of R = 11.36^+0.95_-0.63 km, each reported as the posterior credible interval bounded by the 16 favors softer dense matter equations of state and is highly consistent with constraints derived from gravitational wave measurements of neutron star binary mergers. The hot regions are inferred to be non-antipodal, and hence inconsistent with a pure centered dipole magnetic field.

The CompactObject package is an open-source software framework developed to constrain the neutron star equation of state (EOS) through Bayesian statistical inference. It integrates astrophysical observational constraints from X-ray timing, gravitational wave events, and radio measurements, as well as nuclear experimental constraints derived from perturbative Quantum Chromodynamics (pQCD) and Chiral Effective Field Theory (χEFT). The package supports a diverse range of EOS models, including meta-model like and several physics-motivated EOS models. It comprises three independent components: an EOS generator module that currently provides seven EOS choices, a Tolman-Oppenheimer-Volkoff (TOV) equation solver, that allows the determination of the Mass Radius and Tidal deformability as observables, and a comprehensive Bayesian inference workflow module, including a complete pipeline for implementing EOS Bayesian inference. Each component can be used independently in different scientific research contexts, such as nuclear physics and astrophysics. In addition, CompactObject is designed to work in synergy with existing software such as CompOSE, allowing the use of the CompOSE EOS database to extend the EOS options available.