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At young ages, when radiation from the host star is high, and the planet is hot and inflated after formation, planetary atmospheric mass loss can be extremely strong compared to older planets. In turn, stellar winds are faster and denser for young stars compared to evolved main-sequence stars. Their interaction with escaping planetary atmospheres can substantially affect atmospheric mass loss rates, as well as the observable signatures of escaping atmospheres, with both effects expected to occur differently for young and evolved planets. We perform a comparative study of two systems around stars of similar masses but very different ages (50~Myr and 9~Gyr): TOI-942 and TOI-421. Both stars host two sub-Neptune-like planets at similar orbits and in similar mass ranges, which allows a direct comparison of the atmospheric escape and interactions with the stellar winds in the young and old systems. We perform the 3D atmospheric modeling of the four planets in TOI-942 and TOI-421 systems and make the theoretical predictions of possible observational signatures in Ly-alpha absorption. We find that accounting for the stellar wind interacting with planetary atmospheres is crucial for the interpretation of the observations for young planets. Additionally, we show that a particular energy distribution along the XUV spectra has a minor effect on the atmospheric mass-loss rates, but it is of crucial importance for modeling the Ly-alpha absorption and therefore for interpretation of observations., Comment: 19 pages, 9+3 Figures (including Appendix); Accepted for publication in MNRAS

Large planetesimals and planetary embryos ranging from several hundred to a few thousand kilometers can develop magma oceans through mutual collisions, gravitational energy, and the heating of short-lived radioactive elements. After the evaporation of the protoplanetary gas disk, one can divide such planetary embryos into two distinct populations. If they grow to a certain mass of about >0.5 MEarth before the dissipation of the disk, they will start to accrete a substantial primordial hydrogen-dominated atmosphere, while the gravitational potential of the smaller ones (≤0.5 MEarth) will be too low to support this type of primordial atmosphere. For the smaller planetary embryos, the initial magma ocean will subsequently solidify, and a steam atmosphere will be catastrophically outgassed that, if it does not condense, may be lost efficiently via hydrodynamic escape. The escaping H-atoms will further drag heavier trace elements like noble gases and outgassed moderately volatile elements (MVEs) such as K, Na, Si, and Mg into space. For the larger population of planetary embryos, however, the magma ocean below the primordial atmosphere will not solidify until most of the gaseous envelope will be lost, thereby providing favorable conditions for MVEs to be dissolved within such atmosphere. In our first study (Benedikt et al. 2020), we applied an upper atmosphere hydrodynamic escape model that includes the dragging of heavier species by escaping H-atoms and investigated atmospheric and elemental escape from planetary embryos between 1 MMoon and 1.5 MMars (that is, the population of small protoplanets that does not accrete a primordial hydrogen-dominated atmosphere) by assuming that the noble gases and MVEs mostly reside within the escaping atmosphere. Our results indicated that the steam atmospheres and the embedded trace elements will be lost efficiently before they condense for masses ≤0.5 MMars and orbital distances up to 1 AU. For heavier embryos of up to 1.5 MMars the atmosphere together with the trace elements can only be lost completely if a shallow magma ocean remains below the gaseous envelope which might be achieved through frequent impacts onto the planetary embryo. For embryos with masses ≤MMoon, on the other hand, the gravity is too weak for a dense atmosphere to build up against the high magma ocean related surface temperatures and all outgassed elements will escape immediately into space. The studied planetary embryos will, therefore, be severely depleted in noble gases and MVEs. In a follow-up study (Erkaev et al. 2022), we are currently focusing on the loss of the heat producing element 40K from initially bigger planetary embryos (that is, the population of protoplanets that was able to accrete a substantial primordial atmosphere). Contrary to our first study, we additionally applied equilibrium condensation models with the equilibrium chemistry GGCHEM code (Woitke et al. 2018) and found that for magma ocean surface temperatures of ≥2500 K no condensates that fix potassium are thermally stable, and 40K isotopes indeed populate such a primordial atmosphere to a great extent. By applying a sophisticated multispecies hydrodynamic upper atmosphere evolution model to study the loss of the atmosphere together with 40K, we found that depending on the initial size of the protoplanet and the early evolution of the host star, this process can indeed remove substantial amounts of 40K from protoplanetary bodies that are ≥0.5 MEarth. This effect alone can, together with the loss of MVEs from the smaller planetary embryos that serve as building blocks for the bigger ones, result in a wide variety of different potassium abundances at the fully grown planet. Since different abundances of heat producing elements have a significant influence onto the subsequent thermal and tectonic evolution of a planet, and therewith connected, on its tectonic modes (e.g., O’Neill et al. 2020), the process of early hydrodynamic escape of the heat producing isotope 40K can significantly impact the habitability, since not all rocky planets will end up with the "right" amount of heat production in its interior. However, this process cannot be viewed separately; other factors will additionally determine the initial heat budget of a planet such as collisional erosion, the feeding zone of the growing protoplanet or the initial composition of the protoplanetary disk. References: Benedikt, M.R., Scherf, M., Lammer, H., Marcq, E., Odert, P., Leitzinger, M., Erkev, N.V., Escape of rock-forming volatile elements and noble gases from planetary embryos, Icarus, 347, 113772, 2020.Erkaev, N.V., Scherf, M., Herbort, O., Lammer, H., Odert, P., Kubyshkina, D., Leitzinger, M., Woitke, P., O’Neill, C., Modification of the radioactive heat budget of Earth-like exoplanets by the loss of primordial atmospheres, Mon. Not. R. Ast. Soc., under revision, 2022.O’Neill, C., O’Neill, H.S.C., Jellinek, A.M., On the Distribution and Variation of Radioactive Heat Producing Elements Within Meteorites, the Earth, and Planets, Space Sci. Rev., 216, id.37, 2020.Woitke, P., C. Helling, Hunter, G.H., Millard, J.D., Turner, G.E., Worters, M., Blecic, J., Stock, J.W., Equilibrium chemistry down to 100 K. Impact of silicates and phyllosilicates on the carbon to oxygen ratio, Astron. Astrophys. 614, id.A1, 2018.

The warm- and hot-Neptune-type planets are known to experience significant atmospheric mass loss and are easier to observe and characterize in comparison to terrestrial-like planets. They represent, therefore, interesting targets in the context of planetary atmospheric evolution and star-planet interaction. The majority of studies, however, employ hydrodynamic simulations relying on simplified approaches in describing photoionization processes, or, on the other hand, use high-level photoionization solvers not accounting for dynamical effects.In this study, we aim to outline for which types of planets in the Neptune-like mass range the non-LTE effects become important (in particular - in terms of atmospheric mass loss) and to which extent the hydrodynamic effects (as adiabatic expansion) influence the theoretically predicted transmission spectra.To achieve this goal, we combine our 1D hydrodynamic upper atmosphere model (Kubyshkina et al., 2018) with the latest version of the non-LTE photoionization and radiative transfer code Cloudy (Ferland et al., 2017), which accounts for ionization and dissociation, atomic level transitions and chemical reactions for the lightest chemical elements up to zink. Thus, the former is responsible for resolving the hydrodynamic outflow and the latter solves the realistic photoionization and heating of the planetary atmosphere. We verify this scheme by comparing our results for a dozen of the high profile planets with the predictions of Salz et al., 2016, which use a similar approach.We apply this hybrid framework to model the upper atmospheres of a range of Neptune-like and terrestrial-like planets with masses between 1 and 50 Mearth, changing systematically the orbital parameters (and thus, equilibrium temperature), and the irradiation level from the host star. We find, that for the majority of warm and hot Neptunes, accounting for realistic non-LTE ionization/heating affects significantly the basic parameters of planetary atmospheres, predicting cooler, slower, and denser outflow compared to the predictions of the pure hydrodynamic model. The predictions of the hydrodynamic and hybrid models become closer at the highest levels of stellar radiation.In turn, accounting for hydrodynamic effects, in particular for expansion cooling, considerably affects the predictions of Cloudy models, and is therefore important for the interpretation of observations.

Exoplanets in the mass range between Earth and Saturn show a large spread in radii/densities for a given planetary mass. The most approaches to explain this spread and the distribution of planetary properties therein can be split into two groups. The first considers the planetary formation paths as the primary mechanism shaping this distribution, and the second group considers the radius spread as a consequence of the atmospheric evolution driven by the atmospheric mass loss. The majority of the latter studies, however, consider only the observed radius spread with some theoretical underlying mass distribution, as for most of the Kepler planets the mass is unknown.In this study, we examine the mass-radius distribution of the observed planets with masses between 1 and 108 Earth masses with the aim to understand to which extent it can be explained by the evolution of planetary atmospheres driven by thermal contraction and the hydrodynamic escape, and in which regions of the parameters state the initial parameters of planets set up by specific formation processes are critical for the final (gygayears old) state.Our modeling framework accounts simultaneously for the realistic atmospheric mass loss by interpolating within the grid of upper atmosphere models and for the thermal evolution of planets by means of the MESA code. As the atmospheric mass loss on the long timescales is strongly affected by high energy stellar radiation, we also account for the whole range of different possible stellar evolution histories as represented by the Mors code. We consider the grid of model planets in the mass range given above evolving at different orbital separations (corresponding to the equilibrium temperatures of ~500-1700 K) around the solar mass star. As initial parameters for our atmosphere evolution models, we adopt the predictions of the analytical approximations based on formation models (Mordasini 2020) and consider the two possible scenarios: planets formed in the inner disk (relatively small initial atmospheres) and beyond the snow line (large initial atmospheres) with consequent inward migration at the early phase of the planetary system evolution.The whole radius spread predicted using this approach outlines well the observed distribution (including about 240 planets with mass and radius uncertainties below 45% and 15% respectively), except for a group of very close in (within ~0.1 AU) massive (~70-110 Mearth) planets with radii comparable to the Jupiter radius. The radii of these planets can not be reproduced by our models even by assuming the atmospheric mass fractions above 80% without some additional heating source. A strong correlation of the radii with equilibrium temperature (Rpl~Teq0.7) suggests that the inflation mechanism is similar to that of the so-called "inflated Jupiters", where a range of possible explanations was suggested including the tidal interaction with the host star, vertical heat transport towards the deep atmospheric levels or the Ohmic dissipation.The more detailed analysis shows that the low-mass end of the mass-radius distribution (below 10-15 Earth masses) is dominated by the effect of the atmospheric mass loss (and thus extremely dependent on the activity evolution history of the host star) and weakly depend on the initial parameters, and thus, on the specific formation mechanism of the exoplanets. For more massive planets, though some of them can be significantly affected by the atmospheric mass loss, the initial conditions become important and the variability in the possible stellar histories can only explain about one fourth of the whole spread. Thus, for explaining the upper boundary of the spread above ~20 Mearth one needs to consider the voluminous initial atmospheres which can be explained by the formation at the large distance from the host star. However, the activity history of the host star can be theoretically resolved using the present-day radii of the companion planets for the significant fraction of planets with masses up to ~60 Mearth.Finally, the detailed comparison between the model predictions and the observations within different Teq intervals reveals a relatively small (~6%) but a presumably systematic group of the outliers with radii considerably smaller than the lower boundary predicted by our models for Teq10 Mearth) the accretion models predict the initial atmospheric mass fraction order of 10%, and the total atmospheric mass loss throughout the evolution according to our models is insufficient to remove this much of the atmospheric material. This suggests, that the formation mechanisms and structures of these planets are considerably different from our assumption of the hydrogen-dominated atmospheres accreted onto the rocky core.

The evolution of the atmospheres of low and intermediate-mass planets is strongly connected to the physical properties of their host stars. The types and the past activities of planet-hosting stars can, therefore, affect the overall planetary population. We perform a comparative study of sub-Neptune-like planets orbiting stars of different masses and different evolutionary histories. As a model of atmospheric evolution, we employ our own framework combining planetary evolution in MESA with a realistic prescription of the escape of hydrogen-dominated atmospheres. We discuss general patterns of the evolved population as a function of planetary and stellar parameters. The final populations look qualitatively similar in terms of the atmospheres' survival around different stars, but quantitatively different, with this difference accentuated for planets orbiting more massive stars. We will discuss the potential input from different atmospheric escape mechanisms in shaping these populations.

In this research note, we outline the extension of the grid of upper atmosphere models first presented in Kubyshkina et al. (2018a). The original grid is based on a 1D hydrodynamic model and consists of about 7000 models covering planets of the size from Earth to twice Neptune at orbits corresponding to equilibrium temperatures between 300 and 2000 K around solar-like (0.4 to 1.3 solar mass) stars. The extended and revised grid of models consists of 10235 points and covers a planetary mass range of up to 109 Earth masses, which allows one to outline the transition between low- and high-gravity hot planets in short orbital separations. We prepared the interpolation tool allowing one to use the grid to define the mass-loss of a planet that falls into the parameter range of the grid. We provide a comparison of our results to common analytical models., 3 pages, 1 figure. Research Note AAS

The two planetary systems TOI-942 and TOI-421 share many similar characteristics, apart from their ages (50~Myr and 9~Gyr). Each of the stars hosts two sub-Neptune-like planets at similar orbits and in similar mass ranges. In this paper, we aim to investigate whether the similarity of the host stars and the configuration of the planetary systems can be taken as proof that the two systems were formed and evolved in a similar way. In paper I of this series, we performed a comparative study of these two systems using 3D modeling of atmospheric escape and its interaction with the stellar wind, for the four planets. We demonstrated that though the strong wind of the young star has a crucial effect on observable signatures, its effect on the atmospheric mass loss is minor in the evolutionary context. Here, we use atmosphere evolution models to track the evolution of planets in the younger system TOI-942 and also to constrain the past of the TOI-421 system. We demonstrate that despite all the similarities, the two planetary systems are on two very different evolutionary pathways. The inner planet in the younger system, TOI-942, will likely lose all of its atmosphere and become a super-Earth-like planet, while the outer planet will become a typical sub-Neptune. Concerning the older system, TOI-421, our evolution modeling suggests that they must have started their evolution with very substantial envelopes, which can be a hint of formation beyond the snow line., Comment: 9 pages, 4 figures; Accepted for publication in MNRAS

Using 3D radiative MHD simulations and Lyman-$��$ transit calculations, we investigate the effect of magnetic fields on the observational signatures of atmospheric escape in exoplanets. Using the same stellar wind, we vary the planet's dipole field strength ($B_p$) from 0 to 10G. For $B_p3$G in the blue wing) the absorption increases caused by the growing volume of the magnetosphere. Finally we show that transits below and above the mid-disc differ caused by the asymmetry of the double tail structure., Accepted for publication in MNRAS. 12 pages, 8 figures

We constrain the planetary atmospheric mass fraction at the time of the dispersal of the protoplanetary disk and the evolution of the stellar rotation rate for a dozen multi-planet systems that host sub-Neptunes and/or super-Earths. We employ a custom-developed Python code that we have dubbed Pasta (Planetary Atmospheres and Stellar roTation rAtes), which runs within a Bayesian framework to model the atmospheric evolution of exoplanets. The code combines MESA stellar evolutionary tracks, a model describing planetary structures, a model relating stellar rotation and activity level, and a model predicting planetary atmospheric mass-loss rates based on the results of hydrodynamic simulations. Through a MCMC scheme, we retrieved the posterior PDFs of all considered parameters. For ages older than about 2 Gyr, we find a median spin-down (i.e. $P(t)\propto t^y$) of $\bar{y}=0.38_{-0.27}^{+0.38}$, indicating a rotation decay slightly slower than classical literature values ($\approx$0.5), though still within $1\sigma$. At younger ages, we find a median spin-down (i.e. $P(t)\propto t^x$) of $\bar{x}=0.26_{-0.19}^{+0.42}$, which is below what is observed in young open clusters, though within $1\sigma$. However, these two results are likely due to a selection bias as the systems suitable to be analysed by Pasta contain at least one planet with a hydrogen-dominated atmosphere, implying that the host star has more likely evolved as a slow rotator. We further look for correlations between the initial atmospheric mass fraction of the considered planets and system parameters, but without finding any. The TESS, CHEOPS, and PLATO missions are going to be instrumental in identifying and precisely measuring systems amenable to Pasta's analysis and can thus potentially constrain planet formation and stellar evolution., Comment: 38 pages (15 in the main text), 30 figures (8 in the main text), 2 tables. Accepted for publication in A&A

The population of known low- to intermediate-mass exoplanets shows a large spread in densities, which is believed to be due to the diversity of planetary atmospheres and thus controlled by planetary atmospheric mass loss. One of the main drivers of long-term atmospheric escape is the absorption of high-energy XUV radiation from the host star. For main sequence solar-like stars, rotation and XUV radiation are closely connected, with faster rotating stars being XUV brighter and with both rotation and XUV decreasing with time. This evolution, however, does not follow a unique path, as stars born with the same mass and metallicity can have widely different initial rotation rates. This non-uniqueness holds up to about 1 Gyr, while atmospheric escape from exoplanets is strongest. The atmospheric mass loss through this period is often deciding the future of the planet and its position in the observed population. Therefore, the diversity of possible stellar histories can be an uncertain factor affecting the predictions of population studies. Here, I explore its relevance for different planets and different host stars., Comment: 9 pages, 5 figures, proceedings of the XMM-Newton Workshop 2021 "A High-Energy View of Exoplanets and their Environments". Original article can be found at https://onlinelibrary.wiley.com/doi/10.1002/asna.20210077

As the number of confirmed exoplanets has increased, so too has the diversity in their physical parameters, namely their mass and radius. A common practice is to place these planets on a Mass-Radius diagram with various calculated density curves corresponding to some bulk composition. However, these lines don’t necessarily correspond to the structure of the planet found using interior models, particularly for low mass planets with masses less than 20 M⊕ and 4 R⊕, which we call “sub-Neptunes.” Planets in this range can have highly degenerate solutions with no solar system analog, from so-called “ocean worlds” to small dense cores with extended primary composition atmospheres. We have created a model that is able to cover the range of solutions possible for sub-Neptunes, with various levels of complexity for both the interior and atmosphere. This includes both an isothermal and semi-grey atmosphere, along with a high-pressure solar composition envelope when atmospheric pressures exceed approximately 1000 bar. We then apply this model to known sub-Neptunes located in the extended habitable zone of their star using a hydrogen-helium dominated atmosphere. An atmospheric escape model is used to investigate the longevity of the atmosphere and its effect on the overall habitability of the planet.

Context: The energy-limited (EL) atmospheric escape approach is used to estimate mass-loss rates for a broad range of planets that host hydrogen-dominated atmospheres as well as for performing atmospheric evolution calculations. Aims: We aim to study the applicability range of the EL approximation. Methods: We revise the EL formalism and its assumptions. We also compare its results with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1 $M_{\oplus}$ and 39 $M_{\oplus}$, 1 $R_{\oplus}$ and 10 $R_{\oplus}$, and 300 and 2000 K, respectively. Results: Within the grid boundaries, we find that the EL approximation gives a correct order of magnitude estimate for mass-loss rates for about 76% of the planets, but there can be departures from hydrodynamic simulations by up to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the EL approximation to within one order of magnitude have intermediate gravitational potentials as well as low-to-intermediate equilibrium temperatures and irradiation fluxes of extreme ultraviolet and X-ray radiation. However, for planets with low or high gravitational potentials, or high equilibrium temperatures and irradiation fluxes, the approximation fails in most cases. Conclusions: The EL approximation should not be used for planetary evolution calculations that require computing mass-loss rates for planets that cover a broad parameter space. In this case, it is very likely that the EL approximation would at times return mass-loss rates of up to several orders of magnitude above or below those predicted by hydrodynamic simulations. For planetary atmospheric evolution calculations, interpolation routines or approximations based on grids of hydrodynamic models should be used instead., Comment: 12 pages, 7 figures, Published in A&A in June 2021; Revised on 9.11.2021 to correct typo in equation 2

We report the discovery of a super-Earth and a sub-Neptune transiting the star HD 15337 (TOI-402, TIC 120896927), a bright (V=9) K1 dwarf observed by the Transiting Exoplanet Survey Satellite (TESS) in Sectors 3 and 4. We combine the TESS photometry with archival HARPS spectra to confirm the planetary nature of the transit signals and derive the masses of the two transiting planets. With an orbital period of 4.8 days, a mass of 7.51(+1.09)(-1.01) M_Earth, and a radius of 1.64+/-0.06 R_Earth, HD 15337b joins the growing group of short-period super-Earths known to have a rocky terrestrial composition. The sub-Neptune HD 15337c has an orbital period of 17.2 days, a mass of 8.11(+1.82)(-1.69) M_Earth, and a radius of 2.39+/-0.12 R_Earth, suggesting that the planet might be surrounded by a thick atmospheric envelope. The two planets have similar masses and lie on opposite sides of the radius gap, and are thus an excellent testbed for planet formation and evolution theories. Assuming that HD 15337c hosts a hydrogen-dominated envelope, we employ a recently developed planet atmospheric evolution algorithm in a Bayesian framework to estimate the history of the high-energy (extreme ultraviolet and X-ray) emission of the host star. We find that at an age of 150 Myr, the star possessed on average between 3.7 and 127 times the high-energy luminosity of the current Sun., Comment: Published in ApJ Letters

We study the dependence of the flapping oscillations on the magnetotail current sheet bending, which is caused by the dipole tilt. Observations show that flapping waves propagate from the center of the current sheet to its flanks with a velocity one order of magnitude less than typical Alfven speed. For our analysis we use the double gradient model (Erkaev et al., 2009) of the flapping oscillations, which predicts a small minimum of the total pressure (gas plus magnetic) across the current layer. It is the depth of the potential well in the total pressure which defines the period and the speed of the flapping waves. Using the extension of the Kan/Manankova equilibriums for the non-zero dipole tilt we investigate the depth of the potential well with respect to the current sheet bending rate. We show that with the growth of the dipole tilt angle the depth of the potential well becomes smaller, the period of the flapping oscillations increases, and oscillations become nonlinear. There exists the critical tilt angle, where the potential well disappears and flapping regime changes from oscillations to instability.

There is a point of view that solar wind factors, which break the magnetotail symmetry, are more effective in triggering the magnetospheric substorm. To clarify the question we use a database of substorm onsets and found the evident dependence of the substorm probability on the solar wind flow direction jumps (asymmetric factor), while distribution of the substorm occurrence on the solar wind number density jumps (symmetric factor) is homogeneous. The theoretical interpretation is based on the extension of the existing symmetric Kan model for a bent current sheet. Allowing the model tilt angle to vary in time, we found that the induced electric field penetrates to the central region of the bent current sheet. If the solar wind direction jump increases the bending, then induced electric field thins the current sheet and thus stimulates the reconnection. In the opposite case the current sheet thickens. We claim that this effect is sufficient (provides twice or more thinning of the current sheet in 10 min).

Flapping waves are most noticeable large-scale perturbations of the magnetotail current sheet, whose nature is still under discussion. They represent rather slow (an order of magnitude less than typical Alfven speed) waves propagating from the center of the sheet to its flanks with a typical speed of 20–60 km/s, amplitude of 1–2 Re and quasiperiod of 2–10 min. The double-gradient MHD model, which was elaborated in Erkaev et al. (2007) predicts two (kink and sausage) modes of the flapping waves with differences in their geometry and propagation velocity, but the mode structure is hard to resolve observationally. We investigate the possibility of mode identification by observing the rotation of magnetic field and plasma velocity vectors from a single spacecraft. We test theoretical results by analyzing the flapping oscillations observed by Time History of Events and Macroscale Interactions during Substorms spacecraft and confirm that character of observed rotation is consistent with kink mode determination made by using multispacecraft methods. Also, we checked how the existence of some obstructive conditions, such as noise, combined modes, and multiple sources of the flapping oscillations, can affect on the possibility of the modes separation with suggested method.

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 $\Lambda$ 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 $\Lambda$ 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 $\Lambda$ < 15-35 shrinks to smaller radii so that their $\Lambda$ 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 $\Lambda$ < 15-35, when they orbit M-dwarfs. For old, hydrogen-dominated planets in this range of parameters, $\Lambda$ 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., Comment: Accepted for publication by A&A

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] MEARTH in planetary mass, [1:10] REARTH in planetary radius, [300:2000] K in equilibrium temperature, [0.4:1.3] MSUN in host star's mass, [0.002:1.3] au in orbital separation, and about [10^{26}:5*10^{30}] erg/s 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., Comment: 7 pages, 3 Figures, 2 Tables, published

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 (, 11 pages, 7 figures

The long-term evolution of hydrogen-dominated atmospheres of sub-Neptune-like planets is mostly controlled by two factors: a slow dissipation of the gravitational energy acquired at the formation (known as thermal evolution) and atmospheric mass loss. Here, we use MESA to self-consistently couple the thermal evolution model of lower atmospheres with a realistic hydrodynamical atmospheric evaporation prescription. To outline the main features of such coupling, we simulate planets with a range of core masses (5-20 Mearth) and initial atmospheric mass fractions (0.5-30%), orbiting a solar-like star at 0.1 au. In addition to our computed evolutionary tracks, we also study the stability of planetary atmospheres, showing that the atmospheres of light planets can be completely removed within 1 Gyr, and that compact atmospheres have a better survival rate. From a detailed comparison between our results and the output of the previous-generation models, we show that coupling between thermal evolution and atmospheric evaporation considerably affects the thermal state of atmospheres for low-mass planets and, consequently, changes the relationship between atmospheric mass fraction and planetary parameters. We, therefore, conclude that self-consistent consideration of the thermal evolution and atmospheric evaporation is of crucial importance for evolutionary modeling and a better characterization of planetary atmospheres. From our simulations, we derive an analytical expression between the planetary radius and atmospheric mass fraction at different ages. In particular, we find that, for a given observed planetary radius, the predicted atmospheric mass fraction changes as age^0.11., Comment: 15 pages, 9 figures. The data underlying this article are available in Zenodo Repository, at https://doi.org/10.5281/zenodo.4022393

The evolution of the atmospheres of low and intermediate-mass planets is strongly connected to the physical properties of their host stars. The types and the past activities of planet-hosting stars can, therefore, affect the overall planetary population. In this paper, we perform a comparative study of sub-Neptune-like planets orbiting stars of different masses and different evolutionary histories. We discuss the general patterns of the evolved population as a function of parameters and environments of planets. As a model of the atmospheric evolution, we employ the own framework combining planetary evolution in MESA with the realistic prescription of the escape of hydrogen-dominated atmospheres. {We find that the final populations look qualitatively similar in terms of the atmospheres survival around different stars, but qualitatively different, with this difference accentuated for planets orbiting more massive stars. We show that a planet has larger chances of keeping its primordial atmosphere in the habitable zone of a solar mass star compared to M or K dwarfs and if it starts the evolution having a relatively compact envelope.} We also address the problem of the uncertain initial temperatures (luminosities) of planets and show that this issue is only of particular importance for planets exposed to extreme atmospheric mass-losses., Comment: 18 pages, 13 figures. Accepted for publication in MNRAS

Substorm initiation still remains an unsolved problem, even though there is a consensus among most researchers that its main stages include dayside reconnection and substorm expansion. Dayside reconnection results in magnetotail flux buildup to a certain critical level, after which [or after the interplanetary magnetic field (IMF) Bz turns northward] the substorm expansion begins. One problem with the above scenario is that the critical amount of magnetic flux differs from one substorm to another, and not every northward turning of the IMF Bz triggers a substorm. We suggest that an important factor in substorm dynamics may be the variable shape and alignment of the magnetospheric tail current sheet, which bends and warps in response to diurnal/seasonal changes of the Earth’s dipole tilt angle and also in response to more rapid changes of the solar wind flow direction. Both of these factors may be important, if one assumes that the deformed current sheet becomes unstable at lower values of the tail lobe magnetic flux/pressure than the planar sheet. To investigate this idea, we examined large multi-year sets of THEMIS, Cluster, and Geotail data and established a relationship between the tail lobe Bx and the dipole tilt angle. Further examinations of substorm events during 2005–2010 supported the hypothesis that their probability and intensity indeed depended on the concurrent values of the tilt angle.