Caption: A log-log plot of escape velocities (probably from a reference surface radius) versus some reference temperature for representative Solar System objects showing lines above which the specified gases (labeled above the lines) undergo total??? atmospheric escape (down to some reference minimum level) since the Solar System formation (4.6 Gyr BP) ???. The Solar System objects are approximately to scale and the actual data points are the centered black dots (which CANNOT always be seen or maybe are NOT shown for the smaller Solar System objects).

Features:

1. The specifications of the plot are NOT complete, and so one can only rely on it with some caution.

   In particular, total atmospheric escape requires specifying some time over which it is judged to happen. One can only guess here that the author means since Solar System formation (4.6 Gyr BP).

   Of course, total atmospheric escape can happen over millions to billions of years depending on the astro-body's escape velocity and surface temperature. This is, of course, implied by the plot.

   Note also yours truly thinks the results in the plot are from idealized calculations, and so are only approximate for the real Solar System objects in any case.

   Howsoever, the plot shows the main trend: atmospheric escape increases from upper left to lower right: i.e., as astro-body's escape velocity ↓ and surface temperature ↑, atmospheric escape ↑.

2. The reference surface radii are NOT specified, but they are probably the mean radii for the solid surfaces for the rocky bodies and rocky-icy bodies and the 1 bar radii for the gas giants. The 1 bar radius is the radius where the pressure is 1 bar = 100 kPa (exactly): the pressure increases with depth for pressure-supported astro-bodies. Note that standard Earth atmosphere pressure = 1 atm = 101.325 kPa = 1.01325 bar = 14.696 Psi.

3. The temperatures for the airless worlds are probably their effective temperatures: i.e., the temperatures they would have if they radiated the energy they absorb (but NOT reflect) from the Sun exactly like blackbody radiators---and this is very close to exactly correct for their surface temperatures.

   The temperature for the Earth is probably the Earth mean surface temperature 287 K (1961--1990). The Venus temperature may be from somewhere high in the Venusian atmosphere (see Wikipedia: Atmosphere of Venus: Troposphere). It's NOT the surface temperature which is 740 K (see Wikipedia: Atmosphere of Venus). For Titan (which has its Titanian atmosphere), the temperature is the surface temperature.

   The temperatures for the gas giants may be those at the 1 bar radiis.

4. Atmospheric escape is the loss of atmospheric gases to outer space. There are several processes, but the main one of interest is just that gas molecules (or atoms for monatomic gases which we include hereafter without further mention) from the upper atmosphere with escape velocity can escape to infinity (see Wikipedia: Atmospheric escape: Thermal escape mechanisms). The escape happens in the upper atmosphere where the molecules can avoid collisions when on an escape trajectories.

   Now atmospheric gases almost always have a Maxwell-Boltzmann (MB) distribution of velocities which formally only goes to zero at infinite velocity. So there is always a high-velocity tail to the MB distribution. The higher the temperature, the bigger the tail of molecules. So higher temperature in the upper atmosphere increases atmospheric escape.

   Now the MB maximum velocity v=(2kT/m)**(1/2), where Boltzmann's constant k = 1.380 649*10**(-23) = (8.617333 262... )*10**(-5) eV/K (exact) ≅ 10**(-4) eV/K , T is temperature, and m is molecule mass. The high-velocity tail of the MB distribution is correlated with the MB maximum velocity.

   So as T ↑, atmospheric escape ↑ and as m ↑, atmospheric escape ↓.

5. Now recall the escape velocity formula for spherically symmetric astro-body

    
     v_escape = sqrt(2GM/R) = (11.180 km/s) * sqrt[(M/M_⊕)/(R/R_eq_⊕)]  , 

   where gravitational constant G = 6.67430(15)*10**(-11) (MKS units), M is the mass of the spherically symmetric astro-body, R is the radius of the spherically symmetric astro-body, and the 2nd version of the formula is written in terms of Earth units as indicated by the Earth symbol ⊕.

   Now note that as M/R ↑, v_escape ↑, atmospheric escape ↓ since fewer molecule have the necessary escape velocity.

6. The above discussion of the MB distribution and escape velocity makes the trends in the plot are understandable:
   1. surface temperature T ↑, atmospheric escape ↑.
   2. molecule mass m ↑, atmospheric escape ↓.
   3. astro-body M/R ↑, v_escape ↑, atmospheric escape ↓.

7. We note the following salient features of the astro-bodies shown in the plot:
   1. The gas giants have retained all atmospheric gases.
   2. Earth and Venus have lost hydrogen and helium. Mostly lost. They still have some by continuing geological release (i.e., rock outgassing) of hydrogen and helium embedded in their rock.
   3. Mars CANNOT hold water vapor over geological time, but it does have ice and very probably subsurface liquid water. Some water vapor is detected, but this is from slow release of Mars's non-vapor water.
   4. The Titanian atmosphere (its lower atmosphere) is primarily composed of nitrogen (N) (94.2%) (rather unreactive molecular nitrogen N_2???), methane (CH_4) (5.65%), and hydrogen (H) (0.099%) (molecular hydrogen (H_2)???). So the plot is NOT completely adequate for Titan.
   5. The airless worlds (i.e., those astro-bodies with almost NO atmosphere) can hold on to xenon, but they probably do NOT have much. Note airless worlds have almost NO atmosphere, but there is always a tenuous atmosphere if you look closely enough due to continuing outgassing from rock or accumulation from the solar wind.

8. After thermal atmospheric escape, probably the next most important atmospheric escape process is solar wind sputtering atmospheric escape where the solar wind blows off molecules from the upper atmospheres. This process is most important for Solar System objects lacking a strong magnetic field which shields the objects from the direct solar wind. The Martian atmosphere is believed to have been strongly depleted by solar wind sputtering atmospheric escape (see Wikipedia: Atmosphere of Mars: Atmospheric escape on modern Mars).

9. Astro-bodies shown on the plot: Callisto Earth ⊕, Europa, Ganymede, Io, Jupiter ♃, Mars ♂, Mercury ☿, Moon ☽, Neptune ♆, Pluto ♇, Saturn ♄, Triton, Titan, Triton, Uranus ↑☉,♅, Venus ♀.

10. Gases shown on the plot: ammonia (NH_3), carbon dioxide (CO_2), helium (He,Z=2), hydrogen (H, Z=1) (probably molecular hydrogen (H_2)), methane (CH_4), nitrogen (N, Z=7) (probably molecular nitrogen N_2), oxygen O (Z=8) (probably molecular oxygen (O_2)), water vapor (H_2O) xenon (Xe,Z=54).