A numerical magnetohydrodynamic scheme using the hydrostatic approximation

In gravitationally stratified fluids, length scales are normally much greater in the horizontal direction than in the vertical one. When modelling these fluids it can be advantageous to use the hydrostatic approximation, which filters out vertically propagating sound waves and thus allows a greater timestep. We briefly review this approximation, which is commonplace in atmospheric physics, and compare it to other approximations used in astrophysics such as Boussinesq and anelastic, finding that it should be the best approximation to use in context such as radiative stellar zones, compact objects, stellar or planetary atmospheres and other contexts. We describe a finite-difference numerical scheme which uses this approximation, which includes magnetic fields.Comment: 15 pages, 18 figures, accepted for publication by MNRA

Fast and slow magnetic deflagration fronts in Type I X-ray bursts

Type I X-ray bursts are produced by thermonuclear runaways that develop on accreting neutron stars. Once one location ignites, the flame propagates across the surface of the star. Flame propagation is fundamental in order to understand burst properties like rise time and burst oscillations. Previous work quantified the effects of rotation on the front, showing that the flame propagates as a deflagration and that the front strongly resembles a hurricane. However the effect of magnetic fields was not investigated, despite the fact that magnetic fields strong enough to have an effect on the propagating flame are expected to be present on many bursters. In this paper we show how the coupling between fluid layers introduced by an initially vertical magnetic field plays a decisive role in determining the character of the fronts that are responsible for the Type I bursts. In particular, on a star spinning at 450 Hz (typical among the bursters) we test seed magnetic fields of $10^{7} - 10^{10}$ G and find that for the medium fields the magnetic stresses that develop during the burst can speed up the velocity of the burning front, bringing the simulated burst rise time close to the observed values. By contrast, in a magnetic slow rotator like IGR J17480--2446, spinning at 11 Hz, a seed field $\gtrsim 10^9$ G is required to allow localized ignition and the magnetic field plays an integral role in generating the burst oscillations observed during the bursts.Comment: Pubblished on MNRA

Flame Propagation on the Surfaces of Rapidly Rotating Neutron Stars during Type I X-ray Bursts

We present the first vertically resolved hydrodynamic simulations of a laterally propagating, deflagrating flame in the thin helium ocean of a rotating accreting neutron star. We use a new hydrodynamics solver tailored to deal with the large discrepancy in horizontal and vertical length scales typical of neutron star oceans, and which filters out sound waves that would otherwise limit our timesteps. We find that the flame moves horizontally with velocities of order $10^5$ cm s$^{-1}$, crossing the ocean in few seconds, broadly consistent with the rise times of Type I X-ray bursts. We address the open question of what drives flame propagation, and find that heat is transported from burning to unburnt fuel by a combination of top-to-bottom conduction and mixing driven by a baroclinic instability. The speed of the flame propagation is therefore a sensitive function of the ocean conductivity and spin: we explore this dependence for an astrophysically relevant range of parameters and find that in general flame propagation is faster for slower rotation and higher conductivity.Comment: Accepted for publication by MNRA

Rotational effects in thermonuclear Type I Bursts: equatorial crossing and directionality of flame spreading

In a previous study on thermonuclear (type I) nursts on accreting neutron stars we addressed and demonstrated the importance of the effects of rotation, through the Coriolis force, on the propagation of the burning flame. However, that study only analysed cases of longitudinal propagation, where the Coriolis force coefficient $2\Omega\cos\theta$ was constant. In this paper, we study the effects of rotation on propagation in the meridional (latitudinal) direction, where the Coriolis force changes from its maximum at the poles to zero at the equator. We find that the zero Coriolis force at the equator, while affecting the structure of the flame, does not prevent its propagation from one hemisphere to another. We also observe structural differences between the flame propagating towards the equator and that propagating towards the pole, the second being faster. In the light of the recent discovery of the low spin frequency of burster IGR~J17480-2446 rotating at 11 Hz (for which Coriolis effects should be negligible) we also extend our simulations to slow rotation.Comment: Accepted for publication by MNRA

On the dependence of X-ray burst rate on accretion and spin rate

Nuclear burning and its dependence on the mass accretion rate are fundamental ingredients for describing the complicated observational phenomenology of neutron stars in binary systems. Motivated by high quality burst rate data emerging from large statistical studies, we report general calculations relating bursting rate to mass accretion rate and neutron star rotation frequency. In this first work we neglect general relativistic effects and accretion topology, though we discuss where their inclusion should play a role. The relations we derive are suitable for different burning regimes and provide a direct link between parameters predicted by theory and what is to be expected in observations. We illustrate this for analytical relations of different unstable burning regimes that operate on the surface of an accreting neutron star. We also use the observed behaviour of burst rate to suggest new constraints on burning parameters. We are able to provide an explanation for the long standing problem of the observed decrease of burst rate with increasing mass accretion that follows naturally from these calculations: when accretion rate crosses a certain threshold, ignition moves away from its initially preferential site and this can cause a net reduction of the burst rate due to the effects of local conditions that set local differences in both burst rate and stabilization criteria. We show under which conditions this can happen even if locally the burst rate keeps increasing with accretion.Comment: Accepted for publication on Ap

The jet-disk symbiosis without maximal jets: 1-D hydrodynamical jets revisited

In this work we discuss the recent criticism by Zdziarski of the maximal jet model derived in Falcke & Biermann (1995). We agree with Zdziarski that in general a jet's internal energy is not bounded by its rest-mass energy density. We describe the effects of the mistake on conclusions that have been made using the maximal jet model and show when a maximal jet is an appropriate assumption. The maximal jet model was used to derive a 1-D hydrodynamical model of jets in agnjet, a model that does multiwavelength fitting of quiescent/hard state X-ray binaries and low-luminosity active galactic nuclei. We correct algebraic mistakes made in the derivation of the 1-D Euler equation and relax the maximal jet assumption. We show that the corrections cause minor differences as long as the jet has a small opening angle and a small terminal Lorentz factor. We find that the major conclusion from the maximal jet model, the jet-disk symbiosis, can be generally applied to astrophysical jets. We also show that isothermal jets are required to match the flat radio spectra seen in low-luminosity X-ray binaries and active galactic nuclei, in agreement with other works.Comment: 7 pages, accepted by A&

Dynamics of Laterally Propagating Flames in X-ray Bursts. I. Burning Front Structure

We investigate the structure of laterally-propagating flames through the highly-stratified burning layer in an X-ray burst. Two-dimensional hydrodynamics simulations of flame propagation are performed through a rotating plane-parallel atmosphere, exploring the structure of the flame. We discuss the approximations needed to capture the length and time scales at play in an X-ray burst and describe the flame acceleration observed. Our studies complement other multidimensional studies of burning in X-ray bursts.Comment: Submitted to Ap

Superburst oscillations: ocean and crustal modes excited by Carbon-triggered Type I X-ray bursts

Accreting neutron stars (NS) can exhibit high frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. The frequencies can be offset from the spin frequency of the NS by several Hz, and can drift by 1-3 Hz. One possible explanation is a mode in the bursting ocean, the frequency of which would decrease (in the rotating frame) as the burst cools, hence explaining the drifts. Most burst oscillations have been observed during H/He triggered bursts, however there has been one observation of oscillations during a superburst; hours' long Type I X-ray bursts caused by unstable carbon burning deeper in the ocean. This paper calculates the frequency evolution of an oceanic r-mode during a superburst. The rotating frame frequency varies during the burst from 4-14 Hz, and is sensitive to the background parameters, in particular the temperature of the ocean and ignition depth. This calculation is compared to the superburst oscillations observed on 4U-1636-536. The predicted mode frequencies ($\sim$ 10 Hz) would require a spin frequency of $\sim$ 592 Hz to match observations; 6 Hz higher than the spin inferred from an oceanic r-mode model for the H/He triggered burst oscillations. This model also over-predicts the frequency drift during the superburst by 90 %.Comment: Accepted for publication in MNRA

The low luminosity behaviour of the 4U 0115+63 Be/X-ray transient

The Be/X-ray transient 4U 0115+63 exhibited a giant, type-II outburst in October 2015. The source did not decay to its quiescent state but settled in a meta-stable plateau state (a factor ~10 brighter than quiescence) in which its luminosity slowly decayed. We used XMM-Newton to observe the system during this phase and we found that its spectrum can be well described using a black-body model with a small emitting radius. This suggests emission from hot spots on the surface, which is confirmed by the detection of pulsations. In addition, we obtained a relatively long (~7.9 ksec) Swift/XRT observation ~35 days after our XMM-Newton one. We found that the source luminosity was significantly higher and, although the spectrum could be fitted with a black-body model the temperature was higher and the emitting radius smaller. Several weeks later the system started a sequence of type-I accretion outbursts. In between those outbursts, the source was marginally detected with a luminosity consistent with its quiescent level. We discuss our results in the context of the three proposed scenarios (accretion down to the magnestospheric boundary, direct accretion onto neutron star magnetic poles or cooling of the neutron star crust) to explain the plateau phase.Comment: 8 pages, 4 figures, 2 tables, accepted for publication in MNRA