Estimation of the Appropriate Length Scale to Use with the Quench Level Approximation for Obtaining Chemical Abundances

Michael D. Smith (NRC, NASA/GSFC)

The ``quench level'' approximation for estimating the observed abundance of chemically reacting species in the presence of convective dynamics states that the chemical reaction is quenched at the level where the time scales for the chemical reaction and for convective dynamics are equal. The dynamical time constant, tex2html_wrap_inline14 , can be computed using tex2html_wrap_inline16 , where L is a length scale and K is the vertical eddy diffusion coefficient. Usually K is left as a free parameter, and lacking any better information, L is taken to be a scale height.

Here we show that the length scale, L, can be estimated by comparing the results of three different simple mathematical ``models'' for convective dynamics. Each of the three models uses a different fundamental quantity in describing the strength or efficiency of mixing that depends on the unknown length scale, L, in a different way. By demanding that the three models give consistent results, we arrive at an independent estimate of L. We find that the appropriate value of L is different for different chemical reactions, and can be far from a scale height. As an example, we find that L=0.14 scale heights is appropriate for the estimation of the isotopic enrichment of (D/H) in CH tex2html_wrap_inline36 over (D/H) in H tex2html_wrap_inline38 . Using L=0.14 scale heights leads to a value of 1.17 on Jupiter at a typical value of tex2html_wrap_inline42 cm tex2html_wrap_inline44 sec tex2html_wrap_inline46 compared to 1.21 when L=1.0 scale heights is used. This indicates that greater care should be taken when using the quench level approximation to estimate chemical abundances.