Erratum: ``The Internal Energy for Molecular Hydrogen in Gravitationally Unstable Protoplanetary Disks'' (ApJ, 656, L89 [2007])

Details Erratum: ``The Internal Energy for Molecular Hydrogen in Gravitationally Unstable Protoplanetary Disks'' (ApJ, 656, L89 [2007]) Erratum: ``The Internal Energy for Molecular Hydrogen in Gravitationally Unstable Protoplanetary Disks'' (ApJ, 656, L89 [2007])

May 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007apj...660l.175b&link_type=abstract

The Astrophysical Journal, Volume 660, Issue 2, pp. L175-L175.

Astronomy and Astrophysics

Astrophysics

1

Scientific paper

In the above-mentioned Letter, we stated that Boss uses a discontinuous internal energy for H2, where H2 contributes 3kT/4mp to the specific internal energy e for T<=100 K and 5kT/4mp for T>100 K, based on his own citations to A. P. Boss (ApJ, 277, 768 [1984]). It was brought to our attention by A. P. Boss (2007, private communication) that he now uses a quadratic interpolation for e between 100 and 200 K (see Fig. 1, left panel). This change is not mentioned in the literature but is alluded to in A. P. Boss (ApJ, 346, 336 [1989]). According to Boss, the interpolation has been used in all his simulations since Boss (1989).
In Figure 1 (right panel), we also illustrate the consequences for Γ1 of Boss's latest e approximation by calculating the specific heat at constant volume cv=de/dT and by relating that to Γ1 (see J. P. Cox & R. T. Giuli, Principles of Stellar Structure [New York: Gordon & Breach, 1968]). This curve is compared with curves for pure para-hydrogen (short-dashed curve), a 3:1 ortho/para-hydrogen mixture (long-dashed curve), where the species are treated as independent, and an equilibrium mixture (solid curve). Because fragmentation becomes more likely as Γ1 is lowered (W. K. M. Rice, G. Lodato, & P. J. Armitage, MNRAS, 364, L56 [2005]), Boss's approximation between 100 and 200 K is likely to make his disks susceptible to fragmentation for that temperature range.
We would like to thank A. P. Boss for his discussions and clarification of his code.

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