Excitation and charge transfer in H-H+ collisions at 5-80 keV and application to astrophysical shocks
Tseliakhovich, Dmitriy ; Hirata, Christopher M. ; Heng, Kevin
In: Monthly Notices of the Royal Astronomical Society, 2012, vol. 422, no. 3, p. 2357-2371
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- In astrophysical regimes where the collisional excitation of hydrogen atoms is relevant, the cross-sections for the interactions of hydrogen atoms with electrons and protons are necessary for calculating line profiles and intensities. In particular, at relative velocities exceeding ∼1000 km s−1, collisional excitation by protons dominates over that by electrons. Surprisingly, the H-H+ cross-sections at these velocities do not exist for atomic levels of n≥ 4, forcing researchers to utilize extrapolation via inaccurate scaling laws. In this study, we present a faster and improved algorithm for computing cross-sections for the H-H+ collisional system, including excitation and charge transfer to the n≥ 2 levels of the hydrogen atom. We develop a code named bdscx which directly solves the Schrödinger equation with variable (but non-adaptive) resolution and utilizes a hybrid spatial-Fourier grid. Our novel hybrid grid reduces the number of grid points needed from ∼4000n6 (for a ‘brute force', Cartesian grid) to ∼2000n4 and speeds up the computation by a factor of ∼50 for calculations going up to n= 4. We present (l, m)-resolved results for charge transfer and excitation final states for n= 2-4 and for projectile energies of 5-80 keV, as well as fitting functions for the cross-sections. The ability to accurately compute H-H+ cross-sections to n= 4 allows us to calculate the Balmer decrement, the ratio of Hα to Hβ line intensities. We find that the Balmer decrement starts to increase beyond its largely constant value of 2-3 below 10 keV, reaching values of 4-5 at 5 keV, thus complicating its use as a diagnostic of dust extinction when fast (∼1000 km s−1) shocks are impinging upon the ambient interstellar medium