arXiv subjects

Wynn C. G. Ho

Publications and source records attributed to Wynn C. G. Ho.

At least 37 records · Page 2Linked to original sources

arXiv2024

Rapid spin changes around a magnetar fast radio burst

Magnetars are neutron stars with extremely high magnetic fields that exhibit various X-ray phenomena such as sporadic sub-second bursts, long-term persistent flux enhancements, and variable rates of rotation period change. In 2020, a fast radio burst (FRB), akin to cosmological millisecond-duration radio bursts, was detected from the Galactic magnetar SGR 1935+2154, confirming the long-suspected association between some FRBs and magnetars. However, the mechanism for FRB generation in magnetars remains unclear. Here we report the X-ray discovery of an unprecedented double glitch in SGR 1935+2154 within a time interval of approximately nine hours, bracketing an FRB that occurred on October 14, 2022. Each glitch involved a significant increase in the magnetar's spin frequency, being among the largest abrupt changes in neutron star rotation ever observed. Between the glitches, the magnetar exhibited a rapid spin-down phase, accompanied by a profound increase and subsequent decline in its persistent X-ray emission and burst rate. We postulate that a strong, ephemeral, magnetospheric wind provides the torque that rapidly slows the star's rotation. The trigger for the first glitch couples the star's crust to its magnetosphere, enhances the various X-ray signals, and spawns the wind that alters magnetospheric conditions that might produce the FRB.

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arXiv2024

First detection of polarization in X-rays for PSR B0540-69 and its nebula

We report on X-ray polarization measurements of the extra-galactic Crab-like PSR B0540-69 and its Pulsar Wind Nebula (PWN) in the Large Magellanic Cloud (LMC), using a ~850 ks Imaging X-ray Polarimetry Explorer (IXPE) exposure. The PWN is unresolved by IXPE. No statistically significant polarization is detected for the image-averaged data, giving a 99% confidence polarization upper limit (MDP99) of 5.3% in 2-8 keV energy range. However, a phase-resolved analysis detects polarization for both the nebula and pulsar in the 4-6 keV energy range. For the PWN defined as the off-pulse phases, the polarization degree (PD) of (24.5 ${\pm}$ 5.3)% and polarization angle (PA) of (78.1 ${\pm}$ 6.2)° is detected at 4.6$σ$ significance level, consistent with the PA observed in the optical band. In a single on-pulse window, a hint of polarization is measured at 3.8$σ$ with polarization degree of (50.0 ${\pm}$ 13.1)% and polarization angle of (6.2 ${\pm}$ 7.4)°. A 'simultaneous' PSR/PWN analysis finds two bins at the edges of the pulse exceeding 3$σ$ PD significance, with PD of (68 ${\pm}$ 20)% and (62 ${\pm}$ 20)%; intervening bins at 2-3$σ$ significance have lower PD, hinting at additional polarization structure.

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arXiv2023

MUSE observations of the optical nebula surrounding the central compact object in the Vela Junior Supernova Remnant

Central Compact Objects (CCOs), neutron stars found near the centre of some Supernova Remnants (SNRs), have been almost exclusively studied in X-rays and are thought to lack the wind nebulae typically seen around young, rotation-powered pulsars. We present the first, spatially-resolved, morphological and spectroscopic study of the optical nebula observed at the location of CXOU J085201.4-461753, the CCO in the heart of the Vela Junior SNR. It is currently the only Galactic CCO with a spatially coincident nebula detected at optical wavelengths, whose exact nature remains uncertain. New MUSE integral field spectroscopy data confirm that the nebula, shaped like a smooth blob extending 8" in diameter, is dominated by [N II]$λλ$6548,6583 emission. The data reveals a distinct and previously unobserved morphology of the H$α$ emission, exhibiting an arc-like shape reminiscent of a bow shock nebula. We observe a significantly strong [N II] emission relative to H$α$, with the [N II]$λλ$6548,6583 up to 34 times the intensity of the H$α$ emission within the optical nebula environment. Notably, the [N II] and H$α$ structures are not spatially coincident, with the [N II] nebula concentrated to the south of the CCO and delimited by the H$α$ arc-like structure. We detect additional emission in [N I], He I, [S II], [Ar III], [Fe II], and [S III]. We discuss our findings in the light of a photoionization or Wolf-Rayet nebula, pointing to a very massive progenitor and further suggesting that very massive stars do not necessarily make black holes.

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arXiv2023

Prospects for Time-Domain and Multi-Messenger Science with AXIS

The Advanced X-ray Imaging Satellite (AXIS) promises revolutionary science in the X-ray and multi-messenger time domain. AXIS will leverage excellent spatial resolution (<1.5 arcsec), sensitivity (80x that of Swift), and a large collecting area (5-10x that of Chandra) across a 24-arcmin diameter field of view to discover and characterize a wide range of X-ray transients from supernova-shock breakouts to tidal disruption events to highly variable supermassive black holes. The observatory's ability to localize and monitor faint X-ray sources opens up new opportunities to hunt for counterparts to distant binary neutron star mergers, fast radio bursts, and exotic phenomena like fast X-ray transients. AXIS will offer a response time of <2 hours to community alerts, enabling studies of gravitational wave sources, high-energy neutrino emitters, X-ray binaries, magnetars, and other targets of opportunity. This white paper highlights some of the discovery science that will be driven by AXIS in this burgeoning field of time domain and multi-messenger astrophysics.

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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.

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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.

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arXiv2023

New dynamical tide constraints from current and future gravitational wave detections of inspiralling neutron stars

Previous theoretical works using the pre-merger orbital evolution of coalescing neutron stars to constrain properties of dense nuclear matter assume a gravitational wave phase uncertainty of a few radians, or about a half cycle. However, recent studies of the signal from GW170817 and next generation detector sensitivities indicate actual phase uncertainties at least twenty times better. Using these refined estimates, we show that future observations of nearby sources like GW170817 may be able to reveal neutron star properties beyond just radius and tidal deformability, such as the matter composition and/or presence of a superfluid inside neutron stars, via tidal excitation of g-mode oscillations. Data from GW170817 already limits the amount of orbital energy that is transferred to the neutron star to <2x10^47 erg and the g-mode tidal coupling to Qmode<10^-3 at 50 Hz (5x10^48 erg and 4x10^-3 at 200 Hz), and future observations and detectors will greatly improve upon these constraints. In addition, analysis using general parameterization models that have been applied to the so-called p-g instability show that the instability already appears to be restricted to regimes where the mechanism is likely to be inconsequential; in particular, we show that the number of unstable modes is <<100 at <~100 Hz, and next generation detectors will essentially rule out this mechanism (assuming that the instability remains undetected). Finally, we illustrate that measurements of tidal excitation of r-mode oscillations in nearby rapidly rotating neutron stars are within reach of current detectors and note that even non-detections will limit the inferred inspiralling neutron star spin rate to <20 Hz, which will be useful when determining other parameters such as neutron star mass and tidal deformability.

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arXiv2023

A NICER View on the 2020 Magnetar-Like Outburst of PSR J1846-0258

We report on our monitoring of the strong-field magnetar-like pulsar PSR J1846-0258 with the Neutron Star Interior Composition Explorer (NICER) and the timing and spectral evolution during its outburst in August 2020. Phase-coherent timing solutions were maintained from March 2017 through November 2021, including a coherent solution throughout the outburst. We detected a large spin-up glitch of magnitude Δν/ν= 3 X 10^{-6} at the start of the outburst and observed an increase in pulsed flux that reached a factor of more than 10 times the quiescent level, a behavior similar to that of the 2006 outburst. Our monitoring observations in June and July 2020 indicate that the flux was rising prior to the SWIFT announcement of the outburst on August 1, 2020. We also observed several sharp rises in the pulsed flux following the outburst and the flux reached quiescent level by November 2020. The pulse profile was observed to change shape during the outburst, returning to the pre-outburst shape by 2021. Spectral analysis of the pulsed emission of NICER data shows that the flux increases result entirely from a new black body component that gradually fades away while the power-law remains nearly constant at its quiescent level throughout the outburst. Joint spectral analysis of NICER and simultaneous NuSTAR data confirms this picture. We discuss the interpretation of the magnetar-like outburst and origin of the transient thermal component in the context of both a pulsar-like and a magnetar-like model.

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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.

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arXiv2022

Constraints on neutron star superfluidity from the cooling neutron star in Cassiopeia A using all Chandra ACIS-S observations

Analysis of Chandra observations of the neutron star (NS) in the centre of the Cassiopeia A supernova remnant taken in the subarray (FAINT) mode of the ACIS detector performed by Posselt and collaborators revealed, after inclusion of the most recent (May 2020) observations, a significant decrease of the source surface temperature from 2006 to 2020. The obtained cooling rate is consistent with those obtained from analysis of the 2000$-$2019 data taken in the GRADED mode of the ACIS detector, which is potentially more strongly affected by instrumental effects. We performed a joint spectral analysis using all ACIS data to constrain the NS parameters and cooling rate. We constrain the mass of the Cassiopeia A NS at $M=1.55\pm0.25~M_\odot$, and its radius at $R=13.5\pm 1.5$ km. The surface temperature cooling rate is found to be $2.2\pm 0.3$ per cent in 10 years if the absorbing hydrogen column density is allowed to vary and $1.6\pm 0.2$ per cent in 10 years if it is fixed. The observed cooling can be explained by enhanced neutrino emission from the superfluid NS interior due to Cooper Pair Formation (CPF) process. Based on analysis of all ACIS data, we constrain the maximal critical temperature of triplet neutron pairing within the NS core at $(4-9.5)\times 10^{8}$ K. In accordance with previous studies, the required effective strength of the CPF neutrino emission is at least a factor of 2 higher than existing microscopic calculations suggest.

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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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arXiv2022

Timing six energetic rotation-powered X-ray pulsars, including the fast-spinning young PSR J0058-7218 and Big Glitcher PSR J0537-6910

Measuring a pulsar's rotational evolution is crucial to understanding the nature of the pulsar. Here we provide updated timing models for the rotational evolution of six pulsars, five of which are rotation phase-connected using primarily NICER X-ray data. For the newly-discovered fast energetic young pulsar, PSR J0058-7218, we increase the baseline of its timing model from 1.4 days to 8 months and not only measure more precisely its spin-down rate nudot = (-6.2324+/-0.0001)x10^-11 Hz s^-1 but also for the first time the second time derivative of spin rate nuddot = (4.2+/-0.2)x10^-21 Hz s^-2. For the fastest and most energetic young pulsar, PSR J0537-6910 (with 16 ms spin period), we detect 4 more glitches, for a total of 15 glitches over 4.5 years of NICER monitoring, and show that its spin-down behavior continues to set this pulsar apart from all others, including a long-term braking index n = -1.234+/-0.009 and interglitch braking indices that asymptote to <~ 7 for long times after a glitch. For PSR J1101-6101, we measure a much more accurate spin-down rate that agrees with a previous value measured without phase-connection. For PSR J1412+7922 (also known as Calvera), we extend the baseline of its timing model from our previous 1-year model to 4.4 years, and for PSR J1849-0001, we extend the baseline from 1.5 years to 4.7 years. We also present a long-term timing model of the energetic pulsar, PSR J1813-1749, by fitting previous radio and X-ray spin frequencies from 2009-2019 and new ones measured here using 2018 NuSTAR and 2021 Chandra data.

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arXiv2021

Evidence for a Compact Object in the Aftermath of the Extra-Galactic Transient AT2018cow

The brightest Fast Blue Optical Transients (FBOTs) are mysterious extragalactic explosions that may represent a new class of astrophysical phenomena. Their fast time to maximum brightness of less than a week and decline over several months and atypical optical spectra and evolution are difficult to explain within the context of core-collapse of massive stars which are powered by radioactive decay of Nickel-56 and evolve more slowly. AT2018cow (at redshift of 0.014) is an extreme FBOT in terms of rapid evolution and high luminosities. Here we present evidence for a high-amplitude quasi-periodic oscillation (QPO) of AT2018cow's soft X-rays with a frequency of 224 Hz (at 3.7$σ$ significance level or false alarm probability of 0.02%) and fractional root-mean-squared amplitude of >30%. This signal is found in the average power density spectrum taken over the entire 60-day outburst and suggests a highly persistent signal that lasts for a billion cycles. The high frequency (rapid timescale) of 224 Hz (4.4 ms) argues for a compact object in AT2018cow, which can be a neutron star or black hole with a mass less than 850 solar masses. If the QPO is the spin period of a neutron star, we can set limits on the star's magnetic field strength. Our work highlights a new way of using high time-resolution X-ray observations to study FBOTs.

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arXiv2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740$+$6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument (NICER XTI) event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint NANOGrav and CHIME/Pulsar wideband radio timing measurements of arXiv:2104.00880. We use XMM European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740$+$6620 to be $12.39_{-0.98}^{+1.30}$ km and $2.072_{-0.066}^{+0.067}$ M$_{\odot}$ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully-ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is $\log_{10}(T$ [K]$)=5.99_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

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arXiv2021

A month of monitoring the new magnetar Swift J1555.2-5402 during an X-ray outburst

The soft gamma-ray repeater Swift J1555.2-5402 was discovered by means of a 12-ms duration short burst detected with Swift BAT on 2021 June 3. Then 1.6 hours after the first burst detection, NICER started daily monitoring of this X-ray source for a month. The absorbed 2-10 keV flux stays nearly constant at around 4e-11 erg/s/cm2 during the monitoring timespan, showing only a slight gradual decline. A 3.86-s periodicity is detected, and the time derivative of this period is measured to be 3.05(7)e-11 s/s. The soft X-ray pulse shows a single sinusoidal shape with a root-mean-square pulsed fraction that increases as a function of energy from 15% at 1.5 keV to 39% at 7 keV. The equatorial surface magnetic field, characteristic age, and spin-down luminosity are derived under the dipole field approximation to be 3.5e+14 G, 2.0 kyr, and 2.1e+34 erg/s, respectively. An absorbed blackbody with a temperature of 1.1 keV approximates the soft X-ray spectrum. Assuming a source distance of 10 kpc, the peak X-ray luminosity is ~8.5e+35 erg/s in the 2--10 keV band. During the period of observations, we detect 5 and 37 short bursts with Swift/BAT and NICER, respectively. Based on these observational properties, especially the inferred strong magnetic field, this new source is classified as a magnetar. We also coordinated hard X-ray and radio observations with NuSTAR, DSN, and VERA. A hard X-ray power-law component that extends up to at least 40 keV is detected at 3-sigma significance. The 10-60 keV flux, which is dominated by the power-law component, is ~9e-12 erg/s/cm2 with a photon index of ~1.2. The pulsed fraction has a sharp cutoff above 10 keV, down to ~10% in the hard-tail component band. No radio pulsations are detected during the DSN nor VERA observations. We place 7σ upper limits of 0.043mJy and 0.026 mJy on the flux density at S-band and X-band, respectively.

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arXiv2021

X-ray bounds on cooling, composition, and magnetic field of the Cassiopeia A neutron star and young central compact objects

We present analysis of multiple Chandra and XMM-Newton spectra, separated by 9-19 years, of four of the youngest central compact objects (CCOs) with ages < 2500 yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1-513353 (G330.2+1.0), 1WGA J1713.4-3949 (G347.3-0.5), and XMMU J172054.5-372652 (G350.1-0.3). By fitting these spectra with thermal models, we attempt to constrain each CCO's long-term cooling rate, composition, and magnetic field. For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a decreasing temperature at a ten-year rate of 2.2+/-0.2 or 2.8+/-0.3 percent (1sigma error) for a constant or changing X-ray absorption, respectively. We obtain cooling rate upper limits of 17 percent for CXOU J160103.1-513353 and 6 percent for XMMU J172054.5-372652. For the oldest CCO, 1WGA J1713.4-3949, its temperature seems to have increased by 4+/-2 percent over a ten year period. Assuming each CCO's preferred distance and an emission area that is a large fraction of the total stellar surface, a non-magnetic carbon atmosphere spectrum is a good fit to spectra of all four CCOs. If distances are larger and emission areas are somewhat smaller, then equally good spectral fits are obtained using a hydrogen atmosphere with B <= 7x10^10 G or B >= 10^12 G for CXOU J160103.1-513353, B <= 10^10 G or B >= 10^12 G for XMMU J172054.5-372652, and non-magnetic hydrogen atmosphere for 1WGA J1713.4-3949. In a unified picture of CCO evolution, our results suggest most CCOs, and hence a sizable fraction of young neutron stars, have a surface magnetic field that is low early in their life but builds up over several thousand years.

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arXiv2021

Model-independent constraints on superfluidity from the cooling neutron star in Cassiopeia A

We present a new model-independent (applicable for a broad range of equations of state) analysis of the neutrino emissivity due to triplet neutron pairing in neutron star cores. We find that the integrated neutrino luminosity of the Cooper Pair Formation (CPF) process can be written as a product of two factors. The first factor depends on the neutron star mass, radius and maximal critical temperature of neutron pairing in the core, $T_{Cn \mathrm{max}}$, but not on the particular superfluidity model; it can be expressed by an analytical formula valid for many nucleon equations of state. The second factor depends on the shape of the critical temperature profile within the star, the ratio of the temperature $T$ to $T_{Cn \mathrm{max}}$, but not on the maximal critical temperature itself. While this second factor depends on the superfluidity model, it obeys several model-independent constraints. This property allows one to analyse the thermal evolution of neutron stars with superfluid cores without relying on a specific model of their interiors. The constructed expressions allow us to perform a self-consistent analysis of spectral data and neutron star cooling theory. We apply these findings to the cooling neutron star in the Cassiopeia A supernova remnant using 14 sets of observations taken over 19 years. We constrain $T_{Cn\mathrm{max}}$ to the range of $ (5-10)\times 10^8$ K. This value depends weakly on the equation of state and superfluidity model, and will not change much if cooling is slower than the current data suggest. We also constrain the overall efficiency of the CPF neutrino luminosity.

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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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