arXiv subjects

Tuomo Salmi

Publications and source records attributed to Tuomo Salmi.

At least 37 records · Page 2Linked to original sources

arXiv2025

Modelling polarized X-ray pulses from accreting millisecond pulsars with X-PSI, using different hot spot locations and shapes

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.

astro-ph.HE↗

arXiv2025

Scaling relations for the uncertainty in neutron star radius inferred from pulse profile modelling: the effect of spin rate

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 $1.6\,M_{\mathrm{\odot}}$ 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 $\sim 200$ 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.

astro-ph.HE↗

arXiv2024

Discovery of Polarized X-Ray Emission from the Accreting Millisecond Pulsar SRGA J144459.2-604207

We report on the discovery of polarized X-ray emission from an accreting millisecond pulsar. During a 10-day-long coverage of the February 2024 outburst of SRGA J144459.2-604207, the Imaging X-ray Polarimetry Explorer (IXPE) detected an average polarization degree of the 2-8 keV emission of 2.3% +/- 0.4% at an angle of 59° +/- 6° (East of North; uncertainties quoted at the 1$σ$ confidence level). The polarized signal shows a significant energy dependence with a degree of 4.0% +/- 0.5% between 3 and 6 keV and < 1.5% (90% c.l.) in the 2-3 keV range. We used NICER, XMM-Newton, and NuSTAR observations to obtain an accurate pulse timing solution and perform a phase-resolved polarimetric analysis of IXPE data. We did not detect any significant variability of the Stokes parameters Q and U with the spin and the orbital phases. We used the relativistic rotating vector model to show that a moderately fan-beam emission from two point-like spots at a small magnetic obliquity ($\simeq$ 10°) is compatible with the observed pulse profile and polarization properties. IXPE also detected 52 type-I X-ray bursts, with a recurrence time $Δt_{rec}$ increasing from 2 to 8 h as a function of the observed count rate $C$ as as $Δt_{rec} \simeq C^{-0.8}$ We stacked the emission observed during all the bursts and obtained an upper limit on the polarization degree of 8.5% (90% c.l.).

astro-ph.HE↗

arXiv2024

A NICER View of PSR J1231$-$1411: A Complex Case

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 $12.6 \pm 0.3$ km and the mass to be $1.04_{-0.03}^{+0.05}$ $M_\odot$, 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 $R_{\mathrm{eq}} = 13.5_{-0.5}^{+0.3}$ 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.

astro-ph.HE↗

arXiv2024

Exploring Waveform Variations among Neutron Star Ray-tracing Codes for Complex Emission Geometries

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.

astro-ph.HE↗

arXiv2024

The Radius of the High-mass Pulsar PSR J0740+6620 with 3.6 yr of NICER Data

We report an updated analysis of the radius, mass, and heated surface regions of the massive pulsar PSR J0740+6620 using Neutron Star Interior Composition Explorer (NICER) data from 2018 September 21 to 2022 April 21, a substantial increase in data set size compared to previous analyses. Using a tight mass prior from radio timing measurements and jointly modeling the new NICER data with XMM-Newton data, the inferred equatorial radius and gravitational mass are $12.49_{-0.88}^{+1.28}$ km and $2.073_{-0.069}^{+0.069}$ $M_\odot$ respectively, each reported as the posterior credible interval bounded by the $16\,\%$ and $84\,\%$ quantiles, with an estimated systematic error $\lesssim 0.1$ km. This result was obtained using the best computationally feasible sampler settings providing a strong radius lower limit but a slightly more uncertain radius upper limit. The inferred radius interval is also close to the $R=12.76_{-1.02}^{+1.49}$ km obtained by Dittmann et al., when they require the radius to be less than $16$ km as we do. The results continue to disfavor very soft equations of state for dense matter, with $R<11.15$ km for this high-mass pulsar excluded at the $95\,\%$ probability. The results do not depend significantly on the assumed cross-calibration uncertainty between NICER and XMM-Newton. Using simulated data that resemble the actual observations, we also show that our pipeline is capable of recovering parameters for the inferred models reported in this paper.

astro-ph.HE↗

arXiv2024

Constraining the Properties of the Thermonuclear Burst Oscillation Source XTE J1814-338 Through Pulse Profile Modelling

Pulse profile modelling (PPM) is a comprehensive relativistic ray-tracing technique employed to determine the properties of neutron stars. In this study, we apply this technique to the Type I X-ray burster and accretion-powered millisecond pulsar XTE J1814-338, extracting its fundamental properties using PPM of its thermonuclear burst oscillations. Using data from its 2003 outburst, and a single uniform temperature hot spot model, we infer XTE J1814-338 to be located at a distance of $7.2^{+0.3}_{-0.4}$ kpc, with a mass of $1.21^{+0.05}_{-0.05}$ M$_\odot$ and an equatorial radius of $7.0^{+0.4}_{-0.4}$ km. Our results also offer insight into the time evolution of the hot spot but point to some potential shortcomings of the single uniform temperature hot spot model. We explore the implications of this result, including what we can learn about thermonuclear burst oscillation mechanisms and the importance of modelling the accretion contribution to the emission during the burst.

astro-ph.HE↗

arXiv2024

Constraining the dense matter equation of state with new NICER mass-radius measurements and new chiral effective field theory inputs

Pulse profile modeling of X-ray data from NICER is now enabling precision inference of neutron star mass and radius. Combined with nuclear physics constraints from chiral effective field theory ($χ$EFT), and masses and tidal deformabilities inferred from gravitational wave detections of binary neutron star mergers, this has lead to a steady improvement in our understanding of the dense matter equation of state (EOS). Here we consider the impact of several new results: the radius measurement for the 1.42$\,M_\odot$ pulsar PSR J0437$-$4715 presented by Choudhury et al. (2024), updates to the masses and radii of PSR J0740$+$6620 and PSR J0030$+$0451, and new $χ$EFT results for neutron star matter up to 1.5 times nuclear saturation density. Using two different high-density EOS extensions -- a piecewise-polytropic (PP) model and a model based on the speed of sound in a neutron star (CS) -- we find the radius of a 1.4$\,M_\odot$ (2.0$\,M_\odot$) neutron star to be constrained to the 95% credible ranges $12.28^{+0.50}_{-0.76}\,$km ($12.33^{+0.70}_{-1.34}\,$km) for the PP model and $12.01^{+0.56}_{-0.75}\,$km ($11.55^{+0.94}_{-1.09}\,$km) for the CS model. The maximum neutron star mass is predicted to be $2.15^{+0.14}_{-0.16}\,$$M_\odot$ and $2.08^{+0.28}_{-0.16}\,$$M_\odot$ for the PP and CS model, respectively. We explore the sensitivity of our results to different orders and different densities up to which $χ$EFT is used, and show how the astrophysical observations provide constraints for the pressure at intermediate densities. Moreover, we investigate the difference $R_{2.0} - R_{1.4}$ of the radius of 2$\,M_\odot$ and 1.4$\,M_\odot$ neutron stars within our EOS inference.

astro-ph.HE↗

arXiv2024

Discovery of a strong rotation of the X-ray polarization angle in the galactic burster GX 13+1

Weakly magnetized neutron stars in X-ray binaries show complex phenomenology with several spectral components that can be associated with the accretion disk, boundary and/or spreading layer, a corona, and a wind. Spectroscopic information alone is, however, not enough to disentangle these components. Additional information about the nature of the spectral components and in particular the geometry of the emission region can be provided by X-ray polarimetry. One of the objects of the class, a bright, persistent, and rather peculiar galactic Type I X-ray burster was observed with the Imaging X-ray Polarimetry Explorer (IXPE) and the X-ray Multi-Mirror Mission Newton (XMM-Newton). Using the XMM-Newton data we estimated the current state of the source as well as detected strong absorption lines associated with the accretion disk wind. IXPE data showed the source to be significantly polarized in the 2-8 keV energy band with the overall polarization degree (PD) of 1.4% at a polarization angle (PA) of -2 degrees (errors at 68% confidence level). During the two-day long observation, we detected rotation of the PA by about 70 degrees with the corresponding changes in the PD from 2% to non-detectable and then up to 5%. These variations in polarization properties are not accompanied by visible changes in spectroscopic characteristics. The energy-resolved polarimetric analysis showed a significant change in polarization, from being strongly dependent on energy at the beginning of the observation to being almost constant with energy in the later parts of the observation. As a possible interpretation, we suggest the presence of a constant component of polarization, strong wind scattering, or different polarization of the two main spectral components with individually peculiar behavior. The rotation of the PA suggests a 30-degree misalignment of the neutron star spin from the orbital axis.

astro-ph.HE↗

arXiv2024

A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437$\unicode{x2013}$4715

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 J0437$\unicode{x2013}$4715. 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 $M = 1.418 \pm 0.037$ M$_\odot$ (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% and 84% quantiles. This radius 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.

astro-ph.HE↗

arXiv2023

Effects of scattering in the accretion funnel on the pulse profiles of accreting millisecond pulsars

The hotspot emission of accreting millisecond pulsars (AMPs) undergoes scattering in the accretion flow between the disk inner radius and the neutron star surface. The scattering optical depth of the flow depends on the photon emission angle, which is a function of the pulse phase, and reaches its maximum when the hotspot is closest to the observer. At sufficiently large optical depths the observed pulse profile should develop a secondary minimum, the depth of which depends on the accretion rate and the emission geometry. Such a dip evolving with the accretion rate might explain the phase shift and pulse profile evolution observed in AMPs during outbursts. Accounting for scattering is important for accurate modeling of the AMP pulse profiles in order to improve the accuracy of determination of the neutron star parameters, such as their masses and radii. In this paper we present a simplified analytical model for the Thomson optical depth of the accretion funnel, and apply it to simulating the pulse profiles. We show that scattering in the accretion funnel has a significant effect on the pulse profiles at accretion rates of $\dot{M} \gtrsim 10^{-10}~{M}_\odot\, \mathrm{yr}^{-1}$. Our model predicts a gradual evolution of the pulse profile with the accretion rate that appears to be consistent with the observations.

astro-ph.HE↗

arXiv2023

Pulse Profile Modelling of Thermonuclear Burst Oscillations II: Handling variability

Pulse profile modelling is a relativistic ray-tracing technique that can be used to infer masses, radii and geometric parameters of neutron stars. In a previous study, we looked at the performance of this technique when applied to thermonuclear burst oscillations from accreting neutron stars. That study showed that ignoring the variability associated with burst oscillation sources resulted in significant biases in the inferred mass and radius, particularly for the high count rates that are nominally required to obtain meaningful constraints. In this follow-on study, we show that the bias can be mitigated by slicing the bursts into shorter segments where variability can be neglected, and jointly fitting the segments. Using this approach, the systematic uncertainties on the mass and radius are brought within the range of the statistical uncertainty. With about 10$^6$ source counts, this yields uncertainties of approximately 10% for both the mass and radius. However, this modelling strategy requires substantial computational resources. We also confirm that the posterior distributions of the mass and radius obtained from multiple bursts of the same source can be merged to produce outcomes comparable to that of a single burst with an equivalent total number of counts.

astro-ph.HE↗

arXiv2023

Atmospheric Effects on Neutron Star Parameter Constraints with NICER

We present an analysis of the effects of uncertainties in the atmosphere models on the radius, mass, and other neutron star parameter constraints for the NICER observations of rotation-powered millisecond pulsars. To date, NICER has applied the X-ray pulse profile modeling technique to two millisecond-period pulsars: PSR J0030+0451 and the high-mass pulsar PSR J0740+6620. These studies have commonly assumed a deep-heated, fully ionized hydrogen atmosphere model, although they have explored the effects of partial-ionization and helium composition in some cases. Here, we extend that exploration and also include new models with partially ionized carbon composition, externally heated hydrogen, and an empirical atmospheric beaming parameterization to explore deviations in the expected anisotropy of the emitted radiation. None of the studied atmosphere cases have any significant influence on the inferred radius of PSR J0740+6620, possibly due to its X-ray faintness, tighter external constraints, and/or viewing geometry. In the case of PSR J0030+0451, both the composition and ionization state could significantly alter the inferred radius. However, based on the evidence (prior predictive probability of the data), partially ionized hydrogen and carbon atmospheres are disfavored. The difference in the evidence for ionized hydrogen and helium atmospheres is too small to be decisive for most cases, but the inferred radius for helium models trends to larger sizes around or above 14-15 km. External heating or deviations in the beaming that are less than $5\,\%$ at emission angles smaller than 60 degrees, on the other hand, have no significant effect on the inferred radius.

astro-ph.HE↗

arXiv2023

Polarized radiation from an accretion shock in accreting millisecond pulsars using exact Compton scattering formalism

Pulse profiles of accreting millisecond pulsars can be used to determine neutron star (NS) parameters, such as their masses and radii, and therefore provide constraints on the equation of state of cold dense matter. Information obtained by the Imaging X-ray Polarimetry Explorer (IXPE) can be used to decipher pulsar inclination and magnetic obliquity, providing ever tighter constraints on other parameters. In this paper, we develop a new emission model for accretion-powered millisecond pulsars based on thermal Comptonization in an accretion shock above the NS surface. The shock structure was approximated by an isothermal plane-parallel slab and the Stokes parameters of the emergent radiation were computed as a function of the zenith angle and energy for different values of the electron temperature, the Thomson optical depth of the slab, and the temperature of the seed blackbody photons. We show that our Compton scattering model leads to a significantly lower polarization degree of the emitted radiation compared to the previously used Thomson scattering model. We computed a large grid of shock models, which can be combined with pulse profile modeling techniques both with and without polarization included. In this work, we used the relativistic rotating vector model for the oblate NS in order to produce the observed Stokes parameters as a function of the pulsar phase. Furthermore, we simulated the data to be produced by IXPE and obtained constraints on model parameters using nested sampling. The developed methods can also be used in the analysis of the data from future satellites, such as the enhanced X-ray Timing and Polarimetry mission.

astro-ph.HE↗

arXiv2023

An updated mass-radius analysis of the 2017-2018 NICER data set of PSR J0030+0451

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 characterising dense matter. Two independent analyses found a mass of $\sim 1.3-1.4\,\mathrm{M_\odot}$ and a radius of $\sim 13\,$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 reanalyse, 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 jointly analyse also 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 multi-modal 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 $\sim [1.4 \mathrm{M_\odot}, 11.5$ km] and $\sim [1.7 \mathrm{M_\odot}, 14.5$ 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.

astro-ph.HE↗

arXiv2023

X-PSI Parameter Recovery for Temperature Map Configurations Inspired by PSR J0030+0451

In the last few years, the NICER collaboration has provided mass and radius inferences, via pulse profile modeling, for two pulsars: PSR J0030+0451 and PSR J0740+6620. Given the importance of these results for constraining the equation of state of dense nuclear matter, it is crucial to validate them and test their robustness. We therefore explore the reliability of these results and their sensitivity to analysis settings and random processes, including noise, focusing on the specific case of PSR J0030+0451. We use X-PSI, one of the two main analysis pipelines currently employed by the NICER collaboration for mass and radius inferences. With synthetic data that mimic the PSR J0030+0451 NICER data set, we evaluate the recovery performances of X-PSI under conditions never tested before, including complex modeling of the thermally emitting neutron star surface. For the test cases explored, our results suggest that X-PSI is capable of recovering the true mass and radius within reasonable credible intervals. This work also reveals the main vulnerabilities of the analysis: a significant dependence on noise and the presence of multi-modal structure in the posterior surface. Noise particularly impacts our sensitivity to the analysis settings and widths of the posterior distributions. The multi-modal structure in the posterior suggests that biases could be present if the analysis is unable to exhaustively explore the parameter space. Convergence testing, to ensure an adequate coverage of the parameter space and a suitable representation of the posterior distribution, is one possible solution to these challenges.

astro-ph.HE↗

arXiv2023

Pulse Profile Modeling of Thermonuclear Burst Oscillations I: The Effect of Neglecting Variability

We study the effects of the time-variable properties of thermonuclear X-ray bursts on modeling their millisecond-period burst oscillations. We apply the pulse profile modeling technique that is being used in the analysis of rotation-powered millisecond pulsars by the Neutron Star Interior Composition Explorer (NICER) to infer masses, radii, and geometric parameters of neutron stars. By simulating and analyzing a large set of models, we show that overlooking burst time-scale variability in temperatures and sizes of the hot emitting regions can result in substantial bias in the inferred mass and radius. To adequately infer neutron star properties, it is essential to develop a model for the time variable properties or invest a substantial amount of computational time in segmenting the data into non-varying pieces. We discuss prospects for constraints from proposed future X-ray telescopes.

astro-ph.HE↗

arXiv2023

The Radius of PSR J0740+6620 from NICER with NICER Background Estimates

We report a revised analysis for the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, studied previously with joint fits to NICER and XMM-Newton data by Riley et al. (2021) and Miller et al. (2021). We perform a similar Bayesian estimation for the pulse-profile model parameters, except that instead of fitting simultaneously the XMM-Newton data, we use the best available NICER background estimates to constrain the number of photons detected from the source. This approach eliminates any potential issues in the cross-calibration between these two instruments, providing thus an independent check of the robustness of the analysis. The obtained neutron star parameter constraints are compatible with the already published results, with a slight dependence on how conservative the imposed background limits are. A tighter lower limit causes the inferred radius to increase, and a tighter upper limit causes it to decrease. We also extend the study of the inferred emission geometry to examine the degree of deviation from antipodality of the hot regions. We show that there is a significant offset to an antipodal spot configuration, mainly due to the non-half-cycle azimuthal separation of the two emitting spots. The offset angle from the antipode is inferred to be above 25 degrees with 84% probability. This seems to exclude a centered-dipolar magnetic field in PSR J0740+6620.

astro-ph.HE↗