Parametric analysis of modeled ion escape from Mars

We develop a parametric fit to the results of a detailed magnetohydrodynamic (MHD) study of the response of ion escape rates (O⁺, and ) to strongly varied solar forcing factors, as a way to efficiently extend the MHD results to different conditions. We then use this to develop a second, evolutionary model of solar forced ion escape. We treat the escape fluxes of ion species at Mars as proportional to the product of power laws of four factors - that of the EUV flux R_euv, the solar wind particle density R_ρ, its velocity (squared) R_v², and the interplanetary magnetic field pressure R_B², where forcing factors are expressed in units of the current epoch-averaged values. Our parametric model is: , where ?(i) is the escape flux of ion i. We base our study on the results of just six provided MHD model runs employing large forcing factor variations, and thus construct a successful, first-order parametric model of the MHD program. We perform a five-dimensional least squares fit of this power law model to the MHD results to derive the flux normalizations and the indices of the solar forcing factors. For O⁺, we obtain the values, 1.73 × 10²⁴ s⁻¹, 0.782, 0.251, 0.382, and 0.214, for ?₀, α, β, γ, and δ, respectively. For , the corresponding values are 1.68 × 10²⁴ s⁻¹, −0.393, 0.798, 0.967, and 0.533. For , they are 8.66 × 10²² s⁻¹, −0.427, 1.083, 1.214, and 0.690. The fit reproduces the MHD results to an average error of about 5%, suggesting that the power laws are broadly representative of the MHD model results. Our analysis of the MHD model shows that by itself an increase in R_EUV enhances O⁺ loss, but suppresses the escape of and , whereas increases in solar wind (i.e., in , and R_B², with R_euv constant) favors the escape of heavier ions more than light ions. The ratios of escaping ions detectable at Mars today can be predicted by this parametric fit as a function of the solar forcing factors. We also use the parametric model to compute escape rates over martian history. This second parametric model expresses ion escape functions of one variable (per ion), ?(i) = ?₀(i)(t/t₀)^−ξ(i). The ξ(i) are linear combinations of the epoch-averaged ion escape sensitivities, which are seen to increase with ion mass. We integrate the and oxygen ion escape rates over time, and find that in the last 3.85 Gyr, Mars would have lost about mbars of , and of water (from O⁺ and ) from ion escape.     

Rosetta-Alice observations of exospheric hydrogen and oxygen on Mars

The European Space Agency’s Rosetta spacecraft, en route to a 2014 encounter with comet 67P/Churyumov-Gerasimenko, made a gravity assist swing-by of Mars on 25 February 2007, closest approach being at 01:54 UT. The Alice instrument on board Rosetta, a lightweight far-ultraviolet imaging spectrograph optimized for in situ cometary spectroscopy in the 750-2000 Å spectral band, was used to study the daytime Mars upper atmosphere including emissions from exospheric hydrogen and oxygen. Offset pointing, obtained five hours before closest approach, enabled us to detect and map the H i Lyman-α and Lyman-β emissions from exospheric hydrogen out beyond 30,000 km from the planet’s center. These data are fit with a Chamberlain exospheric model from which we derive the hydrogen density at the 200 km exobase and the H escape flux. The results are comparable to those found from the Ultraviolet Spectrometer experiment on the Mariner 6 and 7 fly-bys of Mars in 1969. Atomic oxygen emission at 1304 Å is detected at altitudes of 400-1000 km above the limb during limb scans shortly after closest approach. However, the derived oxygen scale height is not consistent with recent models of oxygen escape based on the production of suprathermal oxygen atoms by the dissociative recombination of .     

The production of nitrogen atoms on Mars and their escape

Quantitative calculations of the escape rate of nitrogen by photodissociation and photoionization, by photoelectron impact processes, by chemical reactions and by dissociative recombination are reported. It is shown that the predicted present escape rate of 2.0 × 10⁵ atoms cm^?2 S^?1 is consistent with the measured ¹⁵N/¹⁴N isotope ratio. A minimum of 4.0 × 10²² cm^?2 S^?1 is obtained for the initial reservoir of N₂. The production rates of N(⁴S) and N(²D) atoms in the atmosphere are obtained and the altitude profile of N(²D) is calculated.     

Photochemical escape of oxygen from Mars: A comparison of the exobase approximation to a Monte Carlo method

The non-thermal escape of neutral O atoms from Mars at the current epoch is largely due to dissociative recombination of :

     

Isotope fractionation in the photochemical escape of O from Mars

The production of energetic and escaping neutral O atoms at the current epoch in the martian thermosphere is thought to be dominated by the dissociative recombination process:

     

Estimation of the escape of photoelectrons from Mars in 2004 liberated by the ionization of carbon dioxide and atomic oxygen

Photoelectron peaks in the atmosphere of Mars caused by the ionization of carbon dioxide and atomic oxygen by solar 30.4 nm photons have been observed by the Electron Spectrometer (ELS), a component of the Mars Express (MEx) Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) experiment. Ionization mostly occurs at the Mars exobase with the majority of the photoionized electron flux trapped in the remanent and induced magnetic field, with a portion of that flux escaping the planet down its tail. Since Mars is overall charge neutral, the number of electrons must be identical to the number of ion charges which escape the planet. An estimate of the fraction of the total number of escaping electrons is obtained for the year 2004, specifically those produced by the ionization of carbon dioxide and atomic oxygen by solar 30.4 nm photons. In achieving this process, an illustrative example pass is used to show how the electron spectrum is adjusted for the potential on the spacecraft; then the region of the electron spectrum which shows photoelectron peaks is integrated over energy, yielding a flux of 5.74 × 10⁶ electrons/(cm² s sr). This technique is then applied to a subset of 22 sample averaged spectra from the 2004 data (5 January 2004 through 25 January 2005), yielding an average result of 4.15 × 10⁶ electrons/(cm² s sr) for the 22 cases. The observation cone of 33.75° is used to integrate over solid angle (assuming the flux is constant), giving 4.39 × 10⁶ electrons/(cm² s). This average value was taken as representative of the full data interval. Frequency of occurrence statistics showing about a 6.2% occurrence rate for the 2004 data is applied to give an average escape flux from Mars of 2.72 × 10⁵ electrons/(cm² s) during 2004. By estimating the outflow area as 1.16 × 10¹⁸ cm² at X = −1.5 R_Mars the electron escape rate of 3.14 × 10²³ electrons/s is obtained. Thus about 9.92 × 10³⁰ electrons or 16.5 Mmole of electrons escaped Mars during 2004 due to the ionization of carbon dioxide and atomic oxygen by the He 30.4 nm line. Due to the caveats of the analysis, these derived escape rates should be considered lower limits on the total electron escape rate from Mars.     

The combined effects of escape and magnetic field histories at Mars

Mars is thought to have hosted large amounts of water and carbon dioxide at primitive epochs. The morphological analysis of the surface of Mars shows that large bodies of water were probably present in the North hemisphere at late Noachian (3.7–4 Gyr ago). Was this water solid or liquid? For maintaining liquid water at this time, when the Sun was (likely) less bright than now, a CO₂ atmosphere of typically 2 bars is required. Can sputtering, still presently acting at the top of the Martian atmosphere, have removed such a dense atmosphere over the last 3.5–4 Gyr? What was the fate of the 100–200 m global equivalent layer of water present at late Noachian? When did Martian magnetic dynamo vanish, initiating a long period of intense escape by sputtering? Because sputtering efficiency is highly non-linear with solar EUV flux, with a logarithmic slope of ≈7:Φ_sput≈Φ_EUV⁷, resulting in enhanced levels of escape at primitive epochs, when the sun was several times more luminous than now in the EUV, there is a large uncertainty on the cumulated amount of volatiles removed to space. This amount depends primarily on two factors: (i) the exact value of the non-linearity exponent (≈7 from existing models, but this value is rather uncertain), (ii) the exact time when the dynamo collapsed, activating sputtering at epochs when intense EUV flux and solar wind activity prevailed in the solar system. Both parameters are only crudely known at the present time, due the lack of direct observation of sputtering from Martian orbit, and to the incomplete and insufficiently spatially resolved map of the crustal magnetic field. Precise timing of the past Martian dynamo can be investigated through the demagnetisation signature associated with impact craters. A designated mission to Mars would help in answering this crucial question: was water liquid at the surface of Mars at late Noachian? Such a mission would consist of a low periapsis (≈100 km) orbiter, equipped with a boom-mounted magnetometer, for mapping the magnetic field, as well as adequate in situ mass and energy spectrometers, for a full characterization of escape and of its response to solar activity variations. Surface based observations of atmospheric noble gas isotopic ratios, which keep the signatures of past escape processes, including sputtering for the lightest of them (Ne, Ar), would bring a key constraint for escape models extrapolated back to the past.     

Monte Carlo computations of the escape of atomic nitrogen from Mars

Monte Carlo simulations were carried out to compute the escape flux of atomic nitrogen for the low and high solar activity martian thermospheres. The total escape of atomic nitrogen at low and high solar activities was found to be 3.03×¹⁰⁵ and , respectively. The escape flux of atomic nitrogen at low and high solar activities from photodissociation of N₂ was found to be 2.75×¹⁰⁵ and , respectively. The remainder of the contribution is from dissociative recombination, which is only important at high solar activity were it comprises about 25% of the total escape. The relative contributions to the total N escape flux from thermal motion of the background atmosphere, winds and co-rotation, and photoionization and subsequent solar wind pickup are also considered here. We find that the total predicted escape fluxes are observed to increase by 20 and 25% at low and high solar activities owing to thermal motion of the background atmosphere. At low and high solar activities, we find that the co-rotation and wind velocities combined translate to a maximum transferable energy of ∼0.0103 and 0.0181 eV, respectively, and that the total escape flux contribution from winds and co-rotation is negligible. Photoionization was found to be a minor process only impacting those source atoms produced with energies close to the escape energy, between 1.5 and 2 eV. The contributions to the total escape fluxes at low and high solar activities from photoionization and subsequent solar wind pickup are found to be about 8 and 13%, respectively.     

Heavy ion escape from Mars, influence from solar wind conditions and crustal magnetic fields

We have used more than 4 years of Mars Express ion data to estimate the escape of heavy ions ( and ) from Mars. To take the limited field of view of the instrument into account, the data has been binned into spatial bins and angular bins to create average distribution functions for different positions in the near Mars space. The net escape flux for the studied low solar activity period, between May 2007 and May 2011, is 2.0 ± 0.2 × 10²⁴ s⁻¹. The escape has been calculated independently for four different quadrants in the Y_MSO − Z_MSO plane, south, dusk, north and dawn. Escape is highest from the northern and dusk quadrants, 0.6 ± 0.1 × 10²⁴ s⁻¹, and smallest from the south and dawn quadrants, 0.4 ± 0.1 × 10²⁴ s⁻¹. The flux ratio of molecular ( and ) to O⁺ ions is 0.9 ± 0.1, averaged over all quadrants. The flux difference between the north and south quadrants is statistically significant, and is presumed to be due to the presence of significant crustal magnetic fields in the southern hemisphere, reducing the outflow. The difference between the dawn and dusk quadrants is likely due to the magnetic tension associated with the nominal Parker angle spiral, which should lead to higher average magnetic tension on the dusk side. The escape increases during periods of high solar wind flux and during times when co-rotating interaction regions (CIR) affect Mars. In the latter case the increase is a factor 2.4-2.9 as compared to average conditions.     

Mass fractionation during transonic escape and implications for loss of water from Mars and Venus

Hydrodynamic escape of hydrogen from a planetary atmosphere can remove heavier gases as well as hydrogen, provided that the escape rate is sufficiently large. Here, analytic approximations for the degree of mass fractionation of a trace species during hydrodynamic escape are compared with accurate numerical solutions for the case of transonic outflow. Even the simplest analytic approximation is found to be surprisingly good, despite numerous assumptions made in the course of its derivation. The analytic approximations are most accurate when the ratio of molecular weights of the heavier and lighter constituents is large so that nonlinear terms in the momentum equation for the heavy constituent become small. The simplest analytic formula is readily generalized to the case where a heavy constituent is also a major species. Application of the generalized formula to hypothetical episodes of hydrodynamic escape from Venus and Mars suggests that both hydrogen and oxygen could have escaped; thus, substantial quantities of water may have been lost without the need to oxidize large amounts of the crust. Mars could have lost large amounts of rare gases in this manner, but if so it may also have lost significant quantities of carbon dioxide and nitrogen. Venusian argon and neon isotope ratios indicate that Venus lost little or no argon and 50% or less of its original complement of neon. Terrestrial noble gas patterns resemble those that would have resulted had an initially Venus-like Earth undergone a short-lived but locally very energetic escape event.     

Exospheric density and escape fluxes of atomic isotopes on Venus and Mars

Energetic neutrals in dissociative recombinations near or above the exobase provide an important component of exospheric density and escape fluxes. Plasma thermal velocities provide the main contribution to the velocity spread and an exact integral for the escape flux applicable in marginal cases is found for a simple atmosphere and collisional cut-off. Atomic fragments from recombination of diatomic oxygen and nitrogen ions in the Venus and Mars atmospheres are examined and density integrals derived. The oxygen escape flux on Mars is half that previously estimated and there is very little isotope preference supplementing diffusive separation. However, escape of the heavier ¹⁵N isotope is low by a factor two. Reinterpretation of its 75% enrichment as detected by Viking leads to a range 0.4–1.4 mbar for the primeval nitrogen content on Mars.     

Mars atmospheric escape and evolution; interaction with the solar wind

This tutorial deals with the question of atmospheric escape on Mars. After a brief introduction describing the general context of Mars escape studies, we will present in Section 2 a simplified theory of thermal escape, of both Jeans and hydrodynamic types. The phenomenon of hydrodynamic escape, still hypothetical and not proved to have ever existed on terrestrial planets, will be treated with the help of two well known examples: (i) the isotopic fractionation of xenon in Mars and Earth atmospheres, (ii) the paradox of missing oxygen in Venus atmosphere. In Section 3, a simplified approach of non-thermal escape will be developed, treating in a specific way the different kinds of escape (photochemical escape, ion sputtering, ion escape and ionospheric outflow). As a matter of illustration, some calculations of the relative contributions of these mechanisms, and of their time evolutions, will be given, and the magnitude of the total amount of atmosphere lost by non-thermal escape will be estimated. Section 4 will present the state of knowledge concerning the constraints derived from Mars isotopic geochemistry in terms of past escape and evolution. Finally, a few conclusions, which are more interrogations, will be proposed.     

Ion escape from Mars as a function of solar wind conditions: A statistical study

The influence of solar EUV and solar wind conditions on ion escape at Mars is investigated using ion data from the Aspera-3 instrument on Mars Express, combined with solar wind proxy data obtained from the Mars Global Surveyor (MGS) spacecraft. A solar EUV flux proxy based on data from the Earth position, scaled and shifted in time for Mars, is used to study relatively long time scale changes related to solar EUV variability. Data from May 2004 until November 2005 has been used. A clear dependence on the strength of the subsolar magnetic field as inferred from MGS measurements is seen in the ion data. The region of significant heavy ion flows is compressed and the heavy ion flux density is higher for high subsolar magnetic field strength. Because of the difference in outflow area, the difference in estimated total outflow is somewhat less than the difference in average flux density. We confirm previous findings that escaping planetary ions are mainly seen in the hemisphere into which the solar wind electric field is pointed. The effect is more pronounced for the high subsolar magnetic field case.The average ion motion has a consistent bias towards the direction of the solar wind electric field, but the main motion is in the antisunward direction. The antisunward flow velocity increases with tailward distance, reaching above at 2 to 3 martian radii downtail from Mars for O⁺ ions. Different ion species reach approximately the same bulk flow energy. We did not find any clear correlation between the solar EUV flux and the ion escape distribution or rate, probably because the variation of the solar EUV flux over our study interval was too small. The results indicate that the solar wind and its magnetic field directly interacts with the ionosphere of Mars, removing more ions for high subsolar magnetic field strength. The interaction region and the tail heavy ion flow region are not perfectly shielded from the solar wind electric field, which accelerates particles over relatively large tail distances.     

Nonthermal escape of hydrogen and deuterium from Venus and implications for loss of water

Nonthermal escape processes responsible for the escape of hydrogen and deuterium from Venus are examined for present and past atmospheres. Three mechanisms are important for the escape of hydrogen from the present atmosphere: (a) charge exchange of plasmaspheric H⁺ with exospheric H, (b) impact of exospheric hot O atoms on H, and (c) ion molecule reactions involving O⁺ and H₂. However, in the past when the H abundance was higher, the charge-exchange mechanism would be the strongest. The H escape flux increases rapidly with increasing hydrogen abundance in the upper atmosphere and saturates at a value of 1 × 10¹⁰ cm^?2 sec^?1 emerging primarily from the day side when the H mixing ratio at the homopause is 2 × 10^?3. This corresponds to an H₂O mixing ratio of 1 × 10^?3 at the cold trap and ～15% at the surface. Deuterium would also escape by the charge-exchange mechanism and a D/H enrichment by a factor of ～1000 over the nonthermal escape regime is expected, which could have lasted over the last 3 billion years. Coincidentally, the onset of hydrodynamic flow leading to efficient H escape occurs just at the H₂O mixing ratio at which the charge-exchange escape flux saturates. Thus it is possible that Venus has lost an Earth-equivalent ocean of water over geologic time. If so, either the D/H enrichment has been kept low by modest outgassing of juvenile water or Venus started out with a D/H ratio of ～4.0 × 10^?6.     

Loss of water from Venus. I. Hydrodynamic escape of hydrogen

A one-dimensional photochemical-dynamic model is used to study hydrodynamic loss of hydrogen from a primitive, water-rich atmosphere on Venus. The escape flux is calculated as a function of the H₂O mixing ratio at the atmospheric cold trap. The cold-trap mixing ratio is then related in an approximate fashion to the H₂O concentration in the lower atmosphere. Hydrodynamic escape should have been the dominant loss process for hydrogen when the H₂O mass mixing ratio in the lower atmosphere exceeded ～0.1. The escape rate would have depended upon the magnitude of the solar ultraviolet flux and the atmospheric euv heating efficiency and, to a lesser extent, on the O₂ content of the atmosphere. The time required for Venus to have lost the bulk of a terrestrial ocean of water is on the order of a billion years. Deutrium would have been swept away along with hydrogen if the escape rate was high enough, but some D/H enrichment should have occurred as the escape rate slowed down.     

Precursors of Mars: Constraints from nitrogen and oxygen isotopic compositions of martian meteorites

Abstract— We present an approach to assess the nature of materials involved in the accretion of Mars by the planet's nitrogen (δ¹⁵N) and oxygen (Δ¹⁷O) isotopic compositions as derived from data on martian meteorites. δ¹⁵N for Mars has been derived from nitrogen and xenon systematics, while Δ¹⁷O has been taken from the literature data. These signatures indicate that Mars has most probably accreted from enstatite and ordinary chondritic materials in a ratio of 74:26 and may not have a significant contribution from the carbonaceous (CI, CM, or CV) chondrites. This is consistent with the chromium isotopic (?⁵³Cr) signatures of martian meteorites and the bulk planet Fe/Si ratio for Mars as suggested by the moment of inertia factor (I/MR²) obtained from the Mars Pathfinder data. Further, a simple homogeneous accretion from the above two types of materials is found to be consistent with the planet's moment of inertia factor and the bulk composition of the mantle. But, it requires a core with 6.7 wt% Si, which is consistent with the new results from the high pressure and temperature melting experiments and chemical data on the opaque minerals in enstatite chondrites.     

Ion escape at Mars: Comparison of a 3-D hybrid simulation with Mars Express IMA/ASPERA-3 measurements

We have analysed ion escape at Mars by comparing ASPERA-3/Mars Express ion measurements and a 3-D quasi-neutral hybrid model. As Mars Express does not have a magnetometer onboard, the analysed IMA data are from an orbit when the IMF clock angle was possible to determine from the magnetic field measurements of Mars Global Surveyor. We found that fast escaping planetary ions were observed at the place which, according to the 3-D model, is anticipated to contain accelerated heavy ions originating from the martian ionosphere. The direction of the interplanetary magnetic field was found to affect noticeably which regions can be magnetically connected to Mars Express and to the overall 3-D Mars-solar wind interaction.     

The diurnal and solar cycle variation of the charge exchange induced hydrogen escape flux

Using ion temperature and density data at specific points and times in June 1969 provided by the OGO 6 satellite, and altitude profiles of the ion and electron temperature and concentration provided by the Arecibo radar facility over the period February 1972–April 1974, the diurnal and solar cycle variation of the charge exchange induced hydrogen escape flux was investigated. It was calculated that for low to moderate solar activity at Arecibo, the diurnal ratio of the maximum-to-minimum charge exchange induced hydrogen escape flux was approximately 6 with a peak around noon and a minimum somewhere between 0100 and 0300 h L.T. This study of a limited amount of OGO 6 and Arecibo data seems to indicate that the charge exchange induced hydrogen escape flux increases as the F_10.7 flux increases for low to moderate solar activity.     

The time-scale of escape from star clusters

In this paper a cluster is modelled as a smooth potential (due to the cluster stars) plus the steady tidal field of the Galaxy. In this model there is a minimum energy below which stars cannot escape. Above this energy, however, the time-scale on which a star escapes varies with the orbital parameters of the star (mainly its energy) in a way which we attempt to quantify, with both theoretical arguments and computer simulations. Within the limitations of the model we show that the time-scale is long enough to complicate the interpretation of full N -body simulations of clusters, and that stars above the escape energy may remain bound to the cluster for about a Hubble time.