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.
Abstract
Stellar coronal mass ejections (CMEs) may play an important role in mass- and angular momentum loss of young Sun-like stars. If occurring frequently, they may also have a strong effect on ...planetary evolution by increasing atmospheric erosion. So far it has not been possible to infer the occurrence frequency of stellar CMEs from observations. Based on their close relation with flares on the Sun, we develop an empirical model combining solar flare–CME relationships with stellar flare rates to estimate the CME activity of young Sun-like and late-type main-sequence stars. By comparison of the obtained CME mass-loss rates with observations of total mass-loss rates, we find that our modelled rates may exceed those from observations by orders of magnitude for the most active stars. This reveals a possible limit to the extrapolation of such models to the youngest stars. We find that the most uncertain component in the model is the flare–CME association rate adopted from the Sun, which does not properly account for the likely stronger coronal confinement in active stars. Simple estimates of this effect reveal a possible suppression of CME rates by several orders of magnitude for young stars, indicating that this issue should be addressed in more detail in the future.
Context. The thermal and chemical structures of the upper atmospheres of planets crucially influence losses to space and must be understood to constrain the effects of losses on atmospheric ...evolution. Aims. We develop a 1D first-principles hydrodynamic atmosphere model that calculates atmospheric thermal and chemical structures for arbitrary planetary parameters, chemical compositions, and stellar inputs. We apply the model to study the reaction of the Earth’s upper atmosphere to large changes in the CO2 abundance and to changes in the input solar XUV field due to the Sun’s activity evolution from 3 Gyr in the past to 2.5 Gyr in the future. Methods. For the thermal atmosphere structure, we considered heating from the absorption of stellar X-ray, UV, and IR radiation, heating from exothermic chemical reactions, electron heating from collisions with non-thermal photoelectrons, Joule heating, cooling from IR emission by several species, thermal conduction, and energy exchanges between the neutral, ion, and electron gases. For the chemical structure, we considered ~500 chemical reactions, including 56 photoreactions, eddy and molecular diffusion, and advection. In addition, we calculated the atmospheric structure by solving the hydrodynamic equations. To solve the equations in our model, we developed the Kompot code and have provided detailed descriptions of the numerical methods used in the appendices. Results. We verify our model by calculating the structures of the upper atmospheres of the modern Earth and Venus. By varying the CO2 abundances at the lower boundary (65 km) of our Earth model, we show that the atmospheric thermal structure is significantly altered. Increasing the CO2 abundances leads to massive reduction in thermospheric temperature, contraction of the atmosphere, and reductions in the ion densities indicating that CO2 can significantly influence atmospheric erosion. Our models for the evolution of the Earth’s upper atmosphere indicate that the thermospheric structure has not changed significantly in the last 2 Gyr and is unlikely to change signficantly in the next few Gyr. The largest changes that we see take place between 3 and 2 Gyr ago, with even larger changes expected at even earlier times.
ABSTRACT This is the second paper in a series where we build a self-consistent model to simulate the mass-loss process of a close-orbit magnetized giant exoplanet, so-called hot Jupiter (HJ). In this ...paper we generalize the hydrodynamic (HD) model of an HJ's expanding hydrogen atmosphere, proposed in the first paper, to include the effects of intrinsic planetary magnetic field. The proposed self-consistent axisymmetric 2D magnetohydrodynamics model incorporates radiative heating and ionization of the atmospheric gas, basic hydrogen chemistry for the appropriate account of major species composing HJ's upper atmosphere and related radiative energy deposition, and and Ly cooling processes. The model also takes into account a realistic solar-type X-ray/EUV spectrum for calculation of intensity and column density distribution of the radiative energy input, as well as gravitational and rotational forces acting in a tidally locked planet-star system. An interaction between the expanding atmospheric plasma and an intrinsic planetary magnetic dipole field leads to the formation of a current-carrying magnetodisk that plays an important role for topology and scaling of the planetary magnetosphere. A cyclic character of the magnetodisk behavior, composed of consequent phases of the disk formation followed by the magnetic reconnection with the ejection of a ring-type plasmoid, has been discovered and investigated. We found that the mass-loss rate of an HD 209458b analog planet is weakly affected by the equatorial surface field <0.3 G, but is suppressed by an order of magnitude at the field of 1 G.
Context.
The energy-limited atmospheric escape approach is widely 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 energy-limited atmospheric escape approximation.
Methods.
We revise the energy-limited atmospheric escape formalism and the involved assumptions. We also compare the results of the energy-limited formalism with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1
M
⊕
and 39
M
⊕
, 1
R
⊕
and 10
R
⊕
, and 300 and 2000 K, respectively.
Results.
Within the grid boundaries, we find that the energy-limited 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 two to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the energy-limited approximation to within one order of magnitude have intermediate gravitational potentials (≈2.5–5.5 ×10
8
J kg
−1
) 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 energy-limited 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 energy-limited 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.
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.
Context. The heating efficiency ηhν 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 ηhν 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 ηhν 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→ H transition region in the upper atmosphere. Results. The heating by XUV radiation of hydrogen-dominated upper atmospheres does not reach higher values than 20% above the main thermosphere altitude, if the participation of photoelectron impact processes is included. Conclusions. Hydrogen-escape studies from exoplanets that assume ηhν values that are ≥20% probably overestimate the thermal escape or mass-loss rates, while those who assumed values that are <20% produce more realistic atmospheric-escape rates.
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.
ABSTRACT
Coronal mass ejections (CMEs) may have major importance for planetary and stellar evolution. Stellar CME parameters, such as mass and velocity, have yet not been determined statistically. So ...far only a handful of stellar CMEs has been detected mainly on dMe stars using spectroscopic observations. We therefore aim for a statistical determination of CMEs of solar-like stars by using spectroscopic data from the ESO phase 3 and Polarbase archives. To identify stellar CMEs, we use the Doppler signal in optical spectral lines being a signature of erupting filaments that are closely correlated to CMEs. We investigate more than 3700 h of on-source time of in total 425 dF-dK stars. We find no signatures of CMEs and only few flares. To explain this low level of activity, we derive upper limits for the non-detections of CMEs and compare those with empirically modelled CME rates. To explain the low number of detected flares, we adapt a flare power law derived from EUV data to the H α regime, yielding more realistic results for H α observations. In addition, we examine the detectability of flares from the stars by extracting Sun-as-a-star H α light curves. The extrapolated maximum numbers of observable CMEs are below the observationally determined upper limits, which indicates that the on-source times were mostly too short to detect stellar CMEs in H α. We conclude that these non-detections are related to observational biases in conjunction with a low level of activity of the investigated dF-dK stars.
The origin and evolution of planetary protoatmospheres in relation to the protoplanetary disk is discussed. The initial atmospheres of planets can mainly be related via two formation scenarios. If a ...protoplanetary core accretes mass and grows inside the gas disk, it can capture H
2
, He and other gases from the disk. When the gas of the disk evaporates, the core that is surrounded by the H
2
/He gas envelope is exposed to the high X-ray and extreme ultraviolet flux and stellar wind of the young host star. This period can be considered as the onset of atmospheric escape. It is shown that lower mass bodies accrete less gas and depending on the host stars radiation environment can therefore lose the gaseous envelope after tens or hundreds of million years. Massive cores may never get rid of their captured hydrogen envelopes and remain as sub-Neptunes, Neptunes or gas giants for their whole life time. Terrestrial planets which may have lost the captured gas envelope by thermal atmospheric escape, or which accreted after the protoplanetary nebula vanished will produce catastrophically outgassed steam atmospheres during the magma ocean solidification process. These steam atmospheres consist mainly of water and CO
2
that was incorporated into the protoplanet during its accretion. Planets, which are formed in the habitable zone, solidify within several million years. In such cases the outgassed steam atmospheres cool fast, which leads to the condensation of water and the formation of liquid oceans. On the other hand, magma oceans are sustained for longer if planets form inside a critical distance, even if they outgassed a larger initial amount of water. In such cases the steam atmosphere could remain 100 million years or for even longer. Hydrodynamic atmospheric escape will then desiccate these planets during the slow solidification process.
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