Impact erosion

The two main cases in the solar system where theories of atmospheric evolution call for massive atmospheric loss are the problem of water loss on Venus and the loss of a hypothetical dense CO2 atmosphere on Mars. For Titan the question is the converse - accounting for the lack of atmospheric N2 loss, and that is plausibly accounted for by the solar wind shielding provided by Saturn's magnetic field and the low EUV flux at such large distances from the Sun. There may have been blowoff early in Titan's history, but on an icy body there are plenty of volatile reservoirs available to restock an atmosphere. Hydrodynamic escape of hydrogen from photodissociated water provides a plausible mechanism for the Venus case, but we still don't have a good way to get rid of a 2 bar Early Mars atmosphere, except for the remote possibility that solar wind erosion could do the trick. If there is no way to lose such a dense greenhouse atmosphere from Early Mars, then explanations for the apparently warm and wet early climate of that planet must be sought elsewhere. It is likely, however, that impact erosion could provide much of the needed loss mechanism. Impact erosion could be similarly important for Mars-sized bodies elsewhere in the Universe. One should be cautious about concluding that the way things happened in the solar system are the way things must happen elsewhere, but still the fact that Earth and Venus retain thick atmospheres while Mars does not suggests that Mars-sized bodies may be susceptible to loss of atmosphere. One would like to know what the possible mechanisms are, and whether there are circumstances in which a Mars-sized body could retain an atmosphere at temperatures warm enough to be habitable and without the shielding effect of a nearby giant planet.

The impact history in the inner portion of a planetary system, where rocky planets form, can be divided up into five broad stages:

• The Early Accretion stage, in which small planetesimals are colliding to form larger objects, which in turn aggregate into a broad spectrum of still larger objects.

• The Late Accretion stage, in which most of the aggregation is complete, but there are still a number of planet-sized bodies in nearby orbits. According to simulations, Lunar to Mars sized bodies are common at this stage, and one or more giant impacts are likely. In our own Solar System, there is evidence that Earth, Venus and Mars all experienced a giant impact at some point

• The Sweep stage, in which each planet has attained nearly its ultimate size, and is sweeping up much smaller debris in the vicinity of its orbit. The impacts in this stage are still frequent, but involve collisions with bodies much smaller than the planet. There are no giant impactors left.

• The Late Heavy Bombardment, in which a second swarm of impactors originating from perturbations of mass stored in more distant orbits encounters the inner system. In our Solar System the Late Heavy Bombardment occurred around 3.8 billion years ago. It is not known what caused this bombardment, where the mass came from, or whether such bombardments are a generic feature of the late stages of planetary system formation. Indeed, it is not even completely clear whether the Late Heavy Bombardment is really distinct from the sweep stage. In any event, the period of impacts that could substantially erode atmospheres came to a close with the Late Heavy Bombardment, about one billion years after the beginning of the formation of our Solar System. This number can be taken as a rough guide to the time scale of impact erosion in other planetary systems, though in systems without a Late Heavy Bombardment the period when inner planets are subject to impact erosion probably would end up to 300 million years earlier.

• The Steady State Bombardment stage, in which nearby sources of impactor mass have been used up. During this stage there are infrequent collisions by objects drawn from the pool of cometary and asteroidal material. Large objects of this class are only occasionally flung into planet-crossing orbits by long term chaotic gravitational interactions, though inconsequential encounters with very small objects (as in meteor showers) occur on a nearly continuous basis.

Impact erosion is a crucial factor in the process by which a planet forms and retains an atmosphere as it accretes by collision of planetesimals, but in the following we will be principally concerned with impacts that occur in the later stages of the process -the sweep phase and the Late Heavy Bombardment (if it is present). In this stage the planet has attained close to its ultimate mass and most of the impactors are much less massive than the target planet but there is still enough impactor mass available to cause significant atmospheric erosion. We will also offer a few remarks on the consequences of giant impacts which preceed the sweep stage. The long period of steady state impacts which follow the sweep stage and continue to this day can have cataclysmic consequences such as the mass extinction triggered by the Cretaceous-Tertiary impact, but these impacts are too small and too infrequent to cause much atmospheric erosion.

In impact erosion, the source of energy available to accelerate parts of the the atmosphere to escape velocity is the kinetic energy of the impactor. This energy depends on the mass of the impactor and the velocity with which it encounters the planet. When an impactor is dropped onto a much more massive planet from a great distance, it will strike the planet with a velocity equal to the planet's escape velocity, provided the impactor is initially at rest relative to the planet. This is a simple consequence of conservation of kinetic plus potential energy. It can be shown that because objects in neighboring orbits travel at different speeds, gravitational interactions cause the typical impact speed to be somewhat greater than the escape velocity. However, the enhancement is seldom as much as 20%, so throughout the following we will simply take the escape velocity as the characteristic impact speed. The scaling of impact velocity with escape velocity eliminates much of the intuitive effect of planetary size on impact erosion: though the atmosphere of a small planet is less gravitationally bound than that of a large planet, the typical impactor energy is also less for a small planet.

The case of satellites is quite different, since there we need to take into account the gravity of the parent body as well as that of the satellite. Consider the case of Titan, which orbits Saturn at a distance of 1.22 • 109m. At this distance, the gravitational acceleration of Saturn is .025 m/s2. The corresponding escape velocity from Saturn for an object starting at this orbit is 7.9 km/s, which is also the speed an object dropped from infinity reaches under the gravitational influence of Saturn, upon reaching Titan's orbit. In comparison, the escape velocity from Titan is only 2.6 km/s. Under the joint influence of both gravitational fields, the impactor speed would be approximately %/2.62 + 7.92, or 8.3 km/s. In reality, the encounter speed could be somewhat greater, depending on the geometry of the impact, since one should also take into account the orbital speed of Titan, which is 5.5 km/s. The enhancement of impactor velocity for satellites allows the atmosphere to be eroded by a much smaller total mass of impactors than would be required if the body were a planet in an orbit of its own. This effect is overwhelmed, however, by the fact that a satellite must compete for impacts with the much larger planet it is orbiting. Impacts are received in proportion to the cross section areas of the bodies, so the satellite receives many fewer impacts than it would if it were a planet in its own orbit, all other things being equal. For Titan, the ratio of impacts is 0.002, so this effect ups the required mass of available impactors in the orbit by a factor of 500. In the estimates to follow, we'll use the term "Titan-P" to refer to a Titan-like body in a planetary orbit of its own, reserving the name "Titan" for the actual satellite subject to the effects of Saturn.

In a similar vein, the classic theory of impact erosion from planets assumes impactors in fairly circular orbits originating not far from the planet being, impacted, with the planet itself assumed to be in a fairly circular orbit. Recent simulations of planet formation indicate that there can be stages in which planetesimals have highly eccentric orbits. Indeed the catalog of extrasolar planets is rife with systems having very eccentric orbits. When the impactor or planet has an eccentric orbit, the impact velocity can considerably exceed the planet's escape velocity, much as was the case for impacts on satellites. In this case, the planet's parent star plays much the same role as a satellite's parent planet. If eccentric impacts are common, they tend to tilt the balance in favor of greater atmospheric erosion from small planets, since the eccentric impacts decouple impact energy from the strength of a planet's gravity. The understanding of this effect is rapidly evolving, and so we will merely flag it here as a subject worthy of the readers' attention. Our discussion in the following will be mostly based on the classic scaling of impact energy.

The typical impact speed is much greater than the typical speed of sound. For example, an Earthlike body would have an impact speed of over 11,000 m/s, whereas the speed of sound in air at 300K is only 347 m/s. Since pressure and density modifications can travel no faster than the speed of sound, the impactor carves a cylinder into the atmosphere leaving a near-vacuum in its wake. The walls of the cylinder have little time to close in, and the flow just ahead of the impactor cannot know about the presence of the planet's surface far below. The situation is not like a piston slowly compressing a column of air. Instead, the drag force on the impactor is solely dependent on the instantaneous density and temperature just ahead of its position at any time, and on the velocity and cross-section area of the impactor.

Any amount of energy delivered to the planet could, in principle, cause some amount of atmosphere to be accelerated to escape velocity. The key question in determining how much atmosphere actually escapes is the volume of atmosphere over which the energy is diluted. Striking a match releases about 1000 J of energy, which is enough to cause 16 milligrams of air to escape from Earth. It doesn't happen, though, because the energy released is too diluted to cause any gas to escape. The fluid dynamics governing partioning of energy upon impact is complicated and difficult to simulate accurately. Nonetheless, simulations and theory point to a few simple principles upon which estimates of impact erosion can be based.

We can distinguish three classes of impacts:

• Small impacts, which dissipate their energy in the atmosphere. Simulations indicate that these do not cause much atmospheric escape.

• Intermediate sized impacts which dissipate most of their energy when striking the ground or ocean, but which are still small compared to the target planet and therefore do not significantly accelerate the planet as a whole. In this case, the impactor still has a great deal of energy left upon striking the solid or liquid surface of a planet. The the energy is released in a concentrated burst which can lead to considerable erosion of the portion of the atmosphere in the vicinity of the impact.

• Giant impacts, in which the impactor has mass comparable to the target planet. These can cause total blowoff of an atmosphere since the shocked planet acts like a piston which can accelerate nearly the entire mass of the atmosphere to escape velocity.

The energy required for an impactor to reach the surface with most of its energy left depends on how massive the atmosphere is. Any impactor at all will reach the surface of the Moon, but hardly anything gets through to the surface of Venus - which is why the surface of Venus is characterized by just a few but very large impact craters. The drag force exerted on a high speed sphere of radius r is CDpanr2U2, where U is the speed of the body, rhoa is the atmospheric density and CD is a dimensionless number which asymptotes to values near unity for very supersonic flow. When passing through an atmosphere of thickness H (estimated as the density scale height), the work done against the object is CDpanr2U2H. We'll assume that the initial velocity is high enough that the additional work done by the force of gravity after the projectile encounters the atmosphere can be neglected. Then, equating the work done by drag to the kinetic energy 2MU2 for a body of mass M, we find that the condition for the body to reach the surface with some of its initial energy left is M > 2CDpanr2H. Since CD « 1, this condition says that the mass of the body must exceed twice the mass of the cylinder of atmosphere having the same cross section area as the body. Writing M = |nr3pi, where pi is the impactor density, we find r > |(pa/pi)H for CD = 1. For Earth's present atmosphere, this yields a critical radius of a mere 3.5m, assuming a silicate impactor having a density of 3000kg/m3. For the atmosphere of Venus, the critical radius is a more impressive 340 m.

Exercise 8.7.9 Estimate the critical radius for a silicate impactor to penetrate the 7mb atmosphere of present Mars.

Let's focus next on the effect of intermediate impacts. When the impactor reaches the surface, most of its energy is turned into heat, which creates a shock wave which travels outwards from the point of impact, accelerating the atmosphere. Some of the energy also goes into vaporizing the solid surface, which adds mass to the gas that must be ejected, and steals energy that could otherwise be used to feed escape; this is a refinement we shall not pursue quantitatively. Fluid mechanical simulations and analytic shock wave solutions indicate that once a critical energy is reached, essentially all the atmosphere in a narrow cone above the impact is ejected, as shown in the left panel of Fig. 8.6. As the mass of the impactor is increased, the angle of the cone widens, until it reaches the point where all the atmosphere above a plane tangent to the sphere at the point of impact is blown off. Further increases in the mass of the impactor cause little or no additional escape, until the size class of giant impacts is approached. There is a narrow range of impactor masses between the mass where a narrow cone is first blown off and the mass at which the whole tangent slice is blown off. Therefore, one can get a reasonable impact of impact erosion by non-giant impacts by simply assuming that all impactors with a mass below that required to blow off a tangent slice cause no loss, whereas all impactors with mass above this critical mass cause loss of one tangent slice of the atmosphere.

Now we are prepared to answer the key question of how the susceptibility to impact erosion scales with the size of the planet and the thickness of its atmosphere. There are two ingredients

Figure 8.6: Portion of atmosphere subject to impact erosion by non-giant impacts. The left panel shows the portion potentiallly eroded by small impacts; very small impactors dissipate their energy before reaching the ground and cause little or no erosion. The right panel shows the limiting erosion by a larger impactor, which can erode all the atmosphere above the tangent plane to the planet's surface at the point of impact. Increasing the mass of the impactor does not yield much further erosion, until the giant-impact class, able to significantly accelerate the entire target planet, is reached.

Figure 8.6: Portion of atmosphere subject to impact erosion by non-giant impacts. The left panel shows the portion potentiallly eroded by small impacts; very small impactors dissipate their energy before reaching the ground and cause little or no erosion. The right panel shows the limiting erosion by a larger impactor, which can erode all the atmosphere above the tangent plane to the planet's surface at the point of impact. Increasing the mass of the impactor does not yield much further erosion, until the giant-impact class, able to significantly accelerate the entire target planet, is reached.

to this estimate: the critical impactor mass needed to blow off a tangent slice of the atmosphere, and the fraction of atmospheric mass eroded by each such impact. The critical mass is important because it says how big an impactor has to be to cause significant erosion; this affects the erosion rate because there are many more small impactors than there are big impactors. To estimate the mass of atmosphere above a tangent plane, we represent the atmosphere as a uniform density layer with density pa and depth H equal to the scale height at a mean atmospheric temperature T. With this approximation, the mass above a tangent plane is simply paH2 a, where a is the radius of the planet. The energy needed to cause this amount of mass to escape to space is 2v^paH2a, while the energy of an impactor of mass m is 2mv2 where Vi is the speed of the impactor. However, since v-i « ve, the velocity terms cancel and we find that the critical impactor mass is mc « paH2a, i.e. the mass of atmosphere above the tangent plane. Note that paH is the mass of atmosphere per unit area of the planet's surface. We will find it convenient to use this quantity as our basic measure of the amount of atmosphere remaining on the planet. In terms of the surface pressure paH « Ps/g, according to the hydrostatic relation.

For fixed paH,the critical mass scales with Ha = RTa/g, but since g = |Gppa where pp is the mean density of the planet, we find that the critical mass is

4 Gpp

Thus, for fixed atmospheric mass per unit area, the critical impactor mass is independent of the size of the planet. While the critical mass formula does not discriminate by size of planet, it does say that massive atmospheres (in the sense of large paH) are more difficult to erode than tenuous atmospheres, because larger impactors are needed to trigger erosion in the more massive case, but there are fewer large impactors than small impactors. For a given mass spectrum of impactors,

mc (kg)

rc,silicate (km)

rc,ice (km)

Ne

mtot/m Earth

Earth, 1bar N2,280K

5.5-1014

3.5

5.2

3003

1.0 •10-3

Mars, 2bar CO2,280K

2.6-1015

5.9

8.7

951

0.7 -10-3

Mars, 100 mbar C02,220K

1.0-1014

2.0

2.9

1210

0.18 -10-3

Venus, 90bar C02, 700K

9.2-1016

19.4

28.3

1623

7.1 -10-3

Venus, 1bar N2, 280K

6.4-1014

3.7

5.4

2582

0.94 -10-3

Titan-P,1.5bar N2,80K

5.0-1015

7.4

10.8

585

0.6 -10-3

Titan ,1.5bar N2,80K

5.0-1014

3.4

5.0

585

94. -10-3

Super-Earth, 1bar N2,280K

3.2-1014

3.0

4.3

8778

2.3 -10-3

Table 8.4: Table of impact erosion parameters for various bodies. mc is the critical mass required to blow off a tangent slice, and the rc columns give the corresponding impactor radii (in km) for silicate or icy impactors. Ne is the number of impacts with m > mc which are required to deplete most of the atmosphere, and mtot is the total available impactor mass in orbit required to yield this number of impacts. The calculations of mtot depend on the mass distribution; results in this table assume a power law distribution with q = 1.5 and the maximum impactor mass m+ equal to one tenth the mass of Earth's Moon. The "Titan-P" case gives results for a hypothetical Titan-like body in an orbit of its own, while the "Titan" case includes the effects of Saturn, including the competition with Saturn for available inpactor mass. The "Super-Earth" case is for a planet with the same density as Earth and with a mass of 5 Earth masses.

Table 8.4: Table of impact erosion parameters for various bodies. mc is the critical mass required to blow off a tangent slice, and the rc columns give the corresponding impactor radii (in km) for silicate or icy impactors. Ne is the number of impacts with m > mc which are required to deplete most of the atmosphere, and mtot is the total available impactor mass in orbit required to yield this number of impacts. The calculations of mtot depend on the mass distribution; results in this table assume a power law distribution with q = 1.5 and the maximum impactor mass m+ equal to one tenth the mass of Earth's Moon. The "Titan-P" case gives results for a hypothetical Titan-like body in an orbit of its own, while the "Titan" case includes the effects of Saturn, including the competition with Saturn for available inpactor mass. The "Super-Earth" case is for a planet with the same density as Earth and with a mass of 5 Earth masses.

erosion of a massive atmosphere is initially slow and intermittent, accelerating and becoming more steady as erosion proceeds and the atmosphere becomes less massive. For a satellite, mc must be reduced by a factor of (ve/vi)2, which is about 0.1 for Titan.

The quantity 3RT/Gpp has the dimensions of a length squared; we'll use the symbol t2 to refer to it. The length scale t depends on the density of the planet and the composition and temperature of the atmosphere, but not on the mass of either the planet or the atmosphere. It varies little over a wide range of planetary situations. For a 1bar N2 atmosphere at 280K on Earth, t = 233km. For a 2bar Early Mars CO2 atmosphere at 280K, t = 220km. For a 1.5 bar N2 atmosphere on Titan at 80K, t = 213km. Some typical values of critical impactor mass and size are given in Table 8.4. Note that the critical mass is mostly controlled by the mass path paH, rather than the size of the planet. The Early Mars case with a 2 bar atmosphere and the Titan-P case actually require larger impacts to erode than the present Earth case. The massive atmosphere of Venus is hard to erode, but if Venus ever went through a period when it had a 1 bar atmophere, it would be essentially as easy to erode as Earth. Generally speaking, erosion of Earthlike atmospheres is sustained by impactors with radii of a few kilometers or more, and somewhat larger impactors are required for the Early Mars case. As the Early Mars atmosphere erodes down to surface pressures of 100mb, one can make do with impactors of somewhat over a third the size, or one twentieth of the mass. The table also includes a Super-Earth case based on the extrasolar planet Gliese 581c, which has a mass about five times that of Earth. The critical impactor size is slightly lower than for Earth, because the surface gravity is higher and hence a 1 bar atmosphere on the Super-Earth has less mass per unit area than a 1 bar atmosphere on Earth.

For each impactor exceeding the critical mass, the fraction of atmosphere eroded is napaH2/(4npaHa2), which is 4H/a or equivalently 412/a?. Thus, the fraction of atmosphere eroded per supercritical impact decreases quadratically with the radius of the planet, all other things being equal. This is the main reason that small planets are more susceptible to impact erosion than large planets. The characteristic number, Ne, of supercritical impacts needed to substantially erode the atmosphere is 4a2/tt2. If the impactors arrive in sequence and the atmosphere has a chance to adjust back to uniform coverage of the planet between impacts, then this number of impactors would erode the atmosphere down to a mass of 1/e of its initial mass, given that after each impact there is less mass left to erode and each supercritical impact just takes away a fixed fraction of what is there. The values of Ne for some planets of interest are given in Table 8.4. This number is primarily controlled by the size of the planet, ranging from about 600 for Titan to about 3000 for Earth and about 9000 for a Super-Earth. The colder Mars case with a thin atmosphere requires more impactors than the hot Mars case with a 26ar atmosphere because the scale height is smaller in the former case.

To complete the story, we must estimate the total mass of impactors that must hit the planet in order to get the number of supercritical impacts (Ne) required for subtantial erosion. We will carry out this estimate for a late stage in planetary formation, when the planet in question is by far the largest thing near its orbit and the remaining debris near the orbit is all small compared to the planet; our planet is at this stage the big kid on the block, subject to small to intermediate impacts as it sweeps up a late veneer of the remaining debris. We can define a catchment basin for the planet, consisting of the range of orbits for which the debris is more likely to impact the planet under investigation rather than some other planet. As time goes on, essentially all of the mass in this catchment basin will eventually impact the planet. (This part of the story will be slightly modified for satellites). It is this total mass we shall estimate. For given total mass in the catchment basin, a small planet like Mars will take longer to sweep up the debris, than a larger planet such as Earth, in proportion to the relative cross section areas. Thus, for a small planet, erosion by intermediate impacts will carry on for a longer time than for a large planet. For Mars, the late stage of the erosion process will last 3.5 longer than it would for Earth, all other things being equal. This time scale comparison may be a significant factor in accounting for the present tenuous atmosphere of Mars, since Mars can regenerate an atmosphere if it loses it early on when it is still tectonically active, but not if the loss occurs later, when the planet's interior has frozen out and has ceased outgassing volatiles.

To proceed further we must make some assumption about the mass distribution of impactors, because of the role of the critical mass mc in determining how much atmosphere gets blown off by an individual impact. The optimal distribution for erosion would have all the impactors of equal size mc. Making impactors smaller reduces the erosion because the impactor is unable to blow off a tangent slice, and making the impactors larger wastes impactor mass because a large (but not giant) impact can't blow off more than a tangent mass. Information about the mass distribution and total available mass of impactors comes to us mainly from the cratering record of rocky planets, and among those primarily from the Moon and Mars (which have well-preserved surfaces not much subject to erosion). The estimates are highly uncertain, and uncertainties in the impactor distribution almost certainly overwhelm uncertainties in the detailed fluid dynamics governing how much mass is blown off by an individual impact. The mass spectrum of impactors can also be estimated from the mass distribution in today's asteroid belt. These estimates are generally compatible with estimates derived from the cratering record. Information about the timing if the impacts, and the rate of decay in the inner Solar system, comes from looking at the cratering record in younger resurfaced terrain, and in the Lunar case, from direct radiometric dating of crater crater samples returned to Earth for analysis.

Let N(m) be the number of impactors with mass greater than m. This is the function we need to know. The mass spectrum n(m) is given by dN/dm = —n(m). Equivalently, n(m)dm is the number of impactors in the mass range between m — dm/2 and m + dm/2. The distribution of crater radii on any individual body has been found to approximately obey an r-3 power law, where r is the crater radius. This power law captures the basic crater distribution for moons of Jupiter and Saturn, as well as for the inner planets, though the details of the deviations from the ideal power law are different between the outer solar system and the inner solar system. The corrections to the r-3 law are strikingly similar between Mercury, the Moon and Mars. This provides strong evidence that the entire inner Solar System was subject to the same population of impactors. Because crater radius scales with a power of impact energy, the crater distribution implies a power law distribution of impactor energy. Since impact velocity is approximately constant for any given body, the impact energy is proportional to the impact mass for a given body, implying a power law distribution for impactor mass. Specifically, numerical simulations and study of thermonuclear bomb craters imply that crater radius scales approximately with E1/3 (i.e. m1/3 forimpactors. If the crater diameter distribution is n(r), we get the corresponding mass distribution by writing n(r)dr = n(m1/3)d(m1/3) = frac13n(m1/3)m-2/3dm (8.46)

from which we identify frac13n(m1/3)m-2/3 as the mass spectrum. The r-3 crater radius power law thus implies an m-5/3 power law for impactor mass. Use of more detailed fits to the crater data along with alternate crater-size models, as well as direct fits to asteroidal mass distribution, yield exponents between 1.5 and 1.8.

Suppose now that n(m) a: m-q for some exponent q. The total mass of impactors is m n(m) dm, and the blowup of n(m) at small m does not cause the total mass to diverge as long as q < 2. On the other hand, the number of small impactors is infinite for q > 1, as is the case for the observed distribution. However, for q > 1 the total mass of large impactors diverges if the power law continues out to infinite mass. Thus, to make physical sense, the power law must be truncated at some mass m+, which represents the largest mass impactor in the population. With this assumption, the total mass in the distribution is finite, and we can write a normalized distribution as

where, mtot is the total mass of impactors. It is presumed that n = 0 for m > m+.

Exercise 8.7.10 Verify that m+ is the total mass of impactors implied by the distribution in Eq. 8.47. Find the cumulative distribution N(m) and discuss how this behaves for m+ ^ to with mtot fixed.

The total number of impactors with mass greater than mc is r m+ 2

From this, we set N(mc) equal to Ne, which tells us the required total mass mtot, given q and m+. The special case of satellites is treated by reducing mc according to the estimate of impactor velocity enhancement, and multiplying the value of mtot by the ratio of area of the primary to area of the satellite, so as to take into account the proportion of total available impactors that hit the satellite rather than the primary.

The results of this calculation of mtot are given in the final column of Table 8.4. These calculations were carried out with q =1.5 and m+ = 7.35 • 1021kg, which is one tenth the mass of the Earth's moon. It takes rather little impactor mass in the late stage veneer to deplete the atmosphere of an Earthlike planet - only a tenth of a percent of Earth's mass, which is not an unreasonable amount to be left over after the assembly of an Earth-sized planet. An important result is that if Mars were to start out with a 2bar CO2 atmosphere (as suggested by some climate calculations based on evidence for warm,wet early conditions), its atmosphere would not be much more subject to erosion than Earth's. The mass of available impactors required to erode such a

Martian atmosphere would be fully 70% of the corresponding mass for Earth. The main reason the estimates are so similar is that a 2bar atmosphere on Mars has much more mass per unit area than Earth's atmosphere, requiring a higher critical mass of impactor as compared to Earth. A more tenuous Martian atmosphere is much more erodable than Earth's, as illustrated by the 100 mb Mars case in the table. Similarly, if Venus had an Earthlike atmosphere, its atmosphere would be essentially as erodable as Earth's, whereas the actual dense Venus atmosphere requires about seven times as much available impactor mass to erode. The hypothetical Super-Earth case is only a bit less subject to erosion than Earth, in this case because a 1 bar atmosphere on a large planet has less mass per unit area than Earth's atmosphere. The importance of the atmospheric mass effect shows also in the hypothetical planetary Titan case, which, owing to its very massive atmospherre, requires nearly as much available impactor mass to erode as does the 2 bar Early Mars case. The real Titan, in contrast, is very difficult to erode, requiring an available impactor mass of nearly a tenth of Earth's mass, owing to the competition with Saturn for impacts.

The essential puzzle posed by the results of Table 8.4 is that it looks quite plausible that Earth's atmosphere would be subject to loss by impact erosion in the sweep stage, and that a dense Early Mars atmosphere would not be appreciably less erodable than Earth. How, then, to account for the present tenuous Martian atmosphere, while Earth has a substantial atmosphere remaining? One potential factor is that Earth's atmosphere was indeed lost by impact erosion, but was regenerated by outgassing from the interior. Consistent with this picture, we note that while Mars requires nearly as much available impactor mass a Earth, this impactor mass is delivered over a much longer time, owing to the smaller cross section of Mars. Combined with the relatively early shutdown of tectonic activity and hence outgassing on Mars (owing to its small size) it could be that the essential difference between the planets resides not so much in ability to hold an atmosphere as in ability to regenerate an atmosphere. A severe difficulty with this picture, however, is the abundance of N2 in Earth's atmosphere. A CO2 or water vapor atmosphere could be easily regenerated, but it is not easy to hide enough N2 in the mantle to allow this component to be regenerated. And recall that Venus has even more N2 in its atmospherere than Earth, suggesting that even if Venus went through an early stage with far less CO2 in its atmosphere, it did not suffer total atmosphere loss by impacts during that stage. Could it be that there is an ability to sequester a bar or two of N2 in a planet's mantle? Could it be that Earth started out with much more N2 in its atmosphere and that what we have today i the small bit left over after substantial impact erosion? Or could it be that the mass of impactors was not in fact sufficient to deplete Earth's atmosphere and that the tenuous Martian atmosphere has some other explanation? Perhaps it never generated a dense atmosphere, because it never received enough oxygen-bearing material to turn carbon into carbonate and CO2. Perhaps Mars lost its atmosphere in a chance giant impact which got rid of Martian N2, whereas Earth's Moon-forming impact was not big enough to get rid of all the N2 . If a giant impact got rid of most of the primordial N2 on Mars, then perhaps the rest could have been gotten rid of by nonthermal escape and solar wind erosion. But if Mars lost its atmosphere too early (especially its ability to generate a dense CO2 atmosphere) then it becomes hard to account for the large, extensive water-carved channels on Mars, some of which suggest persistence of active surface hydrology up to 3.5 billion years ago, with episodic recurrence of less extensive river networks extending billions of years later. More precise dating of these hydrological features, which will come ultimately with sample return missions from Mars, will go far to help resolve these puzzles. Still, the Mystery of the Missing Martian Atmosphere is likely to remain one of the Big Questions for a long while to come.

How do giant impacts fit into the picture? Giant impacts do not come in a continuous stream, but Lunar to Mars-sized bodies are common enough in the late stages of planetary formation that it is likely that one or more giant impact occurs before the planet attains its final size. The very existence of the Moon provides evidence that Earth experienced a giant impact, while the anomalous retrograde rotation of Venus has been taken as evidence that a giant impact occurred there as well. The Martian crust exhibits a striking dichotomy between rugged thick-crusted and heavily cratered Southern Hemisphere highlands and smoother, thinner Northern Hemisphere lowlands; this has sometimes been taken as having resulted from a giant impact, though one smaller in relative scale than Earth's Moon-forming impact. A single giant impact can blow off an entire atmosphere, but this is not inevitable; depending on the energy of the impactor, there can be a substantial proportion of the original atmosphere left. The issues in reconciling the histories of Earth and Mars are essentially the same as for the sweep stage impact erosion: how to account for the story of N2 on Earth (or Venus, for that matter)? And how to account for the hydrology of Early Mars if a giant impact blew off the primordial Martian atmosphere but the planet was unable to regenerate a new CO2 atmosphere by outgassing?

It should be kept in mind that impacts can also be an important source of volatiles. Comets can directly bring in volatiles such at CO2, water and methane. Moreover, the high pressure and temperature during the impact shock can cook water vapor out of hydrated minerals such as serpentine. Similarly, impacts can release CO2 from carbonates in the crust. Carbonates are not primary planet-forming substances, but could be formed in the process of accretion through reaction between primary forms of carbon, oxygen, water and silicates. If this happens, CO2 can be retained within carbonate even when some atmospheric loss event has blown away an earlier atmosphere, and this CO2 can be released as a result of later impacts at a rate that can be much faster than the release associated with volcanic activity.

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  • Camelia Smallburrow
    What is impact erosion loss of volatiles?
    10 months ago

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