Quiescent Low-mass X-ray Binaries Research Articles

Bayesian analysis of a relativistic hadronic model constrained by recent astrophysical observations

ABSTRACTWe use Bayesian analysis in order to constrain the equation of state for nuclear matter from astrophysical data related to the recent measurements from the NICER mission, LIGO/Virgo collaboration, and probability distributions of mass and radius from other 12 sources, including thermonuclear busters, and quiescent low-mass X-ray binaries. For this purpose, we base our study on a relativistic hadronic mean field model including an ω − ρ interaction. Our results indicate optimal ranges for some bulk parameters at the saturation density, namely, effective mass, incompressibility, and symmetry energy slope (L0). For instance, we find $L_0 = 50.79^{+15.16}_{-9.24}$ MeV (Case 1) and $L_0 = 75.06^{+8.43}_{-4.43}$ MeV (Case 2) in a 68 per cent confidence interval for the two cases analysed (different input ranges for L0 related to the PREX-II data). The respective parametrizations are in agreement with important nuclear matter constraints, as well as observational neutron star data, such as the dimensionless tidal deformability of the GW170817 event. From the mass–radius curves obtained from these best parametrizations, we also find the ranges of 11.97 km ≤ R1.4 ≤ 12.73 km (Case 1) and 12.34 km ≤ R1.4 ≤ 13.06 km (Case 2) for the radius of the $1.4\, \mathrm{M}_\odot$ neutron star.

Periodic X-ray sources in the massive globular cluster 47 Tucanae: Evidence for dynamically formed cataclysmic variables

ABSTRACT We present a systematic study of periodic X-ray sources in the massive globular cluster 47 Tuc, utilizing deep archival Chandra observations that resolve the cluster core and recently available eROSITA observations that cover the cluster outskirt. By applying the Gregory-Loredo algorithm, we detect 20 periodic signals among 18 X-ray sources, ranging between 205–95731 s. Fourteen periods are newly discovered in the X-ray band. We classify these periodic sources into four quiescent low-mass X-ray binaries, 1 ms pulsar, two coronally-active binaries, and eleven cataclysmic variables (CVs) based on their X-ray temporal and spectral properties, as well as multiband information. Despite a small sample subject to potential selection bias against faint and non-magnetic CVs, the 11 CVs together define an orbital period distribution significantly different from that of the CVs previously found in the solar neighbourhood and the Galactic bulge. In particular, there exists in 47 Tuc an apparent paucity of short-period CVs below the period gap, which might be attributed to a high occupation fraction of non-magnetic CVs. Also characteristic of the 47 Tuc CVs are an overabundance of long-period CVs with a subgiant donor, a substantial fraction of CVs within the period gap, and a steep radial surface density profile. These are best understood as a group of CVs having recently formed via dynamical interactions in the dense cluster core. Despite sufficient sensitivity of the X-ray data, only one periodic source is found between one-third of the half-light radius and the tidal radius, the nature of which is unclear.

EROSITA study of the globular cluster 47 Tucanae

Aims. We present the results of the analysis of five observations of the globular clutser 47 Tucanae (47 Tuc) with the extended Roentgen Survey with an Imaging Telescope Array (eROSITA) on board the Spektrum-Roentgen-Gamma (Spektr-RG, SRG). We study the X-ray population in the field of one of the most massive globular clusters in our Milky Way. We focused on the classification of point-like sources in the field of 47 Tuc. The unresolved dense core of 47 Tuc (1.7 radius) and also sources that show extended emission are excluded from this study. Methods. We applied different methods of X-ray spectral and timing analysis together with multi-wavelength studies to classify the X-rays sources in the field of 47 Tuc. Results. We detected 888 point-like sources in the energy range of 0.2–5.0 keV. We identified 126 background active galactic nuclei and 25 foreground stars. One of the foreground stars is classified as a variable M dwarf. We also classified 14 X-ray sources as members of 47 Tuc, including one symbiotic star, two quiescent low-mass X-ray binaries, and four cataclysmic variables. There are also five X-ray sources that can either be a cataclysmic variable or a contact binary, and also one X-ray source can be an active binary (type RS CVn). We identified one X-ray binary that belongs to the Small Magellanic Cloud. Moreover, we calculated the X-ray luminosity function of 47 Tuc. No significant population that seems to belong to the globular cluster is observed in the energy range of 0.5–2.0 keV using eROSITA observations.

The Disk Veiling Effect of the Black Hole Low-mass X-Ray Binary A0620-00*

Abstract The optical light curves of quiescent black hole low-mass X-ray binaries often exhibit significant nonellipsoidal variabilities, showing the photospheric radiation of the companion star is veiled by other sources of optical emission. Assessing this “veiling” effect is critical to the black hole mass measurement. Here in this work, we carry out a strictly simultaneous spectroscopic and photometric campaign on the prototype of black hole low-mass X-ray binary A0620-00. We find that for each observation epoch, the extra optical flux beyond a pure ellipsoidal modulation is positively correlated with the fraction of veiling emission, indicating the accretion disk contributes most of the nonellipsoidal variations. Meanwhile, we also obtain a K2V spectral classification of the companion, as well as the measurements of the companion’s rotational velocity v sin i = 83.8 ± 1.9 km s−1 and the mass ratio between the companion and the black hole q = 0.063 ± 0.004.

Combining Electromagnetic and Gravitational-Wave Constraints on Neutron-Star Masses and Radii.

We perform a joint Bayesian inference of neutron-star mass and radius constraints based on GW170817, observations of quiescent low-mass x-ray binaries (QLMXBs), photospheric radius expansion x-ray bursting sources, and x-ray timing observations of J0030+0451. With this dataset, the form of the prior distribution still has an impact on the posterior mass-radius curves and equation of state (EOS), but this impact is smaller than recently obtained when considering QLMXBs alone. We analyze the consistency of the electromagnetic data by including an "intrinsic scattering" contribution to the uncertainties, and find only a slight broadening of the posteriors. This suggests that the gravitational-wave and electromagnetic observations of neutron-star structure are providing a consistent picture of the neutron-star mass-radius curve and the EOS.

Nuclear Symmetry Energies at Supra-saturation Densities Extracted from Observations of Neutron Stars and Gravitational Waves

The high-density behavior of nuclear symmetry energy is the most uncertain part of the Equation of State (EOS) of dense neutron-rich nucleonic matter. It has significant ramifications in understanding properties of nuclear reactions induced by rare isotopes, neutron stars and gravitational waves from various sources. To infer the underlying EOS of dense neutron-rich nuclear matter from observables of neutron stars is the longstanding neutron star inverse-structure problem. To make progress in solving this problem, we advanced two inversion approaches: (1) the direct inversion in the three-dimensional high-density EOS parameter space and (2) Bayesian inference of six EOS parameters statistically. Neutron star observational data obtained so far, especially their radii from analyzing gravitational waves (e.g., via the tidal deformability) from GW170817 and X-rays from quiescent low-mass X-ray binaries can already help constrain significantly the nuclear EOS up to about twice the saturation density of nuclear matter. In particular, the nuclear symmetry energy at twice the saturation density of nuclear matter E sym(2ρ 0) is found to be MeV at 68% confidence level.

Constraining the equation of state of dense nuclear matter using thermal emission of neutron stars

In this work, the equation of state (EoS) of the dense matter in the core of neutron stars (NSs) is based on a recently proposed meta-modeling of nuclear matter composed of nucleons, which can be parametrized by empirical quantities such as the energy density at saturation density or the nuclear incompressibility modulus. We use a set of recent observations of the thermal emission of seven NSs in quiescent low-mass X-ray binaries (qLMXBs) in order to find some constraints on the parameters of the meta-model, and thus on the nuclear EoS. This is done in a Bayesian statistical framework using Markov Chain Monte Carlo (MCMC) methods, to perform a simultaneous analysis over the seven sources. For the first time, the theoretical modeling of the EoS is directly implemented in the data analysis. We obtain constraints on the slope of the symmetry energy, MeV, and give the first estimation of its curvature, MeV, and on the isoscalar skewness parameter, MeV. Radii of about 12 km are preferred with a good fit statistic, yielding a nuclear EoS that is consistent with observational data and recent gravitational waves signals from NSs coalescence.

New Constraints on the Nuclear Equation of State from the Thermal Emission of Neutron Stars in Quiescent Low-mass X-Ray Binaries

Abstract This paper presents a new analysis of the thermal emission from the neutron star (NS) surface to constrain the dense matter equation of state. We employ an empirical parameterization of the equation of state with a Markov Chain Monte Carlo approach to consistently fit the spectra of quiescent low-mass X-ray binaries in globular clusters with well-measured distances. Despite previous analyses predicting low NS radii, we show that it is possible to reconcile the astrophysical data with nuclear physics knowledge with or without including a prior on the slope of the symmetry energy L sym. With this empirical parameterization of the equation of state, we obtain radii of the order of about 12 km without worsening the fit statistic. More importantly, we obtain the following values for the slope of the symmetry energy, its curvature K sym, and the isoscalar skewness parameter Q sat: MeV, MeV, and MeV. These are the first measurements of the empirical parameters K sym and Q sat. Their values are only weakly impacted by our assumptions, such as the distances or the number of free empirical parameters, provided the latter are taken within a reasonable range. We also study the weak sensitivity of our results to the set of sources analyzed, and we identify a group of sources that dominates the constraints. The resulting masses and radii obtained from this empirical parameterization are also compared to other measurements from electromagnetic observations of NSs and gravitational wave signals from the NS–NS merger GW170817.

Simultaneous fitting of neutron star structure and cooling data

Using a model for the equation of state and composition of dense matter and the magnitude of singlet proton superconductivity and triplet neutron superfluidity, we perform the first simultaneous fit of neutron star masses and radii determined from observations of quiescent low-mass x-ray binaries and luminosities and ages determined from observations of isolated neutron stars. We find that the Vela pulsar strongly determines the values inferred for the superfluid/superconducting gaps and the neutron star radius. We find, regardless of whether or not the Vela pulsar is included in the analysis, that the threshold density for the direct Urca process lies between the central density of 1.7 and 2 solar mass neutron stars. We also find that two solar mass stars are unlikely to cool principally by the direct Urca process because of the suppression by neutron triplet superfluidity.

Prospecting for periods with LSST – low-mass X-ray binaries as a test case

The Large Synoptic Survey Telescope (LSST) will provide for unbiased sampling of variability properties of objects with $r$ mag $<$ 24. This should allow for those objects whose variations reveal their orbital periods ($P_{orb}$), such as low mass X-ray binaries (LMXBs) and related objects, to be examined in much greater detail and with uniform systematic sampling. However, the baseline LSST observing strategy has temporal sampling that is not optimised for such work in the Galaxy. Here we assess four candidate observing strategies for measurement of $P_{orb}$ in the range 10 minutes to 50 days. We simulate multi-filter quiescent LMXB lightcurves including ellipsoidal modulation and stochastic flaring, and then sample these using LSST's operations simulator (OpSim) over the (mag, $P_{orb}$) parameter space, and over five sightlines sampling a range of possible reddening values. The percentage of simulated parameter space with correctly returned periods ranges from $\sim$23 %, for the current baseline strategy, to $\sim$70 % for the two simulated specialist strategies. Convolving these results with a $P_{orb}$ distribution, a modelled Galactic spatial distribution and reddening maps, we conservatively estimate that the most recent version of the LSST baseline strategy will allow $P_{orb}$ determination for $\sim$18 % of the Milky Way's LMXB population, whereas strategies that do not reduce observations of the Galactic Plane can improve this dramatically to $\sim$32 %. This increase would allow characterisation of the full binary population by breaking degeneracies between suggested $P_{orb}$ distributions in the literature. Our results can be used in the ongoing assessment of the effectiveness of various potential cadencing strategies.

On obtaining neutron star mass and radius constraints from quiescent low-mass X-ray binaries in the Galactic plane

X-ray spectral analysis of quiescent low-mass X-ray binaries (LMXBs) has been one of the most common tools to measure the radius of neutron stars (NSs) for over a decade. So far, this method has been mainly applied to NSs in globular clusters, primarily because of their well-constrained distances. Here, we study Chandra data of seven transient LMXBs in the Galactic plane in quiescence to investigate the potential of constraining the radius (and mass) of the NSs inhabiting these systems. We find that only two of these objects had X-ray spectra of sufficient quality to obtain reasonable constraints on the radius, with the most stringent being an upper limit of $R\lesssim$14.5 km for EXO 0748-676 (for assumed ranges for mass and distance). Using these seven sources, we also investigate systematic biases on the mass/radius determination; for Aql X-1 we find that omitting a power-law spectral component when it does not seem to be required by the data, results in peculiar trends in the obtained radius with changing mass and distance. For EXO 0748-676 we find that a slight variation in the lower limit of the energy range chosen for the fit leads to systematically different masses and radii. Finally, we simulated Athena spectra and found that some of the biases can be lifted when higher quality spectra are available and that, in general, the search for constraints on the equation of state of ultra-dense matter via NS radius and mass measurements may receive a considerable boost in the future.

An Ultradeep Chandra Catalog of X-Ray Point Sources in the Galactic Center Star Cluster

Abstract We present an updated catalog of X-ray point sources in the inner 500″ (∼20 pc) of the Galactic center (GC), where the nuclear star cluster (NSC) stands, based on a total of ∼4.5 Ms of Chandra observations taken from 1999 September to 2013 April. This ultradeep data set offers unprecedented sensitivity for detecting X-ray sources in the GC, down to an intrinsic 2–10 keV luminosity of 1.0 × 1031 erg s−1. A total of 3619 sources are detected in the 2–8 keV band, among which ∼3500 are probable GC sources and ∼1300 are new identifications. The GC sources collectively account for ∼20% of the total 2–8 keV flux from the inner 250″ region where detection sensitivity is the greatest. Taking advantage of this unprecedented sample of faint X-ray sources that primarily traces the old stellar populations in the NSC, we revisit global source properties, including long-term variability, cumulative spectra, luminosity function, and spatial distribution. Based on the equivalent width and relative strength of the iron lines, we suggest that in addition to the arguably predominant population of magnetic cataclysmic variables (CVs), nonmagnetic CVs contribute substantially to the detected sources, especially in the lower-luminosity group. On the other hand, the X-ray sources have a radial distribution closely following the stellar mass distribution in the NSC, but much flatter than that of the known X-ray transients, which are presumably low-mass X-ray binaries (LMXBs) caught in outburst. This, together with the very modest long-term variability of the detected sources, strongly suggests that quiescent LMXBs are a minor (less than a few percent) population.

The radius of the quiescent neutron star in the globular cluster M13

X-ray spectra of quiescent low-mass X-ray binaries containing neutron stars can be fit with atmosphere models to constrain the mass and the radius. Mass-radius constraints can be used to place limits on the equation of state of dense matter. We perform fits to the X-ray spectrum of a quiescent neutron star in the globular cluster M13, utilizing data from ROSAT, Chandra and XMM-Newton, and constrain the mass-radius relation. Assuming an atmosphere composed of hydrogen and a 1.4${\rm M}_{\odot}$ neutron star, we find the radius to be $R_{\rm NS}=12.2^{+1.5}_{-1.1}$ km, a significant improvement in precision over previous measurements. Incorporating an uncertainty on the distance to M13 relaxes the radius constraints slightly and we find $R_{\rm NS}=12.3^{+1.9}_{-1.7}$ km (for a 1.4${\rm M}_{\odot}$ neutron star with a hydrogen atmosphere), which is still an improvement in precision over previous measurements, some of which do not consider distance uncertainty. We also discuss how the composition of the atmosphere affects the derived radius, finding that a helium atmosphere implies a significantly larger radius.

Constraining the mass and radius of neutron stars in globular clusters

We analyze observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions are preferred over other models and interpretations of the data with a Bayes factor of 8 or more, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.

Milky Way globular cluster metallicity and low-mass X-ray binaries: the red giant influence

Galactic and extragalactic studies have shown that metal-rich globular clusters (GCs) are approximately three times more likely to host bright low-mass X-ray binaries (LMXBs) than metal-poor GCs. There is no satisfactory explanation for this metallicity effect. We tested the hypothesis that the number density of red giant branch (RGB) stars is larger in metal-rich GCs, and thus potentially the cause of the metallicity effect. Using Hubble Space Telescope photometry for 109 unique Milky Way GCs, we investigated whether RGB star density was correlated with GC metallicity. Isochrone fitting was used to calculate the number of RGB stars, which were normalized by the GC mass and fraction of observed GC luminosity, and determined density using the volume at the half-light radius $r_{h}$. The RGB star number density was weakly correlated with metallicity [Fe/H], giving Spearman and Kendall Rank test $p$-values of 0.00016 and 0.00021 and coefficients $r_{s} = 0.35$ and $\tau = 0.24$ respectively. This correlation may be biased by a possible dependence of $r_{h}$ on [Fe/H], although studies have shown that $r_{h}$ is correlated with Galactocentric distance and independent of [Fe/H]. The dynamical origin of the $r_{h}$-metallicity correlation (tidal stripping) suggests that metal-rich GCs may have had more active dynamical histories, which would promote LMXB formation. No correlation between the RGB star number density and metallicity was found when using only the GCs that hosted quiescent LMXBs. A complete census of quiescent LMXBs in our Galaxy is needed to further probe the metallicity effect, which will be possible with the upcoming launch of eROSITA.

NEUTRON STAR MASS–RADIUS CONSTRAINTS OF THE QUIESCENT LOW-MASS X-RAY BINARIES X7 AND X5 IN THE GLOBULAR CLUSTER 47 TUC

ABSTRACT We present Chandra/ACIS-S subarray observations of the quiescent neutron star (NS) low-mass X-ray binaries X7 and X5 in the globular cluster 47 Tuc. The large reduction in photon pile-up compared to previous deep exposures enables a substantial improvement in the spectroscopic determination of the NS radius and mass of these NSs. Modeling the thermal emission from the NS surface with a non-magnetized hydrogen atmosphere and accounting for numerous sources of uncertainties, we obtain for the NS in X7 a radius of km for an assumed stellar mass of M = 1.4 M ⊙ (68% confidence level). We argue, based on astrophysical grounds, that the presence of a He atmosphere is unlikely for this source. Due to the excision of data affected by eclipses and variable absorption, the quiescent low-mass X-ray binary X5 provides less stringent constraints, leading to a radius of km, assuming a hydrogen atmosphere and a mass of M = 1.4 M ⊙. When combined with all existing spectroscopic radius measurements from other quiescent low-mass X-ray binaries and Type I X-ray bursts, these measurements strongly favor radii in the 9.9–11.2 km range for a ∼1.5 M ⊙ NS and point to a dense matter equation of state that is somewhat softer than the nucleonic ones that are consistent with laboratory experiments at low densities.

Neutron star radii, universal relations, and the role of prior distributions

We investigate constraints on neutron star structure arising from the assumptions that neutron stars have crusts, that recent calculations of pure neutron matter limit the equation of state of neutron star matter near the nuclear saturation density, that the high-density equation of state is limited by causality and the largest high-accuracy neutron star mass measurement, and that general relativity is the correct theory of gravity. We explore the role of prior assumptions by considering two classes of equation of state models. In a first, the intermediate- and high-density behavior of the equation of state is parameterized by piecewise polytropes. In the second class, the high-density behavior of the equation of state is parameterized by piecewise continuous line segments. The smallest density at which high-density matter appears is varied in order to allow for strong phase transitions above the nuclear saturation density. We critically examine correlations among the pressure of matter, radii, maximum masses, the binding energy, the moment of inertia, and the tidal deformability, paying special attention to the sensitivity of these correlations to prior assumptions about the equation of state. It is possible to constrain the radii of $1.4~\mathrm{M}_{\odot}$ neutron stars to a be larger than 10 km, even without consideration of additional astrophysical observations, for example, those from photospheric radius expansion bursts or quiescent low-mass X-ray binaries. We are able to improve the accuracy of known correlations between the moment of inertia and compactness as well as the binding energy and compactness. We also demonstrate the existence of a correlation between the neutron star binding energy and the moment of inertia.

Neutron Star Physics and EOS

Neutron stars are important because measurement of their masses and radii will determine the dense matter equation of state. They will constrain the nuclear matter symmetry energy, which controls the neutron star matter pressure and the interior composition, and will influence the interpretation of nuclear experiments. Astrophysical observations include pulsar timing, X-ray bursts, quiescent low-mass X-ray binaries, pulse profiles from millisecond pulsars, neutrino observations from gravitational collapse supernovae,and gravitational radiation from compact object mergers. These observations will also constrain the neutron star interior, including the properties of superfluidity there, and determine the existence of a possible QCD phase transition.

Limits on thermal variations in a dozen quiescent neutron stars over a decade

n quiescent low-mass X-ray binaries (qLMXBs) containing neutron stars, the origin of the thermal X-ray component may be either release of heat from the core of the neutron star, or continuing low-level accretion. In general, heat from the core should be stable on time-scales <104 yr, while continuing accretion may produce variations on a range of time-scales. While some quiescent neutron stars (e.g. Cen X-4, Aql X-1) have shown variations in their thermal components on a range of time-scales, several others, particularly those in globular clusters with no detectable non-thermal hard X-rays (fit with a power law), have shown no measurable variations. Here, we constrain the spectral variations of 12 low-mass X-ray binaries in three globular clusters over ∼10 years. We find no evidence of variations in 10 cases, with limits on temperature variations below 11 per cent for the seven qLMXBs without power-law components, and limits on variations below 20 per cent for three other qLMXBs that do show non-thermal emission. However, in two qLMXBs showing power-law components in their spectra (NGC 6440 CX 1 and Terzan 5 CX 12) we find marginal evidence for a 10 per cent decline in temperature, suggesting the presence of continuing low-level accretion. This work adds to the evidence that the thermal X-ray component in quiescent neutron stars without power-law components can be explained by heat deposited in the core during outbursts. Finally, we also investigate the correlation between hydrogen column density (NH) and optical extinction (AV) using our sample and current models of interstellar X-ray absorption, finding NH(cm−2) = (2.81 ± 0.13) × 1021AV.

REJECTING PROPOSED DENSE MATTER EQUATIONS OF STATE WITH QUIESCENT LOW-MASS X-RAY BINARIES

Neutrons stars are unique laboratories to discriminate between the various proposed equations of state of matter at and above nuclear density. One sub-class of neutron stars - those inside quiescent low-mass X-ray binaries (qLMXBs) - produce a thermal surface emission from which the neutron star radius (R_NS) can be measured, using the widely accepted observational scenario for qLMXBs, assuming unmagnetized H atmospheres. In a combined spectral analysis, this work first reproduces a previously published measurement of the \rns, assumed to be the same for all neutron stars, using a slightly expanded data set. The radius measured is R_NS = 9.4 +/-1.2 km. On the basis of spectral analysis alone, this measured value is not affected by imposing an assumption of causality in the core. However, the assumptions underlying this R_NS measurement would be falsified by the observation of any neutron star with a mass >2.6 Msun, since radii <11 km would be rejected if causality is assumed, which would exclude most of the R_NS parameter space obtained in this analysis. Finally, this work directly tests a selection of dense matter equations of states: WFF1, AP4, MPA1, PAL1, MS0, and three versions of equations of state produced through chiral effective theory. Two of those, MSO and PAL1, are rejected at the 99% confidence level, accounting for all quantifiable uncertainties, while the other cannot be excluded at >99% certainty.