Figure 1.2: Altitude proles of the Venus ionospheric composition based on the Pioneer Venus Orbiter observations (adapted from Brace and Kliore, 1991). The left panel shows the daytime ionosphere and the right panel the nighttime ionosphere.
Earth, Venus is a very dry planet. According to Donahue and Russell (1997) "the question that begs to be answered is whether this water [in the Venus atmosphere] is mostly the remnant of an early abundant supply of water, most of whose hydrogen has escaped to space, or, instead, consists to a large extent of water that has been introduced comparatively recently by comets or by volcanic outgassing."
See Figure 1.4 for comparison of water, carbon dioxide and nitrogen inventories of Venus, Earth and Mars.
Since young Venus and Earth had presumably similar atmospheres, most of the original Venus water must have disappeared (e.g. Donahue and Russell, 1997).
Approximately 2×1020kg of water may have escaped during the 4.6-billion-year evolution of the Solar System (Luhmann, 1986). This equals to 6.7×1045 water molecules of which 4.5 ×1045 are hydrogen atoms and 2.2× 1045 oxygen atoms.
Moreover, 4.6 billions years is about1.45×1017 seconds, which gives average escape rates of 3.1×1028 hydrogen atoms per second and of 1.5×1028 oxygen atoms per second.
1.2 Atmospheric escape
Atmospheric particles can be lost from a planet in several ways. Escape mecha-nisms can be categorized according to whether they are thermal or non-thermal pro-cesses and whether associated escaping particles are charged ions or neutral atoms or molecules (see, for example, Lundin et al., 2007).
In thermal equilibrium the velocities of particles are distributed according to the Maxwell-Boltzmann distribution. The most probable speed of a particle in thermal equilibrium is given by
vth =
r2kBT
m . (1.1)
Figure 1.3: Altitude proles of the density of hot oxygen atoms in the Venus dayside exosphere from models for dissociative recombination and from the Pioneer Venus Orbiter data (from Gröller et al., 2010).
A particle can escape from an atmosphere at the planetocentric distanceR if its velocity exceeds the escape velocity from a gravitational eld of a planet:
vesc =
r2GMP
R , (1.2)
where MP is the mass of the planet. For Venus the escape velocity is 10.36 km s−1 which equals to kinetic energy of 0.56 eV for a hydrogen atom and to kinetic energy of 8.9 eV for an oxygen atom.
However, atmospheres are collisional at low altitudes and particles cannot make their way straight from surface to space. The exobase is the lower boundary of the uppermost part of a planetary atmosphere, the exosphere. It is dened to be at the altitude at which the mean free path of a particle is the same as the atmospheric scale height. Above the exobase particles are not colliding frequently and move in ballistic trajectories.
The basic form of thermal escape of neutral particles from a planetary
atmo-1.2. ATMOSPHERIC ESCAPE 7
Figure 1.4: Estimated inventories of volatiles, easily vaporizing elements or chemical compounds, on Venus, Earth and Mars. The bars show the lower limit of the total abundances and the lled parts the atmospheric content (from McBride and Gilmour, 2004).
sphere is described by the Jeans equation (Chamberlain and Hunten, 1987):
F = vth 2√
πn(1 +x)e−x [m−2s−1], (1.3) where vth, n and x are the most probable thermal velocity and number density of particles at the exobase and the thermal escape parameter, respectively. The escape parameterx is dened as
x = GMPm
kBTexoRexo = v2esc
vth2 , (1.4)
where Texo is the temperature at the exobase, Rexo planetocentric distance of the exobase andvesc andvththe escape and thermal velocities of particles at the exobase, respectively.
From Equation 1.3 it can be seen that the thermal escape ux is a function of the gravitational potential energy at the exobase. The escape ux decreases expo-nentially in concert with increasing gravitational potential energy. Heavy particle species are more bound to a planetary atmosphere than light species. Also, massive planets can retain lighter species more easily in their atmospheres with respect to less massive planets. McBride and Gilmour (2004) state that if the average speed of particle species (at the exobase) is less than about one-sixth of the escape ve-locity, a planet can retain the species in its atmosphere for a period of time of the
Figure 1.5: Conditions of thermal escape of dierent particle species from the So-lar System planets. For planets one-sixth of the escape velocity and the exobase temperature are shown (dots). The red lines give the average thermal velocities of particle species as a function of temperature. Planets above a certain line are able to retain the species in question in their atmospheres from thermal escape for a period of time of the same order of magnitude as the age of the Solar System (from McBride and Gilmour, 2004).
same order of magnitude as the age of the Solar System. Figure 1.5 summarizes the conditions of thermal escape of dierent particle species from the Solar System planets. Note that the Venus exobase temperature is signicantly lower than that of the Earth. This is due to the radiative cooling eect of CO2 at 15-µm infrared wavelength (Keating and Bougher, 1992).
Venus is massive enough to gravitationally bind neutral oxygen particles. Only a small fraction of the total oxygen is subject to the Jeans escape. On the other hand, hydrogen particles may have been easy to remove from the Venus atmosphere during its evolution. If original Venus water molecules were photodissociated in the atmosphere, hydrogen may have freely escaped from the exoshere. Remaining oxygen could have then reacted with the surface rocks and be absorbed in the Venus soil (Luhmann, 1986). Another possible explanation how heavy elements such as oxygen may have escape from Venus is related to the fact that the planet has no detectable intrinsic magnetic eld and the solar wind interacts directly with its ionosphere.