Thermally driven escape from Pluto’s atmosphere: A combined fluid/kinetic model

A combined fluid/kinetic model is developed to calculate thermally driven escape of N₂ from Pluto’s atmosphere for two solar heating conditions: no heating above 1450 km and solar minimum heating conditions. In the combined model, one-dimensional fluid equations are applied for the dense part of the atmosphere, while the exobase region is described by a kinetic model and calculated by the direct simulation Monte Carlo method. Fluid and kinetic parts of the model are iteratively solved in order to maintain constant total mass and energy fluxes through the simulation region. Although the atmosphere was found to be highly extended, with an exobase altitude at ～6000 km at solar minimum, the outflow remained subsonic and the escape rate was within a factor of two of the Jeans rate for the exobase temperatures determined. This picture is drastically different from recent predictions obtained solely using a fluid model which, in itself, requires assumptions about atmospheric density, flow velocity and energy flux carried away by escaping molecules at infinity. Gas temperature, density, velocity and heat flux versus radial distance are consistent between the hydrodynamic and kinetic model up to the exobase, only when the energy flux across the lower boundary and escape rate used to solve the hydrodynamic equations is obtained from the kinetic model. This limits the applicability of fluid models to atmospheric escape problems. Finally, the recent discovery of CO at high altitudes, the effect of Charon and the conditions at the New Horizon encounter are briefly considered.     

Aeronomical evidence for higher CO2 levels during Earth’s Hadean epoch

According to recent simulations of the Earth’s thermosphere, the exospheric temperature is not expected to rise above 7000-8000 K even under extreme solar EUV conditions anticipated for the early Earth. Rather, when the solar EUV flux exceeds some critical value, the escaping flow of the bulk upper thermosphere starts cooling it due to adiabatic expansion, which results in a decrease of the exobase temperature. Under these extreme conditions, the exobase might have expanded above the magnetopause and the magnetosphere had not been able to protect the upper atmosphere against strong non-thermal erosion by the solar wind.This study shows that a nitrogen-rich terrestrial atmosphere with a present-day composition would have been removed within a few million years during the extreme EUV and solar wind conditions that are expected to have prevailed before the late heavy bombardment period ∼3.8 Ga ago. Our results suggest that a CO₂ amount in the early nitrogen-rich terrestrial atmosphere of at least two orders of magnitude higher than the present-time level was needed to confine the upper atmosphere after the onset of the geodynamo within the shielding magnetosphere and thus might have protected it from complete destruction.     

Energy deposition of pickup ions and heating of Titan's atmosphere

The deposition of energy, escape of atomic and molecular nitrogen and heating of the upper atmosphere of Titan are studied using a Direct Simulation Monte Carlo method. It is found that the globally averaged flux of deflected magnetospheric atomic nitrogen ions and molecular pickup ions deposit more energy in Titan's upper atmosphere than solar radiation. The energy deposition in this region determines the atmospheric loss and the production of the nitrogen neutral torus. The temperature structure near the exobase is also calculated. It is found that, due to the inclusion of the molecular pickup ions more energy is deposited closer to the exobase than assumed in earlier plasma ion heating calculations. Although the temperature at the exobase is only a few degrees larger than it is at depth, the density above the exobase is enhanced by the incident plasma.     

The density and temperature structure near the exobase of Saturn from Cassini UVIS solar occultations

We analyzed 15 solar occultations observed by the Cassini UVIS instrument to constrain the density and temperature structure near the exobase of Saturn. We retrieved the density of H₂ and thus the temperature at altitudes higher than 1900 km above the 1 bar level by analyzing the ionization continuum of H₂ at wavelengths shorter than 804 Å. We find that the exospheric temperature ranges from 370 K to 540 K, with a typical uncertainty of less than 20 K. According to our data the temperature increases with latitude from the equator to the poles by 100–150 K. At similar latitudes, the temperature varies by 20–50 K at different times with no evidence for any systematic diurnal trend so far. Based on our data, the exobase of Saturn is 2700–3000 km above the 1 bar level and the thermal escape parameter near the exobase ranges from 260 to 340, implying that thermal escape from Saturn is firmly in the Jeans regime. The mixing ratio of H₂ is close to unity at all altitudes below the exobase. We find that the pressure levels in the thermosphere deviate significantly from a simple spheroid predicted by potential theory. This is consistent with significant meridional temperature variations in the lower thermosphere. A global analysis of the temperature structure at different depths in the atmosphere is required to constrain both the shape and the deposition and redistribution of energy in the upper atmosphere further.     

Influence of the Earth's rotation and of possible perturbations,on the exobase and exospheric hydrogen densities

In this study, we try to refine the relation existing between the exobase temperature and density distributions of atomic hydrogen around the Earth (assuming that the zero net ballistic flux condition is satisfied all over the critical level). We find essentially that neither local heating in high latitude regions, nor the addition of proton fluxes around the Earth, induce large perturbations in the equatorial density distribution (less than 10 per cent). On the other hand, certain local heating can give large perturbations in the global density distribution (more than 50 per cent).The effect of the Earth's rotation is also studied. We find that at the exobase the density distribution of atomic hydrogen lags about one hour behind the temperature distribution. At higher altitudes this time lag increases, reaching 5–6 hr at 20 Earth radii.We show also that, due to a density inversion which takes place at 2 Earth radii, if the minimum of density at the exobase is on the dayside, above 2 Earth radii, a maximum of density is then on the dayside when going higher, due to the rotational effect, that density maximum shifts towards the evening, reaching early parts of the night at 20 Earth radii.     

Titan’s atomic hydrogen corona

Based on measurements performed by the Hydrogen Deuterium Absorption Cell (HDAC) aboard the Cassini orbiter, Titan’s atomic hydrogen exosphere is investigated. Data obtained during the T9 encounter are used to infer the distribution of atomic hydrogen throughout Titan’s exosphere, as well as the exospheric temperature.The measurements performed during the flyby are modeled by performing Monte Carlo radiative transfer calculations of solar Lyman-α radiation, which is resonantly scattered on atomic hydrogen in Titan’s exosphere. Two different atomic hydrogen distribution models are applied to determine the best fitting density profile. One model is a static model that uses the Chamberlain formalism to calculate the distribution of atomic hydrogen throughout the exosphere, whereas the second model is a Particle model, which can also be applied to non-Maxwellian velocity distributions.The density distributions provided by both models are able to fit the measurements although both models differ at the exobase: best fitting exobase atomic hydrogen densities of n_H = (1.5 ± 0.5) × 10⁴ cm⁻³ and n_H = (7 ± 1) × 10⁴ cm⁻³ were found using the density distribution provided by both models, respectively. This is based on the fact that during the encounter, HDAC was sensitive to altitudes above about 3000 km, hence well above the exobase at about 1500 km. Above 3000 km, both models produce densities which are comparable, when taking into account the measurement uncertainty.The inferred exobase density using the Chamberlain profile is a factor of about 2.6 lower than the density obtained from Voyager 1 measurements and much lower than the values inferred from current photochemical models. However, when taking into account the higher solar activity during the Voyager flyby, this is consistent with the Voyager measurements. When using the density profile provided by the particle model, the best fitting exobase density is in perfect agreement with the densities inferred by current photochemical models.Furthermore, a best fitting exospheric temperature of atomic hydrogen in the range of T_H = (150-175) ± 25 K was obtained when assuming an isothermal exosphere for the calculations. The required exospheric temperature depends on the density distribution chosen. This result is within the temperature range determined by different instruments aboard Cassini. The inferred temperature is close to the critical temperature for atomic hydrogen, above which it can escape hydrodynamically after it diffused through the heavier background gas.     

A semi-analytical approach to time-dependent coronal expansion

In this paper we point out the existence of a special class of solutions to the nonlinear hydrodynamic equations describing the time-dependent solar wind, namely that for which the velocity profile is time-invariant but the density at each point of the corona changes exponentially with time. Theoretical velocity curves are calculated for the case of isothermal expansion and compared with the Parker model for steady-state expansion. These solutions can be used to obtain quantitative estimates for the degree of departure from the latter of a real corona undergoing evolution on a finite time scale.On leave from Los Alamos Scientific Laboratory, Los Alamos, N.M., U.S.A.     

Magnetospheric plasma sputtering of Io's atmosphere

The existence of an atmosphere at Io is presumed and used as a starting point to generate neutral coronae produced by magnetospheric ion sputtering from the exobase and to calculate injection of neutrals and ions into the plasma torus. Several different exobase heights, temperatures, and compositions are used to characterize the neutral and ion ejection processes associated with possible atmospheres. Collision ejection from the sputter-produced corona is shown to be an important supply of neutrals for all atmospheres considered. The net injection rates are compared with estimates of the rates required to populate the plasma torus. We show that by including the sputtered atmospheric corona produced by assuming an unattenuated incident ion flux, the supply rate to the torus can be satisfied with an exobase very close to the surface. An exobase close to the surface would imply that the atmosphere at Io is not robust enough to support a fully photodissociated corona and that a significant fraction of the incident plasma ions can penetrate to the surface, providing a sputter source of atmospheric gas. Conversely, a high exobase could only be consistent with the estimated supply rates if the incident plasma flux is attenuated or deflected. The results presented scale approximately with the magnitude of the incident ion flux and, therefore, can be used as knowledge of both the plasma flow and atmospheric composition improve.     

Towards a Better Understanding of a Hydrodynamic Plasma-Gas Coupling by Charge Exchange Processes

Previous models of the interaction of the solar and interstellar hydrodynamic flows have clearly recognized the need to correctly describe the charge-exchange induced coupling of these flows. Neutral atoms and protons are coupled by mass-, momentum-, and energy- exchange terms due to charge exchange collisions between ionized and neutral particle species. However, treating as implified case of this problem, namely the penetration of an H-atom flow through the plasma wall ahead of the heliopause, we demonstrate that the exchange terms previously used in hydrodynamic treatments lead to a singularity with an O-type critical point at the sonic point of the H-atom flow. At this point a continuous integration of the hydrodynamic set of differential equations is impeded. We show that the remedy of this problem is given by a more accurate formulation of the momentum exchange term for the regime of quasi- and sub-sonic H-atom flows. Using a momentum exchange term derived from basic kinetic Boltzmann principles we now obtain a characteristic equation with an X-type critical point which allows to present a continuous solution from supersonic to subsonic flow conditions. Under these new auspices the already often treated problem of the penetration of interstellar H-atoms into the inner heliosphere has urgently to be revisited, since H-atoms are more effectively decelerated at their penetration into the inner heliosphere and are more strongly deflected to the flanks of the heliopause. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diagnostics of horizontal velocity field in the solar atmosphere: Line Ba II λ 455.403 nm

We proposed a method for diagnostics of the horizontal velocity field based on 2D observations at the center of the solar disk with high spatial and temporal resolution. The method consists in semiempirical modeling of the solar atmosphere by solving the inverse radiative transfer problem and subsequent obtaining horizontal velocities by solution of the corresponding hydrodynamic equations. We investigated the diagnostic capabilities of the line Ba II λ 455.403 nm (considering hyperfine structure and isotope splitting) for studying the horizontal velocity field of the nonhomogeneous solar atmosphere.     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

Hydrodynamic instability of the solar nebula in the presence of a planetary core

When a planetary core composed of condensed matter is accumulated in the primitive solar nebula, the gas of the nebula becomes gravitationally concentrated as an envelope surrounding the planetary core. Models of such gaseous envelopes have been constructed subject to the assumption that the gas everywhere is on the same adiabat as that in the surrounding nebula. The gaseous envelope extends from the surface of the core to the distance at which the gravitational attraction of core plus envelope becomes equal to the gradient of the gravitational potential in the solar nebula; at this point the pressure and temperature of the gas in the envelope are required to attain the background values characteristics of the solar nebula. In general, as the mass of the condensed core increases, increasing amounts of gas became concentrated in the envelope, and these envelopes are stable against hydrodynamic instabilities. However, the core mass then goes through a maximum and starts to decrease. In most of the models tested, the envelopes were hydrodynamically unstable beyond the peak in the core mass. An unstable situation was always created if it was insisted that the core mass contain a larger amount of matter than given by these solutions. For an initial adiabat characterized by a temperature of 450°K and a pressure of 5 × 10^?6 atm, the maximum core mass at which instability occurs is approximately 115 earth masses; this value is rather insensitive to the position in the solar nebula or to the background pressure of the solar nebula. However, if the adiabat is lowered, then the core mass corresponding to instability is decreased. Since the core masses found by Podolak and Cameron for the giant planets are significantly less than the critical core mass corresponding to the initial solar nebula adiabat, we conclude that the giant planets obtained their large amounts of hydrogen and helium by a hydrodynamic collapse process in the solar nebula only after the nebula had been subjected to a considerable period of cooling.     

On the stability of the solar wind

The stability of the solar wind is studied in the case of spherical symmetry and constant temperature. It is shown that the stability problem must be formulated as a mixed initial and boundary-value problem in which are prescribed the perturbation values of velocity and density at an initial time and additionally the velocity perturbation at the base of the corona for all times. The solution is constructed by linear superposition of normal solutions, which contain the time only in an exponential factor. The stability problem becomes a singular eigenvalue problem for the amplitudes of the velocity and pressure perturbations, since additionally to the boundary condition at the base of the corona one must add the condition that the amplitudes behave regularly at the critical point. It is proved that only stable eigenvalues exist.     

Propagation of solar generated disturbances through the solar wind critical points: One-dimensional analysis

We investigate the proper method for mathematically simulating the formation of an interplanetary disturbance (IPD) in the subsonic, sub-Alfvénic region near the solar surface within the constraints of one-dimensional hydrodynamic and magnetohydrodynamic (MHD) analyses. We then numerically simulate the subsequent propagation of the IPD through the solar wind critical points in the equatorial plane to the outer corona. We show that, if the IPD is initiated outside the critical points, it always contains both a forward and reverse shock (a shock pair). This result contrasts with observations indicating that shock pairs at 1 AU which can be associated with solar events are rare occurrences in the solar wind. On the other hand, IPDs initiated inside the critical points contain only a forward shock at the leading edge. When the magnetic field is included in the simulation and the IPD is originated inside the critical points, the IPD contains a forward shock at its leading edge followed by large-amplitude, nonlinear, MHD waves which are convected outward by the solar wind. Unlike shock pairs, MHD waves are often observed in the solar wind. Hence, we conclude that physically realistic studies of the propagation of IPD which are assumed to originate near the solar surface must (1) initiate the IPD inside the critical points and (2) include the magnetic field. Although this conclusion is based on a one-dimensional analysis, we speculate that it would be equally valid in multi-dimensions.     

An Operable Solution Approach to Interplanetary Hydrodynamic Shock Waves

In this paper, an operable solution approach is proposed to solve interplanetary hydrodynamic shock waves propagating in the interplanetary medium of solar wind background derived from Parker's hydrodynamic model. In our case the problem concerned is reduced to a set of ordinary differential equations (ODEs) involving the solar wind background parameters velocity v0(r), density 0(r), and pressure p0(r). The entire information for the shock can be obtained easily by obtaining the numerical solutions to the set of ODEs.     

Hydromagnetic-gravity wave critical levels in the solar atmosphere

It is shown that the discontinuous jump in the vertical wave energy flux of slow hydromagnetic-gravity waves, occurring at a critical level, which is accompanied by wave absorption, and the existence of a reflection point imply that slow waves are trapped in the solar atmosphere. Thus such a system behaves as a leaky wave guide.     

Observation of the hydrogen corona with SPICAM on Mars Express

A series of seven dedicated Lyman-α observations of exospheric atomic hydrogen in the martian corona were performed in March 2005 with the ultraviolet spectrometer SPICAM on board Mars Express. Two types of observations are analyzed, observations at high illumination (for a solar zenith angle SZA equal to 30°) and observations at low illumination (for a solar zenith angle equal to 90° (terminator), and near the south pole). The measured Lyman-α emission is interpreted as purely resonant scattering of solar photons. Because the Lyman-α emission is optically thick, we use a forward model to analyze this data. Below the exobase, the hydrogen density is described by a diffusive model and above the exobase, it follows Chamberlain's approach without satellite particles. For different hydrogen density profiles between 80 and 50,000 km, the volume emission rates are computed by solving the radiative transfer equation. Such an approach has been used to analyze the Mariner 6, 7 exospheric Lyman-α data during the late 1960s. A reasonable fit of the set of observations is obtained assuming an exobase temperature between 200 and 250 K and an exobase density of ∼1-4 × 10⁵ cm⁻³ in good agreement with photochemical models. However, when considering the average exospheric temperature of 200 K measured by other methods [Leblanc, F., Chaufray, J.Y., Witasse, O., Lilensten, J., Bertaux, J.-L., 2006a. J. Geophys. Res. 111 (E9), doi:10.1029/2005JE002664. E09S11; Leblanc, F., Chaufray, J.-Y., Bertaux, J.-L., 2007. Geophys. Res. Lett. 34, doi:10.1029/2006GL028437. L02206; Bougher, S.W., Engel, S., Roble, R.G., Foster, B., 2000. J. Geophys. Res. 105, 17669-17692; Mazarico, E., Zuber, M.T., Lemoine, F.G., Smith, D.E., 2007. J. Geophys. Res. 112, doi:10.1029/2006JE002734. E05014] a supplementary hot population is needed above the exobase to reconcile Lyman-α measurements with these previous measurements, particularly for the observations at low SZA. In this case, the densities and temperatures at the exobase for the two populations are 1.0±0.2×¹⁰⁵ cm⁻³ and T=200 K and 1.9±0.5×¹⁰⁴ cm⁻³ and T>500 K for the cold and hot populations respectively at low SZA. At high SZA, the densities and temperatures are equal to 2±0.4×¹⁰⁵ cm⁻³ and T=200 K and n=1.2±0.5×¹⁰⁴ cm⁻³ and T>500 K. These high values of the hot hydrogen component are not presently supported by the theory. Moreover, it is important to underline that the two population model remains relatively poorly constrained by the limited range of altitude covered by the present set of SPICAM measurements and cannot be unambiguously identified because of the global uncertainty of our model and of SPICAM measurements. For a one population solution, an average water escape rate of 7.5 × 10⁻⁴ precipitable μm/yr is estimated, yielding a lifetime of 13,000 years for the average present water vapor content of 10 precipitable microns.     

Conditions for collisional growth of a grain aggregate

Collisional growth of grain aggregates is a critical process in the early stage of planet formation. A collision between grain aggregates is numerically simulated by means of a smoothed particle hydrodynamic code, treating a grain aggregate as a continuum media. A model for mechanical response of a grain aggregate is developed based on published experimental data. Free parameters of the model are the bulk modulus, compressive, shear, and tensile strengths of a grain aggregate, and impact velocity. I have determined three conditions for the growth of an aggregate within the mechanical response model. (1) Compressive strength is the smallest among the three components of strengths. (2) Impact velocity is as low as 4% of the sound speed of an aggregate. (3) Effective restoration of the strengths is necessary due to reconnection between grains followed by compaction of an aggregate. Possibilities of these conditions in the solar nebula are discussed.     

A one-dimensional gasdynamical model of magnetospheric convection

The plasma flow in the equatorial plane of the magnetosphere is examined within the framework of a one-dimensional model in which all quantities are supposed to depend only on the distance along the Sun-Earth axis. The following models are considered: (1) the gasdynamical model in which the Ampère force is ignored, (2) the magnetohydrodynamical model in which the normal component of the Ampère force on the magnetopause is taken into account. The flow regime is calculated in the region including two regions: (1) the layer of the return flow where flow velocity is directed from the Sun, (2) the region of convection where the velocity is directed toward the Sun - on the assumption that the form of the magnetopause and the distribution of the solar wind pressure on the magnetopause are known.The following physical mechanisms are taken into account: (1) the appearance of a centrifugal force owing to the magnetopause curvature, the centrifugal force partly compensating for the solar wind pressure; (2) the existence of the critical point which is analogous to the point of transition through the local sound velocity in the Laval nozzle or in the Parker model of the solar corona. The thickness of the layer of the return flow and the velocity of convection in the magnetosphere are calculated; and the following peculiarities are found: (1) in the gasdynamical model the convection regime is only possible with high velocities corresponding to the substorm, (2) in the magnetohydrodynamic model the convection velocity and the thickness of the layer of the return flow are reduced; the reduction being connected to the fact that the pressure of the solar wind is partially compensated for by the jump of the magnetic pressure on the magnetopause.