arXiv subjects

N. V. Erkaev

Publications and source records attributed to N. V. Erkaev.

At least 19 recordsLinked to original sources

arXiv2023

On the required mass for exoplanetary radio emission

The detection of radio emission from an exoplanet would constitute the best way to determine its magnetic field. Indeed, the presence of a planetary magnetic field is a necessary condition for radio emission via the Cyclotron Maser Instability. The presence of a magnetic field is, however, not sufficient. At the emission site, the local cyclotron frequency has to be sufficiently high compared to the local plasma frequency. As strong stellar insolation on a low-mass planet can lead to an extended planetary atmosphere, the magnetospheric plasma frequency depends on the planetary mass, its orbital distance, and its host star. We show that an extended planetary atmosphere can quench the radio emission. This seems to be true, in particular, for an important fraction of the planets less massive than approximately two Jupiter masses and with orbital distances below $\sim$0.2 AU. Most of the best candidates suggested by radio scaling laws lie in this parameter space. Taking this effect quenching into account will have important implications for the target selection of observation campaigns. At the same time, this effect will have consequences for the interpretation of observational data.

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arXiv2022

The Exosphere as a Boundary: Origin and Evolution of Airless Bodies in the Inner Solar System and Beyond Including Planets with Silicate Atmospheres

In this review we discuss all the relevant solar/stellar radiation and plasma parameters and processes that act together in the formation and modification of atmospheres and exospheres that consist of surface-related minerals. Magma ocean degassed silicate atmospheres or thin gaseous envelopes from planetary building blocks, airless bodies in the inner Solar System, and close-in magmatic rocky exoplanets such as CoRot-7b, HD219134b and 55 Cnc e are addressed. The depletion and fractionation of elements from planetary embryos, which act as the building blocks for protoplanets are also discussed. In this context the formation processes of the Moon and Mercury are briefly reviewed. The Lunar surface modification since its origin by micrometeoroids, plasma sputtering, plasma impingement as well as chemical surface alteration and the search of particles from the early Earth's atmosphere that were collected by the Moon on its surface are also discussed. Finally, we address important questions on what can be learned from the study of Mercury's environment and its solar wind interaction by MESSENGER and BepiColombo in comparison with the expected observations at exo-Mercurys by future space-observatories such as the JWST or ARIEL and ground-based telescopes and instruments like SPHERE and ESPRESSO on the VLT, and vice versa.

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arXiv2020

Nitrogen Atmospheres of the Icy Bodies in the Solar System

This brief review will discuss the current knowledge on the origin and evolution of the nitrogen atmospheres of the icy bodies in the solar system, particularly of Titan, Triton and Pluto. An important tool to analyse and understand the origin and evolution of these atmospheres can be found in the different isotopic signatures of their atmospheric constituents. The $^{14}$N/$^{15}$N ratio of the N$_2$-dominated atmospheres of these bodies serve as a footprint of the building blocks from which Titan, Triton and Pluto originated and of the diverse fractionation processes that shaped these atmospheres over their entire evolution. Together with other measured isotopic and elemental ratios such as $^{12}$C/$^{13}$C or Ar/N these atmospheres can give important insights into the history of the icy bodies in the solar system, the diverse processes that affect their N$_2$-dominated atmospheres, and the therewith connected solar activity evolution. Titan's gaseous envelope most likely originated from ammonia ices with possible contributions from refractory organics. Its isotopic signatures can yet be seen in the - compared to Earth - comparatively heavy $^{14}$N/$^{15}$N ratio of 167.7, even though this value slightly evolved over its history due to atmospheric escape and photodissociation of N$_2$. The origin and evolution of Pluto's and Triton's tenuous nitrogen atmospheres remain unclear, even though it might be likely that their atmospheres originated from the protosolar nebula or from comets. An in-situ space mission to Triton such as the recently proposed Trident mission, and/or to the ice giants would be a crucial cornerstone for a better understanding of the origin and evolution of the icy bodies in the outer solar system and their atmospheres in general.

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arXiv2020

Escape and evolution of Titan's N$_2$ atmosphere constrained by $^{14}$N/$^{15}$N isotope ratios

We apply a 1D upper atmosphere model to study thermal escape of nitrogen over Titan's history. Significant thermal escape should have occurred very early for solar EUV fluxes 100 to 400 times higher than today with escape rates as high as $\approx 1.5\times 10^{28}$ s$^{-1}$ and $\approx 4.5\times 10^{29}$ s$^{-1}$, respectively, while today it is $\approx 7.5\times 10^{17}$ s$^{-1}$. Depending on whether the Sun originated as a slow, moderate or fast rotator, thermal escape was the dominant escape process for the first 100 to 1000 Myr after the formation of the solar system. If Titan's atmosphere originated that early, it could have lost between $\approx 0.5 - 16$ times its present atmospheric mass depending on the Sun's rotational evolution. We also investigated the mass-balance parameter space for an outgassing of Titan's nitrogen through decomposition of NH$_3$-ices in its deep interior. Our study indicates that, if Titan's atmosphere originated at the beginning, it could have only survived until today if the Sun was a slow rotator. In other cases, the escape would have been too strong for the degassed nitrogen to survive until present-day, implying later outgassing or an additional nitrogen source. An endogenic origin of Titan's nitrogen partially through NH$_3$-ices is consistent with its initial fractionation of $^{14}$N/$^{15}$N $\approx$ 166 - 172, or lower if photochemical removal was relevant for longer than the last $\approx$ 1,000 Myr. Since this ratio is slightly above the ratio of cometary ammonia, some of Titan's nitrogen might have originated from refractory organics.

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arXiv2020

Modeling the Ly$α$ transit absorption of the hot Jupiter HD 189733b

Hydrogen-dominated atmospheres of hot exoplanets expand and escape 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 exoplanets, indicating such extended atmospheres. For the hot Jupiter HD 189733b, this absorption shows temporal variability. Variations in stellar XUV emission and/or stellar wind conditions have been invoked to explain this effect. We apply a 1D hydrodynamic upper atmosphere model and a 3D MHD stellar wind flow model to study the effect of variations of the stellar XUV and wind conditions on the neutral hydrogen distribution, including the production of energetic neutral atoms (ENAs), and the related Ly$α$ transit signature. We obtain comparable, albeit slightly higher Ly$α$ absorption as observed in 2011 with a stellar XUV flux of $1.8\times10^4$ erg cm$^{-2}$ s$^{-1}$, rather typical activity conditions for this star. Flares similar to the one observed 8 h before the transit are unlikely to have caused a significant modulation of the transit signature. 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 on the stellar wind parameters. Since the transit absorption can be modeled with typical stellar XUV and wind conditions, it is possible that the non-detection 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/spatial variations in Ly$α$ affecting the determination of the transit absorption.

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arXiv2020

Stellar Driven Evolution of Hydrogen-Dominated Atmospheres from Earth-Like to Super-Earth-Type Exoplanets

In the present chapter we present the results of evolutionary studies of exoplanetary atmospheres. We mostly focus on the sub- to super-Earth domain, although these methods are applicable to all types of exoplanets. We consider both thermal and nonthermal loss processes. The type of thermal loss mechanism depends on so-called escape parameter $β$, which is the ratio of the gravitational energy of a particle to its thermal energy. While $β$ is decreasing, an exoplanet switches from classical Jeans to modified Jeans and finally to blow-off escape mechanisms. During blow-off the majority of the atmospheric particles dispose of enough energy to escape the planet's gravity field. This leads to extreme gas losses. Although nonthermal losses never exceed blow-off escape, they are of significant importance for planets with relatively weak Jeans-type escape. From the diversity of nonthermal escape mechanisms, in the present chapter we focus on ion pickup and discuss the importance of other loss mechanisms. The general conclusion of the chapter is, that escape processes strongly shape the evolution of the exoplanets and determine, if the planet loses its atmosphere due to erosion processes or, on the contrary, stays as mini-Neptune type body, which can probably not be considered as a potential habitat as we know it.

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arXiv2019

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

The influence of the hydrogen hydrodynamic upper atmosphere escape, driven by the solar soft X-ray and extreme ultraviolet radiation (XUV) flux, on an expected magma ocean outgassed steam atmosphere of early Venus is studied. By assuming that the young Sun was either a weak or moderate 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 gas 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 H$_2$O 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.

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arXiv2019

The Kepler-11 system: evolution of the stellar high-energy emission and {initial planetary} atmospheric mass fractions

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 retains 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 2.45g 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 1-10 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.

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arXiv2019

Transit Ly-$α$ signatures of terrestrial planets in the habitable zones of M dwarfs

We modeled the transit signatures in the Lya line of a putative Earth-sized planet orbiting in the HZ of the M dwarf GJ436. We estimated the transit depth in the Lya line for an exo-Earth with three types of atmospheres: a hydrogen-dominated atmosphere, a nitrogen-dominated atmosphere, and a nitrogen-dominated atmosphere with an amount of hydrogen equal to that of the Earth. We calculated the in-transit absorption they would produce in the Lya line. We applied it to the out-of-transit Lya observations of GJ 436 obtained by the HST and compared the calculated in-transit absorption with observational uncertainties to determine if it would be detectable. To validate the model, we also used our method to simulate the deep absorption signature observed during the transit of GJ 436b and showed that our model is capable of reproducing the observations. We used a DSMC code to model the planetary exospheres. The code includes several species and traces neutral particles and ions. At the lower boundary of the DSMC model we assumed an atmosphere density, temperature, and velocity obtained with a hydrodynamic model for the lower atmosphere. We showed that for a small rocky Earth-like planet orbiting in the HZ of GJ436 only the hydrogen-dominated atmosphere is marginally detectable with the STIS/HST. Neither a pure nitrogen atmosphere nor a nitrogen-dominated atmosphere with an Earth-like hydrogen concentration in the upper atmosphere are detectable. We also showed that the Lya observations of GJ436b can be reproduced reasonably well assuming a hydrogen-dominated atmosphere, both in the blue and red wings of the Lya line, which indicates that warm Neptune-like planets are a suitable target for Lya observations. Terrestrial planets can be observed in the Lya line if they orbit very nearby stars, or if several observational visits are available.

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arXiv2018

Supermassive Hot Jupiters Provide More Favourable Conditions for the Generation of Radio Emission via the Cyclotron Maser Instability - A Case Study Based on Tau Bootis b

We investigate under which conditions supermassive hot Jupiters can sustain source regions for radio emission, and whether this emission could propagate to an observer outside the system. We study Tau Bootis b-like planets (a supermassive hot Jupiter with 5.84 Jupiter masses and 1.06 Jupiter radii), but located at different orbital distances (between its actual orbit of 0.046 AU and 0.2 AU). Due to the strong gravity of such planets and efficient radiative cooling, the upper atmosphere is (almost) hydrostatic and the exobase remains very close to the planet, which makes it a good candidate for radio observations. We expect similar conditions as for Jupiter, i.e. a region between the exobase and the magnetopause that is filled with a depleted plasma density compared with cases where the whole magnetosphere cavity is filled with hydrodynamically outward flowing ionospheric plasma. Thus, unlike classical hot Jupiters like the previously studied planets HD 209458b and HD 189733b, supermassive hot Jupiters should be in general better targets for radio observations.

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arXiv2017

Young planets under extreme UV irradiation. I. Upper atmosphere modelling of the young exoplanet K2-33b

The K2-33 planetary system hosts one transiting ~5 R_E planet orbiting the young M-type host star. The planet's mass is still unknown, with an estimated upper limit of 5.4 M_J. The extreme youth of the system (<20 Myr) gives the unprecedented opportunity to study the earliest phases of planetary evolution, at a stage when the planet is exposed to an extremely high level of high-energy radiation emitted by the host star. We perform a series of 1D hydrodynamic simulations of the planet's upper atmosphere considering a range of possible planetary masses, from 2 to 40 M_E, and equilibrium temperatures, from 850 to 1300 K, to account for internal heating as a result of contraction. We obtain temperature profiles mostly controlled by the planet's mass, while the equilibrium temperature has a secondary effect. For planetary masses below 7-10 M_E, the atmosphere is subject to extremely high escape rates, driven by the planet's weak gravity and high thermal energy, which increase with decreasing mass and/or increasing temperature. For higher masses, the escape is instead driven by the absorption of the high-energy stellar radiation. A rough comparison of the timescales for complete atmospheric escape and age of the system indicates that the planet is more massive than 10 M_E.

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arXiv2017

Escape and fractionation of volatiles and noble gases from Mars-sized planetary embryos and growing protoplanets

Planetary embryos form protoplanets via mutual collisions, which can lead to the development of magma oceans. During their solidification, large amounts of the mantles' volatile contents may be outgassed. The resulting H$_2$O/CO$_2$ dominated steam atmospheres may be lost efficiently via hydrodynamic escape due to the low gravity and the high stellar EUV luminosities. Protoplanets forming later from such degassed building blocks could therefore be drier than previously expected. We model the outgassing and subsequent hydrodynamic escape of steam atmospheres from such embryos. The efficient outflow of H drags along heavier species (O, CO$_2$, noble gases). The full range of possible EUV evolution tracks of a solar-mass star is taken into account to investigate the escape from Mars-sized embryos at different orbital distances. The envelopes are typically lost within a few to a few tens of Myr. Furthermore, we study the influence on protoplanetary evolution, exemplified by Venus. We investigate different early evolution scenarios and constrain realistic cases by comparing modeled noble gas isotope ratios with observations. Starting from solar values, consistent isotope ratios (Ne, Ar) can be found for different solar EUV histories, as well as assumptions about the initial atmosphere (either pure steam or a mixture with accreted H). Our results generally favor an early accretion scenario with a small amount of accreted H and a low-activity Sun, because in other cases too much CO$_2$ is lost during evolution, which is inconsistent with Venus' present atmosphere. Important issues are likely the time at which the initial steam atmosphere is outgassed and/or the amount of CO$_2$ which may still be delivered at later evolutionary stages. A late accretion scenario can only reproduce present isotope ratios for a highly active young Sun, but then very massive steam atmospheres would be required.

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arXiv2017

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

We investigate the interaction between the magnetized stellar wind plasma and the partially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphere of non- or weakly magnetized hot Jupiters. We use the well-studied hot Jupiter HD 209458b as an example for similar exoplanets, assuming a negligible intrinsic magnetic moment. For this planet, the stellar wind plasma interaction forms an obstacle in the planet's upper atmosphere, in which the position of the magnetopause is determined by the condition of pressure balance between the stellar wind and the expanded atmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show that the neutral atmospheric atoms penetrate into the region dominated by the stellar wind, where they are ionized by photo-ionization and charge exchange, and then mixed with the stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show that an induced magnetic field forms in front of the planetary obstacle, which appears to be much stronger compared to those produced by the solar wind interaction with Venus and Mars. Depending on the stellar wind parameters, because of the induced magnetic field, the planetary obstacle can move up to ~0.5-1 planetary radii closer to the planet. Finally, we discuss how estimations of the intrinsic magnetic moment of hot Jupiters can be inferred by coupling hydrodynamic upper planetary atmosphere and MHD stellar wind interaction models together with UV observations. In particular, we find that HD 209458b should likely have an intrinsic magnetic moment of 10-20% that of Jupiter.

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arXiv2016

Aeronomical constraints to the minimum mass and maximum radius of hot low-mass planets

Stimulated by the discovery of a number of close-in low-density planets, we generalise the Jeans escape parameter taking hydrodynamic and Roche lobe effects into account. We furthermore define $Λ$ as the value of the Jeans escape parameter calculated at the observed planetary radius and mass for the planet's equilibrium temperature and considering atomic hydrogen, independently of the atmospheric temperature profile. We consider 5 and 10 $M_{\oplus}$ planets with an equilibrium temperature of 500 and 1000 K, orbiting early G-, K-, and M-type stars. Assuming a clear atmosphere and by comparing escape rates obtained from the energy-limited formula, which only accounts for the heating induced by the absorption of the high-energy stellar radiation, and from a hydrodynamic atmosphere code, which also accounts for the bolometric heating, we find that planets whose $Λ$ is smaller than 15-35 lie in the "boil-off" regime, where the escape is driven by the atmospheric thermal energy and low planetary gravity. We find that the atmosphere of hot (i.e. $T_{\rm eq}\gtrapprox$ 1000 K) low-mass ($M_{\rm pl}\lessapprox$ 5 $M_{\oplus}$) planets with $Λ$ < 15-35 shrinks to smaller radii so that their $Λ$ evolves to values higher than 15-35, hence out of the boil-off regime, in less than $\approx$500 Myr. Because of their small Roche lobe radius, we find the same result also for hot (i.e. $T_{\rm eq}\gtrapprox$ 1000 K) higher mass ($M_{\rm pl}\lessapprox$ 10 $M_{\oplus}$) planets with $Λ$ < 15-35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, $Λ$ should therefore be $\geq$15-35, which provides a strong constraint on the planetary minimum mass and maximum radius and can be used to predict the presence of aerosols and/or constrain planetary masses, for example.

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arXiv2016

On the ultraviolet anomalies of the WASP-12 and HD 189733 systems: Trojan satellites as a plasma source

We suggest an additional possible plasma source to explain part of the phenomena observed for the transiting hot Jupiters WASP-12b and HD 189733b in their ultraviolet (UV) light curves. In the proposed scenario, material outgasses from the molten surface of Trojan satellites on tadpole orbits near the Lagrange points L$_4$ and L$_5$. We show that the temperature at the orbital location of WASP-12b is high enough to melt the surface of rocky bodies and to form shallow lava oceans on them. In case of WASP-12b, this leads to the release of elements such as Mg and Ca, which are expected to surround the system. The predicted Mg and Ca outgassing rates from two Io-sized WASP-12b Trojans are $\approx 2.2 \times 10^{27}$ s$^{-1}$ and $\approx 2.2 \times 10^{26}$ s$^{-1}$, respectively. Trojan outgassing can lead to the apparent lack of emission in Mg{\sc ii}\,h\&k and Ca{\sc ii}\,H\&K line cores of WASP-12. For HD 189733b, the mechanism is only marginally possible due to the lower temperature. This may be one of the reasons that couldn't explain the early ingress of HD 189733b observed in the far-UV (FUV) C{\sc ii} doublet due to absence of carbon within elements outgassed by molten lava. We investigate the long-term stability region of WASP-12b and HD 189733b in case of planar and inclined motion of these satellites and show that unlike the classical exomoons orbiting the planet, Io-sized Trojans can be stable for the whole systems life time.

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arXiv2016

Identifying the "true" radius of the hot sub-Neptune CoRoT-24b by mass loss modelling

For the hot exoplanets CoRoT-24b and CoRoT-24c, observations have provided transit radii R$_{\rm T}$ of 3.7$\pm$0.4 R$_{\oplus}$ and 4.9$\pm$0.5 R$_{\oplus}$, and masses of $\le$5.7 M$_{\oplus}$ and 28$\pm$11 M$_{\oplus}$, respectively. We study their upper atmosphere structure and escape applying an hydrodynamic model. Assuming R$_{\rm T} \approx$ R$_{\rm PL}$, where R$_{\rm PL}$ is the planetary radius at the pressure of 100 mbar, we obtained for CoRoT-24b unrealistically high thermally-driven hydrodynamic escape rates. This is due to the planet's high temperature and low gravity, independent of the stellar EUV flux. Such high escape rates could last only for $<$100 Myr, while R$_{\rm PL}$ shrinks till the escape rate becomes less than or equal to the maximum possible EUV-driven escape rate. For CoRoT-24b, R$_{\rm PL}$ must be therefore located at $\approx 1.9-2.2$ R$_{\oplus}$ and high altitude hazes/clouds possibly extinct the light at R$_{\rm T}$. Our analysis constraints also the planet's mass to be 5$-$5.7 M$_{\oplus}$. For CoRoT-24c, R$_{\rm PL}$ and R$_{\rm T}$ lie too close together to be distinguished in the same way. Similar differences between R$_{\rm PL}$ and R$_{\rm T}$ may be present also for other hot, low-density sub-Neptunes.

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arXiv2016

Thermal mass loss of protoplanetary cores with hydrogen-dominated atmospheres: The influences of ionization and orbital distance

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.

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arXiv2015

The Evolution of Stellar Rotation and the hydrogen atmospheres of habitable-zone Terrestrial Planets

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.

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