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.

/pdf/a-nicer-view-of-psr-j0030-0451-millisecond-pulsar-parameter-1uyudonltc.pdf

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

Magnetic fields are present in a wide variety of stars throughout the HR diagram and play a role at basically all evolutionary stages, from very-low-mass dwarfs to very massive stars, and from young star-forming molecular clouds and protostellar accretion discs to evolved giants/supergiants and magnetic white dwarfs/neutron stars. These fields range from a few μG (e.g., in molecular clouds) to TG and more (e.g., in magnetic neutron stars); in nondegenerate stars in particular, they feature large-scale topologies varying from simple nearly axisymmetric dipoles to complex nonaxsymmetric structures, and from mainly poloidal to mainly toroidal topologies. After recalling the main techniques of detecting and modeling stellar magnetic fields, we review the existing properties of magnetic fields reported in cool, hot, and young nondegenerate stars and protostars, and discuss our understanding of the origin of these fields and their impact on the birth and life of stars.

Magnetic Fields of Nondegenerate Stars

Magnetic fields are present in a wide variety of stars through out the HR diagram and play a role at basically all evolutionary stages, from very-low- mass dwarfs to very massive stars, and from young star-forming molecular clouds and protostellar accretion discs to evolved gi- ants/supergiants and magnetic white dwarfs/neutron stars. These fields range from a fewG (e.g., in molecular clouds) to TG and more (e.g., in magnetic neutron stars); in non-degenerate stars in particular, they feature large-scale topologies varying f rom simple nearly-axisymmetric dipoles to complex non-axsymmetric structures, and from mainly poloidal to mainly toroidal topology. After recalling the main techniques of detecting and modelling stellar magnetic fields, we review the existing properties of magnetic fields reported in cool, hot and young non-degenerate stars and protostars, and discuss our understanding of the origin of these fields and their impact on the birth and life of stars.

Magnetic fields of non-degenerate stars

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.

Accretion through circumstellar disks plays an important role in star formation and in establishing the properties of the regions in which planets form and migrate. The mechanisms by which protostellar and protoplanetary disks accrete onto low-mass stars are not clear; angular momentum transport by magnetic fields is thought to be involved, but the low-ionization conditions in major regions of protoplanetary disks lead to a variety of complex nonideal magnetohydrodynamic effects whose implications are not fully understood. Accretion in pre-main-sequence stars of masses ≲1M⊙ (and in at least some 2–3-M⊙ systems) is generally funneled by the stellar magnetic field, which disrupts the disk at scales typically of order a few stellar radii. Matter moving at near free-fall velocities shocks at the stellar surface; the resulting accretion luminosities from the dissipation of kinetic energy indicate that mass addition during the T Tauri phase over the typical disk lifetime ∼3 Myr is modest in terms of stellar evo...

Accretion onto Pre-Main-Sequence Stars

We investigate the rotational equilibrium state of disk-accreting magnetized stars using axisymmetric magnetohydrodynamic (MHD) simulations. In this "locked" state, the spin-up torque balances the spin-down torque so that the net average torque on the star is zero. We investigated two types of initial conditions: (I) a relatively weak stellar magnetic field and a high coronal density and (II) a stronger stellar field and a lower coronal density. We observed that for both initial conditions the rotation of the star is locked to the rotation of the disk. In the second case, the radial field lines carry significant angular momentum out of the star. However, this did not appreciably change the condition for locking of the rotation of the star. We find that in the equilibrium state the corotation radius rco is related to the magnetospheric radius rA as rco/rA ≈ 1.2-1.3 for case I and rco/rA ≈ 1.4-1.5 for case II. We estimated periods of rotation in the equilibrium state for classical T Tauri stars, dwarf novae, and X-ray millisecond pulsars.

https://iopscience.iop.org/article/10.1086/497000/pdf

Locking of the Rotation of Disk-Accreting Magnetized Stars

Disc accretion to rotating stars with complex magnetic fields is investigated using full 3D magnetohydrodynamic (MHD) simulations. The studied magnetic configurations include superpositions of misaligned dipole and quadrupole fields and off-centre dipoles. The simulations show that when the quadrupole component is comparable to the dipole component, the magnetic field has a complex structure with three major magnetic poles on the surface of the star and three sets of loops of field lines connecting them. A significant amount of matter flows to the quadrupole 'belt', forming a ring-like hotspot on the star. If the maximum strength of the magnetic field on the star is fixed, then we observe that the mass accretion rate, the torque on the star and the area covered by hotspots are several times smaller in the quadrupole-dominant cases than in the pure dipole cases. The influence of the quadrupole component on the shape of the hotspots becomes noticeable when the ratio of the quadrupole and dipole field strengths Bq /B d ≥ 0.5. It becomes dominant in determining the shape of the hotspots when Bq /B d ≥ 1. We conclude that if the quadrupole component is larger than the dipole one, then the shape of the hotspots is determined by the quadrupole field component. In the case of an off-centre dipole field, most of the matter flows through a one-armed accretion stream, forming a large hotspot on the surface, with a second much smaller secondary spot. The light curves may have simple, sinusoidal shapes, thus mimicking stars with pure dipole fields. Or, they may be complex and unusual. In some cases, the light curves may be indicators of a complex field, in particular if the inclination angle is known independently. We also note that in the case of complex fields, magnetospheric gaps are often not empty, and this may be important for the survival of close-in exosolar planets.

Three-dimensional simulations of accretion to stars with complex magnetic fields

Disc accretion to a rotating star with a non-dipole magnetic ﬁeld is investigatedfor the ﬁrst time in full three-dimensional (3D) magnetohydrodynamic (MHD) simula-tions. We investigated the cases of (1) pure dipole, (2) pure quadrupole, and (3) dipoleplus quadrupole ﬁelds. The quadrupole magnetic moment D is taken to be parallelto the dipole magnetic moment µ, and both are inclined relative to the spin axis ofthe star Ω at an angle Θ. Simulations have shown that in each case the structure ofthe funnel streams and associated hot spots on the surface of the star have speciﬁcfeatures connected with the magnetic ﬁeld conﬁguration. In the pure dipole case mat-ter accretes in two funnel streams which form two arch-like spots near the magneticpoles. In the case of a pure quadrupole ﬁeld, most of the matter ﬂows through thequadrupole “belt” forming a ring-shaped hot region on the magnetic equator. In thecase of a dipole plus quadrupole ﬁeld, magnetic ﬂux in the northern magnetic hemi-sphere is larger than that in the southern, and the quadrupole belt and the ring aredisplaced to the south. The stronger the quadrupole, the closer the ring is to the mag-netic equator. At suﬃciently large Θ, matter also ﬂows to the south pole, forming a hotspot near the pole. The light curves have a variety of diﬀerent features which makesit diﬃcult to derive the magnetic ﬁeld conﬁguration from the light curves. There arespeciﬁc features which are diﬀerent in cases of dipole and quadrupole dominated mag-netic ﬁeld: (1) Angular momentum ﬂow between the star and disc is more eﬃcient inthe case of the dipole ﬁeld; (2) Hot spots are hotter and brighter in case of the dipoleﬁeld because the matter accelerates over a longer distance compared with the ﬂow ina quadrupole case.Key words: accretion, accretion discs - magnetic ﬁelds - MHD - stars: magneticﬁelds.

/pdf/accretion-to-stars-with-non-dipole-magnetic-fields-u2xlz0o5vv.pdf

Accretion to stars with non-dipole magnetic fields

The magnetic field of the classical T Tauri star V2129 Oph can be modelled approximately by superposing slightly tilted dipole and octupole moments, with polar magnetic field strengths of 0.35 and 1.2 kG, respectively, as observed by Donati et al. Here we construct a numerical model of V2129 Oph incorporating this result and simulate accretion on to the star using a three-dimensional magnetohydrodynamic code. Simulations show that the disc is truncated by the dipole component and matter flows towards the star in two funnel streams. Closer to the star, the flow is redirected by the octupolar component, with some of the matter flowing towards the high-latitude poles, and the rest into the octupolar belts. The shape and position of the spots differ from those in a pure dipole case, where crescent-shaped spots are observed at the intermediate latitudes.



Simulations show that if the disc is truncated at the distance of r≈ 6.2R★ which is comparable with the corotation radius, rcor≈ 6.8 R★, then the high-latitude polar spot dominates, but the accretion rate obtained from the simulations (and from the accompanying theoretical calculations) is about an order of magnitude lower than the observed one. The accretion rate matches the observed one if the disc is disrupted much closer to the star, at 3.4R★. However, in that case the octupolar belt spots strongly dominate. In the intermediate case of r≈ 4.3R★, the polar spots are sufficiently bright, and the accretion rate is within the error bar of the observed accretion rate, and this model can explain the observations. However, an even better match has been obtained in experiments with a dipole field twice as strong compared with one suggested by Donati et al.



The torque on the star from the disc–magnetosphere interaction is small, and the time-scale of spin evolution, 2 × 107–6 × 108  yr is longer than the 2 × 106 yr age of V2129 Oph. This means that V2129 Oph probably lost most of its angular momentum in the early stages of its evolution, possibly, during the stage when it was fully convective, and had a stronger magnetic field. The propeller mechanism could also be responsible for the rapid spin-down.



The external magnetic flux of the star is strongly influenced by the disc: the field lines connecting the disc and the star inflate and form magnetic towers above and below the disc. The potential (vacuum) approximation is still valid inside the Alfven (magnetospheric) surface where the magnetic stress dominates over the matter stress.

/pdf/global-3d-simulations-of-disc-accretion-on-to-the-classical-23duvlay4a.pdf

Global 3D simulations of disc accretion on to the classical T Tauri star V2129 Oph

The magnetic field of the classical T Tauri star V2129 Oph can be modeled approximately by superposing slightly tilted dipole and octupole moments, with polar magnetic field strengths of 0.35kG and 1.2kG respectively (Donati et al. 2007). Here we construct a numerical model of V2129 Oph incorporating this result and simulate accretion onto the star. Simulations show that the disk is truncated by the dipole component and matter flows towards the star in two funnel streams. Closer to the star, the flow is redirected by the octupolar component, with some of the matter flowing towards the high-latitude poles, and the rest into the octupolar belts. The shape and position of the spots differ from those in a pure dipole case, where crescent-shaped spots are observed at the intermediate latitudes. Simulations show that if the disk is truncated at the distance of 6.2 R_* which is comparable with the co-rotation radius, 6.8 R_*, then the high-latitude polar spots dominate, but the accretion rate obtained from the simulations is about an order of magnitude lower than the observed one. The accretion rate matches the observed one if the disk is disrupted much closer to the star, at 3.4 R_*. However, the octupolar belt spots strongly dominate. Better match has been obtained in experiments with a dipole field twice as strong. The torque on the star from the disk-magnetosphere interaction is small, and the time-scale of spin evolution, 2 x10^7-10^9 years is longer than the 2x10^6 years age of V2129 Oph. The external magnetic flux of the star is strongly influenced by the disk: the field lines connecting the disk and the star inflate and form magnetic towers above and below the disk. The potential (vacuum) approximation is still valid inside the Alfven (magnetospheric) surface where the magnetic stress dominates over the matter stress.

Min Long

Papers

Locking of the Rotation of Disk-Accreting Magnetized Stars

Three-dimensional simulations of accretion to stars with complex magnetic fields

Accretion to stars with non-dipole magnetic fields

Global 3D simulations of disc accretion on to the classical T Tauri star V2129 Oph

Global 3D Simulations of Disc Accretion onto the classical T Tauri Star V2129 Oph