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Register a new userIonization Equilibrium Timescales in Collisional Plasmas
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Astrophysical shocks or bursts from a photoionizing source can disturb the typical collisional plasma found in galactic interstellar media or the intergalactic medium. The spectrum emitted by this plasma contains diagnostics that have been used to determine the time since the disturbing event, although this determination becomes uncertain as the elements in the plasma return to ionization equilibrium. A general solution for the equilibrium timescale for each element arises from the elegant eigenvector method of solution to the problem of a non-equilibrium plasma described by Masai (1984) and Hughes & Helfand (1985). In general the ionization evolution of an element Z in a constant electron temperature plasma is given by a coupled set of Z+1 first order differential equations. However, they can be recast as Z uncoupled first order differential equations using an eigenvector basis for the system. The solution is then Z separate exponential functions, with the time constants given by the eigenvalues of the rate matrix. The smallest of these eigenvalues gives the scale of slowest return to equilibrium independent of the initial conditions, while conversely the largest eigenvalue is the scale of the fastest change in the ion population. These results hold for an ionizing plasma, a recombining plasma, or even a plasma with random initial conditions, and will allow users of these diagnostics to determine directly if their best-fit result significantly limits the timescale since a disturbance or is so close to equilibrium as to include an arbitrarily-long time.
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We report on high-resolution X-ray spectroscopy of the ultracompact X-ray binary pulsar 4U 1626-67 with Chandra/HETGS acquired in 2010, two years after the pulsar experienced a torque reversal. The well-known strong Ne and O emission lines with Keplerian profiles are shown to arise at the inner edge of the magnetically-channeled accretion disk. We exclude a photoionization model for these lines based on the absence of sharp radiative recombination continua. Instead, we show that the lines arise from a collisional plasma in the inner-disk atmosphere, with $Tsimeq 10^7$ K and $n_e sim 10^{17}$ cm^(-3). We suggest that the lines are powered by X-ray heating of the optically-thick disk inner edge at normal incidence. Comparison of the line profiles in HETGS observations from 2000, 2003, and 2010 show that the inner disk radius decreased by a factor of two after the pulsar went from spin-down to spin-up, as predicted by magnetic accretion torque theory. The inner disk is well inside the corotation radius during spin-up, and slightly beyond the corotation radius during spin-down. Based on the disk radius and accretion torque measured during steady spin-up, the pulsars X-ray luminosity is $2times 10^{36}$ erg/s, yielding a source distance of 3.5(+0.2-0.3) kpc. The mass accretion rate is an order of magnitude larger than expected from gravitational radiation reaction, possibly due to X-ray heating of the donor. The line profiles also indicate a binary inclination of 39(+20-10) degrees, consistent with a 0.02 Msun donor star. Our emission measure analysis favors a He white dwarf or a highly-evolved H-poor main sequence remnant for the donor star, rather than a C-O or O-Ne white dwarf. The measured Ne/O ratio is 0.46+-0.14 by number. In an appendix, we show how to express the emission measure of a H-depleted collisional plasma without reference to a H number density.
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