Neutron Star Atmosphere Models Research Articles

Ray-traced spectra of a hot neutron star for various metallicities

General relativity strongly affects the observed spectra of compact objects. New models of hot nonrotating neutron star (NS) atmospheres are presented for various chemical compositions. We demonstrate the influence of strong gravity on the value of the hardening factor measured by a distant observer. We prepare new xspec fitting packages based on our extended numerical models for hot NS atmospheres in order to use them for a spectral analysis in the X-ray domain. For the Schwarzschild metric, ray-tracing calculations were performed to determine the observational appearance of the continuum emission of an NS. The grid of intensity spectra emerging from the NS surface was computed with the code which solves the model atmosphere equations with an accurate treatment of the Compton scattering of photons on free electrons in fully relativistic thermal motion. For the single value of the surface gravity, $ =14.34$ (cgs), the emerging specific intensity spectra were then ray-traced from the surface to the distant observer with the code across the spacetime of a nonrotating NS obtained using the lo library. The color-correction factors were determined for a large grid of models of different chemical compositions for surface gravities from the critical gravity $ g_ crit $ up to $15.00$ (cgs), and for effective temperatures in the range of $10^ eff $ K. Comptonized spectra seen at the source rest frame display hardening factors in the range from 1.4 up to 2.0 in the case of a highly luminous metal-rich atmosphere. The ratio of the color temperature $T_ c $ to the effective temperature $T_ eff $ for ray-traced spectra is in the range $0.9-1.4$. In the strong gravity regime, the structure of a hot atmosphere strongly depends on the surface gravity, luminosity, and atmospheric metal abundance of the NS. The theoretical hardening factors of the ray-traced spectra are systematically lower then the hardening factors of spectra at the source by about 30<!PCT!> on average.

Multiwavelength Pulsations and Surface Temperature Distribution in the Middle-aged Pulsar B1055–52

We present a detailed study of the X-ray emission from PSR B1055–52 using XMM-Newton observations from 2019 and 2000. The phase-integrated X-ray emission from this pulsar is poorly described by existing models of neutron star atmospheres. Instead, we confirm that, similar to other middle-aged pulsars, the best-fitting spectral model consists of two blackbody components, with substantially different temperatures and emitting areas, and a nonthermal component characterized by a power law. Our phase-resolved X-ray spectral analysis using this three-component model reveals variations in the thermal emission parameters with the pulsar’s rotational phase. These variations suggest a nonuniform temperature distribution across the neutron star’s surface, including the cold thermal component and probable hot spot(s). Such a temperature distribution can be caused by external and internal heating processes, likely a combination thereof. We observe very high pulse fractions, 60%–80% in the 0.7–1.5 keV range, dominated by the hot blackbody component. This could be related to temperature nonuniformity and potential beaming effects in an atmosphere. We find indication of a second hot spot that appears at lower energies (0.15–0.3 keV) than the first hot spot (0.5–1.5 keV) in the X-ray light curves and is offset by about half a rotation period. This finding aligns with the nearly orthogonal rotator geometry suggested by radio observations of this interpulse pulsar. If the hot spots are associated with polar caps, a possible explanation for their temperature asymmetry could be an offset magnetic dipole and/or an additional toroidal magnetic field component in the neutron star crust.

Detection of pulsed X-ray emission from the isolated neutron star candidate eRASSU J131716.9–402647

The X-ray source eRASSU J131716.9–402647 was recently identified from observations with Spectrum Roentgen Gamma (SRG)/eROSITA as a promising X-ray dim isolated neutron star (XDINS) candidate on the premise of a soft energy distribution, absence of catalogued counterparts, and a high X-ray-to-optical flux ratio. Here, we report the results of a multi-wavelength observational campaign with XMM-Newton, NICER and the FORS2 instrument at the ESO-VLT. We found in both the XMM-Newton and NICER data that the X-ray emission is strongly pulsed at a period of 12.757 s (pulsed fraction pf = (29.1 ± 2.6)% in the 0.2–2 keV band). The pulse profile is double-humped, and the pulsed fraction increases with energy. The XMM-Newton and NICER epochs allow us to derive a 3σ upper limit of Ṗ ≤ 8 × 10−11 s s−1 on the spin-down rate of the neutron star. The source spectrum is well described by a purely thermal continuum, either a blackbody with kT ∼ 95 eV or a magnetised neutron star atmosphere model with kT ∼ 35 eV. Similarly to other thermally emitting isolated neutron stars, we found in either case strong deviations from the continuum, a broad absorption feature at energy ∼260 eV and a narrow one around 590 eV. The FORS2 instrument at ESO-VLT has not detected the optical counterpart (mR > 27.5 mag, 5σ detection limit), implying an X-ray-to-optical flux ratio of 104 at least. The properties of eRASSU J131716.9–402647 strongly resemble those of a highly magnetised isolated neutron star and favour an XDINS or high-B pulsar nature.

X-ray pulsar GRO J1008−57 as an orthogonal rotator

X-ray polarimetry is a unique way to probe the geometrical configuration of highly magnetized accreting neutron stars (X-ray pulsars). GRO J1008−57 is the first transient X-ray pulsar observed at two different flux levels by the Imaging X-ray Polarimetry Explorer (IXPE) during its outburst in November 2022. We find the polarization properties of GRO J1008−57 to be independent of its luminosity, with the polarization degree varying between nondetection and about 15% over the pulse phase. Fitting the phase-resolved spectro-polarimetric data with the rotating vector model allowed us to estimate the pulsar inclination (130°, which is in good agreement with the orbital inclination), the position angle (75°) of the pulsar spin axis, and the magnetic obliquity (∼74°). This makes GRO J1008−57 the first confidently identified nearly orthogonal rotator among X-ray pulsars. We discuss our results in the context of the neutron star atmosphere models and theories of the axis alignment of accreting pulsars.

The Neutron Star Population in M28: A Joint Chandra/GBT Look at Pulsar Paradise

We present the results of a deep study of the neutron star (NS) population in the globular cluster M28 (NGC 6626), using the full 330 ks 2002–2015 ACIS data set from the Chandra X-ray Observatory and coordinated radio observations taken with the Green Bank Telescope (GBT) in 2015. We investigate the X-ray luminosity (L X ), spectrum, and orbital modulation of the seven known compact binary millisecond pulsars in the cluster. We report two simultaneous detections of the redback PSR J1824−2452I (M28I) and its X-ray counterpart at L X = [8.3 ± 0.9] × 1031 erg s−1. We discover a double-peaked X-ray orbital flux modulation in M28I during its pulsar state, centered around pulsar inferior conjunction. We analyze the spectrum of the quiescent NS low-mass X-ray binary to constrain its mass and radius. Using both hydrogen and helium NS atmosphere models, we find an NS radius of R = 9.2–11.5 km and R = 13.0–17.5 km, respectively, for an NS mass of 1.4 M ⊙ (68% confidence ranges). We also search for long-term variability in the 46 brightest X-ray sources and report the discovery of six new variable low-luminosity X-ray sources in M28.

Constraining the properties of dense neutron star cores: the case of the low-mass X-ray binary HETE J1900.1–2455

ABSTRACT Measuring the time evolution of the effective surface temperature of neutron stars can provide invaluable information on the properties of their dense cores. Here, we report on a new Chandra observation of the transient neutron star low-mass X-ray binary HETE J1900.1–2455, which was obtained ≈2.5 yr after the end of its ≈10-yr long accretion outburst. The source is barely detected during the observation, collecting only six net photons, all below 2 keV. Assuming that the spectrum is shaped as a neutron star atmosphere model, we perform a statistical analysis to determine a 1σ confidence upper range for the neutron star temperature of ≈30–39 eV (for an observer at infinity), depending on its mass, radius, and distance. Given the heat injected into the neutron star during the accretion outburst, estimated from data provided by all-sky monitors, the inferred very low temperature suggests that the core either has a very high heat capacity or undergoes very rapid neutrino cooling. While the present data do not allow us to disentangle these two possibilities, both suggest that a significant fraction of the dense core is not superfluid/superconductor. Our modelling of the thermal evolution of the neutron star predicts that it may still cool further, down to a temperature of ≃15 eV. Measuring such a low temperature with a future observation may provide constraints on the fraction of baryons that is paired in the stellar core.

Observations of GRO J1744–28 in quiescence with XMM-Newton

We report on the deep observations of the “bursting pulsar” GRO J1744–28, which were performed with XMM-Newton and aimed to clarify the origin of its X-ray emission in quiescence. We detect the source at a luminosity level of ∼1034 erg s−1 with an X-ray spectrum that is consistent with the power law, blackbody, or accretion-heated neutron star atmosphere models. The improved X-ray localization of the source allowed us to confirm the previously identified candidate optical counterpart as a relatively massive G/K III star at 8 kpc close to the Galactic center, implying an almost face-on view of the binary system. Although we could only find a nonrestricting upper limit on the pulsed fraction of ∼20%, the observed hard X-ray spectrum and strong long-term variability of the X-ray flux suggest that the source is also still accreting when not in outburst. The luminosity corresponding to the onset of centrifugal inhibition of accretion is thus estimated to be at least two orders of magnitude lower than previously reported. We discuss this finding in the context of previous studies and argue that the results indicate a multipole structure in the magnetic field with the first dipole term of ∼1010 G, which is much lower than previously assumed.

Strengthening the bounds on the r-mode amplitude with X-ray observations of millisecond pulsars

ABSTRACT R-mode oscillations have been shown to have a significant potential to constrain the composition of fast spinning neutron stars. Due to their high rotation rates, millisecond pulsars (MSPs) provide a unique platform to constrain the properties of such oscillations, if their surface temperatures can be inferred. We present the results of our investigations of archival X-ray data of a number of MSPs, as well as recent XMM–Newton observations of PSR J1810+1744 and PSR J2241−5236. Using the neutron star atmosphere model and taking into account various uncertainties, we present new bounds on the surface temperature of these sources. Thereby, we significantly strengthen previous bounds on the amplitude of the r-mode oscillations in MSPs and find rigorous values as low as α ≲ 3 × 10−9. This is by now about three orders of magnitude below what standard saturation mechanisms in neutron stars could provide, which requires very strong dissipation in the interior, strongly pointing towards a structurally complex or exotic composition of these sources. At such low temperatures, sources could even be outside of the instability region, and taking into account the various uncertainties, we obtain for an observed surface temperature a simple frequency bound below which r-modes are excluded in slower spinning pulsars.

Observational appearance of rapidly rotating neutron stars

Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity (ν*∼ 200–600 Hz). First, we investigate the effects of rapid rotation on the observational appearance of a NS. We propose analytical formulae relating gravitational mass and equatorial radius of the rapidly rotating NS to the massMand radiusRof a non-rotating NS of the same baryonic mass using accurate fully relativistic computations. We assume that the NS surface emission is described by the Planck function with two different emission patterns: the isotropic intensity and that corresponding to the electron-scattering dominated atmosphere. For these two cases we compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild approximation, where light bending is computed in Schwarzschild metric, but frame dragging and quadrupole moment of a NS are approximately accounted for in the photon redshift calculations. In particular, we determine the solid angle at which a rotating NS is seen by a distant observer, the observed colour temperature and the blackbody normalization. Then, we investigate how rapid rotation affects the results of NS radius determination using the cooling tail method applied to the X-ray burst spectral evolution. We approximate the local spectra from the NS surface by a diluted blackbody with the luminosity-dependent dilution factor using previously computed NS atmosphere models. We then generalize the cooling tail method to the case of a rapidly rotating NS to obtain the most probable values ofMandRof the corresponding non-rotating NS with the same baryonic mass. We show that the NS radius could be overestimated by 3–3.5 km for face-on stars ofR ≈ 11 km rotating atν*= 700 Hz if the version of the cooling tail method for a non-rotating NS is used. We apply the method to an X-ray burst observed from the NS rotating atν* ≈ 532 Hz in SAX J1810.8−2609. The resulting radius of the non-rotating NS (assumingM = 1.5M⊙) becomes 11.8 ± 0.5 km if it is viewed at inclinationi = 60° andR = 11.2 ± 0.5 km for a face-on view, which are smaller by 0.6 and 1.2 km than the radius obtained using standard cooling tail method ignoring rotation. The corresponding equatorial radii of these rapidly rotating NSs are 12.3 ± 0.6 km (fori = 60°) and 11.6 ± 0.6 km (fori = 0°).

XMM–Newton observations of a gamma-ray pulsar J0633+0632: pulsations, cooling and large-scale emission

ABSTRACT We report results of XMM–Newton observations of a γ-ray pulsar J0633+0632 and its wind nebula. We reveal, for the first time, pulsations of the pulsar X-ray emission with a single sinusoidal pulse profile and a pulsed fraction of 23 ± 6 per cent in the 0.3–2 keV band. We confirm previous Chandra findings that the pulsar X-ray spectrum consists of thermal and non-thermal components. However, we do not find the absorption feature that was previously detected at about 0.8 keV. Thanks to the greater sensitivity of XMM–Newton, we get stronger constraints on spectral model parameters compared to previous studies. The thermal component can be equally well described by either blackbody or neutron star atmosphere models, implying that this emission is coming from either hot pulsar polar caps with a temperature of about 120 eV or from the colder bulk of the neutron star surface with a temperature of about 50 eV. In the latter case, the pulsar appears to be one of the coolest among other neutron stars of similar ages with estimated surface temperatures. We discuss cooling scenarios relevant to this neutron star. Using an interstellar absorption–distance relation, we also constrain the distance to the pulsar to the range of 0.7–2 kpc. Besides the pulsar and its compact nebula, we detect regions of weak large-scale diffuse non-thermal emission in the pulsar field and discuss their possible nature.

X-ray spectral analysis of the neutron star in SNR 1E 0102.2−7219

ABSTRACT We re-analysed numerous archival Chandra X-ray observations of the bright supernova remnant (SNR) 1E 0102.2−7219 in the Small Magellanic Cloud, to validate the detection of a neutron star (NS) in the SNR by Vogt et al. Careful attention to the background is necessary in this spectral analysis. We find that a blackbody + power-law model is a decent fit, suggestive of a relatively strong B field and synchrotron radiation, as in a normal young pulsar, though the thermal luminosity would be unusually high for young pulsars. Among realistic NS atmosphere models, a carbon atmosphere with B = 1012 G best fits the observed X-ray spectra. Comparing its unusually high thermal luminosity ($L_{\mathrm{ bol}} = 1.1_{-0.5}^{+1.6}\times 10^{34}$ erg s−1) to other NSs, we find that its luminosity can be explained by decay of an initially strong magnetic field (as in magnetars or high B-field pulsars) or by slower cooling after the supernova explosion. The nature of the NS in this SNR (and of others in the Magellanic Clouds) could be nicely confirmed by an X-ray telescope with angular resolution like Chandra, but superior spectral resolution and effective area, such as the Lynx concept.

Evaluating the evidence of multipolar surface magnetic field in PSR J0108–1431

ABSTRACTPSR J0108–1431 is an old pulsar where the X-ray emission is expected to have a thermal component from the polar cap and a non-thermal component from the magnetosphere. Although the phase-integrated spectra are fit best with a single non-thermal component modelled with a power law (PL) of photon index Γ = 2.9, the X-ray pulse profiles do show the presence of phase-separated thermal and non-thermal components. The spectrum extracted from half the rotational phase away from the X-ray peak fits well with either a single blackbody (BB) or a neutron star atmosphere (NA) model, whereas the spectrum from the rest of the phase range is dominated by a PL. From Bayesian analysis, the estimated BB area is smaller than the expected polar cap area for a dipolar magnetic field with a probability of 86 per cent, whereas the area estimate from the NA model is larger with a probability of 80 per cent. Due to the ambiguity in the thermal emission model, the polar cap area cannot be reliably estimated and hence cannot be used to understand the nature of the surface magnetic field. Instead, we can infer the presence of multipolar magnetic field from the misalignment between the pulsar’s thermal X-ray peak and the radio emission peak. For J0108–1431, we estimated a phase-offset Δϕ > 0.1 between the thermal polar cap emission peak and the radio emission peak and argue that this is best explained by the presence of a multipolar surface magnetic field.

The neutron star mass and radius of Aql X‐1 from quiescent X‐ray emissions

We report the quiescent spectra of neutron star (NS) in Aql X‐1 from XMM‐Newton and Chandra. The NS atmosphere model, NSATMOS, is applied to fit the quiescent spectra. The Monte Carlo Markov Chain algorithm is used to constrain the NS mass and radius in Aql X‐1. We find that the absolute flux calibration between XMM‐Newton and Chandra for Aql X‐1 is in good agreement with each other. The NS mass and radius of Aql X‐1 are obtained.

Possible Phase-dependent Absorption Feature in the X-Ray Spectrum of the Middle-aged PSR J0659+1414

Abstract We report on the energy-resolved timing and phase-resolved spectral analysis of X-ray emission from PSR J0659+1414 observed with XMM-Newton and NuSTAR. We find that the new data rule out the previously suggested model of the phase-dependent spectrum as a three-component (two blackbodies + power law) continuum, which shows large residuals between 0.3 and 0.7 keV. Fitting neutron star atmosphere models or several blackbodies to the spectrum does not provide a better description of the spectrum and requires spectral model components with unrealistically large emission region sizes. The fits improve significantly if we add a phase-dependent absorption feature with central energy 0.5–0.6 keV and equivalent width up to ≈50 eV. We detected the feature for about half of the pulse cycle. Energy-resolved pulse profiles support the description of the spectrum with a three-component continuum and an absorption component. The absorption feature could be interpreted as an electron cyclotron line originating in the pulsar magnetosphere and broadened by the nonuniformity of the magnetic field along the line of sight. The significant phase variability in the thermal emission from the entire stellar surface may indicate multipolar magnetic fields and a nonuniform temperature distribution. The strongly pulsed nonthermal spectral component detected with NuSTAR in the 3–20 keV range is well fit by a power-law model with a photon index Γ = 1.5 ± 0.2.

Accretion heated atmospheres of X-ray bursting neutron stars

Some thermonuclear (type I) X-ray bursts at the neutron star surfaces in low-mass X-ray binaries take place during hard persistent states of the systems. Spectral evolution of these bursts is well described by the atmosphere model of a passively cooling neutron star when the burst luminosity is high enough. The observed spectral evolution deviates from the model predictions when the burst luminosity drops below a critical value of 20–70% of the maximum luminosity. The amplitude of the deviations and the critical luminosity correlate with the persistent luminosity, which leads us to suggest that these deviations are induced by the additional heating of the accreted particles. We present a method for computation of the neutron star atmosphere models heated by accreted particles assuming that their energy is released via Coulomb interactions with electrons. We computed the temperature structures and the emergent spectra of the atmospheres of various chemical compositions and investigate the dependence of the results on the velocity of accreted particles, their temperature and the penetration angle. We show that the heated atmosphere develops two different regions. The upper one is the hot (20–100 keV) corona-like surface layer cooled by Compton scattering, and the deeper, almost isothermal optically thick region with a temperature of a few keV. The emergent spectra correspondingly have two components: a blackbody with the temperature close to that of the isothermal region and a hard Comptonized component (a power law with an exponential decay). Their relative contribution depends on the ratio of the energy dissipation rate of the accreted particles to the intrinsic flux from the neutron star surface. These spectra deviate strongly from those of undisturbed, passively cooling neutron star atmospheres, with the main differences being the presence of a high-energy tail and a strong excess in the low-energy part of the spectrum. They also lack the iron absorption edge, which is visible in the spectra of undisturbed low-luminosity atmospheres with solar chemical composition. Using the computed spectra, we obtained the dependences of the dilution and color-correction factors as functions of relative luminosities for pure helium and solar abundance atmospheres. We show that the helium model atmosphere heated by accretion corresponding to 5% of the Eddington luminosity describes well the late stages of the X-ray bursts in 4U 1820−30.

Broad-band high-energy emissions of the redback millisecond pulsar PSR J2129–0429

We present the first results from a joint XMM-Newton and NuSTAR observation of the gamma-ray emitting millisecond pulsar compact binary PSR J2129-0429. X-ray emission up to about 40 keV is detected and the joint spectrum can be modeled with a power-law plus a neutron star atmosphere model. At a distance of 1.4 kpc, the 0.3-79 keV luminosity is $3.56\times10^{32}$ erg s$^{-1}$. We also detected the 0.64-day binary orbital period with a double-peaked structure across the wavebands. By combining the updated Fermi GeV data, we modeled the broadband spectral energy distribution as well as the X-ray modulation with an intrabinary model involving shock interaction between pulsar wind and outflow from the companion star. Lastly, we reported a high-resolution X-ray image provided by Chandra to rule out the proposed pulsar wind nebula associated with PSR J2129-0429.

The quiescent state of the neutron-star X-ray transient GRS 1747−312 in the globular cluster Terzan 6

We studied the transient neutron-star low-mass X-ray binary GRS 1747−312, located in the globular cluster Terzan 6, in its quiescent state after its outburst in August 2004, using an archival XMM–Newton observation. A source was detected in this cluster and its X-ray spectrum can be fitted with the combination of a soft, neutron-star atmosphere model and a hard, power-law model. Both contributed roughly equally to the observed 0.5–10 keV luminosity (∼4.8 × 1033 erg s−1). This type of X-ray spectrum is typically observed for quiescent neutron-star X-ray transients that are perhaps accreting in quiescence at very low rates. Therefore, if this X-ray source is the quiescent counterpart of GRS 1747−312, then this source is also accreting at low levels in-between outbursts. Since source confusion is a likely problem in globular clusters, it is quite possible that part, if not all, of the emission we observed is not related to GRS 1747−312, and is instead associated with another source or conglomeration of sources in the cluster. Currently, it is not possible to determine exactly which part of the emission truly originates from GRS 1747−312, and a Chandra observation (when no source is in outburst in Terzan 6) is needed to be conclusive. Assuming that the detected emission is due to GRS 1747−312, we discuss the observed results in the context of what is known about other quiescent systems. We also investigated the thermal evolution of the neutron star in GRS 1747−312, and inferred that GRS 1747−312 can be considered a typical quiescent system under our assumptions.

Further constraints on neutron star crustal properties in the low-mass X-ray binary 1RXS J180408.9−342058

We report on two new quiescent {\it XMM-Newton} observations (in addition to the earlier {\it Swift}/XRT and {\it XMM-Newton} coverage) of the cooling neutron star crust in the low-mass X-ray binary 1RXS J180408.9$-$342058. Its crust was heated during the $\sim$4.5 month accretion outburst of the source. From our quiescent observations, fitting the spectra with a neutron star atmosphere model, we found that the crust had cooled from $\sim$ 100 eV to $\sim$73 eV from $\sim$8 days to $\sim$479 days after the end of its outburst. However, during the most recent observation, taken $\sim$860 days after the end of the outburst, we found that the crust appeared not to have cooled further. This suggested that the crust had returned to thermal equilibrium with the neutron star core. We model the quiescent thermal evolution with the theoretical crustal cooling code NSCool and find that the source requires a shallow heat source, in addition to the standard deep crustal heating processes, contributing $\sim$0.9 MeV per accreted nucleon during outburst to explain its observed temperature decay. Our high quality {\it XMM-Newton} data required an additional hard component to adequately fit the spectra. This slightly complicates our interpretation of the quiescent data of 1RXS J180408.9$-$342058. The origin of this component is not fully understood.

XMM-Newton observations of the γ-ray pulsar J0633+0632

We briefly report the results of XMM-Newton X-ray observations of the γ-ray pulsar J0633+0632. We detected, for the first time, X-ray pulsations from J0633+0632 with the pulsar period. The pulse profile is typical for spin-modulated thermal emission from the surface of a neutron star. The pulsed fraction in the 0.3–2 keV band is 23 ± 6%. We confirmed previous results that the X-ray spectrum of J0633+0632 contains a non-thermal power law and a thermal (described either by the blackbody or the neutron star atmosphere models) components. However, XMM-Newton observations do not confirm the absorption line in the pulsar spectrum at ≈ 0.8 keV found in the Chandra data (Danilenko et al 2015 PASA 32 e038).Using the interstellar absorption–distance relations, we constrained the distance to the pulsar in the range of 0.7–2.2 kpc.

Neutron star mass and radius measurements from atmospheric model fits to X-ray burst cooling tail spectra

Observations of thermonuclear X-ray bursts from accreting neutron stars (NSs) in low-mass X-ray binary systems can be used to constrain NS masses and radii. Most previous work of this type has set these constraints using Planck function fits as a proxy: both the models and the data are fit with diluted blackbody functions to yield normalizations and temperatures which are then compared against each other. Here, for the first time, we fit atmosphere models of X-ray bursting NSs directly to the observed spectra. We present a hierarchical Bayesian fitting framework that uses state-of-the-art X-ray bursting NS atmosphere models with realistic opacities and relativistic exact Compton scattering kernels as a model for the surface emission. We test our approach against synthetic data, and find that for data that are well-described by our model we can obtain robust radius, mass, distance, and composition measurements. We then apply our technique to Rossi X-ray Timing Explorer observations of five hard-state X-ray bursts from 4U 1702-429. Our joint fit to all five bursts shows that the theoretical atmosphere models describe the data well but there are still some unmodeled features in the spectrum corresponding to a relative error of 1-5% of the energy flux. After marginalizing over this intrinsic scatter, we find that at 68% credibility the circumferential radius of the NS in 4U 1702-429 is R = 12.4+-0.4 km, the gravitational mass is M=1.9+-0.3 Msun, the distance is 5.1 < D/kpc < 6.2, and the hydrogen mass fraction is X < 0.09.