Research Summary

Starting with an analytical calculation of the thermonuclear depletion of lithium, beryllium, and boron in contracting, fully convective, pre-main-sequence stars less massive than about 0.5 solar masses, we demonstrated the robustness of using the lithium abundance for constraining cluster ages. Because these low mass stars are fully convective, we can accurately model them as fully mixed polytropes (index 3/2) with the assumption that the effective temperature is fixed. The destruction rate of lithium, beryllium, and boron are strong functions of central temperature, and so the transition from the star having an abundance of these elements to having a deficit is rapid. This is fortunate, as it is easy to determine if a star is depleted, but difficult to determine by how much.

Although our calculation assumes a fixed effective temperature, it does not constrain its value. Our technique then accurately determines the radius, age, and luminosity of the pre-main-sequence star as a function of two observables, elemental abundance and effective temperature. Lithium abundance observations also provide a useful discriminant between stars and brown dwarfs, as the latter do not reach central temperatures hot enough to destroy lithium. By comparing pairs of cluster stars, one with lithium and one without, we determined a minimum age (60 Myr) for α Persei and the Pleiades (105 Myr), in confirmation of that found by Basri et al.

While fitting the reactions, I became interested in the possible effect of a sub-threshold (25.7 keV) resonance in the reaction ⁹Be(p,α)⁶Li. Experiments had been unable to accurately determine the spin and parity of the intermediate state; one of the possible (spin, parity) combinations would allow this reaction to proceed via a level in the compound nucleus ¹⁰B with an s-wave entrance channel. In principle this resonance could be tested by observations of beryllium abundances in sub-solar mass stars.

Many accreting neutron stars exihibit X-ray bursts (called type I) which canonically appear as a rapid brightening on a timescale of order 1 s, followed by a roughly exponential decay. The recurrence times, energetics, and spectral properties of these bursts are consistent with them being due to unstable burning of accreted H/He.

For neutron stars rapidly accreting pure He (such as on the polar cap of an accretion-powered pulsar), there is a possibility of detecting unstable carbon burning. At super-Eddington local accretion rates, the recurrence times are short enough (hours to days) to make this burning observable.

Recently, large super bursts have been observed from several weakly magnetized neutron stars. One example of which is 4U 1820-30, which accretes pure He from its companion. For this object, the identification of the superburst with a thermonuclear instability in a carbon-rich layer seems secure; there remain many interesting questions about the energetics and evolution of the burst.

Accretion at near-Eddington rates heats the outer atmosphere to temperatures greater than 5  10⁸ K. At this temperature, neutrino emissions from the deep crust (densities greater than neutron drip) and core become important. These rates are relevant for the brightest low-mass X-ray binaries, the Z sources. As the material in the crust is pushed ever deeper by the accumulation of material in overlying layers, a series of compression-induced reactions (electron captures, neutron emissions, and pycnonuclear reactions) release about 1 MeV per accreted baryon (Haensel 1990); this heat is deposited in the region about neutron drip. This heat is then conducted into the deep crust and core and re-emitted as neutrinos. The temperature in the inner crust and core therefore depends on the method of neutrino emission (i.e., modified Urca vs. accelerated mechanisms) and also the degree to which proton and neutron superfluidity suppress that emission.

For low-mass X-ray binaries, accretion over the lifetime of the binary (∼ 10⁹ yr) can replace the entire crust. This crust will differ in composition from the original, which is approximately in nuclear statistical equilibrium. The impurities can drastically reduce the thermal conductivity, which leads to a decrease in the timescale for ohmic decay of crustal magnetic fields.

This work began with a study of how deep the strong magnetic fields of accreting X-ray pulsars could confine the accretion flow, and the consequences for unstable hydrogen/helium burning on the accreting pulsar (2.14 Hz) GRO J1744-28 and unstable carbon burning on more strongly magnetized X-ray pulsars. Following Hameury et al., L. Bildsten & I performed a magnetostatic calculation and found that the magnetic field lines are strongly distorted from vertical (i.e., the mound spreads) when the pressure at its base is greater than about R/H times the magnetic pressure B²/8 π, where R is the radius of the polar cap and H is the thickness of the atmosphere. We applied this to GRO J1744-28 and found that the inferred magnetic field could confine the accretion flow enough to make the burning of hydrogen and helium stable. This would explain the absence of type I X-ray bursts. We expected that as the outburst faded and the accretion rate declined, the local accretion rate would eventually become sub-Eddington and allow unstable burning to begin. The absence of unstable burning (either in the form of type I X-ray bursts or slow flares) raises intriguing questions about the geometry of the polar cap and the ability of the magnetic field to halt a convective burning front.

A more refined calculation of the stability of the accreted material was done my C Litwin, myself, and R Rosner. We found that line-tying to the crust stabilizes short-wavelength ballooning modes until the overpressure at the top of the neutron star crust exceeds the magnetic pressure by a factor ∼8(a/h), where a and h are, respectively, the lateral extent of the accretion region and the density scale height. The most unstable modes are localized within a density scale height above the crust.