---
id: gas
title: Gas Phase Reactions
---

# Gas Phase Reactions

## Gas phase ODEs
The rate of change of the concentration of a gas phase species due to a single two body reaction is

$$ 
\frac{dn_i}{dt} = k_{jk} n_j n_k 
$$

where $k_{jk}$ is the rate of that reaction in units of $cm^{3} s^{-1}$. Since we work in fractional abundances rather than concentrations, we can remove factors of $n_H$ since $n_j=X_jn_H$

$$ 
\frac{dX_i}{dt} = k_{jk} X_j X_k n_H
$$

For reactions between involving only a single body such as ionization by a cosmic ray, we have

$$ 
\frac{dX_i}{dt} = k_{i} X_i
$$

The total rate of change of the fractional abundance of a species due to gas phase reactions is then just the sum of these terms for all reactions where it is a product minus the sum of all reactions where it is a reactant.

As a rule, any part of a reaction ODE which does not depend on abundance (eg the rate itself) is calculated between timesteps by the subroutine ```calculateReactionRates``` in ```rates.f90```. The abundances are include in the ODE calculation itself so they can be updated between steps by the solver.


## Reaction Rates
Gas phase chemistry in UCLCHEM uses either the UMIST Database for Astrochemistry ([McElroy et al. 2013](https://ui.adsabs.harvard.edu/abs/2013A&A...550A..36M/abstract)) or the KIDA database ([Wakelam et al. 2012](https://ui.adsabs.harvard.edu/abs/2012ApJS..199...21W/abstract)). These databases list reactants and products with up to three rate constants which we label $\alpha, \beta, and \gamma$ for thousands of gas phase reactions. We briefly list here the way in which the rates in the above equations are calculated for each reaction type

**Two Body Reactions** use the Kooji-Arrhenius equation.

$$
k = \alpha (\frac{T}{300K})^\beta exp(-\gamma/T)
$$

**Cosmic Ray Protons**
$$
k = \alpha \zeta
$$
**Cosmic Ray induced photons**
$$
k = \alpha (\frac{T}{300K})^\beta \frac{E}{1-\omega} \zeta
$$
**UV Photons**
$$
k = \alpha F_{UV}\exp(-kA_v)
$$

where $\zeta$ is the cosmic ray ionization rate in units of 1.3 10$^-17$ s$^{-1}$, E is the efficiency with which cosmic rays cause ionization, $\omega$ is the dust grain albedo, $F_{UV} \exp(-kA_v)$ is the attenuated UV field.