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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

dnidt=kjknjnk\frac{dn_i}{dt} = k_{jk} n_j n_k

where kjkk_{jk} is the rate of that reaction in units of cm3sβˆ’1cm^{3} s^{-1}. Since we work in fractional abundances rather than concentrations, we can remove factors of nHn_H since nj=XjnHn_j=X_jn_H

dXidt=kjkXjXknH\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

dXidt=kiXi\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 the UMIST12 database. This is a database listing reactants and products with up to three rate constants which we label Ξ±,Ξ²,andΞ³\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 and more information can be found in McElroy et al. 2013

Two Body Reactions use the Kooji-Arrhenius equation.

k=Ξ±(T300K)Ξ²exp(βˆ’Ξ³/T)k = \alpha (\frac{T}{300K})^\beta exp(-\gamma/T)

Cosmic Ray Protons

k=Ξ±ΞΆk = \alpha \zeta

Cosmic Ray induced photons

k=Ξ±(T300K)Ξ²E1βˆ’Ο‰ΞΆk = \alpha (\frac{T}{300K})^\beta \frac{E}{1-\omega} \zeta

UV Photons

k=Ξ±FUVexp⁑(βˆ’kAv)k = \alpha F_{UV}\exp(-kA_v)

where ΞΆ\zeta is the cosmic ray ionization rate in units of 1.3 10βˆ’17^-17 sβˆ’1^{-1}, E is the efficiency with which cosmic rays cause ionization, Ο‰\omega is the dust grain albedo, FUVexp⁑(βˆ’kAv)F_{UV} \exp(-kA_v) is the attenuated UV field.