A) Mercury
 

1. Basic facts Radius - 2435 km Mass - 3.3 x 1026 g Density - 5.43 g/cc Albedo - 0.12 Distance from Sun - 0.3 - 0.46 AU Length of year - 87.97 days Length of day - 58.646 days.  Note that this is exactly 2/3 of the year.

2. Similarity with the Moon: 2.1 Its surface is covered with craters. 2.2 There are regions that look like lunar basins, and regions where there appears to have been lava flows like the lunar Maria. 2.3 It has a low albedo and a color similar to the Moon.

3. Differences from the Moon: 3.1 The Moon always keeps the same face towards the Earth, but Mercury turns three times every two revolutions about the Sun.  When Giovanni Schiaparelli observed Mercury at the end of the 19th century, he could only do so when Mercury was far from the Sun both in distance and in angle.  This happens only rarely, but after a number of years of observing Schiaparelli was able to see features on the surface that repeated.  Because Mercury returns to aphelion every 88 days, one should observe it then, but if the angle is good at one particular time, it will be very bad 88 days later because 88/365 = 0.24, i.e. nearly 1/4, so the Earth will have moved almost a quarter orbit and the observations will be difficult.  Another 88 days will put Mercury back at aphelion and the Earth on the other side of the orbit; again a good time for viewing.  In the meantime, Mercury makes not 2 but 3 full rotations.  Schiapparelli observed Mercury every second orbit, and thought it had made 2 rotations, so he assumed that, like the Moon, it always kept one side towards the Sun.  Just like the Moon is locked into a resonance by the tides raised by the Earth, so Mercury should be locked into a resonance with tides raised by the Sun.  In the early 1960's measurements of the dark side of Mercury showed that the temperature was higher than expected.  The dayside has a temperature of about 700 K and the night side temperature is about 90 K.  If the dark side always faced away from the Sun it should be even colder.  At first people suspected a slight atmosphere that carried heat around from the hot side.  But in 1964, radar signals bounced off Mercury showed that it was rotating slowly.  What about the tidal locking?  Since Mercury's orbit is very eccentric, it is sometimes considerably closer to the Sun than at other times.  At this point, when the tidal forces are the strongest, Mercury moves more quickly in its orbit.  At this speed it would circle the Sun in only 59 days.  This is the spin rate imposed on the planet. 3.2 A second, more important, difference is that the Moon is much less dense than Mercury.  Part of the difference is due to the fact that Mercury is more massive and has greater pressures in the center, but this is a small effect.  Apparently the composition is different.  We know the Moon has a very small core, and is poor in iron. Probably Mercury has a much larger iron core; even larger than that of the Earth. 3.3 Another feature that is found on Mercury but not on the Moon is a scarp.  Scarps are several km high and thousands of km long.  A possible explanation is that because Mercury is larger than the Moon it released more gravitational energy on accretion.  This heat, in addition to core formation, caused a global heating of the planet.  The planet expanded.  As it cooled, it wanted to contract, and caused warping of the solid surface.  Estimates are that the radius of Mercury shrunk some 20 km in this way.  The scarps are the remains of such warps. 3.4 Spectroscopy has revealed a very thin atmosphere of potassium and sodium that are diffuse from the surface.  In 1991 radio telescopes found evidence for sheets of polar ice.  Mariner 10 did not cover the poles.

4. Density and composition: The density of a planet depends on its composition, but also on its mass.  The more massive a planet, the greater the compression of the material, and the greater the density. 4.1 The equation of state: For low (i.e. zero) pressure we can measure the density, ρ0. For somewhat higher pressures we can measure the bulk modulus, K, and assume that it stays constant with pressure.  For most materials K ~ 1011 - 1012 dynes cm-2, and for pressures much less than these values K stays roughly constant.  From the definition of  K we see that and  This is a simple form of an equation of state and can be used to estimate the change in density of a material as a function of pressure.  More sophisticated assumptions can give better equations of state.  In this way we can estimate the uncompressed density of a planet. 4.2 Composition: We see that Mercury is made of the densest material of any of the terrestrial planets. How does this density difference translate into a composition difference?    Water + iron can combine to give the same density as organic material.  How can we differentiate?  Reflection spectroscopy of the surface. 4.3 A crystal is made up of particles attached by springs. The vibrational frequency of this lattice of springs depends on the mass of the molecules making up the lattice as well as the spring constants.  These latter depend on the intermolecular forces.  Photons that hit a mineral surface are absorbed preferentially if they have the same frequency as one of the favored frequencies of the lattice.  So that the signatures of different minerals measured in the laboratory can be compared with observations.  The problem is that different spectra add, so you have to be able to untangle the individual spectra from the combination.  This can be difficult. 4.4 Philosophy:  what would you expect on the basis of cosmogony?  You expect to see these types of constituents. Thus to make up the high density of Mercury you would expect to see a good deal of iron. 4.5 The true composition is probably a mixture of different materials.   The density of a mixture can be found from the following argument:  Suppose we have a mixture of substances denoted by the index, i.  The total volume is the sum of the individual volumes, so   If the mass fraction of each species is denoted by Xi, where Mi = Xi M (M is the mass), we have or ,  where ρ is the density of the mixture and &rhoiare the densities of the individual components.  This relation is known as the additive volume law, and holds as long as there are no interactions between the individual species, so that the volume is preserved.  An alternative formulation of this idea is to define Yi as the volume fraction of the ith species.  In this case, the mass of the ith species is given by YiV&rhoi , and since the masses must add

5. The moment of inertia:  The density distribution inside a planet is one of the main objects of interest for a planetary scientist. 5.1 The mass of the planet is given by  This is really the zeroth moment of the density distribution.  If we would know all of the moments we could work backwards and find the density distribution itself.  Unfortunately this is not possible. 5.2 A second moment can be found from the moment of inertia.   where θ is the colatitude and dm is an element of mass.  If we take a volume element to consist of   Assume symmetry about f, then putting dm = ρdV in the above, gives 5.3 A more convenient quantity is the inertia factor I/MR2. For a body of constant density, we get I = 8πρR5/15 and an inertia factor of 0.4.  For a more centrally condensed body the factor will be less.  The inertia factor for the Moon is 0.39 and for the Earth 0.33. 5.4 The moment of inertia is another (second) moment of the density distribution.  If we could measure all of the moments we could retrieve the density, but this is not possible in practice.  In fact it is extremely difficult to measure the moment of inertia for any other planet. 5.5 There is another way of getting information on the density distribution inside a planet.  A body under the influence of gravity will be a sphere, but if the body is spinning, centrifugal force will cause it to become oblate.  The size of the oblateness will depend on the ratio of the centrifugal to gravitational forces, i.e. on the quantity  ,  where ω = 2π/P is the angular velocity and P is the period of rotation. 5.6 The oblateness, or flattening, of a planet can be measured, and is defined by 5.7 The shape of a planet also influences the gravitational field it produces.  A purely spherical body acts like a point mass, and has a 1/r potential.  An oblate body has a more complex potential, which depends not only on r, but also on the angles.  Just as the point mass potential is characterized by the mass, M, the potential of an oblate body is characterized by M and a series of gravitational moments, Jn.  These can sometimes be measured, and give additional information about the interior structure of a planet. 5.8 If there are no prominent mountains, then the planet is symmetric about the spin axis, and there is no φ-dependence.  If there is symmetry with respect to the equator, then the n's are even.  Very roughly, Jn ~ qn for small q, so that usually J2 is the dominant term.  It can be shown that for small q  5.9 A body moving in a 1/r potential will execute a closed orbit.  If the potential differs from a pure 1/r form, the orbit will not be closed, and the line of apsides will precess.  The rate of precession will depend on the Jn's (mostly J2) and this can be measured if the planet has satellites (natural or artificial).  In this way we can learn something about the internal structure of a planet. 5.10 for Mercury, q ~ 10-6, which is very small.  Mountains on Mercury distort the gravitational field more than this so that J2 = (8 ± 6) x 10-5.  In such a case we cannot learn much about the interior from a measurement of J2.

B) Venus
 
 

1. Basic data Radius - 6052 km Mass - 4.87 x 1027 g Density - 5.24 g cm-3 Albedo - 0.75 Length of day - 243.02 days (retrograde) Length of year - 224.7 days Distance from Sun - 0.723 AU

2. Atmosphere 2.1 Venus has an extensive atmosphere and is completely covered with clouds.  For many years very little was known about the atmosphere and what lay underneath.  In 1967 a Soviet spacecraft arrived at Venus, but did not survive long enough to relay information.  In 1970 Venera 7 landed and in 1972 Venera 8 reached the surface.  An American probe arriving in 1978 sent back information on atmospheric chemistry. 2.2 The Landers measured a surface pressure of 92 bars and a surface temperature of 740 K (the Landers survived for roughly an hour). 2.3 The atmosphere is 96% CO2, 3.5% N2, and traces of Ne, Ar, and sulfur compounds.  There is essentially no water.  The clouds extend from 30 km to 90 km above the surface and consist of drops of H2SO4 between 1 and 10 μm in diameter. 2.4 Winds near the surface are low, about 0.3 to 1 m s-1.  At 50 km altitude, however, they reach 100 m s-1. 2.5 The major weather pattern is a Hadley circulation with hot air rising at the equator and descending at the poles.  Hadley's theory works much better for Venus than for Earth for several reasons 2.6 Venus spins much more slowly, so there are no significant coriolis effects.  Venus' spin axis is only tilted 177.3° (i.e. -2.7°) from the perpendicular compared to 23.5° for the Earth, and its orbit is nearly circular (eccentricity of 0.0068) compared to 0.167 for the Earth, so there are no seasons to influence the distribution of sunlight. 2.7 Venus's temperature is determined by the greenhouse effect so that this too reduces the effect of variations in the solar illumination.  For all these reasons the simple Hadley theory works well. 2.8 The surface temperature is 740 K (day and night).  This is caused by the greenhouse effect.

3. Surface-Atmosphere interaction: The key to understanding the chemistry of Venus' atmosphere (and of terrestrial planetary atmospheres in general) is through the interaction with the surface. 3.1 Radar reflection from the surface of Venus is consistent with the presence of pyrite (FeS2).  The CO2 in the atmosphere will react with this to produce COS and H2S 3.2 The gases can be broken down by UV to form H2, which escapes to space, as well as other gases, such as CO.  These gases have been observed in the Venus atmosphere. 3.3 Sulfur, from the H2S can form sulfur particles, which act as aerosols in Venus’ atmosphere.  These are the dark areas seen in UV photos of Venus.  3.4 Another reaction product is SO2, which combines with water to form H2SO4 drops.  These are the yellow drops that form the clouds we see. 3.5 Additional chemistry is believed to have been responsible for the high temperatures.  On Earth the oceans buffer the atmospheric CO2.  Excess CO2 gets dissolved and  CO2 + H2O → H2CO3  This calcium carbonate precipitates out of the oceans and into carbonate rocks.  The carbonate rocks get subducted into the mantle and the heating breaks up the carbonates into water and CO2.  Volcanism returns these products to the surface. There is as much CO2 in carbonates in the Earth as there is CO2 in the atmosphere of Venus. 3.6 Since Venus is closer to the Sun, the temperature there should be a bit higher.  This means more water vapor in the atmosphere and a stronger greenhouse effect.  This means even more evaporation, and less absorption of CO2.  This means an even stronger greenhouse effect.  In addition, ultraviolet breakdown of water and the subsequent loss of the hydrogen, means that the system is not closed, and the water gets irreversibly lost.  Eventually, all of the oceans on Venus were lost, and there was no sink for the CO2, so it too all went into the atmosphere.  This runaway greenhouse effect is what is believed to have led to the high temperatures on Venus today.  Of course it is possible that Venus had less water to begin with.

4. Venus’ Surface 4.1 Radar mapping of Venus' surface by Pioneer Venus in 1978, and Magellan in 1990 have provided many details about the surface.  Impact craters have been observed.  The largest has a radius of about 80 km, and the smallest about 3 km.  Although smaller craters could have been seen, the thick atmosphere probably prevents smaller meteorites from reaching the surface. 4.2 There are large troughs, the largest being 1400 km long. Volcanoes have also been seen, although it is not yet clear if they are still active. 4.3 Many of the surface features are the result of stresses on the surface material.  In order to understand the source of those stresses, we have to first determine the energy source driving them.  One source is accretion energy.  If a mass dm falls onto a planet from infinity, the energy released is  if the material of the planet (and the planetesimal) has a density ρ, then  and  This is approximately the formula we used in computing the binding energy of the Sun.  As we have seen, a large fraction of this energy is lost through radiation during the formation process itself.  This is especially true if the accretion takes place over a long time. 4.4 When a planet melts the heavier core material can separate out and sink to the bottom. This also provides an energy source due to gravitational energy release, except that here the release occurs in a relatively short time, and the energy is prevented from escaping by the overlying layers. Another difference is that the material is not falling from infinity. 4.5 A possibly more important source of heating is radioactive decay.  The details of the composition of Venus are not known, but measurements of the surface composition at the Venera landing sites shows that it is similar to that of the Earth.  Probably, the rest of the composition is similar as well, but we do not know for sure.

5. Venus Interior 5.1 Since Venus spins so slowly, it does not have a bulge at the equator, and so we cannot tell much about how centrally condensed it is.  All we know is that its mean density is similar (somewhat smaller) to that of the Earth.  This too indicates that the composition should be similar.  We can guess that the structure should be similar as well. 5.2 If we use the same pressure-density relation as for the Earth, and use it to compute a model of Venus we find that we fall short by 40 km.  If we take into account the fact that Venus' mass is slightly lower, so that a given pressure is reached at a greater depth, and higher temperature, then the pressure-density relation must be corrected to allow for this.  This correction reduces the discrepancy to only 20 km, but this is enough to show that the composition is not identical to that of the Earth. 5.3 A possible explanation is the amount of sulfur.  Venus formed closer to the Sun, and therefore may have accreted a different amount of sulfur. 5.4 If the temperature in the region of Venus' formation were above 700 K, the sulfur in the solar nebula would have been in the gas phase.  The core would consist of Fe and Ni and would be denser than the Earth's core by about 10%.  It would also be less massive, since the total amount of core material would be smaller.  This would affect the total density of the planet by about 1%, just enough to explain the discrepancy.  The problem is that we see sulfur on Venus, so it got accreted.  We just don't know how much of the sulfur remained in the mantle and how much got into the core. 5.5 If the temperature were much lower, then most of the heating would come not from the Sun, but from accretion.  This energy would be less than for the Earth because Venus is less massive.  Instead of the Fe forming FeS, it might have formed FeO, which would stay in the mantle. Again, the core would be smaller, and this would account for the discrepancy. 5.6 Venus doesn't have a magnetic field.  This may be because there is no S in the core, so that it is not melted. Or it may be that Venus is not spinning fast enough.

C) Mars
 
 

1. Basic data Radius - 3397 km Mass - 6.4 x 1026 g Density - 3.94 g cm-3 Albedo - 0.25 Length of Year - 686.98 days Length of Day - 24h 37m 26s Distance from Sun - 1.524 AU

2. Overview 2.1 The Martian surface is divided into highlands and lowlands.  The highlands are in the southern and part of the northern region of the planet and are heavily cratered.  They are probably the older part of the planet.  In general, the ground level is higher than the rest of the planet. 2.2 The lowlands are smoother (fewer craters) and probably are younger.  They cover the northern part of the planet.  2.3 At the poles there are ice caps composed of H2O and CO2 ice.  The ice caps show layering, probably due to alternating episodes of vaporization and freezing.  There is dust mixed in with the ice. 2.4 Near the caps there are dune fields.  These are connected to an interesting story.  Markings had been seen on Mars since 1659 when Huygens sketched Syrtis Major, a dark area on Mars.  From 1877 to 1888, Schiapparelli made observations and produced maps of Mars with many named features.  In particular he charted long dark features he called canali - channels in English.  They were mistranslated canals and people started thinking in terms of artificial structures.  In particular the American astronomer, Percival Lowell claimed he saw canals on Mars.  A 1909 story in the Los Angeles Times reports signs of digging on Mars by Lowell and the French astronomer Flammarion.  The idea caught hold in the Western imagination, and science fiction started producing works based on the idea.  H. G. Wells wrote War of the Worlds in 1898 and E. R. Burroughs wrote a series of books about Mars starting in 1912.  An award posted for the first contact with another world specifically excluded Mars because that was too easy.  In 1938 Orson Welles produced a radio version of War of the Worlds that was presented as a news- broadcast.  It was so realistic (and people were so ready to believe that Martians existed and were preparing to invade the Earth) that thousands believed it was the real news, and some even committed suicide out of fear.  One of the observations that had some basis was that of the "wave of darkening" that was observed to proceed from the poles towards the equator in the summer at a rate consistent with the rate of water vapor migration.  This was seen as evidence for the existence of plant life, and as late as 1964 the Encyclopedia Britannica suggested that possibility. The Viking spacecraft discovered the cause of the wave of darkening. 2.5 Seasons on Mars are much more pronounced, especially in the southern hemisphere.  This is because in the southern summer Mars is closer to the Sun.  It is only 2.07 x 108 km as opposed to 2.49 x 108 km, a difference of 20%.  The temperature extremes go from -87 to 17°C.  As a result the southern cap is more affected than the northern one.  Since the ice is largely CO2, which goes directly to the gas phase, and the atmosphere is not very massive to begin with, this causes strong winds, which move dust around.  The dust is bright orange Fe2O3 and it covers dark basaltic rocks.  The dust moves out of the way and the darker rock is revealed.  This looks like a wave of darkening which acts like a wave of plant growth.  In the winter the CO2 refreezes on the cap, and the winds go in the other direction, covering the darker rocks.  The fields of dunes show how this sand is moved around. 2.6 Mars has prominent volcanoes. Olympus Mons is the largest volcano known in the solar system.  It has a height of 26 km, and a diameter of 500 km.  The peak is higher than 96% of the atmosphere.  It is located in a region called Tharsis, which has a number of other volcanoes.  Alba Patera is only 6 km high, but 1600 km in diameter.  Some of the lava flows are 400 km long.  This indicates lavas of a very low viscosity.  One way to lower viscosity of lava is to mix in large quantities of water, but liquid water is not found on Mars.  Another way is to assume that the rock producing the lava is very rich in Fe.  Melting would form FeO, which has a very low viscosity.  The southern highlands also have lava flows, but these are much older. 2.7 Another prominent feature is Valles Marineris, a huge rift valley some 6000 km long.  There are many channels running into the rift, but no liquid water.  There are dendritic channels, which were apparently caused by flowing water.  Since they are found only in very old terrain, it seems that Mars had flowing water in the past.  There are also outflow channels that start in a certain place and flow outward.  Perhaps volcanism melted underground ice, which then flowed away from the place of melting.  Some of these features may have been seen by the early observers, and mistaken for canals, but many canals were just optical illusions. 2.8 The volcanoes sit on the surface and weigh it down.  The very uppermost surface is stiff, because it is cold.  We know that as a material is heated it becomes softer, i.e. its viscosity goes down with increasing temperature.  The stiff part of the planet (near the surface) is called the lithosphere.  The more plastic region is called the asthenosphere.  Even the lithosphere responds to pressures after a while, and might even crack under the weight of a volcano.  Similar cracks are seen in Greenland under the weight of the ice.  Regions like this take a body out of hydrostatic equilibrium.  The Tharsis bulge is an example of a particularly hot area under the surface, which causes the lithosphere to bulge outward at this point.  Such deviations from hydrostatic equilibrium make it difficult to interpret the measured gravitation field and to get a moment of inertia.  Now, observations from the surface of Mars via Viking and Pathfinder have determined that Mars’ inertia factor is 0.364. 2.9 There seems to be a correlation between the heights of the volcanoes and their age.  The oldest volcanoes are only a few km high, while the younger ones are higher.  The height of a volcano may be related to the depth of the magma source.  Suppose the source is at a depth d.  Then the pressure at that depth is P=ρgd.  If the density of the lava is lower, and equal toρ', then let ξ= (ρ-ρ')/ρ'.  The height to which the lava will rise is ρ'g(d+h), and h = ξd.  It is plausible that as Mars cooled, the lithosphere became thicker, and the magma source sank. As a result the volcanoes got higher.  The lithosphere is believed to be 120 - 150 km thick in some regions, and as thin as 20 - 50 km in others.  Since for typical lavas ξ~ 0.1, and h ~ 10 - 20 km, we would expect a lithosphere thickness of 100 - 200 km so that is consistent.

3. Surface processes and evidence for water: 3.1  In addition to tectonic processes, there are also surface processes at work on Mars. Two of these can be included under the heading of weathering. 3.2 There is no liquid water on Mars today, although there is evidence that there was in the past.  This water may still be present as permafrost. 3.3 The reason liquid water could have existed in the past depends on changes in Mars' obliquity.  This is the tilt of Mars' spin axis to the Sun.  The gravitational influence of the Sun and the other planets causes the obliquity to change with time from low values (of the order of 10°) to high values (of the order of 40°).  At low values the poles get little heat and much of the CO2 in the atmosphere gets frozen onto the poles and trapped there.  The atmosphere becomes very thin.  At high obliquity, the poles get more heat and the ice caps are smaller.  This allows more of the CO2 to remain in the atmosphere, and increases the atmospheric pressure.  The higher pressure allows more dust to be suspended in the atmosphere, which allows more heat to be trapped.  This raises the temperature and allows for more water vapor.  This, in turn, raises the temperature even more, etc.  The result is that in the past Mars may have had a significantly different climate, as well as liquid water. 3.4 This potentially fatal state of affairs does not occur on Earth, because our Moon is much larger than Mars' moons and gives the Earth - Moon system a large moment of inertia.  This helps prevent large changes in obliquity. 3.5  A second process of weathering is mechanical weathering. 3.6 Meteorite impacts break down the crust, and overturn the topsoil.  This is called gardening.  The layer of soil is called a regolith.  The regolith of the Moon is estimated to be several meters deep.  Asteroids are also expected to have regoliths. 3.7 Water can also help break up rocks.  As a rock is heated it expands, and can crack.  If water seeps into the cracks, then as the rock cools the water can freeze, and expand, further enlarging the cracks, and helping to break down the rocks. 3.8 Water can also carry soil from one place to another.  The Mississippi river has a discharge rate of 20,000 m3/s during normal times, and 3 times as much during floods. 3.9 Wind can also contribute to mechanical weathering, either by banging small rocks into larger rocks to break them, or by carrying the rocks to different locations.  Sand dunes moving are an example of the latter. 3.10 Chemical weathering changes the atmospheric composition as we have seen. 3.11  Another process is Jeans escape.  In thermal equilibrium the gas molecules in an atmosphere have certain speeds.  If the speed exceeds the escape speed, that particular molecule will escape into space.  There are two major complications.  The first is that the molecule must be moving away from the planet.  Even this is not sufficient.  Even if it is moving away, it may still collide with some other molecule and either slow down or get its direction changed.  In either case its chance of escaping is considerably reduced. 3.12  The pressure at the Earth's surface is 1 bar (106 dynes/cm2) and the temperature is 300 K, so the number density is n = 2 x 1019 part/cm3.  The mean free path that a molecule will travel is l = 1/nσ, where σ, the molecular cross-section, is roughly 10-15 cm2.  This gives a mean free path of l = 5 x 10-5 cm.  The particle will thus change its direction every half-micron of travel, and will almost never escape.  We need to do the computation for a region where the mean free path is much larger. 3.13  In a constant temperature, constant gravitational acceleration atmosphere, the density and pressure vary as e-z/H where z is the altitude, and H = kT/mg  is the scale height.  For altitude changes of the order of H, there are significant changes in the pressure and the density.  If a particle is at the region where the mean free path is of the order of the scale height, and it is moving away from the Earth, the density (an hence the mean free path) will be significantly lowered by the time it moves on mean free path.  The chances of it colliding with another molecule are therefore very small.  This region is called the exobase, and the area above it, the exosphere.  If there will be escape, it will be from the exobase, which is found from the condition that l ~H, i.e. 3.14  The second major complication is that not all molecules have the same speed.  In equilibrium the speeds are distributed according to a Maxwell-Boltzmann distribution.  Even if kT is not high enough to give a mean speed greater than the escape speed, there may still be molecules in the tail of the distribution that are moving fast enough.  Using these two ideas, we can compute the rate of escape of a planetary atmosphere.  Without going through the details, the resulting flux is given by , where m is the mass of the escaping molecule, R is the radius of the planet, g is the acceleration of gravity at the surface, z is the altitude, and the subscript ex refers to conditions at the exobase.  This computation was first done by James Jeans, and is known as Jeans escape.  What is important for us is that the escape flux depends exponentially on the mass of the molecule, so that lighter molecules have a much better chance of escaping.  This mechanism allows for the differential escape of the lighter isotopes of an element.  The effect is largest for the differential loss of H over D, and the D/H ratio on Mars is 5 times that of the Earth, while the 15N/14N ratio is 1.6 times that of the Earth.  Differential Jeans escape is one possible explanation, although, in fact, there are a number of additional complications.