Many problems in the experimental estimation of parameters for models can be solved through use of the likelihood ratio test. Applications of the likelihood ratio, with particular attention to photon counting experiments, are discussed. The procedures presented solve a greater range of problems than those currently in use, yet are no more difficult to apply. The procedures are proved analytically, and examples from current problems in astronomy are discussed.

Parameter estimation in astronomy through application of the likelihood ratio. [satellite data analysis techniques

We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSR J0030+0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray spectral-timing event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsar’s surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass M and equatorial radius R eq are, respectively, and , while the compactness is more tightly constrained; the credible interval bounds reported here are approximately the 16% and 84% quantiles in marginal posterior mass.

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A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation

There are now about 50 known radio pulsars in binary systems, including at least five in double neutron star binaries. In some cases, the stellar masses can be directly determined from measurements of relativistic orbital effects. In others, only an indirect or statistical estimate of the masses is possible. We review the general problem of mass measurement in radio pulsar binaries and critically discuss all current estimates of the masses of radio pulsars and their companions. We find that significant constraints exist on the masses of 21 radio pulsars and on five neutron star companions of radio pulsars. All the measurements are consistent with a remarkably narrow underlying Gaussian mass distribution, m=1.35?0.04 M. There is no evidence that extensive mass accretion (?m0.1 M) has occurred in these systems. We also show that the observed inclinations of millisecond pulsar binaries are consistent with a random distribution, and thus find no evidence for either alignment or counteralignment of millisecond pulsar magnetic fields.

https://iopscience.iop.org/article/10.1086/306742/pdf

Neutron Star Mass Measurements. I. Radio Pulsars

We report on Bayesian parameter estimation of the mass and equatorial radius of the millisecond pulsar PSR J0030$+$0451, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer (NICER) X-ray spectral-timing event data. We perform relativistic ray-tracing of thermal emission from hot regions of the pulsar's surface. We assume two distinct hot regions based on two clear pulsed components in the phase-folded pulse-profile data; we explore a number of forms (morphologies and topologies) for each hot region, inferring their parameters in addition to the stellar mass and radius. For the family of models considered, the evidence (prior predictive probability of the data) strongly favors a model that permits both hot regions to be located in the same rotational hemisphere. Models wherein both hot regions are assumed to be simply-connected circular single-temperature spots, in particular those where the spots are assumed to be reflection-symmetric with respect to the stellar origin, are strongly disfavored. For the inferred configuration, one hot region subtends an angular extent of only a few degrees (in spherical coordinates with origin at the stellar center) and we are insensitive to other structural details; the second hot region is far more azimuthally extended in the form of a narrow arc, thus requiring a larger number of parameters to describe. The inferred mass $M$ and equatorial radius $R_\mathrm{eq}$ are, respectively, $1.34_{-0.16}^{+0.15}$ M$_{\odot}$ and $12.71_{-1.19}^{+1.14}$ km, whilst the compactness $GM/R_\mathrm{eq}c^2 = 0.156_{-0.010}^{+0.008}$ is more tightly constrained; the credible interval bounds reported here are approximately the $16\%$ and $84\%$ quantiles in marginal posterior mass.

/pdf/a-nicer-view-of-psr-j0030-0451-millisecond-pulsar-parameter-16h4tta2pe.pdf

A NICER View of PSR J0030+0451: Millisecond Pulsar Parameter Estimation.

We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5M , a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e = 0.44) orbit around an unevolved companion.

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Binary and Millisecond Pulsars

The classical vacuum gap model of Ruderman & Sutherland, in which spark-associated subbeams of subpulse emission circulate around the magnetic axis due to the E × B drift of spark plasma filaments, provides a natural and plausible physical mechanism of the subpulse drift phenomenon. Moreover, this is the only model with quantitative predictions that can be compared with observa- tions. Recent progress in the analysis of drifting subpulses in pulsars has provided a strong support to this model by revealing a number of subbeams circulating around the magnetic axis in a manner compatible with theoretical predictions. However, a more detailed analysis revealed that the circulation speed in a pure vacuum gap is too high when compared with observations. Moreover, some pul- sars demonstrate significant time variations of the drift rate, including a change of the apparent drift direction, which is obviously inconsistent with the E × B drift scenario in a pure vacuum gap. We attempted to resolve these discrepancies by considering a partial flow of iron ions from the positively charged polar cap, co- existing with the production of outflowing electron-positron plasmas. The model of such charge-depleted acceleration region is highly sensitive to both the critical ion temperature Ti � 10 6 K (above which ions flow freely with the corotational charge density) and the actual surface temperature Ts of the polar cap, heated by the bombardment of ultra-relativistic charged particles. By fitting the obser- vationally deduced drift-rates to the theoretical values, we managed to estimate polar cap surface temperatures in a number of pulsars. The estimated surface temperatures Ts correspond to a small charge depletion of the order of a few percent of the Goldreich-Julian corotational charge density. Nevertheless, the re-

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Drifting subpulses and inner acceleration regions in radio pulsars

A nonstationary polar gap model first proposed by Ruderman & Sutherland is modified and applied to spark-associated pulsar emission at radio wavelengths. It is argued that under physical and geometrical conditions prevailing above pulsar polar cap, highly nonstationary spark discharges do not occur at random positions. Instead, sparks should tend to operate in well determined preferred regions. At any instant the polar cap is populated as densely as possible with a number of two-dimensional sparks with a characteristic dimension as well as a typical distance between adjacent sparks being about the polar gap height. Our model differs, however, markedly from its original "hollow cone" version. The key feature is the quasi-central spark driven by γ-B pair production process and anchored to the local pole of a sunspot-like surface magnetic field. This fixed spark prevents the motion of other sparks toward the pole, restricting it to slow circumferential × drift across the planes of field lines converging at the local pole. We argue that the polar spark constitutes the core pulsar emission and that the annular rings of drifting sparks contribute to conal components of the pulsar beam. We found that the number of nested cones in the beam of typical pulsar should not exceed three; a number also found by Mitra & Deshpande using a completely different analysis. We confront predictions of our model with a variety of pulsar data, including mean profiles morphology and their predicted correlations with properties of the P- pulsar diagram as well as detailed studies of drifting subpulses. We demonstrate that, if the observing geometry is known, the average profile as well as the apparent drift pattern are fully determined by the values of P and . In the accompanying Paper II we develop a self-consistent theory of coherent pulsar radio emission based on the modified polar gap model explored in this paper.

https://iopscience.iop.org/article/10.1086/309394/pdf

Spark Model for Pulsar Radiation Modulation Patterns

We propose a new, self-consistent theory of coherent pulsar radio emission based on the nonstationary sparking model of Ruderman & Sutherland, modified by Gil & Sendyk. The polar cap is populated by a number of sparks with a characteristic perpendicular dimension D approximately equal to the polar gap height scale h, separated from each other also by about D ≈ h. Each spark reappears in approximately the same place on the polar cap for a timescale much longer than its 10 μs lifetime and delivers to the open magnetosphere a sequence of e-e+ clouds that flow orderly along a flux tube of dipolar magnetic field lines. The overlapping of particles with different momenta from consecutive clouds leads to effective two-stream instability, which triggers electrostatic Langmuir waves at the altitudes of about 50 stellar radii. The electrostatic oscillations are modulationally unstable, and their nonlinear evolution results in formation of plasma solitons. Because of relative streaming of electrons and positrons and the corresponding difference in relativistic masses, the pondermotive Miller force acts on them at different rates, which results in the net soliton charge. A characteristic soliton length along magnetic field lines is about 30 cm, so they are capable of emitting coherent curvature radiation at radio wavelengths. A perpendicular cross section of each soliton at radiation altitudes follows from a dipolar spread of a plasma cloud with a characteristic dimension near the star surface of about D ≈ h ≈ 50 m. If Δγ = |γ+ - γ-| ~ 100, then the net soliton charge is about 1021 fundamental charges contained within a volume of about 1014 cm3. For a typical pulsar, there are about 105 solitons associated with each of about 25 sparks operating on the polar cap at any instant. One soliton moving relativistically along dipolar field lines with a Lorentz factor of the order of 100 generates a power of about 1021 ergs s-1 by means of curvature radiation. Then the total power of a typical radio pulsar can be estimated as being about 1027-1028 ergs s-1. The energy of the soliton curvature radiation is supported by kinetic energy of secondary electron-positron plasma created by the primary beam produced by the accelerating potential drop within the polar gap. A significant fraction of kinetic energy generated by sparks is radiated away in the form of the observed coherent radio emission.

The Spark-associated Soliton Model for Pulsar Radio Emission

The method of emission altitude estimation in radio pulsars based on pulse width measurements at the low intensity profile wings is reviewed. Both measurement details and model assumptions are discussed. It is argued that the pulse width measurement technique is sensitive enough to detect the radio emission generated at the beam edge near the last open field lines. We give the refined version of the formula for the radio emission altitudes and compare it with values obtained independently using a method based on measurements of separation between peaks of the outermost profile components. We show that both methods give comparable results.

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Radio emission altitude in pulsars

We consider the curvature radiation of a pointlike charge moving relativistically along curved magnetic field lines through a pulsar magnetospheric electron-positron plasma. We demonstrate that the radiation power is largely suppressed compared with the vacuum case, but still at a considerable level, high enough to explain the observed pulsar luminosities. The outgoing waves are polarized perpendicularly to the plane of the dipolar magnetic field lines. Our results strongly support coherent curvature radiation by the spark-associated solitons as a plausible mechanism of pulsar radio emission.

https://iopscience.iop.org/article/10.1086/379972/pdf

Janusz Gil

Papers

Drifting subpulses and inner acceleration regions in radio pulsars

Spark Model for Pulsar Radiation Modulation Patterns

The Spark-associated Soliton Model for Pulsar Radio Emission

Radio emission altitude in pulsars

Curvature Radiation in Pulsar Magnetospheric Plasma