Thermal Escape Rates Research Articles

Solar cycle and seasonal variability of H in the upper atmosphere of Mars

The complex seasonal, dust, and atmospheric circulation patterns at Mars affect the abundance and spatial extent of water and its photo-dissociated atomic byproduct H. Recent observations by the Mars Atmosphere and Volatile Evolution (MAVEN) mission have been used to constrain the H abundance at the exobase (200 km altitude) as well as its thermal and global escape rate. The MAVEN observations span the last seven years and encompass the effects of the declining phase of Solar Cycle 24 and activating phase of Solar Cycle 25 from mid-perihelion of Mars Year (MY) 32 through most of aphelion of MY36. Results show that there are seasonal as well as solar cycle variations in H exobase temperatures, densities, thermal escape rates, and global escape rates. During perihelion of MYs 32–35, the H exobase density fluctuates with a cadence that corresponds to the approach to perihelion as well as the onset and peak of regional dust storms. Additionally, the abundance of H atoms did not show exceptional variability during the MY34 Global Dust Storm, when compared with trends from adjacent years. Seasonal averages of H exobase densities, thermal escape rates, and global escape rates indicated an order of magnitude difference between perihelion and aphelion, and suggest a water global equivalent layer range of 0.02–13 m lost over 4 billon years. H properties are also found to vary with solar cycle to a lesser extent than with seasons across the MAVEN timeline. Trends show that the exobase density varies inversely with solar activity, while both the thermal and global escape rates vary directly with solar activity. It remains to be seen if the effects of a stronger than recent solar cycle on the upper atmospheric H properties would become more pronounced.

Solar Cycle, Seasonal, and Dust-storm-driven Variations of the Mars Upper Atmospheric State and H Escape Rate Derived from the Lyα Emission Observed by NASA’s MAVEN Mission

Abstract An accurate and systematic quantification of the state variables in the Mars upper atmosphere is important for the study of Mars volatile evolution. In this study, we perform a comprehensive analysis of the Lyα limb scans observed by MAVEN during Martian years 32–35 to quantify the Mars upper atmospheric temperature, the CO2 density, the H density, and the H thermal escape rate. A previously uncharacterized feature of the proton aurora at Mars is reported, which affects the overall shape of the limb scans without introducing peak intensity structures. Our inversion results excluding such scans demonstrate an unambiguous and systematic consistency of the Mars exobase temperature (∼150–280 K) derived from the dayside Lyα emission with those derived from the CO2 + airglow emission and those from atmospheric drag measurements, resolving a long-standing discrepancy between those different estimates. The temperature is shown to be highly predictable over different solar cycles and seasons. However, the H density and escape rate can be episodically enhanced by a factor of ∼2–3, likely driven by dust storms that coincided with the enhancements. During the three Martian years, the averaged thermal escape rates between Mars solar longitude 0°–180° and 210°–330° are 0.6 × 107 cm−2 s−1 and 9.0 × 107 cm−2 s−1, respectively, a factor of 15 seasonal difference, with a factor of ∼7.5 and ∼2 due to temperature and H density variations, respectively. These temperatures and thermal escape rates derived from the thermospheric Lyα emission are generally lower than those derived from the exospheric Lyα emission in the literature, indicating the presence of a hot H population in the Mars exosphere.

Lifetime of a transient atmosphere produced by lunar volcanism

Early in the Moon's history volcanic outgassing may have produced a periodic millibar level atmosphere (Needham and Kring 2017). We examined the relevant atmospheric escape processes and lifetime of such an atmosphere. Thermal escape rates were calculated as a function of atmospheric mass for a range of temperatures including the effect of the presence of a light constituent such as H2. Photochemical escape and atmospheric sputtering were calculated using estimates of the higher EUV and plasma fluxes consistent with the early Sun. The often used surface Jeans calculation carried out in Vondrak (1974) is not applicable for the scale and composition of the atmosphere considered. We show that solar driven non-thermal escape can remove an early CO millibar level atmosphere on the order of ~1 Myr if the average exobase temperature is below ~350–400 K. However, if solar UV/EUV absorption heats the upper atmosphere to temperatures > ~ 400 K thermal escape increasingly dominates the loss rate, and we estimated a minimum lifetime of 100's of years considering energy limited escape.

Two-dimensional model for the martian exosphere: Applications to hydrogen and deuterium Lyman α observations

The analysis of Lyman α observations in the exosphere of Mars has become limited by the assumption of spherical symmetry in the modeling process, as the models are being used to analyze increasingly detailed measurements. In order to overcome this limitation, a two-dimensional density model is presented, which better emulates the density distribution of deuterium and hydrogen atoms in the exosphere of Mars. A two-dimensional radiative transfer model developed in order to simulate multiple scattering of solar Lyman α photons by an asymmetric, non-isothermal hydrogen exosphere, is also presented here. The models incorporate changes in density and temperature structure of the martian atmosphere with radial distance and solar zenith angle. The 2-D models were applied to the MAVEN-IUVS echelle observations of deuterium and hydrogen Lyman α as well as HST Lyman α observations of hydrogen at Mars. The asymmetric 2-D model provided better fits to the data and smaller thermal escape rates in comparison to the symmetric 1-D model for the exosphere of Mars. However, intensity differences between both models became small above ~2.5 martian radii indicating that the exosphere of Mars approaches spherical symmetry at higher altitudes, in agreement with earlier studies. In addition, a new cross calibration of the absolute sensitivities of two instruments on the Hubble Space Telescope and the MAVEN-IUVS echelle mode is presented based on near-simultaneous observations of the geocorona and Mars.

Kramers’ escape rate problem within a non-Markovian description

We compare the thermal escape rates of a Brownian particle, initially trapped into one of the two wells of an asymmetric double-well potential, for thermal Markovian and non-Markovian noise. The Markovian treatment of this problem goes originally back to the studies of Kramers in 1940 and is therefore often referred to as “Kramers’ escape rate problem”. We solve the generalized Langevin equation for the trajectories of the particles numerically and analytically for both limiting cases, Markovian and non-Markovian thermal noise. We compute the escape rate and work out the fundamental differences arising from finite correlation times of the thermal noise.

Solar XUV and ENA‐driven water loss from early Venus' steam atmosphere

AbstractWe present a study on the influence of the upper atmosphere hydrodynamic escape of hydrogen, driven by the solar soft X‐ray and extreme ultraviolet radiation (XUV), on an expected outgassed steam atmosphere of early Venus. By assuming that the young Sun was either a weak or moderately active young G star, we estimated the water loss from a hydrogen dominated thermosphere due to the absorption of the solar XUV flux and the precipitation of solar wind produced energetic hydrogen atoms (ENAs). The production of ENAs and their interaction with the hydrodynamic extended upper atmosphere, including collision‐related feedback processes, have been calculated by means of Monte Carlo models. ENAs that collide in the upper atmosphere deposit their energy and heat the surrounding atmosphere mainly above the main XUV energy deposition layer. It is shown that precipitating ENAs modify the thermal structure of the upper atmosphere, but the enhancement of the thermal escape rates caused by these energetic hydrogen atoms is negligible. Our results also indicate that the majority of oxygen arising from dissociated H2O molecules is left behind during the first 100 Myr. It is thus suggested that the main part of the remaining oxygen has been absorbed by crustal oxidation.

Calculating thermal stability and attempt frequency of advanced recording structures without free parameters

Ensuring a permanent increase of magnetic storage densities is one of the main challenges in magnetic recording. Conventional approaches based on single phase grains are not suitable to achieve this goal, because their grain volume is limited due to the superparamagnetic limit. Grains with graded anisotropy are the most promising candidates to overcome this limit, providing magnetic memory bits with small volumes, low coercivity, and high thermal stability at the same time. Combining micromagnetic simulations with forward flux sampling, a computational method for rare events that has been recently applied to the magnetic nanostructures, we have determined thermal escape rates and attempt frequencies of a graded media grain and two single phase grains of the same geometry. We find that graded anisotropy can increase the thermal stability of a grain by 12 orders of magnitudes from tens of milliseconds to centuries without changing the coercive field.

Extreme hydrodynamic atmospheric loss near the critical thermal escape regime

By considering martian-like planetary embryos inside the habitable zone of solar-like stars we study the behavior of the hydrodynamic atmospheric escape of hydrogen for small values of the Jeans escape parameter $\beta < 3$, near the base of the thermosphere, that is defined as a ratio of the gravitational and thermal energy. Our study is based on a 1-D hydrodynamic upper atmosphere model that calculates the volume heating rate in a hydrogen dominated thermosphere due to the absorption of the stellar soft X-ray and extreme ultraviolet (XUV) flux. We find that when the $\beta$ value near the mesopause/homopause level exceeds a critical value of $\sim$2.5, there exists a steady hydrodynamic solution with a smooth transition from subsonic to supersonic flow. For a fixed XUV flux, the escape rate of the upper atmosphere is an increasing function of the temperature at the lower boundary. Our model results indicate a crucial enhancement of the atmospheric escape rate, when the Jeans escape parameter $\beta$ decreases to this critical value. When $\beta$ becomes $\leq$2.5, there is no stationary hydrodynamic transition from subsonic to supersonic flow. This is the case of a fast non-stationary atmospheric expansion that results in extreme thermal atmospheric escape rates.

Heating efficiency in hydrogen-dominated upper atmospheres

Context. The heating efficiency is defined as the ratio of the net local gas-heating rate to the rate of stellar radiative energy absorption. It plays an important role in thermal-escape processes from the upper atmospheres of planets that are exposed to stellar soft X-rays and extreme ultraviolet radiation (XUV). Aims. We model the thermal-escape-related heating efficiency of the stellar XUV radiation in the hydrogen-dominated upper atmosphere of the extrasolar gas giant HD 209458b. The model result is then compared with previous thermal-hydrogen-escape studies which assumed heating efficiency values between 10-100%. Methods. The photolytic and electron impact processes in the thermosphere were studied by solving the kinetic Boltzmann equation and applying a Direct Simulation Monte Carlo model. We calculated the energy deposition rates of the stellar XUV flux and that of the accompanying primary photoelectrons that are caused by electron impact processes in the H2 to H transition region in the upper atmosphere. Results. The heating by XUV radiation of hydrogen-dominated upper atmospheres does not reach higher than 20% above the main thermosphere altitude, if the participation of photoelectron impact processes is included. Conclusions. Hydrogen-escape studies from exoplanets that assume heating efficiency values that are >= 20 % probably overestimate the thermal escape or mass-loss rates, while those who assumed values that are < 20% probably produce more realistic atmospheric-escape rates.

Stellar wind interaction and pick-up ion escape of the Kepler-11 “super-Earths”

We study the interactions between stellar wind and the extended hydrogen-dominated upper atmospheres of planets and the resulting escape of planetary pick-up ions from the 5 "super-Earths" in the compact Kepler-11 system and compare the escape rates with the efficiency of the thermal escape of neutral hydrogen atoms. Assuming the stellar wind of Kepler-11 is similar to the solar wind, we use a polytropic 1D hydrodynamic wind model to estimate the wind properties at the planetary orbits. We apply a Direct Simulation Monte Carlo Model to model the hydrogen coronae and the stellar wind plasma interaction around Kepler-11b-f within a realistic expected heating efficiency range of 15-40%. The same model is used to estimate the ion pick-up escape from the XUV heated and hydrodynamically extended upper atmospheres of Kepler-11b-f. From the interaction model we study the influence of possible magnetic moments, calculate the charge exchange and photoionization production rates of planetary ions and estimate the loss rates of pick-up H+ ions for all five planets. We compare the results between the five "super-Earths" and in a more general sense also with the thermal escape rates of the neutral planetary hydrogen atoms. Our results show that for all Kepler-11b-f exoplanets, a huge neutral hydrogen corona is formed around the planet. The non-symmetric form of the corona changes from planet to planet and is defined mostly by radiation pressure and gravitational effects. Non-thermal escape rates of pick-up ionized hydrogen atoms for Kepler-11 "super-Earths" vary between approximately 6.4e30 1/s and 4.1e31 1/s depending on the planet's orbital location and assumed heating efficiency. These values correspond to non-thermal mass loss rates of approximately 1.07e7 g/s and 6.8e7 g/s respectively, which is a few percent of the thermal escape rates.

XUV-Exposed, Non-Hydrostatic Hydrogen-Rich Upper Atmospheres of Terrestrial Planets. Part II: Hydrogen Coronae and Ion Escape

We studied the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and the hydrogen-rich upper atmosphere of an Earth-like planet and a "super-Earth" with a radius of 2 R(Earth) and a mass of 10 M(Earth), located within the habitable zone at ∼0.24 AU. We investigated the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pickup ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes that are 1, 10, 50, and 100 times higher compared to that of the present-day Sun were considered, and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions was modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, lead to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ∼1.0×10²⁵ s⁻¹ to ∼5.3×10³⁰ s⁻¹, depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimated the long-time nonthermal ion pickup escape for the studied planets and compared them with the thermal escape. According to our estimates, nonthermal escape of picked-up ionized hydrogen atoms over a planet's lifetime within the habitable zone of an M dwarf varies between ∼0.4 Earth ocean equivalent amounts of hydrogen (EO(H)) to <3 EO(H) and usually is several times smaller in comparison to the thermal atmospheric escape rates.

XUV-exposed, non-hydrostatic hydrogen-rich upper atmospheres of terrestrial planets. Part I: atmospheric expansion and thermal escape.

The recently discovered low-density "super-Earths" Kepler-11b, Kepler-11f, Kepler-11d, Kepler-11e, and planets such as GJ 1214b represent the most likely known planets that are surrounded by dense H/He envelopes or contain deep H₂O oceans also surrounded by dense hydrogen envelopes. Although these super-Earths are orbiting relatively close to their host stars, they have not lost their captured nebula-based hydrogen-rich or degassed volatile-rich steam protoatmospheres. Thus, it is interesting to estimate the maximum possible amount of atmospheric hydrogen loss from a terrestrial planet orbiting within the habitable zone of late main sequence host stars. For studying the thermosphere structure and escape, we apply a 1-D hydrodynamic upper atmosphere model that solves the equations of mass, momentum, and energy conservation for a planet with the mass and size of Earth and for a super-Earth with a size of 2 R(Earth) and a mass of 10 M(Earth). We calculate volume heating rates by the stellar soft X-ray and extreme ultraviolet radiation (XUV) and expansion of the upper atmosphere, its temperature, density, and velocity structure and related thermal escape rates during the planet's lifetime. Moreover, we investigate under which conditions both planets enter the blow-off escape regime and may therefore experience loss rates that are close to the energy-limited escape. Finally, we discuss the results in the context of atmospheric evolution and implications for habitability of terrestrial planets in general.

Outgassing History and Escape of the Martian Atmosphere and Water Inventory

The evolution and escape of the martian atmosphere and the planet’s water inventory can be separated into an early and late evolutionary epoch. The first epoch started from the planet’s origin and lasted ∼500 Myr. Because of the high EUV flux of the young Sun and Mars’ low gravity it was accompanied by hydrodynamic blow-off of hydrogen and strong thermal escape rates of dragged heavier species such as O and C atoms. After the main part of the protoatmosphere was lost, impact-related volatiles and mantle outgassing may have resulted in accumulation of a secondary CO2 atmosphere of a few tens to a few hundred mbar around ∼4–4.3 Gyr ago. The evolution of the atmospheric surface pressure and water inventory of such a secondary atmosphere during the second epoch which lasted from the end of the Noachian until today was most likely determined by a complex interplay of various nonthermal atmospheric escape processes, impacts, carbonate precipitation, and serpentinization during the Hesperian and Amazonian epochs which led to the present day surface pressure.

Wind‐induced atmospheric escape: Titan

Rapid thermospheric flows can significantly enhance the atmospheric loss rates and structures of atmospheric coronae of planetary bodies. Using descriptions of atmospheric escape based on molecular kinetic models, we show that such flows at the exobase of Titan could significantly increase the calculated constituent thermal and nonthermal escape rates. In particular, we show here that the effect of thermospheric winds at the exobase cannot be ignored when calculating the escape of methane from Titan. Such enhancements are likely also relevant to Pluto and exoplanet atmospheres.

Thermally driven atmospheric escape: Monte Carlo simulations for Titan's atmosphere

Recent models of Titan's upper atmosphere were used to reproduce the Cassini measurements of the density vs. altitude by allowing a net upward flow at the exobase. Large mass flow rates were extracted and interpreted due to thermally driven escape to space at a rate that is orders of magnitude larger than the Jeans escape rate. This process is referred to as slow hydrodynamic escape. Direct simulation Monte Carlo (DSMC) models are used here to describe the transition region of Titan's atmosphere where the gas changes from being dominated by collisions to being dominated by ballistic transport. When normalized at an altitude below the exobase to the densities and temperatures calculated in the recent continuum descriptions of the Cassini ion neutral mass spectrometer data, these simulations show no evidence for slow hydrodynamic escape. In addition, above the nominal exobase there is no evidence for the proposed enhancement in the tail of the molecular speed distribution that would be required at these temperatures to give the suggested escape rates. Even simulations at Titan for artificially small Jeans parameters do not give thermal escape rates that deviate enormously from the Jeans estimate. Therefore, we conclude that the suggested upward flow rates extracted from the INMS data, if confirmed, must be due to mass loss by non-thermal processes and/or global transport.

Atmospheres and Plasma Interactions at Saturn's Largest Inner Icy Satellites

We explore the possible existence of atmospheres on Saturn's icy satellites, Mimas, Enceladus, Tethys, Dione, and Rhea. Only the most massive satellite, Rhea, has the potential to hold a thin oxygen atmosphere/exosphere. The masses of the other satellites are too small to retain gravitationally atmospheres in the presence of large thermal escape rates. If the temperature of Rhea's atmosphere is close to its surface temperature, then a molecular oxygen column density of 6 × 1017 m-2 is possible and causes a discernable plasma interaction with Saturn's magnetosphere that can be probed by close flybys of the Cassini spacecraft.

Abrupt Magnetoresistance Jumps Associated with Macroscopic Quantum Tunneling and Weak Localization in Ni Nanowire Arrays

Detailed behavior of abrupt magnetoresistance (MR) jumps in Ni nanowires, embedded into nanoporous alumina membranes, is reported. The observed abrupt elimination of the MR hysteresis by the MR jump indicates an abrupt motion and emission of magnetic domain walls (DWs) from the wires. We find that the temperature dependence of the inverse of the normalized jump magnitude shows a behavior similar to that of the thermal escape and macroscopic quantum tunneling (MQT) rates in Josephson junctions. We also find that the MR jump is sensitive to wire diameters. These observations can be evidence for MQT of magnetic DWs. The presence of a possible weak localization is revealed in the Ni wire, from the logarithmic temperature and magnetic-field dependence of conductance. It should be implied that this weak localization is independent of the MR jump.

MUADEE: A discovery-class mission for exploration of the upper atmosphere of Mars

MUADEE, an acronym for Mars Upper Atmosphere Dynamics, Energetics, and Evolution, was recently selected by NASA as one of several candidates for future Discovery-class missions. MUADEE will use a combination of simple remote and in situ instruments to explore for the first time the Martian upper atmosphere between 60 and 200 km. An understanding of the Dynamics and Energetics of this region will require measurements of atmospheric tides, gravity waves, global circulation and temperature. An understanding of atmospheric Evolution will require an evaluation of the thermal and non-thermal atmospheric escape rates based on measurements of constituent energies and the isotopic ratios of certain atoms. MUADEE will be complementary to the planned Planet B and Mars 94 missions which will focus on the ionosphere, magnetosphere, and solar wind interactions with the planet. MUADEE will also be complementary to the new Mars Surveyor mission which will provide remote measurements of the lower atmosphere. This paper briefly outlines the results of the MUADEE feasibility study that was recently completed by a consortium of scientists and engineers from the University of Michigan, Lockheed Missiles and Space Corporation (our industrial partner), the Jet Propulsion Lab, NASA/Goddard Space Flight Center and co-investigators from the University of Colorado, the University of Texas at Dallas, and the University of Arizona.

The structure of Io's thermal corona and implications for atmospheric escape

We investigate the escape of species from Io's atmosphere using a steady-state model of Io's exospheric corona and its interaction with the Io plasma torus. The corona is assumed to be spherically symmetric with the radial density and compositional structure determined by the gas kinetic temperature, critical level radius, and mixing ratios of the component species. Thermal and nonthermal escape rates are calculated and the results compared with previously estimated torus and neutral cloud supply rates for O, S, Na, and K. Both oxygen- and sulfur-dominated exospheres are considered. Atmospheric sputtering is found to be the major escape mechanism for models in which the plasma flow reaches the critical level. However, such models produce total mass-loading rates an order of magnitude larger than inferred values suggesting that either (1) the structure of the thermal corona is significantly modified by the nonthermal interaction, or (2) substantial plasma flow modification and deflection occurs in the corona at or above the critical level. Assuming that the thermal model is a correct description of the corona, a comparison of these results with the observed near-Io distribution of neutral Na and estimated source rates for the neutral Na jets suggests an extended Na coronal component. Assuming that this component is part of the thermal exosphere, we find that the observations are consistent with an O-dominated corona, an exospheric temperature ~1000 K, a 0.001 critical level mixing ratio of Na, and a critical level radius ~1.5 R_(Io).

Thermal and nonthermal escape mechanisms for terrestrial bodies

A survey is given of the classical thermal escape (Jeans or blowoff) and some eight nonthermal processes involving ions. Diffusional, energetic, and other limitations on the escape flux are discussed. Isotopic fractionation, due to differences in thermal escape rates or diffusive separation, is considered. The dominant processes acting at the five terrestrial planets and six major satellites are summarized. In general, nonthermal processes dominate over the classic thermal ones.