Neutron stars are essentially very heavy (1.4 solar masses!) nuclei, the size of a city (R ~ 10 km), and contain, in their core, matter at densities higher than that inside ordinary nuclei (ρnuc = 2.8 x 1014 g cm-3). The composition of the inner core remains difficult to access both theoretically and observationally. In contrast, the outer part of the star, its crust, where ρ < ρnuc, is amenable to a more reliable theoretical description. Here too theory predicts interesting and exotic phases of matter. Below the atmosphere and a liquid ocean lays the crust composed of a nuclear lattice immersed in an almost ideal relativistic gas of degenerate electrons. With increasing density the nuclei become more and more neutron rich and eventually, at a density ρdrip ~ 4-8 x 1011 g cm-3, called the neutron-drip point, most neutrons can no longer be bound inside nuclei. In this inner crust, matter is made of neutron rich nuclei immersed in an almost perfect gas of degenerate electrons and a quantum liquid of neutrons that are predicted to form a superfluid. Finally, when ρ approaches ~ ¼ ρnuc, theory predicts that nuclei are highly deformed and nuclear shapes, ranging from rods ("spaghetti"), plates ("lasagna"), and tubes ("anti-spaghetti") to bubbles ("swiss-cheese") are expected. This regime is collectively referred to as the nuclear pasta phase and is likely to be a liquid crystal, immersed in the neutron superfluid.
The quasi-persistent sources are a recently discovered class of low-mass X-ray binaries (LMXBs) characterized by long periods of accretion, years to decades, followed by even longer, decades to centuries, periods of quiescence during which no, or very little, accretion is occurring. If the accretor is a neutron star, the accreted matter, mostly H and He, is processed in the atmosphere and ocean by thermo-nuclear reactions into a mix or either iron-peak nuclei or a complex mixture of C/O and heavy, A ≤ 104, nuclei. Under further compression due to the ongoing accretion, complex sequences of reactions, as electron captures and, in the inner crust, neutron emissions and absorption and pycno-nuclear fusions (i.e., induced by the high pressure) continuously transform the nuclei till they are pushed into the pasta phase and eventually into the core where they dissolve. Through these reactions, each accreted nucleon will liberate from 1.5 to 2 MeV of thermal energy and heat the crust. When the accretion outburst is long enough the crust is heated significantly and driven out of thermal equilibrium with the core. After the outburst the subsequent cooling of the crust can be, and has been, observed as illustrated in the left panel of Fig. 1. It is this process, that makes them unique laboratories to study thermal, transport and nuclear processes in the neutron star crust. Surprisingly, recently for two sources that exhibited short (~months) accretion outbursts similar crust cooling curves have been observed, as displayed in the right panel of Fig.1. Although this behavior is not yet understood, its similarity to what is seen in quasi-persistent sources opens up a new observational opportunities because these systems are much more abundant than those which accrete for years to decades.
The seven cooling curves of transient LMXBs observed to date: with long (left panel), and short (right panel) accretion outbursts.
Theoretical modeling of three observed crust coolings for the long outburst sources has met some success, as illustrated in Fig. 1, with even some predictive power as seen in the right panel. In particular, it has been shown that the observed decreasing stellar effective temperature at different times after the end of the outburst is determined by the thermal state of layers of increasing depth: these observations, together with their theoretical modeling, are like pealing an onion, progressively revealing physics of deeper and deeper layers -- tomography of nature's most extreme system. To watch, and interpret in realtime, the relaxation of a neutron star after it has been heated out of equilibrium is an observers delight and a theorists dream come true.
Modelling of observed crust cooling curves. Left panel: MXB 1659-29. Right panel: two possible scenarios for XTE J1701-46, with the latest data point, at day 1906, from the Chandra observation performed in October 2012, which confirms the prediction of scenario ``A''.
Several macroscopic parameters also control the heating and cooling of the crust during and after an outburst: A) the crust thickness, determined by the neutron star mass; B) the initial stellar temperature, determined by the long term accretion history and the core composition that controls its neutrino emission, but potentially observable by observation of the neutron star before the outburst or after it, once the crust has fully relaxed; C) the mass accretion rate during the outburst and the duration of it, which are also directly observed.
Observations will also identify which data are likely affected by residual accretion, which is known to occur at least in some instances, so that those data can be ignored when the crust cooling curves are modeled (two such likely events are marked with "?" in the right panel of Fig. 2). However, not always such instances can be directly recognized and residual accretion therefore is an important issue that will be discussed in the meetings.
X-ray observers are in urgent need of theoretical input from the modellers to select ideal systems for constraining neutron star physics, and to obtain observing time at the most appropriate moments for optimal sampling of the cooling curves. The modellers need improved physics to include in their models, and physicists need modellers to help identify specific microphysics that is important to model observations. In addition, the observers will give vital information about the observed behavior of the sources to the modellers and physicists, what the limitations are on the observational results, as well as what is achievable and realistic observationally wise.
Ongoing discussions between observers, modellers and theorists, which were initiated in the process of putting together this proposal, are already reshaping the scientific agenda of the whole group. This has been an important missing ingredient, and perhaps responsible for the piecemeal approach to this problem until now. The overarching goal is to interpret these fascinating observations in terms of fundamental physical processes that occur inside the neutron star crust. We can only claim to have a basic paradigm of crust relaxation if the predictions of the theory can naturally incorporate source to source and event to event variability in terms of well founded microphysical, astrophysical and observational parameters.
The observations of crust cooling entail detailed monitoring of the systems with the X-ray satellites Chandra, XMM-Newton and Swift. Those satellites are getting old, and there is no replacement planned in the near future. Observationally we might only have a few more years to obtain high quality data of the crust cooling of accreting neutron stars and the time is now for modellers, theoretical physicists and observers to come together to identify the open questions, design optimal observing strategies, develop the theory and perform the modelling required to answer these questions.