X-Ray Ionization of Protoplanetary Disks: Erratum

Details X-Ray Ionization of Protoplanetary Disks: Erratum X-Ray Ionization of Protoplanetary Disks: Erratum

Aug 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997apj...485..920g&link_type=abstract

Astrophysical Journal v.485, p. 920

Astronomy and Astrophysics

Astronomy

18

Errata, Addenda

Scientific paper

In the paper "X-Ray Ionization of Protoplanetary Disks" by A. E. Glassgold, J. Najita, and J. Igea (ApJ, 480, 344 [1997]), there is an error in our calculation of the ionization that changes some quantitative aspects of our results but not the main conclusions. Although equations (1) and (2) give the correct expression for the vertical component of the flux, we neglected to include the extra r/RXR factor in the calculation of the ionization rate, which describes the increased probability for absorption along the slant path length. Another way of understanding this point is to recall that it is easier to use the mean energy and not the flux of the X-rays for calculating the ionization rates. The correct result is obtained by multiplying equation (6) and the subsequent equations (7) and (8) by r/RXR. For the numerical calculations in the published paper, r/RXR = 17.9 (12 R&sun;/RXR)(r/AU), and equation (8) becomes zeta 0=3.00 x 10^{-11} {s}^{-1} sigma tilde _{-22}(kT_{{XR}}/{keV})^{-n}(L_{{XR}}/1029 {ergs} {s}^{-1})(r/{AU})^{-2} .(8) The results in Figure 1, which describe the ionization rate at 1 AU, should be increased by an overall factor of 17.9, and the local electron fractions in Figure 2 should be increased by (r/RXR)1/2, which is 4.23 at 1 AU. The change in the last factor in equation (8) from an inverse cube to an inverse square law means that the iso-ionization curves in Figure 2 are somewhat more horizontal, especially in the vicinity of the critical ionization curve. However, the main qualitative conclusion that we draw from Figure 2 is the same: X-ray ionization produces a layered ionization structure in protoplanetary disks, similar to that obtained by C. F. Gammie using Galactic cosmic rays (ApJ, 457, 355 [1997]). If anything, the case for X-ray ionization is even stronger because the overall effect is almost a factor of 20 larger at 1 AU than we indicated previously. All other aspects of the paper are unchanged.

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