Towards More Reliable Analytic Thermochemical-equilibrium Abundances. (arXiv:1901.03764v1 [astro-ph.EP])
<a href="http://arxiv.org/find/astro-ph/1/au:+Cubillos_P/0/1/0/all/0/1">Patricio Cubillos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Blecic_J/0/1/0/all/0/1">Jasmina Blecic</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Dobbs_Dixon_I/0/1/0/all/0/1">Ian Dobbs-Dixon</a>
Heng & Tsai (2016) developed an analytic framework to obtain
thermochemical-equilibrium abundances for H$_{2}$O, CO, CO$_2$, CH$_4$,
C$_{2}$H$_{2}$, C$_{2}$H$_{4}$, HCN, NH$_3$, and N$_2$ for a system with known
temperature, pressure, and elemental abundances (hydrogen, carbon, nitrogen,
and oxygen). However, the implementation of their approach can become
numerically unstable under certain circumstances, leading to inaccurate
solutions (e.g., ${rm C/O} ge 1$ atmospheres at low pressures). Building up
on their approach, we identified the conditions that prompt inaccurate
solutions, and developed a new framework to avoid them, providing a reliable
implementation for arbitrary values of temperature (200 to $sim$2000 K),
pressure ($10^{-8}$ to $10^{3}$ bar), and CNO abundances ($10^{-3}$ to $sim
10^{2}times$ solar elemental abundances), for hydrogen-dominated atmospheres.
The accuracy our analytic framework is better than 10% for the more abundant
species that have mixing fractions larger than $10^{-10}$, whereas the accuracy
is better than 50% for the less abundant species. Additionally, we added the
equilibrium-abundance calculation of atomic and molecular hydrogen into the
system, and explored the physical limitations of this approach. Efficient and
reliable tools, such as this one, are highly valuable for atmospheric Bayesian
studies, which need to evaluate a large number of models. We implemented our
analytic framework into the textsc{rate} Python open-source package, available
at https://github.com/pcubillos/rate .
Heng & Tsai (2016) developed an analytic framework to obtain
thermochemical-equilibrium abundances for H$_{2}$O, CO, CO$_2$, CH$_4$,
C$_{2}$H$_{2}$, C$_{2}$H$_{4}$, HCN, NH$_3$, and N$_2$ for a system with known
temperature, pressure, and elemental abundances (hydrogen, carbon, nitrogen,
and oxygen). However, the implementation of their approach can become
numerically unstable under certain circumstances, leading to inaccurate
solutions (e.g., ${rm C/O} ge 1$ atmospheres at low pressures). Building up
on their approach, we identified the conditions that prompt inaccurate
solutions, and developed a new framework to avoid them, providing a reliable
implementation for arbitrary values of temperature (200 to $sim$2000 K),
pressure ($10^{-8}$ to $10^{3}$ bar), and CNO abundances ($10^{-3}$ to $sim
10^{2}times$ solar elemental abundances), for hydrogen-dominated atmospheres.
The accuracy our analytic framework is better than 10% for the more abundant
species that have mixing fractions larger than $10^{-10}$, whereas the accuracy
is better than 50% for the less abundant species. Additionally, we added the
equilibrium-abundance calculation of atomic and molecular hydrogen into the
system, and explored the physical limitations of this approach. Efficient and
reliable tools, such as this one, are highly valuable for atmospheric Bayesian
studies, which need to evaluate a large number of models. We implemented our
analytic framework into the textsc{rate} Python open-source package, available
at https://github.com/pcubillos/rate .
http://arxiv.org/icons/sfx.gif
