Compositionally-driven convection in the oceans of accreting neutron stars

At the base of the ocean, matter freezes as it is compressed by continuing accretion, becoming part of the solid crust. Horowitz et al. (2007) carried out molecular dynamics simulations of the freezing of a mixture of 17 species taken from a calculation of rp-process hydrogen and helium burning and hence representative of the kind of mixture expected to make up the ocean of an accreting neutron star (Schatz et al. 2001;Gupta et al. 2007). They found that this mixture underwent chemical separation during crystallization, such that light elements (charge number Z 20) were preferentially left behind in the liquid, whereas heavier elements were preferentially incorporated into the solid. In a previous paper (Medin & Cumming 2010, hereafter Paper I) we showed that this result can be understood by generalizing previous work using fits to the free energies of the liquid and solid states of binary and tertiary plasmas.

In this paper, we address the implications of chemi-cal separation for the structure and composition of the ocean. Horowitz et al. (2007) raised the question of what the steady-state ocean would look like, since the matter entering the crust is enriched in certain elements compared to others, and therefore different from the mean ocean composition. We investigate this question here, and argue that the retention of light elements in the liquid acts as a source of buoyancy that drives a slow but continual mixing of the ocean, enriching it substantially in light elements and leading to a relatively uniform composition with depth. The steady state arises as the ocean enriches in light elements to the point where the composition of the solid that forms upon freezing matches the composition of matter entering the top of the ocean.

One motivation for studying this problem comes from models for superbursts which involve thermally-unstable carbon burning in the deep ocean of the neutron star (Cumming & Bildsten 2001;Strohmayer & Brown 2002). The energy release in these very long duration thermonuclear flashes, inferred from fitting their lightcurves (Cumming et al. 2006), corresponds to carbon fractions of ≈ 20%. This has been challenging to produce in models of the nuclear burning of the accreted hydrogen and helium. If the hydrogen and helium burn unstably, the amount of carbon produced is 1% (Woosley et al. 2004), and whereas stable burning can produce large carbon fractions (Schatz et al. 2003), time-dependent models do not show stable burning at the ≈ 10% Eddington accretion rates of superburst sources (although observationally, superburst sources show evidence that much of the accreted material may not burn in Type I bursts; in ’t Zand et al. 2003).

Perhaps even more problematic than making enough carbon is that carbon ignition models for superbursts require large ocean temperatures ≈ 6 × 10 8 K at the ignition depth, which are difficult to achieve in standard models of crust heating (e.g., Cumming et al. 2006;Keek et al. 2008). Similarly, Brown & Cumming (2009) inferred a large inwards heat flux in the outer crust of the transiently-accreting neutron stars MXB 1659-29 and KS 1731-260 by fitting their cooling curves in quiescence. Both of these observations imply an additional heating source in the outer crust or ocean is needed. In this paper, we begin to address the question of to what extent chemical separation could enrich the ocean in carbon and other light elements, or provide a heat source that could alleviate some of the difficulty of matching the observations of superbursts and transient cooling.

We begin in §2 by reviewing the physics of chemical separation, and discussing the timescales on which accretion, crystallization, diffusion, sedimentation, and convection occur, leading us to a picture of compositionallydriven convection. In §3 we calculate the structure of the steady-state ocean for two simplified models: first, accretion of a two-component mixture composed of Se and either O or Fe; and second, accretion of a mixture of H and He which then burns to pr

…(Full text truncated)…