Studies of planetary atmospheric composition, variability, and evolution require appropriate theoretical and numerical tools to estimate key atmospheric parameters, among which the mass-loss rate is ...often the most important. In evolutionary studies, it is common to use the energy-limited formula, which is attractive for its simplicity but ignores important physical effects and can be inaccurate in many cases. To overcome this problem, we consider a recently developed grid of about 7000 one-dimensional upper-atmosphere hydrodynamic models computed for a wide range of planets with hydrogen-dominated atmospheres from which we extract the mass-loss rates. The grid boundaries are 1:39 in planetary mass, 1:10 in planetary radius, 300:2000 K in equilibrium temperature, 0.4:1.3 in host star's mass, 0.002:1.3 au in orbital separation, and about 1026:5×1030 erg s−1 in stellar X-ray and extreme ultraviolet luminosity. We then derive an analytical expression for the atmospheric mass-loss rates based on a fit to the values obtained from the grid. The expression provides the mass-loss rates as a function of planetary mass, planetary radius, orbital separation, and incident stellar high-energy flux. We show that this expression is a significant improvement to the energy-limited approximation for a wide range of planets. The analytical expression presented here enables significantly more accurate planetary evolution computations without increasing computing time.
There is growing observational and theoretical evidence suggesting that atmospheric escape is a key driver of planetary evolution. Commonly, planetary evolution models employ simple analytic formulae ...(e.g. energy limited escape) that are often inaccurate, and more detailed physical models of atmospheric loss usually only give snapshots of an atmosphere’s structure and are difficult to use for evolutionary studies. To overcome this problem, we have upgraded and employed an existing upper atmosphere hydrodynamic code to produce a large grid of about 7000 models covering planets with masses 1–39 M⊕ with hydrogen-dominated atmospheres and orbiting late-type stars. The modelled planets have equilibrium temperatures ranging between 300 and 2000 K. For each considered stellar mass, we account for three different values of the high-energy stellar flux (i.e. low, moderate, and high activity). For each computed model, we derived the atmospheric temperature, number density, bulk velocity, X-ray and EUV (XUV) volume heating rates, and abundance of the considered species as a function of distance from the planetary centre. From these quantities, we estimate the positions of the maximum dissociation and ionisation, the mass-loss rate, and the effective radius of the XUV absorption. We show that our results are in good agreement with previously published studies employing similar codes. We further present an interpolation routine capable to extract the modelling output parameters for any planet lying within the grid boundaries. We used the grid to identify the connection between the system parameters and the resulting atmospheric properties. We finally applied the grid and the interpolation routine to estimate atmospheric evolutionary tracks for the close-in, high-density planets CoRoT-7 b and HD 219134 b,c. Assuming that the planets ever accreted primary, hydrogen-dominated atmospheres, we find that the three planets must have lost them within a few Myr.
The discovery of transiting 'super-Earths' with inflated radii and known masses, such as Kepler-11b-f, GJ 1214b and 55 Cnc e, indicates that these exoplanets did not lose their nebula-captured ...hydrogen-rich, degassed or impact-delivered protoatmospheres by atmospheric escape processes. Because hydrodynamic blow-off of atmospheric hydrogen atoms is the most efficient atmospheric escape process we apply a time-dependent numerical algorithm which is able to solve the system of 1D fluid equations for mass, momentum and energy conservation to investigate the criteria under which 'super-Earths' with hydrogen-dominated upper atmospheres can experience hydrodynamic expansion by heating of the stellar soft X-rays and extreme ultraviolet (XUV) radiation and thermal escape via blow-off. Depending on orbit location, XUV flux, heating efficiency and the planet's mean density our results indicate that the upper atmospheres of all 'super-Earths' can expand to large distances, so that except for Kepler-11c all of them experience atmospheric mass-loss due to Roche lobe overflow. The atmospheric mass loss of the studied 'super-Earths' is one to two orders of magnitude lower compared to that of 'hot Jupiters' such as HD 209458b, so that one can expect that these exoplanets cannot lose their hydrogen envelopes during their remaining lifetimes.
The atmospheres of close-in planets are strongly influenced by mass loss driven by the high-energy (X-ray and extreme ultraviolet, EUV) irradiation of the host star, particularly during the early ...stages of evolution. We recently developed a framework to exploit this connection and enable us to recover the past evolution of the stellar high-energy emission from the present-day properties of its planets, if the latter retain some remnants of their primordial hydrogen-dominated atmospheres. Furthermore, the framework can also provide constraints on planetary initial atmospheric mass fractions. The constraints on the output parameters improve when more planets can be simultaneously analysed. This makes the Kepler-11 system, which hosts six planets with bulk densities between 0.66 and 2.45 g cm−3, an ideal target. Our results indicate that the star has likely evolved as a slow rotator (slower than 85% of the stars with similar masses), corresponding to a high-energy emission at 150 Myr of between 1 and 10 times that of the current Sun. We also constrain the initial atmospheric mass fractions for the planets, obtaining a lower limit of 4.1% for planet c, a range of 3.7–5.3% for planet d, a range of 11.1–14% for planet e, a range of 1–15.6% for planet f, and a range of 4.7–8.7% for planet g assuming a disc dispersal time of 1 Myr. For planet b, the range remains poorly constrained. Our framework also suggests slightly higher masses for planets b, c, and f than have been suggested based on transit timing variation measurements. We coupled our results with published planet atmosphere accretion models to obtain a temperature (at 0.25 AU, the location of planet f) and dispersal time of the protoplanetary disc of 550 K and 1 Myr, although these results may be affected by inconsistencies in the adopted system parameters. This work shows that our framework is capable of constraining important properties of planet formation models.
We investigate the origin and loss of captured hydrogen envelopes from protoplanets having masses in a range between 'sub-Earth'-like bodies of 0.1 M⊕ and 'super-Earths' with 5 M⊕ in the habitable ...zone at 1 au of a Sun-like G star, assuming that their rocky cores had formed before the nebula gas dissipated. We model the gravitational attraction and accumulation of nebula gas around a planet's core as a function of protoplanetary luminosity during accretion and calculate the resulting surface temperature by solving the hydrostatic structure equations for the protoplanetary nebula. Depending on nebular properties, such as the dust grain depletion factor, planetesimal accretion rates, and resulting luminosities, for planetary bodies of 0.1-1 M⊕ we obtain hydrogen envelopes with masses between ∼2.5 × 1019 and 1.5 × 1026 g. For 'super-Earths' with masses between 2 and 5 M⊕ more massive hydrogen envelopes within the mass range of ∼7.5 × 1023-1.5 × 1028 g can be captured from the nebula. For studying the escape of these accumulated hydrogen-dominated protoatmospheres, we apply a hydrodynamic upper atmosphere model and calculate the loss rates due to the heating by the high soft-X-ray and extreme ultraviolet (XUV) flux of the young Sun/star. The results of our study indicate that under most nebula conditions 'sub-Earth' and Earth-mass planets can lose their captured hydrogen envelopes by thermal escape during the first ∼100 Myr after the disc dissipated. However, if a nebula has a low dust depletion factor or low accretion rates resulting in low protoplanetary luminosities, it is possible that even protoplanets with Earth-mass cores may keep their hydrogen envelopes during their whole lifetime. In contrast to lower mass protoplanets, more massive 'super-Earths', which can accumulate a huge amount of nebula gas, lose only tiny fractions of their primordial hydrogen envelopes. Our results agree with the fact that Venus, Earth, and Mars are not surrounded by dense hydrogen envelopes, as well as with the recent discoveries of low density 'super-Earths' that most likely could not get rid of their dense protoatmospheres.
We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 ...times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass-loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass-loss rates of hydrogen-dominated super-Earths and compare the results to those obtained by the energy-limited escape formula which is widely used for mass-loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over- or underestimate the hydrogen mass-loss rates by amounts that depend on the stellar EUV flux and planetary parameters such as mass, size, effective temperature and EUV absorption radius.
The magnetized supersonic solar wind, when flowing around planets, forms a magnetic barrier near the streamlined surface. The main feature of the magnetic barrier is that the magnetic pressure ...prevails over the plasma pressure. The Hall-MHD model is used to simulate the magnetic barrier in the case of solar wind flow around the atmosphere of Venus. The obtained numerical results are compared with an analytical approximation of the magnetic barrier thickness, which expresses the dependence of the magnetic barrier on solar wind parameters. Particular attention is paid to the physical reasons for the asymmetry of the magnetic barrier caused by the Hall effects, which are mainly concentrated in the boundary layer near the ionopause, where the electric current has a maximum strength. An additional source of asymmetry is also considered, which acts in the same direction and is associated with the influence of the normal component of the electric field on the specific behavior of new atmospheric ions. It is shown that solar wind protons are loaded by new atmospheric ions mainly in the E+ hemisphere. In the case of more intense loading, the boundary of the magnetic barrier and the shock wave are located farther from the ionopause.
•Hall-MHD effects cause a strong magnetic field asymmetry near the Venus ionopause.•Hall-related changes in magnetic and plasma pressures are opposite to each other.•Asymmetry due to Hall effects near Venus increases as solar wind density decreases.•The finite Larmor radius of ions causes an asymmetry additional to the Hall effect.
ABSTRACT Terrestrial planets formed within gaseous protoplanetary disks can accumulate significant hydrogen envelopes. The evolution of such an atmosphere due to XUV driven evaporation depends on the ...activity evolution of the host star, which itself depends sensitively on its rotational evolution, and therefore on its initial rotation rate. In this Letter, we derive an easily applicable method for calculating planetary atmosphere evaporation that combines models for a hydrostatic lower atmosphere and a hydrodynamic upper atmosphere. We show that the initial rotation rate of the central star is of critical importance for the evolution of planetary atmospheres and can determine if a planet keeps or loses its primordial hydrogen envelope. Our results highlight the need for a detailed treatment of stellar activity evolution when studying the evolution of planetary atmospheres.
Data‐Based Modeling of the Magnetosheath Magnetic Field Tsyganenko, N. A.; Semenov, V. S.; Erkaev, N. V.
Journal of geophysical research. Space physics,
November 2023, 2023-11-00, 20231101, Letnik:
128, Številka:
11
Journal Article
Recenzirano
A quantitative model of the magnetosheath (MS) magnetic structure is developed, using a multi‐year set of Geotail, Themis, Cluster, and MMS magnetometer and plasma instrument data. The MS database is ...created using an identification algorithm, based on observed magnetic field magnitudes and proton densities, normalized by their concurrent interplanetary values, followed by additional filtering with the help of standard bow shock (BS) and magnetopause (MP) models. The model architecture is based on the toroidal/poloidal formalism and a coordinate system that naturally accounts for the tailward flaring of both boundaries. The magnetic field expansions include 960 free coefficients, derived by fitting the model to a grand data set, split into independent training and validation subsets with 1,291,380 and 411,933 1‐min records, respectively. The model faithfully reproduces basic types of the interplanetary magnetic field (IMF) wrapping around the MP. Regular IMF sectors result in strongly dawn‐dusk asymmetric draping, with much larger magnitudes at the quasi‐perpendicular dusk side of BS, and weaker at the quasi‐parallel dawn side, where the MS field lines are bent and dragged tailward. Except in the case of the flow‐aligned IMF orientation, the subsolar field steadily grows toward the MP, and the effect is clearly IMF Bz‐dependent: the field and its gradient are larger (smaller) for northward (southward) IMF Bz, implying a pile‐up of the magnetic flux in the first case and stronger reconnection in the second. Model distributions of the MS field magnitude reveal local depressions, associated with polar cusps near the high‐latitude limits of data coverage.
Plain Language Summary
The terrestrial magnetosheath is a relatively wide transition region, separating our planet’s magnetosphere from the undisturbed flow of magnetized solar wind. Due to the sudden compression of the incoming plasma flow at the bow shock and high conductivity of the magnetosheath medium, the relatively weak magnetic field of interplanetary origin undergoes abrupt compression and drapes around the magnetosphere boundary, the magnetopause. Huge amounts of archived spacecraft data accumulated in the world data centers during past decades of space flight made it possible to develop quantitative models of the magnetosheath magnetic field, based on direct in situ observations. This paper presents first results of such a modeling study, providing a closed analytical representation of the magnetosheath magnetic field, driven by input from upstream monitors of the interplanetary medium.
Key Points
A closed empirical model of the magnetosheath magnetic field is developed, based on satellite data and a flexible mathematical architecture
Driven by interplanetary parameters and dipole tilt, the model faithfully reproduces basic features of the IMF draping around the magnetopause
Northward (southward) IMF results in higher (lower) subsolar fields, indicating magnetic flux pile‐up (stronger reconnection), respectively
Context. Hydrogen-dominated atmospheres of hot exoplanets expand and escape hydrodynamically due to the intense heating by the X-ray and extreme ultraviolet (XUV) irradiation of their host stars. ...Excess absorption of neutral hydrogen has been observed in the Ly α line during transits of several close-in gaseous exoplanets, indicating such extended atmospheres. Aims. For the hot Jupiter HD 189733b, this absorption shows temporal variability. We aim to study if variations in stellar XUV emission and/or variable stellar wind conditions may explain this effect. Methods. We applied a 1D hydrodynamic planetary upper atmosphere model and a 3D magnetohydrodynamic stellar wind flow model to study the effect of variations of the stellar XUV irradiation and wind conditions at the planet’s orbit on the neutral hydrogen distribution. This includes the production of energetic neutral atoms (ENAs) and the related Ly α transit signature. Results. We obtain comparable, albeit slightly higher Ly α absorption than that observed in 2011 with a stellar XUV flux of 1.8 × 10 4 erg cm −2 s −1 , rather typical activity conditions for this star. Flares with parameters similar to that observed eight hours before the transit are unlikely to have caused a significant modulation of the transit signature. We find that the resulting Ly α absorption is dominated by atmospheric broadening, whereas the contribution of ENAs is negligible, as they are formed inside the bow shock from decelerated wind ions that are heated to high temperatures. Thus, within our modeling framework and assumptions, we find an insignificant dependence of the absorption on the stellar wind parameters. Conclusions. Since the transit absorption can be modeled with typical stellar XUV and wind conditions, it is possible that the nondetection of the absorption in 2010 was affected by less typical stellar activity conditions, such as a very different magnitude and/or shape of the star’s spectral XUV emission, or temporal and/or spatial variations in Ly α affecting the determination of the transit absorption.
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