Atmospheric Mass Flux as a Function of Ionospheric Emission on Unmagnetized Earth

TL;DR

This paper investigates whether an unmagnetized Earth-like planet can retain its atmosphere under solar wind interaction by quantifying ion escape and solar wind deposition as a function of ionospheric emission $E_m$ using the RHybrid model. Six simulations around a present-day Earth–Venus–based reference emission demonstrate that escape and deposition follow distinct power laws, with a critical emission rate $E_{crit}=1.28 E_{ref}$ where net atmospheric mass change is zero; geologic-timescale extrapolations suggest the total atmospheric mass changes by less than about 3% over 1 Gyr under steady solar driving. The study finds that higher $E_m$ inflates the induced magnetosphere and reduces solar wind penetration, while deposition can rival escape, enabling potential net mass accretion in some regimes. Together, these results imply that intrinsic magnetic fields may not be strictly required for long-term atmospheric retention on Earth-like planets and reveal a possible self-regulating mechanism that drives atmospheres toward mass equilibrium with the solar wind. The work highlights important implications for planetary habitability and motivates future work incorporating neutral chemistry and variable solar conditions.

Abstract

We explore ion escape from, and solar ion deposition to, \hll{an unmagnetized Earth-like planet}. We use RHybrid, an ion-kinetic electron-fluid code to simulate the global plasma interaction of unmagnetized Earth with the solar wind. We vary the global ionospheric emission rate, and quantify the resultant planetary ion escape rates ($O^+$ and $H^+$) and the solar wind deposition rate ($H^+$). We use these results to compute the net mass flux to the atmosphere and find that the solar ion deposition rate could be comparable to planetary ion escape rates. For the emission rates simulated, our results show that under typical solar wind conditions ($v_{sw} = 400 \ km \ s^{-1}$, $n_{sw} = 5 \ cm^{-3}$), the mass of the atmosphere would decrease by less than 3\% over a billion years, indicating that Earth's intrinsic magnetic field may be unnecessary for retention of its atmosphere. Lastly, we present a hypothesis suggesting that ionospheric emission may evolve through time towards a critical emission rate that occurs at a net mass flux of zero.

Figures (6)

• Figure 1: Snapshots in the xy plane from the $0.1E_{ref}$ (left) and $10E_{ref}$ (right) simulation runs. Each snapshot is taken from the end of the run when steady-state has been achieved. The blue circle at x =0, y =0, represents the planetary body. White overlaid vectors depict the direction of velocity vectors. The colorbar shows the speed of the solar wind, which is initialized at 400 km/s on the right side of the figures. The $10E_{ref}$ case has an inflated magnetosphere when compared to the $0.1E_{ref}$
• Figure 2: The x-axis shows the global ion emission rate ($E_m$) in units of the reference rate ($E_{ref}$). The y-axis is in units of ions per second. The data with error bars is shown in log-log space, and overlaid with power laws. Orange and blue are hydrogen and oxygen escape, respectively. Green is solar hydrogen deposition. Error bars represent $1\sigma$ variation on Gaussian fits to equilibrated time series data.
• Figure 3: In the left panel, the x-axis shows the global ion emission rate ($E_m$) in units of the reference rate ($E_{ref}$), and the y-axis shows the net mass change per second. A positive net mass change means that more mass is being deposited than is escaping, quantified in units of proton masses per time. The theoretical maximum limit on solar wind deposition is shown as the black dotted line and the model upper limit is shown as the black dash-dot line. Triangles represent computed net mass flux, and the thick black line is a polynomial fit to the data. Error bars are smaller than the marker size. The solid horizontal line represents a net mass flux of zero, and the solid vertical line represents the corresponding critical global ion emission rate. The right panel visualizes when $E_m$ is less than and greater than $E_{crit}$. Purple dots represent solar wind ions, blue dots represent planetary ions, and the light pink region is the magnetosheath.
• Figure 4: This illustration shows how the modeled solar wind regulates $E_m$, and the total mass, of unmagnetized terrestrial atmospheres. Deviations from $E_{crit}$ cause negative feedback pushing $E_m$ towards $E_{crit}$.
• Figure A1: The escape and deposition rates as a function of time are shown for each of the simulations. The top panel shows $H^+$ escape rates, the middle panel shows $O^+$ escape rates, and the bottom panel shows $H^+$ deposition rates. Higher production rate simulations require more computational time per real time step but reach equilibrium in less real time. The last 10% of each time series (shown in black) is used to produce the data points in Figure 2. While the $2E_{ref}$ escape rate data is oscillatory, the sampled data captures an entire period, thus the effect of the oscillation is represented in the error bar of this data point.