arXiv subjects

Frederick K. Lamb

Publications and source records attributed to Frederick K. Lamb.

At least 19 recordsLinked to original sources

arXiv2026

Systematic Effects of Hydrogen and Helium Atmosphere Mismatch on Radius Inference in PSR~J0740+6620-like Synthetic NICER Data

Constraints on neutron star radii provide insight into the properties of the cold, dense matter in their interiors. Previous studies using synthetic Neutron star Interior Composition Explorer (NICER) pulse waveform data have demonstrated that radius inferences derived therefrom are robust against several classes of modeling systematics. Here we explore the consequences of assuming the wrong atmospheric composition, using synthetic data based on the $\sim 2.1~M_\odot$ pulsar PSR~J0740$+$6620. We find that the assumption of a hydrogen atmosphere when the synthetic data assumed a helium atmosphere, or vice versa, produces little bias in the inferred radius at the spot-to-background ratio of the actual PSR~J0740$+$6620 data. However, when we increase the spot-to-background ratio by a factor of $\sim20$ while keeping the total number of counts fixed at the observed $\sim 5.5\times 10^5$, we find that composition mismatch can produce significantly biased radius estimates while remaining hidden inside a fit with statistically acceptable residuals. Even in these cases, the Bayesian evidence consistently identifies the correct atmospheric model. Our findings reinforce the importance of using the Bayesian evidence for model comparison and goodness-of-fit tests.

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arXiv2026

An Investigation of Systematic Effects from Background Priors on PSR J0740$+$6620 Radius Estimates using Synthetic NICER and XMM-Newton Data

Accurate and precise measurements of neutron star radii provide invaluable information about the cold, dense matter in neutron star cores. Analyses of synthetic X-ray pulse waveform data similar to the data obtained from non-accreting neutron stars using the Neutron star Interior Composition Explorer (NICER) have indicated that mass and radius estimates made using such data are robust against some systematic errors that may be made when modeling these data, such as errors in the assumed pattern of the thermal X-ray emission from the surface of these stars. A potentially important but so far unexplored source of systematic error is misparameterization of unmodulated background components, which can bias the inferred radius, particularly when data from different telescopes are used in the analysis. In this study, we investigate the effects of the background model on radius estimates by jointly analyzing synthetic NICER and XMM-Newton data, using the $\sim 2.1~M_\odot$ pulsar PSR~J0740$+$6620 as a prototypical example. Our analysis shows that even if the background assumed in the model underestimates the actual background by a factor of more than five, the resulting shift of the radius posterior from the true value of the radius corresponds to only $\sim1σ$. In all the cases we examined, the Bayesian evidence for the correct background model is greater than for the incorrect background model. These results add to the evidence that analyses of NICER-like data provide accurate measurements of neutron star radii when the statistical sampling is thorough and the model fits the data well.

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arXiv2024

A More Precise Measurement of the Radius of PSR J0740+6620 Using Updated NICER Data

PSR J0740+6620 is the neutron star with the highest precisely determined mass, inferred from radio observations to be $2.08\pm0.07\,\rm M_\odot$. Measurements of its radius therefore hold promise to constrain the properties of the cold, catalyzed, high-density matter in neutron star cores. Previously, Miller et al. (2021) and Riley et al. (2021) reported measurements of the radius of PSR J0740+6620 based on Neutron Star Interior Composition Explorer (NICER) observations accumulated through 17 April 2020, and an exploratory analysis utilizing NICER background estimates and a data set accumulated through 28 December 2021 was presented in Salmi et al. (2022). Here we report an updated radius measurement, derived by fitting models of X-ray emission from the neutron star surface to NICER data accumulated through 21 April 2022, totaling $\sim1.1$ Ms additional exposure compared to the data set analyzed in Miller et al. (2021) and Riley et al. (2021), and to data from X-ray Multi-Mirror (XMM-Newton) observations. We find that the equatorial circumferential radius of PSR J0740+6620 is $12.92_{-1.13}^{+2.09}$ km (68% credibility), a fractional uncertainty $\sim83\%$ the width of that reported in Miller et al. (2021), in line with statistical expectations given the additional data. If we were to require the radius to be less than 16 km, as was done in Salmi et al. (2024), then our 68% credible region would become $R=12.76^{+1.49}_{-1.02}$ km, which is close to the headline result of Salmi et al. (2024). Our updated measurements, along with other laboratory and astrophysical constraints, imply a slightly softer equation of state than that inferred from our previous measurements.

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arXiv2022

Snowmass 2021 Cosmic Frontier White Paper: The Dense Matter Equation of State and QCD Phase Transitions

Our limited understanding of the physical properties of matter at ultra-high density, high proton/neutron number asymmetry, and low temperature is presently one of the major outstanding problems in physics. As matter in this extreme state is known to only exist stably in the cores of neutron stars (NSs), complementary measurements from electromagnetic and gravitational wave astrophysical observations of NSs, combined with terrestrial laboratory constraints and further theoretical investigations, hold the promise to provide important insight into the properties of matter in a region of the quantum chromodynamics phase space that is otherwise inaccessible. This multidisciplinary endeavor imposes the following requirements for facilities and resources in the upcoming decade and beyond: * A next generation of gravitational wave detectors to uncover more double NS and neutron star-black hole mergers; * Sensitive radio telescopes to find the most massive and fastest spinning NSs; * Large-area, high-time-resolution and/or high angular resolution X-ray telescopes to constrain the NS mass-radius relation; * Suitable laboratory facilities for nuclear physics experiments to constrain the dense matter equation of state; * Funding resources for theoretical studies of matter in this regime; * The availability of modern large-scale high performance computing infrastructure. The same facilities and resources would also enable significant advances in other high-profile fields of inquiry in modern physics such as the nature of dark matter, alternative theories of gravity, nucleon superfluidity and superconductivity, as well as an array of astrophysics, including but not limited to stellar evolution, nucleosynthesis, and primordial black holes.

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arXiv2021

Constraining the Neutron Star Mass--Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

We describe the X-ray pulse profile models we use, and how we use them, to analyze Neutron Star Interior Composition Explorer (NICER) observations of rotation-powered millisecond pulsars to obtain information about the mass-radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. (2019) and Riley et al. (2019) and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. (2019) and Riley et al. (2019) by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass-radius plane that are statistically consistent with one another and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. (2019) that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar's spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in these estimates made using this technique, some of which may warrant further investigation.

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arXiv2019

Constraining the Neutron Star Mass-Radius Relation and Dense Matter Equation of State with NICER. I. The Millisecond Pulsar X-ray Data Set

We present the set of deep Neutron Star Interior Composition Explorer (NICER) X-ray timing observations of the nearby rotation-powered millisecond pulsars PSRs J0437-4715, J0030+0451, J1231-1411, and J2124-3358, selected as targets for constraining the mass-radius relation of neutron stars and the dense matter equation of state via modeling of their pulsed thermal X-ray emission. We describe the instrument, observations, and data processing/reduction procedures, as well as the series of investigations conducted to ensure that the properties of the data sets are suitable for parameter estimation analyses to produce reliable constraints on the neutron star mass-radius relation and the dense matter equation of state. We find that the long-term timing and flux behavior and the Fourier-domain properties of the event data do not exhibit any anomalies that could adversely affect the intended measurements. From phase-selected spectroscopy, we find that emission from the individual pulse peaks is well described by a single-temperature hydrogen atmosphere spectrum, with the exception of PSR J0437-4715, for which multiple temperatures are required.

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arXiv2019

Constraining the Neutron Star Mass-Radius Relation and Dense Matter Equation of State with NICER. II. Emission from Hot Spots on a Rapidly Rotating Neutron Star

We describe the model of surface emission from a rapidly rotating neutron star that is applied to Neutron Star Interior Composition Explorer X-ray data of millisecond pulsars in order to statistically constrain the neutron star mass-radius relation and dense matter equation of state. To ensure that the associated calculations are both accurate and precise, we conduct an extensive suite of verification tests between our numerical codes for both the Schwarzschild + Doppler and Oblate Schwarzschild approximations, and compare both approximations against exact numerical calculations. We find superb agreement between the code outputs, as well as in comparison against a set of analytical and semi-analytical calculations, which combined with their speed, demonstrates that the codes are well-suited for large-scale statistical sampling applications. A set of verified, high-precision reference synthetic pulse profiles is provided to the community to facilitate testing of other independently developed codes.

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arXiv2019

Constraining the equation of state of high-density cold matter using nuclear and astronomical measurements

The increasing richness of data related to cold dense matter, from laboratory experiments to neutron-star observations, requires a framework for constraining the properties of such matter that makes use of all relevant information. Here, we present a rigorous but practical Bayesian approach that can include diverse evidence, such as nuclear data and the inferred masses, radii, tidal deformabilities, moments of inertia, and gravitational binding energies of neutron stars. We emphasize that the full posterior probability distributions of measurements should be used rather than, as is common, imposing a cut on the maximum mass or other quantities. Our method can be used with any parameterization of the equation of state (EOS). We use both a spectral parameterization and a piecewise polytropic parameterization with variable transition densities to illustrate the implications of current measurements and show how future measurements in many domains could improve our understanding of cold catalyzed matter. We find that different types of measurements will play distinct roles in constraining the EOS in different density ranges. For example, better symmetry energy measurements will have a major influence on our understanding of matter somewhat below nuclear saturation density but little influence above that density. In contrast, precise radius measurements or multiple tidal deformability measurements of the quality of those from GW170817 or better will improve our knowledge of the EOS over a broader density range.

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arXiv2019

Determining the Equation of State of Cold, Dense Matter with X-ray Observations of Neutron Stars

The unknown state of matter at ultra-high density, large proton/neutron number asymmetry, and low temperature is a major long-standing problem in modern physics. Neutron stars provide the only known setting in the Universe where matter in this regime can stably exist. Valuable information about the interior structure of neutron stars can be extracted via sensitive observations of their exteriors. There are several complementary techniques that require different combinations of high time resolution, superb spectral resolution, and high spatial resolution. In the upcoming decade and beyond, measurements of the masses and radii of an ensemble of neutron stars using these techniques, based on data from multiple proposed next-generation X-ray telescopes, can produce definitive empirical constraints on the allowed dense matter equation of state.

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arXiv2018

NICER Detects a Soft X-ray Kilohertz Quasi-periodic Oscillation in 4U 0614+09

We report on the detection of a kilohertz quasi-periodic oscillation (QPO) with the Neutron Star Interior Composition Explorer (NICER). Analyzing approximately 165 ks of NICER exposure on the X-ray burster 4U 0614+09, we detect multiple instances of a single-peak upper kHz QPO, with centroid frequencies that range from 400 Hz to 750 Hz. We resolve the kHz QPO as a function of energy, and measure, for the first time, the QPO amplitude below 2 keV. We find the fractional amplitude at 1 keV is on the order of 2% rms, and discuss the implications for the QPO emission process in the context of Comptonization models.

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arXiv2018

A NICER look at the Aql X-1 hard state

We report on a spectral-timing analysis of the neutron star low-mass X-ray binary Aql~X-1 with the Neutron Star Interior Composition Explorer (NICER) on the International Space Station. Aql~X-1 was observed with NICER during a dim outburst in 2017 July, collecting approximately $50$ ks of good exposure. The spectral and timing properties of the source correspond to that of an (hard) extreme island state in the atoll classification. We find that the fractional amplitude of the low frequency ($<0.3$ Hz) band-limited noise shows a dramatic turnover as a function of energy: it peaks at 0.5 keV with nearly 5\% rms, drops to $12\%$ rms at 2 keV, and rises to $15\%$ rms at 10 keV. Through the analysis of covariance spectra, we demonstrate that band-limited noise exists in both the soft thermal emission and the power-law emission. Additionally, we measure hard time lags, indicating the thermal emission at $0.5$ keV leads the power-law emission at 10 keV on a timescale of $\sim100$ ms at $0.3$ Hz to $\sim10$ ms at $3$ Hz. Our results demonstrate that the thermal emission in the hard state is intrinsically variable, and driving the modulation of the higher energy power-law. Interpreting the thermal spectrum as disk emission, we find our results are consistent with the disk propagation model proposed for accretion onto black holes.

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arXiv2018

Erratum: "Determining neutron star masses and radii using energy-resolved waveforms of X-ray burst oscillations" (ApJ, 776, 19 [2013])

This erratum addresses an error in the text of Lo et al. (2013) and more importantly corrects a computational error that was made in all previously published relativistic computations of absolute pulse waveform fluxes produced by hot spots on rotating stars that followed the radiation forward in time from the star to the observer. These computations used an incorrect expression for the differential emitting area on the stellar surface, as measured in the comoving frame. This erratum explains this error, lists all the published papers that contain results affected by this error, and summarizes in a general way why and how the results in Lo et al. (2013) were affected by this error, in a way that makes clear why and how the results in the other papers were affected. The idealized radiation spectra, beaming patterns, and spot shapes assumed in many of the previously reported computations of pulse waveforms very likely introduced systematic errors that are much larger than the relatively small errors introduced by using an incorrect expression for the differential emitting area. This erratum also corrects an error in the caption of Figure 5, an error in the text on page 19, and an incomplete description of our results on page 24.

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arXiv2016

Observational Constraints on Neutron Star Masses and Radii

Precise and reliable measurements of the masses and radii of neutron stars with a variety of masses would provide valuable guidance for improving models of the properties of cold matter with densities above the saturation density of nuclear matter. Several different approaches for measuring the masses and radii of neutron stars have been tried or proposed, including analyzing the X-ray fluxes and spectra of the emission from neutron stars in quiescent low-mass X-ray binary systems and thermonuclear burst sources; fitting the energy-dependent X-ray waveforms of rotation-powered millisecond pulsars, burst oscillations with millisecond periods, and accretion-powered millisecond pulsars; and modeling the gravitational radiation waveforms of coalescing double neutron star and neutron star -- black hole binary systems. We describe the strengths and weaknesses of these approaches, most of which currently have substantial systematic errors, and discuss the prospects for decreasing the systematic errors in each method.

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arXiv2016

Measuring the neutron star equation of state using X-ray timing

One of the primary science goals of the next generation of hard X-ray timing instruments is to determine the equation of state of the matter at supranuclear densities inside neutron stars, by measuring the radius of neutron stars with different masses to accuracies of a few percent. Three main techniques can be used to achieve this goal. The first involves waveform modelling. The flux we observe from a hotspot on the neutron star surface offset from the rotational pole will be modulated by the star's rotation, giving rise to a pulsation. Information about mass and radius is encoded into the pulse profile via relativistic effects, and tight constraints on mass and radius can be obtained. The second technique involves characterising the spin distribution of accreting neutron stars. The most rapidly rotating stars provide a very clean constraint, since the mass-shedding limit is a function of mass and radius. However the overall spin distribution also provides a guide to the torque mechanisms in operation and the moment of inertia, both of which can depend sensitively on dense matter physics. The third technique is to search for quasi-periodic oscillations in X-ray flux associated with global seismic vibrations of magnetars (the most highly magnetized neutron stars), triggered by magnetic explosions. The vibrational frequencies depend on stellar parameters including the dense matter equation of state. We illustrate how these complementary X-ray timing techniques can be used to constrain the dense matter equation of state, and discuss the results that might be expected from a 10m$^2$ instrument. We also discuss how the results from such a facility would compare to other astronomical investigations of neutron star properties. [Modified for arXiv]

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arXiv2015

Determining Neutron Star Properties by Fitting Oblate-Star Waveforms To X-ray Burst Oscillations

We describe sophisticated new Bayesian analysis methods that make it possible to estimate quickly the masses and radii of rapidly rotating, oblate neutron stars by fitting oblate-star waveform models to energy-resolved observations of the X-ray oscillations produced by a hot spot on such stars. We conclude that models that take the oblate shape of the star into account should be used for stars with large radii and rotation rates $>300$ Hz. We find that a 25% variation of the temperature of the hot spot with latitude does not significantly bias estimates of the mass $M$ and equatorial radius $R_{\rm eq}$ derived by fitting a model that assumes a uniform-temperature spot. Our results show that fits of oblate-star waveform models to waveform data can simultaneously determine $M$ and $R_{\rm eq}$ with uncertainties $\lesssim\,$7% if (1) the star's rotation rate is $\gtrsim\,$$600$ Hz; (2) the spot center and observer's sightline are both within $30^\circ$ of the star's rotational equator; (3) the oscillations have a fractional rms amplitude $\gtrsim\,$10%; and (4) $\gtrsim$$10^7$ counts are collected from the star. This is a realistic fractional amplitude, and this many counts could be obtained from a single star by the accepted NICER and proposed LOFT and AXTAR space missions by combining data from many X-ray bursts. These uncertainties are small enough to improve substantially our understanding of cold, ultradense matter.

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arXiv2013

Determining neutron star masses and radii using energy-resolved waveforms of X-ray burst oscillations

Simultaneous, precise measurements of the mass $M$ and radius $R$ of neutron stars can yield uniquely valuable information about the still uncertain properties of cold matter at several times the density of nuclear matter. One method that could be used to measure $M$ and $R$ is to analyze the energy-dependent waveforms of the X-ray flux oscillations seen during some thermonuclear bursts from some neutron stars. These oscillations are thought to be produced by X-ray emission from hotter regions on the surface of the star that are rotating at or near the spin frequency of the star. Here we explore how well $M$ and $R$ could be determined by generating, and analyzing using Bayesian techniques, synthetic energy-resolved X-ray data that we produce assuming a future space mission having 2--30 keV energy coverage and an effective area of 10 m$^2$, such as the proposed \textit{LOFT} or \textit{AXTAR} missions. We find that if the hot spot is within 10$^\circ$ of the rotation equator, both $M$ and $R$ can usually be determined with an uncertainty of about 10% if there are $10^6$ total counts from the spot, whereas waveforms from spots within 20$^\circ$ of the rotation pole provide no useful constraints. These constraints can usually be achieved even if the burst oscillations vary with time and data from multiple bursts must be used to obtain 10$^6$ counts from the hot spot. This is therefore a promising method to constrain $M$ and $R$ tightly enough to discriminate strongly between competing models of cold, high-density matter.

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arXiv2013

Testing the rotating hot spot model using X-ray burst oscillations from 4U 1636-536

Precise and accurate measurements of neutron star masses and radii would provide valuable information about the still uncertain properties of cold matter at supranuclear densities. One promising approach to making such measurements involves analysis of the X-ray flux oscillations often seen during thermonuclear (type 1) X-ray bursts. These oscillations are almost certainly produced by emission from hotter regions on the stellar surface modulated by the rotation of the star. One consequence of the rotation is that the oscillation should appear earlier at higher photon energies than at lower energies. Ford (1999) found compelling evidence for such a hard lead in the tail oscillations of one type 1 burst from Aql X-1. We have therefore analyzed individually the oscillations observed in the tails of the four type 1 bursts from 4U 1636-536 that, when averaged, provided the strongest evidence for a soft lead in the analysis by Muno et al. (2003). We have also analyzed the oscillation observed during the superburst from this star. We find that the data from these five bursts, treated both individually and jointly, are fully consistent with a rotating hot spot model. Unfortunately, the uncertainties in these data are too large to provide interesting constraints on the mass and radius of this star.

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arXiv2011

Accretion onto Stars with Octupole Magnetic Fields: Matter Flow, Hot Spots and Phase Shifts

We show results of global 3D MHD simulations of accretion onto stars with superposition of the dipole and octupole fields, where we vary the ratio between components. Simulations show that if octupolar field strongly dominates at the disc-magnetosphere boundary, then matter flows into the ring-like octupolar poles, forming ring-shape spots at the surface of the star above and below equator. The light-curves are complex and may have two peaks per period. In case where the dipole field dominates, matter accretes in two ordered funnel streams towards poles, however the polar spots are meridionally-elongated due to the action of the octupolar component. In the case when the fields are of similar strengths, both, polar and belt-like spots are present. In many cases the light-curves show the evidence of complex fields, excluding the cases of small inclinations angles, where sinusoidal light-curve %is observed and `hides' the information about the field complexity. We also propose new mechanisms of phase shift in stars with complex magnetic fields. We suggest that the phase shifts can be connected with: (1) temporal variation of the star's intrinsic magnetic field and subsequent redistribution of main magnetic poles; (2) variation of the accretion rate, which causes the disc to interact with the magnetic fields associated with different magnetic moments. We use our model to demonstrate these phase shift mechanisms, and we discuss possible applications of these mechanisms to accreting millisecond pulsars and young stars.

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