Solar wind erosion is a form of nonthermal escape energized by solar wind particles instead of EUV photons. The corona is basically the exosphere of the Sun, and the solar wind is nothing more nor less than hydrodynamic escape of the Solar atmosphere, which is primarily hydrogen ionized to protons. The mechanism is general and applies to virtually all stars, though we will not attempt to discuss here how the stellar wind characteristics vary from star to star, nor the way the stellar wind changes as a star proceeds trhough its lifecycle.
The solar wind consists almost entirely of protons (95this is likely to be the case for all main sequence stars. Solar wind particles are extremely energetic; they fly out with speeds of 300 to
600 km/s or even more, having energy between 8 • 10-17 J and 3.2 • 10-16 J. The solar wind is very tenuous; at the Earth's orbit, it has a density ranging up to 107 particles per cubic meter, leading to a particle flux of 4 • 1012/m2s, though it also fluctuates down to values as low as a tenth as much. The flux at other orbits can be estimated using the inverse-square law. The energy flux in the Solar wind is on the order of 10-3W/m2 at Earth's orbit, which is comparable to the total EUV energy flux. Stellar winds are stronger when a star is young, and decrease over time, with the most pronounced decay occurring in the first billion years of the star's like for G class stars like the Sun. The precise nature of the time evolution is not definitively settled, and ties in with many of the same issues that determine the long term evolution of EUV output.
Based strictly on energetic considerations, it would appear that the solar wind has the potential to cause a great deal of atmospheric erosion even for planets as massive as Earth or Venus, and still more so for Mars. The escape energy for an oxygen atom from Earth or Venus is about 1.7 • 10-18J, so a single solar wind proton has enough energy to knock loose about 120 oxygen atoms if it could be optimally deployed. Taking into account the flux of solar wind protons (reduced by a factor of 4 to allow for averaging over the surface of the planet), this would lead to the loss of 20 bars of oxygen on Venus in the course of a billion years, or about half that much from Earth where the solar wind flux is weaker. For Venus, even this upper bound is only sufficient to remove the oxygen in a 200 meter deep ocean. The oxygen loss estimate for Earth is only relevant to the time after the atmosphere was appreciably oxygenated, but it does indicate that solar wind erosion cannot be a priori ruled out as a factor in evolution of the atmosphere. On Mars, we are principally interested in the process that could lead to the loss of a dense primordial CO2 atmosphere; the solar wind flux is lower at the orbit of Mars, but the excape energy is less. A purely energetic estimate suggests that solar wind erosion could potentially lead to a loss of 8 bars of CO2 in the course of a billion years, which would be more than sufficient to leave Mars in its present state.
However, there are a number of factors that greatly limit the ability of collision with solar wind protons to directly erode the heavier species of an atmosphere. The first is that, in a collision between a proton and a heavier particle, only a small part of the proton's energy is transferred to the heavy particle. For in-line collisions, conservation of energy and momentum during a collision between a light particle of mass m1 and a stationary heavy particle of mass m2 implies that the fraction of incident energy transferred to the heavy species is only 4(m1/m2). For protons colliding with CO2, this amounts to about 10%. Moreover, the light proton reverses in direction in a collision, and therefore tends to escape the planet's gravity well before it can lead to additional escape. Since the typical solar wind proton has enough energy to cause 217 CO2 molecules to escape Mars, even the limited energy depositied could cause nearly 22 molecules to escape, but only if the subsequent collisions of CO2 or its components with the rest of the atmosphere caused 100% efficient escape. This is an unrealistic upper bound, since much of the energy of subsequent collisions will be lost to multiple collisions with simply heat the atmosphere a bit. Thus, if solar wind protons could collide with the Martian atmosphere, the actual loss of CO2 over a billion years would be somewhere between 0.8 bars and 0.08 bars. The former, based on the upper bound, would still be significant, but the latter would relegate solar wind erosion to the role of a minor player. Similar considerations reduce the estimates of oxygen loss from Earth of Venus.
In reality, the effect of planetary and solar electromagnetic fields render the problem far more complicated. For planets with a strong planetary magnetic field, such as Earth, the planetary field very effectively shields the atmosphere from impacts with solar wind protons, and limits erosion to small values. Titan has no magnetic field of its own, but it benefits from shielding by Saturn's magnetic field during the part of its orbit when it is effectively in the solar wind shadow caused by Saturn's field. The same phenomenon is likely to apply generically to moons orbiting gas giants.
Venus has essentially no planetary magnetic field, and Mars has only a very weak one arising from remnant magnetizationof the crust. However, buildup of ionized species in the outer atmosphere still leads to electromagnetic fields that are sufficient to deflect most incident protons and keep them from interacting significantly with the atmosphere. For this reason, direct collisions with protons is not generally considered to be a significant source of erosion of heavy species even for nonmagnetized planets like Mars or Venus.
Heavier ions are less deflected by magnetic fields, and so can penetrate more deeply into the atmosphere. Collisions with heavy ions are also more effective at transferring energy to heavy species. For this reason, it is not the solar wind itself, but secondary acceleration of heavy ions by the solar wind that play the greatest role in solar wind erosion. This is where things get complicated. First of all, you need a supply of heavy ionized species; these are created by ionization due to the EUV flux. On Mars and Early Venus, the heavy ions of principle interest are ionized oxygen atoms, in the Martian case arising from decomposition of CO2 and in the Early Venus case arising from decomposition of H2O if the planet is in a runaway state. The second step is accelerating the oxygen ions to an energy where they can cause escape. This step is not done by collisions with solar wind protons, but rather by the forces exerted by the electromagnetic field carried by the solar wind. The energy still ultimately comes from the energy of the solar wind, but it is transferred by the intermediary of large scale electromagnetic interactions. The calculations necessary to determine the flux and energy of heavy ions are very complex, since they require a model of the electromagnetic field of the solar wind as well as the tracking of a large shower of ions injected into the field. The final stage of the problem is figuring out what happens when an accelerated oxygen ion collides with the atmosphere. When the shower of ions hits the atmosphere, a certain fraction of the target will splashed out backward with sufficient energy to escape the gravitational well. This process is known as sputtering. Sputtering is not nearly 100% efficient at converting incident energy to escaping particles, and the computation of sputtering efficiency is difficult, depending, among other things, on the degree to which the collisions cause the target molecules to dissociate.
Because of the complexities and considerable uncertainties of such calculations, we are in the regrettable position of not being able to guide the reader through any simple robust estimates of the actual likely mass loss due to solar wind erosion; it is a subject for experts and cognoscenti, but a very important one. The articles cited in the Further Readings section for this chapter will provide some introduction to the subject, and the range of numbers that have emerged to date. Most estimates of loss of CO2 from Mars due to solar wind sputtering suggest that 0.1 to 0.2 bars could be lost in this way, though the somewhat controversial calculations of Kass and Yung put the number as high as 1 bar. It thus appears that solar wind erosion is a potentially significant factor for loss of a primordial dense Martian atmosphere, but the the general sentiment is that most of the mass loss would have to occur by other means (probably impact erosion, to be discussed shortly). Solar wind erosion does not seem to provide a viable mass loss mechanism for either the hydrogen or oxygen in a runaway Venus state, despite the planet's proximity to the Sun and even assuming that the Early Venus, like that of today, had no planetary magnetic field. The only situation in which solar wind erosion could have contributed to loss of a Venus ocean is if the loss occurred in the first hundred million years of the life of the Solar system, during which time it has been speculated that the solar wind may have been over a thousand times as intense as it is today. Even then, the loss occurs not by direct erosion or sputtering, but rather by providing enough additional heating to cause hydrodynamic escape of hydrogen with sufficient velocity to drag oxygen along with it. This mechanism bears more resemblance to hydrodynamic escape, with solar wind substituted for EUV as an energy source, then it does to the sputtering mechanisms that have been discussed in connection with Mars. The shielding effect of the Earth's magnetic field limits solar wind erosion to very small values, so that it is not a major factor in atmospheric evolution for Earth.
As in the case of escape driven by other processes, the trickle of escape of heavy species driven by solar wind interactions is pertinent to a rich variety of interesting questions bearing on the observed structures of outer planetary atmospheres today. Many of these questions are important in interpreting the isotopic composition of atmospheres in terms of past atmospheric evolution. However, for the purposes of this book we are principally interested in those mechanisms that cause enough escape to substantially effect the evolution of a planet's climate or habitability. The best guideline we can provide at this point is that, for bodies orbiting G-class stars like the Sun, solar wind erosion should be kept in mind as a sigificant factor in climate evolution for bodies the size of Mars or smaller, which are unshielded by a planetary magnetic field. M-dwarfs, despite being cool, have much higher stellar wind fluxes than the Sun, and could therefore sustain significant atmospheric escape from somewhat larger bodies, especially if they are in close orbits.
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