Parametric analysis of modeled ion escape from Mars

We develop a parametric fit to the results of a detailed magnetohydrodynamic (MHD) study of the response of ion escape rates (O+, O 2 + and CO 2 + ) to strongly varied solar forcing factors, as a way to efficiently extend the MHD results to different conditions. We then use this to develop a second, evolutionary model of solar forced ion escape. We treat the escape fluxes of ion species at Mars as proportional to the product of power laws of four factors – that of the EUV flux Reuv, the solar wind particle density Rρ, its velocity (squared) R v 2 , and the interplanetary magnetic field pressure R B 2 , where forcing factors are expressed in units of the current epoch-averaged values. Our parametric model is: ϕ ( i ) = ϕ 0 ( i ) R euv α ( i ) R ρ β ( i ) R v 2 γ ( i ) R B 2 δ ( i ) , where ϕ(i) is the escape flux of ion i. We base our study on the results of just six provided MHD model runs employing large forcing factor variations, and thus construct a successful, first-order parametric model of the MHD program. We perform a five-dimensional least squares fit of this power law model to the MHD results to derive the flux normalizations and the indices of the solar forcing factors. For O+, we obtain the values, 1.73 × 1024 s−1, 0.782, 0.251, 0.382, and 0.214, for ϕ0, α, β, γ, and δ, respectively. For O 2 + , the corresponding values are 1.68 × 1024 s−1, −0.393, 0.798, 0.967, and 0.533. For CO 2 + , they are 8.66 × 1022 s−1, −0.427, 1.083, 1.214, and 0.690. The fit reproduces the MHD results to an average error of about 5%, suggesting that the power laws are broadly representative of the MHD model results. Our analysis of the MHD model shows that by itself an increase in REUV enhances O+ loss, but suppresses the escape of O 2 + and CO 2 + , whereas increases in solar wind (i.e., in R ρ , R v 2 , and R B 2 , with Reuv constant) favors the escape of heavier ions more than light ions. The ratios of escaping ions detectable at Mars today can be predicted by this parametric fit as a function of the solar forcing factors. We also use the parametric model to compute escape rates over martian history. This second parametric model expresses ion escape functions of one variable (per ion), ϕ(i) = ϕ0(i)(t/t0)−ξ(i). The ξ(i) are linear combinations of the epoch-averaged ion escape sensitivities, which are seen to increase with ion mass. We integrate the CO 2 + and oxygen ion escape rates over time, and find that in the last 3.85 Gyr, Mars would have lost about 25 - 0.19 + 85 mbars of CO 2 + , and 0.64 - 0.34 + 0.62 m of water (from O+ and O 2 + ) from ion escape.