Burial of the polar magnetic field of an accreting neutron star – II. Hydromagnetic stability of axisymmetric equilibria

Abstract

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad-Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as M a = 6 × 10 −4 M , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to M a < 10 −4 M ) into the time-dependent, ideal-magnetohydrodynamic code ZEUS-3D and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in ZEUS-3D. Surprisingly, it is observed that the equilibria are marginally stable for all M a 6 × 10 −4 M ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).

Gravitational waves from surface inhomogeneities of neutron stars

“…Detailed two and three-dimensional MHD simulations [31,32] indicate a lower mass threshold (5×10 −13 M ⊙ for B p ∼ 10 12 G) above which pressure driven instabilities would start operating and matter could not be efficiently confined by the local field in the polar cap. This threshold mass is much smaller than the amount indicated in earlier investigations [14,29,45], but matches very closely with that obtained from simple dimensional estimates in Eq. [15].…”

“…It needs to be noted that some of the recent estimates [14,29,45] place the mass of a magnetically confined accretion column at a much larger value (∆M ∼ 10 −5 M ⊙ ) by allowing for mass-loading beyond the accretion column. This approach makes use of plasma loading on all field lines providing additional lateral support to help form accretion mounds with very large masses.…”

Evolution towards and beyond accretion-induced collapse of massive white dwarfs and formation of millisecond pulsars

“…The exact mechanism for this process is still unknown. It may be related to decay of crustal fields by ohmic dissipation and diffusion from heating via nuclear processing of accreted material (Romani 1990;Geppert & Urpin 1994;Konar & Bhattacharya 1997), burial (screening) of the field (Zhang 1998;Cumming et al 2001;Payne & Melatos 2007), or decay of core fields due to flux tube expulsion from the superfluid interior induced by rotational slow-down in the initial phases of mass accretion (Srinivasan et al 1990); see also review by Bhattacharya (2002). Even a small amount of material accreted may lead to significant B-field decay, contradicting the observational evidence that these binary NSs have accreted large amounts of material.…”

Long-term change in the cyclotron line energy in Hercules X-1

“…Or, whether screening or burial of the magnetic field at the polar caps is possible (Brown & Bildsten 1998;Payne & Melatos 2004;Litwin et al 2001;Payne & Melatos 2007). It needs to be investigated, how much mass could eventually be stored in the magnetically confined mountains, whether matter is continuously leaking out to larger areas of the neutron star surface (due to plasma pressure exceeding the magnetic pressure) and on what timescales an observational effect can be expected.…”