Akshay K. Kulkarni

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc‐magnetosphere boundary. The instability is Rayleigh‐Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, � � 30 ◦ , between the star’s rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.

Unstable Disk Accretion onto Magnetized Stars: First Global Three-dimensional Magnetohydrodynamic Simulations

We report on the first global three-dimensional (3D) MHD simulations of disk accretion onto a rotating magnetized star through the Rayleigh-Taylor instability. The star has a dipole field misaligned relative to the rotation axis by a small angle Θ. Simulations show that, depending on the accretion rate, a star may be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates deep into the magnetosphere through several elongated tongues which deposit matter at random places on the surface of the star, leading to stochastic light curves. In the stable regime, matter accretes in ordered funnel streams and the light curves are almost periodic. A star may switch between these two regimes depending on the accretion rate and may thus show alternate episodes of ordered pulsations and stochastic light curves. In the intermediate regime, both stochastic and ordered pulsations are observed. For -->Θ > 30°, the instability is suppressed and stable accretion through funnel streams dominates.We report on the first global three-dimensional (3D) MHD simulations of disk accretion onto a rotating magnetized star through the Rayleigh-Taylor instability. The star has a dipole field misaligned relative to the rotation axis by a small angle Θ. Simulations show that, depending on the accretion rate, a star may be in the stable or unstable regime of accretion. In the unstable regime, matter penetrates deep into the magnetosphere through several elongated “tongues” which deposit matter at random places on the surface of the star, leading to stochastic light-curves. In the stable regime, matter accretes in ordered funnel streams and the light-curves are almost periodic. A star may switch between these two regimes depending on the accretion rate and may thus show alternate episodes of ordered pulsations and stochastic light-curves. In the intermediate regime, both stochastic and ordered pulsations are observed. For Θ > 30, the instability is suppressed and stable accretion through funnel streams dominates.

Variability Profiles of Millisecond X-Ray Pulsars: Results of Pseudo-Newtonian Three-dimensional Magnetohydrodynamic Simulations

We model the variability profiles of millisecond-period X-ray pulsars. We performed three-dimensional magneto- hydrodynamic simulations of disk accretion to millisecond-period neutron stars with a misaligned magnetic dipole moment, using the pseudo-Newtonian Paczynski-Wiita potential to model general relativistic effects. We found that the shapes of the resulting funnel streams of accreting matter and the hot spots on the surface of the star are quite similar to those for more slowly rotating stars obtained from earlier simulations using the Newtonian potential. The funnel streams and hot spots rotate approximately with the same angular velocity as the star. The spots are bow- shaped (bar-shaped) for small (large) misalignment angles. We found that the matter falling on the star has a higher Mach number when we use the Paczynski-Wiita potential than in the Newtonian case. Having obtained the surface distribution of the emitted flux, we calculated the variability curves of the star, taking into account general rel- ativistic, Doppler, and light-travel time effects. We found that general relativistic effects decrease the pulse frac- tion (flatten the light curve), while Doppler and light-travel time effects increase it and distort the light curve. We also found that the light curves from our hot spots are reproduced reasonably well by spots with a Gaussian flux distribution centered at the magnetic poles. We also calculated the observed image of the star in a few cases and saw that for certain orientations, both the antipodal hot spots are simultaneously visible, as noted by earlier authors. Subject headingg accretion, accretion disks — pulsars: general — X-rays: stars

QPO emission from moving hot spots on the surface of neutron stars: a model

We present recent results of 3D magnetohydrodynamic simulations of neutron stars with small misalignment angles, as regards the features in light curves produced by regular movements of the hot spots during accretion on to the star. In particular, we show that the variation of position of the hot spot created by the infalling matter, as observed in 3D simulations, can produce high-frequency quasi-periodic oscillations (QPOs) with frequencies associated with the inner zone of the disc. Previously reported simulations show that the usual assumption of a fixed hot spot near the polar region is valid only for misalignment angles Θ relatively large. Otherwise, two phenomena challenge the assumption: one is the presence of Rayleigh-Taylor instabilities at the disc-magnetospheric boundary, which produce tongues of accreting matter that can reach the star almost anywhere between the equator and the polar region; the other one is the motion of the hot spot around the magnetic pole during stable accretion. In this paper, we start by showing that both phenomena are capable of producing short-term oscillations in the light curves. We then use Monte Carlo techniques to produce model light curves based on the features of the movements observed, and we show that the main features of kHz QPOs can be reproduced. Finally, we show the behaviour of the frequencies of the moving spots as the mass accretion rate changes, and propose a mechanism for the production of double QPO peaks.

Possible quasi-periodic oscillations from unstable accretion: 3D magnetohydrodynamic simulations

We investigate the photometric variability of magnetized stars, particularly neutron stars, accreting through a magnetic Rayleigh–Taylor-type instability at the disc–magnetosphere interface, and compare it with the variability during stable accretion, with the goal of looking for possible quasi-periodic oscillations (QPOs). The light curves during stable accretion show periodicity at the stars frequency and sometimes twice that, due to the presence of two funnel streams that produce antipodal hotspots near the magnetic poles. On the other hand, light curves during unstable accretion through tongues penetrating the magnetosphere are more chaotic due to the stochastic behaviour of the tongues, and produce noisier power spectra. However, the power spectra do show some signs of quasi-periodic variability. Most importantly, the rotation frequency of the tongues and the resulting hotspots are close to the inner-disc orbital frequency, except in the most strongly unstable cases. There is therefore a high probability of observing QPOs at that frequency in longer simulations. In addition, the light curves in the unstable regime show periodicity at the stars rotation frequency in many of the cases investigated here, again except in the most strongly unstable cases which lack funnel flows and the resulting antipodal hotspots. The noisier power spectra result in the fractional rms amplitudes of the Fourier peaks being smaller. We also study in detail the effect of the misalignment angle between the rotation and magnetic axes of the star on the variability, and find that at misalignment angles ≳25° the stars period always appears in the light curves.

Discovery of drifting high-frequency quasi-periodic oscillations in global simulations of magnetic boundary layers

We report on the numerical discovery of quasi-periodic oscillations (QPOs) associated with accretion through a non-axisymmetric magnetic boundary layer in the unstable regime, when two ordered equatorial streams form and rotate synchronously at approximately the angular velocity of the inner disc. The streams hit the stars surface producing hotspots. Rotation of the spots leads to high-frequency QPOs. We performed a number of simulation runs for different magnetospheric sizes from small to tiny, and observed a definite correlation between the inner disc radius and the QPO frequency: the frequency is higher when the magnetosphere is smaller. In the stable regime, a small magnetosphere forms and accretion through the usual funnel streams is observed, and the frequency of the star is expected to dominate the light curve. We performed exploratory investigations of the case in which the magnetosphere becomes negligibly small and the disc interacts with the star through an equatorial belt. We also performed investigation of somewhat larger magnetospheres where one or two ordered tongues may dominate over other chaotic tongues. In application to millisecond pulsars, we obtain QPO frequencies in the range of 350-990 Hz for one spot. The frequency associated with rotation of one spot may dominate if spots are not identical or antipodal. If the spots are similar and antipodal, then the frequencies are twice as high. We show that variation of the accretion rate leads to drift of the QPO peak.

2D and 3D MHD simulations of disk accretion by rotating magnetized stars: Search for variability

Abstract We performed 2D and full 3D magnetohydrodynamic simulations of disk accretion to a rotating star with an aligned or misaligned dipole magnetic field. We investigated the rotational equilibrium state and derived from simulations the ratio between two main frequencies: the spin frequency of the star and the orbital frequency at the inner radius of the disk. In 3D simulations we observed different features related to the non-axisymmetry of the magnetospheric flow. These features may be responsible for high-frequency quasi-periodic oscillations (QPOs). Variability at much lower frequencies may be connected with restructuring of the magnetic flux threading the inner regions of the disk. Such variability is specifically strong at the propeller stage of evolution.

Modeling of Disk‐Star Interaction: Different Regimes of Accretion and Variability

The appearance and time variability of the accreting millisecond X‐ray pulsars (hereafter AMXPs, e.g. [27]) depends strongly on the accretion rate and the effective viscosity and magnetic diffusivity of the disk‐magnetosphere boundary. The accretion rate is the main parameter which determines the location of the magnetospheric radius of the neutron star. We introduce a classification of accreting neutron stars as a function of the accretion rate and show the corresponding stages obtained from our global 3D magnetohydrodynamic (MHD) simulations and from our axisymmetric MHD simulations. We discuss the expected variability features in these stages of accretion, both periodic and quasi‐periodic (QPOs). We conclude that the periodicity may be suppressed at both very high and very low accretion rates. In addition the periodicity may disappear when ordered funnel flow accretion is replaced by disordered accretion through the interchange instability.

GRMHD simulations of magnetized advection-dominated accretion on a non-spinning black hole: role of outflows: Magnetized advection-dominated accretion

We present results from two long-duration general relativistic magneto-hydrodynamic (GRMHD) simulations of advection-dominated accretion around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200 000 GM/c3 and achieved inflow equilibrium out to a radius ∼90 GM/c2. Even at this relatively large radius, the mass outflow rate is found to be only 60 per cent of the net mass inflow rate into the black hole. The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a shorter time of 100 000 GM/c3. Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius ∼170 GM/c2. Here, becomes equal to at r ∼ 160 GM/c2. Since the mass outflow rates in the two simulations do not show robust convergence with time, it is likely that the true outflow rates are lower than our estimates. The effect of black hole spin on mass outflow remains to be explored. Neither simulation shows strong evidence for convection, though a complete analysis including the effect of magnetic fields is left for the future.

GRMHD Simulations of Magnetized Advection Dominated Accretion on a Non-Spinning Black Hole: Outflows and Convection

We present results from two long-duration general relativistic magneto-hydrodynamic (GRMHD) simulations of advection-dominated accretion around a non-spinning black hole. The first simulation was designed to avoid significant accumulation of magnetic flux around the black hole. This simulation was run for a time of 200 000 GM/c3 and achieved inflow equilibrium out to a radius ∼90 GM/c2. Even at this relatively large radius, the mass outflow rate is found to be only 60 per cent of the net mass inflow rate into the black hole. The second simulation was designed to achieve substantial magnetic flux accumulation around the black hole in a magnetically arrested disc. This simulation was run for a shorter time of 100 000 GM/c3. Nevertheless, because the mean radial velocity was several times larger than in the first simulation, it reached inflow equilibrium out to a radius ∼170 GM/c2. Here, becomes equal to at r ∼ 160 GM/c2. Since the mass outflow rates in the two simulations do not show robust convergence with time, it is likely that the true outflow rates are lower than our estimates. The effect of black hole spin on mass outflow remains to be explored. Neither simulation shows strong evidence for convection, though a complete analysis including the effect of magnetic fields is left for the future.