Bayesian parameter constraints for neutron star masses and radii using X-ray timing observations of accretion-powered millisecond pulsars

We present a Bayesian method to constrain the masses and radii of neutron stars (NSs) using the information encoded in the X-ray pulse profiles of accreting millisecond pulsars. We model the shape of the pulses using “oblate Schwarzschild” approximation, which takes into account the deformed shape of the star together with the special and general relativistic corrections to the photon trajectories and angles. The spectrum of the radiation is obtained from an empirical model of Comptonization in a hot slab in which a fraction of seed black-body photons is scattered into a power-law component. By using an affine-invariant Markov chain Monte Carlo ensemble sampling method, we obtain posterior probability distributions for the different model parameters, especially for the mass and the radius. To test the robustness of our method, we first analysed self-generated synthetic data with known model parameters. Similar analysis was then applied for the observations of SAX J1808.4−3658 by the Rossi X-ray Timing Explorer (RXTE). The results show that our method can reproduce the model parameters of the synthetic data, and that accurate constraints for the radius can be obtained using the RXTE pulse profile observations if the mass is a priori known. For a mass in the range 1.5–1.8 M⊙, the radius of the NS in SAX J1808.4−3658 is constrained between 9 and 13 km. If the mass is accurately known, the radius can be determined with an accuracy of 5% (68% credibility). For example, for the mass of 1.7 M⊙ the equatorial radius is Req = 11.9+0.5−0.4 km. Finally, we show that further improvements can be obtained when the X-ray polarization data from the Imaging X-ray Polarimeter Explorer will become available.

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refnx: neutron and X-ray reflectometry analysis in Python

Journal of Applied Crystallography ◽

10.1107/s1600576718017296 ◽

2019 ◽

Vol 52 (1) ◽

pp. 193-200 ◽

Cited By ~ 16

Author(s):

Andrew R. J. Nelson ◽

Stuart W. Prescott

Keyword(s):

Bayesian Approach ◽

Volume Fraction ◽

Scattering Length ◽

Distribution Functions ◽

Monte Carlo Algorithm ◽

Reproducible Research ◽

Model Parameters ◽

X Ray ◽

Multiple Data Sets ◽

Parameter Constraints

refnx is a model-based neutron and X-ray reflectometry data analysis package written in Python. It is cross platform and has been tested on Linux, macOS and Windows. Its graphical user interface is browser based, through a Jupyter notebook. Model construction is modular, being composed from a series of components that each describe a subset of the interface, parameterized in terms of physically relevant parameters (volume fraction of a polymer, lipid area per molecule etc.). The model and data are used to create an objective, which is used to calculate the residuals, log-likelihood and log-prior probabilities of the system. Objectives are combined to perform co-refinement of multiple data sets and mixed-area models. Prior knowledge of parameter values is encoded as probability distribution functions or bounds on all parameters in the system. Additional prior probability terms can be defined for sets of components, over and above those available from the parameters alone. Algebraic parameter constraints are available. The software offers a choice of fitting approaches, including least-squares (global and gradient-based optimizers) and a Bayesian approach using a Markov-chain Monte Carlo algorithm to investigate the posterior distribution of the model parameters. The Bayesian approach is useful for examining parameter covariances, model selection and variability in the resulting scattering length density profiles. The package is designed to facilitate reproducible research; its use in Jupyter notebooks, and subsequent distribution of those notebooks as supporting information, permits straightforward reproduction of analyses.

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The confrontation of the shock-powered synchrotron maser model with the Galactic FRB 200428

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3374 ◽

2020 ◽

Vol 500 (2) ◽

pp. 2704-2710 ◽

Cited By ~ 2

Author(s):

Yun-Wei Yu ◽

Yuan-Chuan Zou ◽

Zi-Gao Dai ◽

Wen-Fei Yu

Keyword(s):

Line Of Sight ◽

Model Parameters ◽

Observational Constraints ◽

Synchrotron Emission ◽

Physical Processes ◽

X Ray ◽

Emission Efficiency ◽

Free Parameters ◽

Fast Radio Burst ◽

Parameter Constraints

ABSTRACT The association of FRB 200428 with an X-ray burst (XRB) from the Galactic magnetar SGR 1935+2154 offers important implications for the physical processes responsible for the fast radio burst (FRB) phenomena. By assuming that the XRB emission is produced in the magnetosphere, we investigate the possibility that the FRB emission is produced by shock-powered synchrotron maser (SM), which is phenomenologically described with a number of free parameters. The observational constraints on the model parameters indicate that the model can in principle be consistent with the FRB 200428 observations, if the ejecta lunched by magnetar activities can have appropriate ingredients and structures and the shock processes occur on the line of sight. To be specific, a complete burst ejecta should consist of an ultra-relativistic and extremely highly collimated e± component and a sub-relativistic and wide-spreading baryonic component. The internal shocks producing the FRB emission arise from a collision between the e± ejecta and the remnant of a previous baryonic ejecta at the same direction. The parameter constraints depend on the uncertain spectrum and efficiency of the SM emission. While the spectrum is tentatively described by a spectral index of −2, we estimate the emission efficiency to be around 10−4 by requiring that the synchrotron emission of the shocked material cannot be much brighter than the magnetosphere XRB emission.

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Thermal X-ray emission identified from the millisecond pulsar PSR J1909–3744

Astronomy and Astrophysics ◽

10.1051/0004-6361/201732040 ◽

2019 ◽

Vol 627 ◽

pp. A141 ◽

Cited By ~ 2

Author(s):

N. A. Webb ◽

D. Leahy ◽

S. Guillot ◽

N. Baillot d’Etivaux ◽

D. Barret ◽

...

Keyword(s):

Neutron Star ◽

Equation Of State ◽

Thermal Emission ◽

Black Body ◽

Millisecond Pulsar ◽

Distance Measurements ◽

Millisecond Pulsars ◽

X Ray ◽

Link Type

Context. Pulsating thermal X-ray emission from millisecond pulsars can be used to obtain constraints on the neutron star equation of state, but to date only five such sources have been identified. Of these five millisecond pulsars, only two have well-constrained neutron star masses, which improve the determination of the radius via modelling of the X-ray waveform. Aims. We aim to find other millisecond pulsars that already have well-constrained mass and distance measurements that show pulsed thermal X-ray emission in order to obtain tight constraints on the neutron star equation of state. Methods. The millisecond pulsar PSR J1909–3744 has an accurately determined mass, M = 1.54 ± 0.03 M⊙ (1σ error) and distance, D = 1.07 ± 0.04 kpc. We analysed XMM-Newton data of this 2.95 ms pulsar to identify the nature of the X-ray emission. Results. We show that the X-ray emission from PSR J1909–3744 appears to be dominated by thermal emission from the polar cap. Only a single component model is required to fit the data. The black-body temperature of this emission is $ {kT}=0.26^{0.03}_{0.02} $ keV and we find a 0.2–10 keV un-absorbed flux of 1.1 × 10−14 erg cm−2 s−1 or an un-absorbed luminosity of 1.5 × 1030 erg s−1. Conclusion. Thanks to the previously determined mass and distance constraints of the neutron star PSR J1909–3744, and its predominantly thermal emission, deep observations of this object with future X-ray facilities should provide useful constraints on the neutron star equation of state.

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Using quasar X-ray and UV flux measurements to constrain cosmological model parameters

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1855 ◽

2020 ◽

Vol 497 (1) ◽

pp. 263-278 ◽

Cited By ~ 3

Author(s):

Narayan Khadka ◽

Bharat Ratra

Keyword(s):

Cosmological Parameters ◽

Hubble Constant ◽

Acoustic Oscillation ◽

Joint Analysis ◽

Model Parameters ◽

Density Parameter ◽

Current Standard ◽

X Ray ◽

Flux Measurements ◽

Parameter Constraints

ABSTRACT Risaliti and Lusso have compiled X-ray and UV flux measurements of 1598 quasars (QSOs) in the redshift range 0.036 ≤ z ≤ 5.1003, part of which, z ∼ 2.4 − 5.1, is largely cosmologically unprobed. In this paper we use these QSO measurements, alone and in conjunction with baryon acoustic oscillation (BAO) and Hubble parameter [H(z)] measurements, to constrain cosmological parameters in six different cosmological models, each with two different Hubble constant priors. In most of these models, given the larger uncertainties, the QSO cosmological parameter constraints are mostly consistent with those from the BAO + H(z) data. A somewhat significant exception is the non-relativistic matter density parameter Ωm0 where QSO data favour Ωm0 ∼ 0.5 − 0.6 in most models. As a result, in joint analyses of QSO data with H(z) + BAO data the 1D Ωm0 distributions shift slightly towards larger values. A joint analysis of the QSO + BAO + H(z) data is consistent with the current standard model, spatially-flat ΛCDM, but mildly favours closed spatial hypersurfaces and dynamical dark energy. Since the higher Ωm0 values favoured by QSO data appear to be associated with the z ∼ 2 − 5 part of these data, and conflict somewhat with strong indications for Ωm0 ∼ 0.3 from most z < 2.5 data as well as from the cosmic microwave background anisotropy data at z ∼ 1100, in most models, the larger QSO data Ωm0 is possibly more indicative of an issue with the z ∼ 2 − 5 QSO data than of an inadequacy of the standard flat ΛCDM model.

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Structural inversion of gravity data using linear programming

Geophysics ◽

10.1190/1.2197491 ◽

2006 ◽

Vol 71 (3) ◽

pp. J41-J50 ◽

Cited By ~ 11

Author(s):

Tim van Zon ◽

Kabir Roy-Chowdhury

Keyword(s):

Linear Programming ◽

Gravity Data ◽

A Priori ◽

Synthetic Data ◽

Uniform Grid ◽

Model Parameters ◽

Data Set ◽

Test Models ◽

Structural Inversion ◽

Value Decomposition

Structural inversion of gravity data — deriving robust images of the subsurface by delineating lithotype boundaries using density anomalies — is an important goal in a range of exploration settings (e.g., ore bodies, salt flanks). Application of conventional inversion techniques in such cases, using [Formula: see text]-norms and regularization, produces smooth results and is thus suboptimal. We investigate an [Formula: see text]-norm-based approach which yields structural images without the need for explicit regularization. The density distribution of the subsurface is modeled with a uniform grid of cells. The density of each cell is inverted by minimizing the [Formula: see text]-norm of the data misfit using linear programming (LP) while satisfying a priori density constraints. The estimate of the noise level in a given data set is used to qualitatively determine an appropriate parameterization. The 2.5D and 3D synthetic tests adequately reconstruct the structure of the test models. The quality of the inversion depends upon a good prior estimation of the minimum depth of the anomalous body. A comparison of our results with one using truncated singular value decomposition (TSVD) on a noisy synthetic data set favors the LP-based method. There are two advantages in using LP for structural inversion of gravity data. First, it offers a natural way to incorporate a priori information regarding the model parameters. Second, it produces subsurface images with sharp boundaries (structure).

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Searching for X-ray Pulsations from Neutron Stars Using NICER

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317008237 ◽

2017 ◽

Vol 13 (S337) ◽

pp. 187-190 ◽

Cited By ~ 5

Author(s):

Paul S. Ray ◽

Zaven Arzoumanian ◽

Keith C. Gendreau ◽

Keyword(s):

Neutron Star ◽

Neutron Stars ◽

Compact Objects ◽

Large Area ◽

Pulse Profile ◽

Millisecond Pulsars ◽

X Ray ◽

Event Time ◽

Time Stamps ◽

Central Compact Objects

AbstractThe Neutron Star Interior Composition Explorer (NICER) presents an exciting new capability for exploring the modulation properties of X-ray emitting neutron stars, including large area, low background, extremely precise absolute event time stamps, superb low-energy response and flexible scheduling. The Pulsation Searches and Multiwavelength Coordination working group has designed a 2.5 Ms observing program to search for emission and characterize the modulation properties of about 30 known or suspected neutron star sources across a number of source categories. A key early goal will be to search for pulsations from millisecond pulsars that might exhibit thermal pulsations from the surface suitable for pulse profile modeling to constrain the neutron star equation of state. In addition, we will search for pulsations from transitional millisecond pulsars, isolated neutron stars, low-mass X-ray binaries (LMXBs), accretion-powered millisecond pulsars, central compact objects and other sources. We present our science plan and initial results from the first months of the NICER mission, including the discovery of pulsations from the millisecond pulsar J1231–1411.

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

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa287 ◽

2020 ◽

Vol 493 (2) ◽

pp. 1874-1887 ◽

Cited By ~ 1

Author(s):

A Danilenko ◽

A Karpova ◽

D Ofengeim ◽

Yu Shibanov ◽

D Zyuzin

Keyword(s):

Neutron Star ◽

Large Scale ◽

Gamma Ray ◽

Thermal Emission ◽

Absorption Feature ◽

Model Parameters ◽

Pulse Profile ◽

X Ray ◽

Polar Caps ◽

Star Surface

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.

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Spectral analysis of SXP59.0 during its 2017 outburst and properties of the soft excess in X-ray binary pulsars

Astronomy and Astrophysics ◽

10.1051/0004-6361/201833907 ◽

2018 ◽

Vol 619 ◽

pp. A126 ◽

Cited By ~ 1

Author(s):

N. La Palombara ◽

P. Esposito ◽

F. Pintore ◽

L. Sidoli ◽

S. Mereghetti ◽

...

Keyword(s):

Spectral Analysis ◽

Black Body ◽

Emission Lines ◽

Plasma Component ◽

Pulse Profile ◽

X Ray ◽

Photon Index ◽

Body Component ◽

Energy Dependent ◽

Narrow Emission

We report the results provided by the XMM-Newton observation of the X-ray binary pulsar SXP59.0 during its most recent outburst in April 2017. The source was detected at fX(0.2–12 keV) = 8 × 10−11erg cm−2 s−1, one of its highest flux levels reported to date. The measured pulse period was Pspin = 58.949(1) s, very similar to the periods measured in most of the previous observations. The pulsed emission was clearly detected over the whole energy range between 0.2 and 12 keV, but the pulse profile is energy dependent and the pulsed fraction increases as the energy increases. Although the time-averaged EPIC spectrum is dominated by a power-law component (with photon index Γ = 0.76 ± 0.01), the data show an evident soft excess, which can be described with the sum of a black-body and a hot thermal plasma component (with temperatures kTBB = 171+11−14 eV and kTAPEC = 1.09+0.16−0.09 keV, respectively). Moreover, the EPIC and RGS spectra show narrow emission lines due to N, O, Ne, Mg, and Fe. The phase-resolved spectral analysis of the EPIC data shows that the flux of the black-body component varies with the pulse phase, while the plasma component is almost constant. We show that the black-body component can be attributed to the reprocessing of the primary emission by the optically thick material at the inner edge of the accretion disc, while the hot plasma component is due to a diffuse gas far from the accretion region and the narrow emission lines of the RGS spectrum are most probably due to photoionized matter around the accreting source.

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Relativistic rotating vector model for X-ray millisecond pulsars

Astronomy and Astrophysics ◽

10.1051/0004-6361/202038689 ◽

2020 ◽

Vol 641 ◽

pp. A166

Author(s):

Juri Poutanen

Keyword(s):

Neutron Star ◽

Rotation Angle ◽

Vector Model ◽

Emission Region ◽

Pulse Profile ◽

Phase Dependence ◽

Millisecond Pulsars ◽

X Ray ◽

Neutron Star Mass ◽

Neutron Star Radius

The X-ray radiation produced on the surface of accreting magnetised neutron stars is expected to be strongly polarised. A swing of the polarisation vector with the pulsar phase gives a direct measure of the source inclination and magnetic obliquity. In the case of rapidly rotating millisecond pulsars, the relativistic motion of the emission region causes additional rotation of the polarisation plane. Here, we develop a relativistic rotating vector model, where we derive analytical expression for the polarisation angle as a function of the pulsar phase accounting for relativistic aberration and gravitational light bending in the Schwarzschild metric. We show that in the case of fast pulsars the rotation of the polarisation plane can reach tens of degrees, strongly influencing the observed shape of the polarisation angle’s phase dependence. The rotation angle grows nearly linearly with the spin rate but it is less sensitive to the neutron star radius. Overall, this angle is large even for large spots. Our results have implications with regard to the modelling of X-ray polarisation from accreting millisecond pulsars that are to be observed with the upcoming Imaging X-ray Polarimeter Explorer and the enhanced X-ray Timing and Polarimetry mission. The X-ray polarisation may improve constraints on the neutron star mass and radius coming from the pulse profile modelling.

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Mass outflow of the X-ray emission line gas in NGC 4151

Proceedings of the International Astronomical Union ◽

10.1017/s1743921320001660 ◽

2020 ◽

Vol 15 (S359) ◽

pp. 131-135

Author(s):

S. B. Kraemer ◽

T. J. Turner ◽

D. M. Crenshaw ◽

H. R. Schmitt ◽

M. Revalski ◽

...

Keyword(s):

Emission Line ◽

Total Mass ◽

High Energy ◽

Model Parameters ◽

Zeroth Order ◽

Space Telescope ◽

X Ray ◽

Ngc 4151 ◽

Outflow Rate ◽

Mass Outflow

AbstractWe have analyzed Chandra/High Energy Transmission Grating spectra of the X-ray emission line gas in the Seyfert galaxy NGC 4151. The zeroth-order spectral images show extended H- and He-like O and Ne, up to a distance r ˜ 200 pc from the nucleus. Using the 1st-order spectra, we measure an average line velocity ˜230 km s–1, suggesting significant outflow of X-ray gas. We generated Cloudy photoionization models to fit the 1st-order spectra; the fit required three distinct emission-line components. To estimate the total mass of ionized gas (M) and the mass outflow rates, we applied the model parameters to fit the zeroth-order emission-line profiles of Ne IX and Ne X. We determined an M ≍ 5.4 × 105Mʘ. Assuming the same kinematic profile as that for the [O III] gas, derived from our analysis of Hubble Space Telescope/Space Telescope Imaging Spectrograph spectra, the peak X-ray mass outflow rate is approximately 1.8 Mʘ yr–1, at r ˜ 150 pc. The total mass and mass outflow rates are similar to those determined using [O III], implying that the X-ray gas is a major outflow component. However, unlike the optical outflows, the X-ray emitting mass outflow rate does not drop off at r > 100pc, which suggests that it may have a greater impact on the host galaxy.

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