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Register a new userThe Multipolar Magnetic Field of Millisecond Pulsar PSR J0030+0451
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Constantinos Kalapotharakos
Publication date
2020
fields
Physics
and research's language is
English
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Modeling of the NICER X-ray waveform of the pulsar PSR J0030+0451, aimed to constrain the neutron star mass and radius, has inferred surface hot-spots (the magnetic polar caps) that imply significantly non-dipolar magnetic fields. To this end, we investigate magnetic field configurations that comprise offset dipole plus quadrupole components using static vacuum field and force-free global magnetosphere models. Taking into account the compactness and observer angle values provided by Miller et al. (2019) and Riley et al. (2019), we compute geodesics from the observer plane to the polar caps to compute the resulting X-ray light curve. We explore, through Markov chain Monte Carlo techniques, the detailed magnetic field configurations that can reproduce the observed X-ray light curve and have discovered degeneracies, i.e., diverse field configurations, which can provide sufficient descriptions to the NICER X-ray waveforms. Having obtained the force-free field structures, we then compute the corresponding synchronous gamma-ray light curves following Kalapotharakos et al. (2014) these we compare to those obtained by Fermi-LAT, to provide models consistent with both the X-ray and the gamma-ray data, thereby restricting further the multipole field parameters. An essential aspect of this approach is the proper computation of the relative phase between the synchronous X- and gamma-ray light curves. We conclude with a discussion of the broader implications of our study.
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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 pulsars 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.
We report on deep BVR-imaging of the field of the nearby millisecond pulsar PSR J0030+0451 obtained with the ESO/VLT/FORS2. We do not detect any optical counterpart down to B>27.3, V>27.0 and R>27.0 in the immediate vicinity of the radio pulsar position. The closest detected sources are offset by >3, and they are excluded as counterpart candidates by our astrometry. Using our upper limits in the optical, and including recent XMM-Newton X-ray data we show that any nonthermal power-law spectral component of neutron star magnetospheric origin, as suggested by the interpretation of X-ray data, must be suppressed by at least a factor of ~500 in the optical range. This either rules out the nonthermal interpretation or suggests a dramatic spectral break in the 0.003-0.1 keV range of the power-law spectrum. Such a situation has never been observed in the optical/X-ray spectral region of ordinary pulsars, and the origin of such a break is unclear. An alternative interpretation with a purely thermal X-ray spectrum is consistent with our optical upper limits. In this case the X-ray emission is dominated by hot polar caps of the pulsar.
Recent modeling of Neutron Star Interior Composition Explorer(NICER) observations of the millisecond pulsar PSR J0030+0451 suggests that the magnetic field of the pulsar is non-dipolar. We construct a magnetic field configuration where foot points of the open field lines closely resemble the hotspot configuration from NICER observations. Using this magnetic field as input, we perform force-free simulations of the magnetosphere of PSR J0030+0451, showing the three-dimensional structure of its plasma-filled magnetosphere. Making simple and physically motivated assumptions about the emitting regions, we are able to construct the multi-wavelength lightcurves that qualitatively agree with the corresponding observations. The agreement suggests that multipole magnetic structures are the key to modeling this type of pulsars, and can be used to constrain the magnetic inclination angle and the location of radio emission.
We report the parallax and proper motion of millisecond pulsar J0030+0451, one of thirteen known isolated millisecond pulsars in the disk of the Galaxy. We obtained more than 6 years of monthly data from the 305 m Arecibo telescope at 430 MHz and 1410 MHz. We measure the parallax of PSR J0030+0451 to be 3.3 +/- 0.9 mas, corresponding to a distance of 300 +/- 90 pc. The Cordes and Lazio (2002) model of galactic electron distribution yields a dispersion measure derived distance of 317 pc which agrees with our measurement. We place the pulsars transverse space velocity in the range of 8 to 17 km/s, making this pulsar one of the slowest known. We perform a brief census of velocities of isolated versus binary millisecond pulsars. We find the velocities of the two populations are indistinguishable. However, the scale height of the binary population is twice that of the isolated population and the luminosity functions of the two populations are different. We suggest that the scale height difference may be an artifact of the luminosity difference.
Both the mass and radius of the millisecond pulsar PSR J0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASAs NICER mission. In this Letter we study the implications of the mass-radius inference reported for this source by Riley et al. (2019) for the dense matter equation of state (EOS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EOS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EOS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EOS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass-radius likelihood function derived by Riley et al. (2019) using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSR J0030+0451.
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