Труды сотрудников ИВМ СО РАН

/ H. Lammer [et al.] // Mon. Not. Roy. Astron. Soc. - 2013. - Vol. 430, Is. 2. - P1247-1256, DOI 10.1093/mnras/sts705. - Cited References: 85. - NVE, KGK, MLK and HL acknowledge the support by the FWF NFN project S116 'Pathways to Habitability: From Disks to Active Stars, Planets and Life', and the related FWF NFN subprojects, S116 606-N16 'Magnetospheric Electrodynamics of Exoplanets' and S116607-N16 'Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions'. KGK, HL and PO thank also the Helmholtz Alliance project 'Planetary Evolution and Life'. ML and PO acknowledge support from the FWF project P22950-N16. NVE acknowledges support by the RFBR grant No 12-05-00152-a. The authors also acknowledge support from the EU FP7 project IMPEx (No. 262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science working group WG5. The authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team 'Characterizing stellar- and exoplanetary environments'. Finally, we thank an anonymous referee for interesting suggestions and recommendations which helped to improve the article. . - 10. - ISSN 0035-8711РУБ Astronomy & Astrophysics

Аннотация: 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.


Доп.точки доступа:
Lammer, H.; Erkaev, N.V.; Еркаев, Николай Васильевич; Odert, P.; Kislyakova, K.G.; Leitzinger, M.; Khodachenko, M.L.

[Text] / U.V. Amerstorfer [et al.] // Phys. Plasmas. - 2010. - Vol. 17, Is. 7. - Ст. 72901, DOI 10.1063/1.3453705. - Cited References: 26. - This work was supported by the FWF under Project No. P21051-N16 and also by the RFBR under Grant No. 09-05-91000-ANF_a. . - ISSN 1070-664XРУБ Physics, Fluids & Plasmas

Аннотация: Results of two-dimensional nonlinear numerical simulations of the magnetohydrodynamic Kelvin-Helmholtz instability are presented. A boundary layer of a certain width is assumed, which separates the plasma in the upper layer from the plasma in the lower layer. A special focus is given on the influence of a density increase toward the lower layer. The evolution of the Kelvin-Helmholtz instability can be divided into three different phases, namely, a linear growth phase at the beginning, followed by a nonlinear phase with regular structures of the vortices, and finally, a turbulent phase with nonregular structures. The spatial scales of the vortices are about five times the initial width of the boundary layer. The considered configuration is similar to the situation around unmagnetized planets, where the solar wind (upper plasma layer) streams past the ionosphere (lower plasma layer), and thus the plasma density increases toward the planet. The evolving vortices might detach around the terminator of the planet and eventually so-called plasma clouds might be formed, through which ionospheric material can be lost. For the special case of a Venus-like planet, loss rates are estimated, which are of the order of estimated loss rates from observations at Venus. (C) 2010 American Institute of Physics. [doi:10.1063/1.3453705]


Доп.точки доступа:
Amerstorfer, U.V.; Erkaev, N.V.; Еркаев, Николай Васильевич; Taubenschuss, U.; Biernat, H.K.

[Text] / N. V. Erkaev [et al.] // Astrobiology. - 2013. - Vol. 13, Is. 11. - P1011-1029, DOI 10.1089/ast.2012.0957. - Cited References: 92. - M. Gudel, K. G. Kislyakova, M. L. Khodachenko, and H. Lammer acknowledge support by the FWF NFN project S116 601-N16 "Pathways to Habitability: From Disks to Active Stars, Planets and Life" and the related FWF NFN subprojects S116 604-N16 "Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond," S116 606-N16 "Magnetospheric Electrodynamics of Exoplanets," S116 607-N16 "Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies under Extreme Stellar Conditions." K. G. Kislyakova, Yu. N. Kulikov, H. Lammer, and P. Odert thank also the Helmholtz Alliance project "Planetary Evolution and Life." P. Odert and A. Hanslmeier also acknowledge support from the FWF project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No. 262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. The authors thank the International Space Science Institute (ISSI) in Bern and the ISSI team "Characterizing stellar and exoplanetary environments." N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. Finally, the authors thank referee Tian Feng, from the Tsinghua University, Beijing, China, for suggestions and recommendations that helped to improve the work. . - 19. - ISSN 1531-1074РУБ Astronomy & Astrophysics + Biology + Geosciences, Multidisciplinary

Аннотация: The recently discovered low-density super-Earths Kepler-11b, Kepler-11f, Kepler-11d, Kepler-11e, and planets such as GJ 1214b represent the most likely known planets that are surrounded by dense H/He envelopes or contain deep H2O oceans also surrounded by dense hydrogen envelopes. Although these super-Earths are orbiting relatively close to their host stars, they have not lost their captured nebula-based hydrogen-rich or degassed volatile-rich steam protoatmospheres. Thus, it is interesting to estimate the maximum possible amount of atmospheric hydrogen loss from a terrestrial planet orbiting within the habitable zone of late main sequence host stars. For studying the thermosphere structure and escape, we apply a 1-D hydrodynamic upper atmosphere model that solves the equations of mass, momentum, and energy conservation for a planet with the mass and size of Earth and for a super-Earth with a size of 2 R-Earth and a mass of 10 M-Earth. We calculate volume heating rates by the stellar soft X-ray and extreme ultraviolet radiation (XUV) and expansion of the upper atmosphere, its temperature, density, and velocity structure and related thermal escape rates during the planet's lifetime. Moreover, we investigate under which conditions both planets enter the blow-off escape regime and may therefore experience loss rates that are close to the energy-limited escape. Finally, we discuss the results in the context of atmospheric evolution and implications for habitability of terrestrial planets in general. Key Words: Stellar activityLow-mass starsEarly atmospheresEarth-like exoplanetsEnergetic neutral atomsIon escapeHabitability. Astrobiology 13, 1011-1029.

WOS,
Scopus

Держатели документа:
[Erkaev, Nikolai V.] Russian Acad Sci, Siberian Div, Inst Computat Modelling, Krasnoyarsk 660036, Russia
[Erkaev, Nikolai V.] Siberian Fed Univ, Krasnoyarsk, Russia
[Lammer, Helmut
Odert, Petra
Kislyakova, Kristina G.
Khodachenko, Maxim L.
Biernat, Helfried] Austrian Acad Sci, Space Res Inst, A-8010 Graz, Austria
[Odert, Petra
Kislyakova, Kristina G.
Hanslmeier, Arnold] Graz Univ, Inst Phys, Graz, Austria
[Kulikov, Yuri N.] Russian Acad Sci, Polar Geophys Inst, Murmansk, Russia
[Khodachenko, Maxim L.] Moscow MV Lomonosov State Univ, Inst Nucl Phys, Moscow, Russia
[Guedel, Manuel] Univ Vienna, Inst Astrophys, A-1010 Vienna, Austria
ИВМ СО РАН

Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Lammer, H.; Odert, P.; Kulikov, Y.N.; Kislyakova, K.G.; Khodachenko, M.L.; Gudel, M.; Hanslmeier, A.; Biernat, H.K.; FWF NFN project [S116 601-N16, S116 604-N16, S116 606-N16, S116 607-N16]; FWF project [P22950-N16]; EU [262863]; EUROPLANET-RI projects; JRA3/EMDAF; Na2 science WG5; RFBR [12-05-00152-a]

/ K. G. Kislyakova [et al.] // Astrobiology. - 2013. - Vol. 13, Is. 11. - P1030-1048, DOI 10.1089/ast.2012.0958 . - ISSN 1531-1074
Аннотация: We studied the interactions between the stellar wind plasma flow of a typical M star, such as GJ 436, and the hydrogen-rich upper atmosphere of an Earth-like planet and a "super-Earth" with a radius of 2 R Earth and a mass of 10 MEarth, located within the habitable zone at ∼0.24 AU. We investigated the formation of extended atomic hydrogen coronae under the influences of the stellar XUV flux (soft X-rays and EUV), stellar wind density and velocity, shape of a planetary obstacle (e.g., magnetosphere, ionopause), and the loss of planetary pickup ions on the evolution of hydrogen-dominated upper atmospheres. Stellar XUV fluxes that are 1, 10, 50, and 100 times higher compared to that of the present-day Sun were considered, and the formation of high-energy neutral hydrogen clouds around the planets due to the charge-exchange reaction under various stellar conditions was modeled. Charge-exchange between stellar wind protons with planetary hydrogen atoms, and photoionization, lead to the production of initially cold ions of planetary origin. We found that the ion production rates for the studied planets can vary over a wide range, from ∼1.0×1025 s-1 to ∼5.3×1030 s-1, depending on the stellar wind conditions and the assumed XUV exposure of the upper atmosphere. Our findings indicate that most likely the majority of these planetary ions are picked up by the stellar wind and lost from the planet. Finally, we estimated the long-time nonthermal ion pickup escape for the studied planets and compared them with the thermal escape. According to our estimates, nonthermal escape of picked-up ionized hydrogen atoms over a planet's lifetime within the habitable zone of an M dwarf varies between ∼0.4 Earth ocean equivalent amounts of hydrogen (EOH) to <3 EOH and usually is several times smaller in comparison to the thermal atmospheric escape rates. © 2013 Mary Ann Liebert, Inc.

Scopus

Держатели документа:
Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, A-8042 Graz, Austria
Institute of Physics, University of Graz, Graz, Austria
Swedish Institute of Space Physics, Kiruna, Sweden
Institute of Computational Modelling, Siberian Division of the Russian Academy of Sciences, Krasnoyarsk, Russian Federation
SINP, Moscow State University, Moscow, Russian Federation
Polar Geophysical Institute (PGI), Russian Academy of Sciences, Murmansk, Russian Federation
Institute of Astrophysics, University of Vienna, Austria
ИВМ СО РАН

Доп.точки доступа:
Kislyakova, K.G.; Lammer, H.; Holmstrom, M.; Panchenko, M.; Odert, P.; Erkaev, N.V.; Еркаев, Николай Васильевич; Leitzinger, M.; Khodachenko, M.L.; Kulikov, Y.N.; Gudel, M.; Hanslmeier, A.

[Text] / T. Penza [et al.] // Planet Space Sci. - 2008. - Vol. 56, Is. 9. - P1260-1272, DOI 10.1016/j.pss.2008.04.005. - Cited References: 53 . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: We investigate the efficiency of the atmospheric mass loss due to hydrodynamic blow-off over the lifetime of the exoplanet HD209458b by studying numerically its hydrogen wind for host star X-ray and EUV (XUV) fluxes between 1 and 100 times that of the present Sun. We apply a time-dependent numerical algorithm which is able to solve the system of hydrodynamic equations straight through the transonic point of the flow including Roche lobe effects. The mass loss rates are calculated as functions of the absorbed energy in the thermosphere. Depending on the heating efficiency for a hydrogen-rich thermosphere the maximum temperature obtained in our study at 1.5R(p1) by neglecting IR cooling is about 5000-10,000 K for heating efficiencies of 10% and 60%, respectively. We find that the upper atmosphere of HD209458b experiences hydrodynamic blow-off even at such low temperatures if one does not neglect gravitational effects caused by the proximity of the planet to its Roche lobe boundary. Depending on the heating efficiency, we find from the solution of the hydrodynamic equations of mass, momentum, and energy balance that energy-limited mass loss rate estimations overestimate the realistic mass loss rate at present time for HD209458b by several times. Using the maximum heating efficiency for hydrogen-rich atmospheres of 60% we find that HD209458b may experience an atmospheric mass loss rate at present time of about 3.5 x 10(10) g s(-1). The mass loss rate evolves to higher values for higher XUV fluxes expected during the early period of the planet's host star evolution, reaching values of several times 10(12) gs(-1). The integrated mass loss is found to be between 1.8% and 4.4% of the present mass of HD209458b. We found that the influence of the stellar tidal forces on atmospheric loss (the Roche lobe effect) is not significant at 0.045 AU. For a similar exoplanet, but at closer orbital distances <= 0.02 AU, the combined effect of the Roche lobe and the high XUV radiation result in much higher thermal loss rates of about 2.6 x 10(11) g s(-1) and even more for early stages. This leads to a total loss over 4 Gyr of 27.5% of the planetary mass. (c) 2008 Elsevier Ltd. All rights reserved.

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Доп.точки доступа:
Penza, T.; Erkaev, N.V.; Еркаев, Николай Васильевич; Kulikov, Y.N.; Langmayr, D.; Lammer, H.; Micela, G.; Cecchi-Pestellini, C.; Biernat, H.K.; Selsis, F.; Barge, P.; Deleuil, M.; Leger, A.

[Text] / U. V. Amerstorfer [et al.] // Planet Space Sci. - 2007. - Vol. 55, Is. 12. - P1811-1816, DOI 10.1016/j.pss.2007.01.015. - Cited References: 20 . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: In this paper, the Kelvin-Helmholtz instability is studied by solving the ideal MHD equations for a compressible plasma. A transition layer of finite thickness between two plasmas, across which the magnitude of the velocity and the density change, is assumed. Growth rates are presented for the transverse case, i.e., the flow velocity is perpendicular to the magnetic field. If only the velocity changes across the boundary layer and the density is kept constant, an important quantity affecting the growth of the Kelvin-Helmholtz instability is the magnetosonic Mach number, which characterizes compressibility. The growth rates for the case when both, the velocity and the density, change are very sensitive to the ratio of the upper plasma density to the lower plasma density: a decrease of the density ratio yields a decrease of the growth rate. Including a density profile is very important for the application of the Kelvin-Helmholtz instability to the solar wind flow around unmagnetized planets, e.g., Venus, where the plasma density increases from the magnetosheath to the ionosphere. (C) 2007 Elsevier Ltd. All rights reserved.


Доп.точки доступа:
Amerstorfer, U.V.; Erkaev, N.V.; Еркаев, Николай Васильевич; Langmayr, D.; Biernat, H.K.

[Text] / N. V. Erkaev [et al.] // Astron. Astrophys. - 2007. - Vol. 472, Is. 1. - P329-334, DOI 10.1051/0004-6361:20066929. - Cited References: 26 . - ISSN 0004-6361РУБ Astronomy & Astrophysics

Аннотация: Context. A study of the mass loss enhancement for very close "Hot Jupiters" due to the gravitational field of the host star is presented. Aims. The influence of the proximity to a planet of the Roche lobe boundary on the critical temperature for blow-off conditions for estimating the increase of the mass loss rate through hydrodynamic blow-off for close-in exoplanets is investigated. Methods. We consider the gravitational potential for a star and a planet along the line that joins their mass centers and the energy balance equation for an evaporating planetary atmosphere including the effect of the stellar tidal force on atmospheric escape. Results. By studying the effect of the Roche lobe on the atmospheric loss from short-periodic gas giants we derived reasonably accurate approximate formulas to estimate atmospheric loss enhancement due to the action of tidal forces on a "Hot Jupiter" and to calculate the critical temperature for the onset of "geometrical blow-off", which are valid for any physical values of the Roche lobe radial distance. Using these formulas, we found that the stellar tidal forces can enhance the hydrodynamic evaporation rate from TreS-1 and OGLE-TR-56b by about 2 fold, while for HD 209458b we found an enhancement of about 50%. For similar exoplanets which are closer to their host star than OGLE-TR-56b, the mass loss enhancement can be even larger. Moreover, we showed that the effect of the Roche lobe allows "Hot Jupiters" to reach blow-off conditions at temperatures which are less than expected due to the stellar X-ray and EUV heating.


Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Kulikov, Y.N.; Lammer, H.; Selsis, F.; Langmayr, D.; Jaritz, G.F.; Biernat, H.K.

[Text] / M. L. Khodachenko [et al.] // Planet Space Sci. - 2007. - Vol. 55: Symposium on Exoplanets and Planetary Formation (APR 25-30, 2004, Nice, FRANCE), Is. 5. - P631-642, DOI 10.1016/j.pss.2006.07.010. - Cited References: 63 . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: Atmospheric erosion due to CME-caused ion pick-up is investigated here for the first time for short periodic gas giants (so-called "Hot Jupiters") orbiting close to a star, To study the effect of encountering CMEs produced on the inagnetospheres and atmospheres of "Hot Jupiters" we model possible interaction of dense CME plasma with the exoplanet HD209458b (r(pl) = 1.43r(Jup) M(pl) = 0.69 M(jup)), which orbits a 4.0-5.0 Gyr old Sun-like star at a distance of about 0.045 AU. A numerical hydrodynamic model is applied for calculation of the upper atmospheric density and the hydrogen wind of HD209458b Lis a function of planetocentric distance. Taking into account the similarity of HD209458b's host star to Our Sun we use for the study of the ion production and loss rate of H(+) ions the solar CME plasma parameters and apply a numerical test particle model. Tidal-locking of short periodic exoplanets closely located to their host stars should result in weaker intrinsic planetary magnetic moments, as compared to those of the fast rotating Jupiter type planets at much larger orbits. It is shown that in this case the encountering CME plasma can compress the magnetospheric stand-off distance of short periodic "Hot Jupiters" down to the heights Lit which the ionization and pick-LIP of the planetary neutral atmosphere by the CME plasma flow take place. Assuming for the host star of HD209458b the same CME occurrence rate Lis on the Suit, we estimate possible total mass loss rates of HD2094581b due to its collisions with CMEs over the planet lifetime. It has been found that Under different estimations of the value of a planetary magnetic moment, HD209458b Could have lost over its lifetime the mass from 0-2 up to several times of its present mass M(pl). (c) 2006 Elsevier Ltd. All rights reserved.


Доп.точки доступа:
Khodachenko, M.L.; Lammer, H.; Lichtenegger, H.I.M.; Langmayr, D.; Erkaev, N.V.; Еркаев, Николай Васильевич; Griessmeier, J.M.; Leitner, M.; Penz, T.; Biernat, H.K.; Motschmann, U.; Rucker, H.O.

[Text] / G. F. Jaritz [et al.] // Astron. Astrophys. - 2005. - Vol. 439, Is. 2. - P771-775, DOI 10.1051/0004-6361:20052946. - Cited References: 32 . - ISSN 0004-6361РУБ Astronomy & Astrophysics

Аннотация: Theoretical studies and recent observational evidence of the expansion of the atmospheres of short-periodic exoplanets show that the atmospheres extend up to several planetary radii. This indicates that the atmospheres experience blow-off conditions. Because of the short orbital distance to their host stars, the expansion of the upper atmosphere is no longer radially symmetric, but depends on the direction to the central body, resulting in a deformation of the expanded atmosphere. We show the connection between atmospheric expansion, tidal forces and effects of the Roche potential and find that HD209458 b, OGLE-TR-10 b and OGLE-TR-111 b are most likely in a state of classical hydrodynamical blow-off because the distance where blow-off can occur is less than the distance to the Lagrangian point L1. On the other hand, OGLE-TR-56 b, OGLE-TR-113 b, OGLE-TR-132 b and TreS-1 experience a geometrical blow-off defined by the Roche lobe as proposed by Lecavelier des Etangs et al. (2004, A&A, 418, L1). Our results have important implications for the evolution of short periodic gas giants, because the Roche lobe overflow of the atmosphere can lead to lower mass loss rates over the exoplanets history, compared to gas giants which experience hydrodynamic expansion and loss unaffected by this boundary. Thus, massive exoplanets like OGLE-TR-56 b in very close orbital distances are subject to geometrical blow-off conditions, this results in a total mass loss for this particular exoplanet of the order of about 3 x 10(-2) M-pl over the planets age, even if current mass loss rates of about 2 x 10(11) g s(-1) are calculated. If the exoplanet effected by the geometrical blow-off is more massive, the mass loss rate is even lower. However, giant exoplanets like HD209458 b, OGLE-TR-10 b and OGLE-TR-111 b at orbital distances of about 0.05 AU may experience classical hydrodynamic blow-off conditions, which can result in higher mass loss rates. Thus, such planets may shrink to their core sizes during the X-ray and EUV active periods of their host stars as proposed by Lammer et al. ( 2003, ApJ, L121, 598) and Bara. e et al. (2004, A& A, 419, L13).


Доп.точки доступа:
Jaritz, G.F.; Endler, S.; Langmayr, D.; Lammer, H.; Griessmeier, J.M.; Erkaev, N.V.; Еркаев, Николай Васильевич; Biernat, H.K.

[Text] / N. V. Erkaev [et al.] // Astrophys. J. Suppl. Ser. - 2005. - Vol. 157, Is. 2. - P396-401, DOI 10.1086/427904. - Cited References: 48 . - ISSN 0067-0049РУБ Astronomy & Astrophysics

Аннотация: During the past years, more than 130 giant planets were discovered in extrasolar planetary systems. Because of the fact that the orbital distances are very close to their host stars, these planets are embedded in a dense stellar wind, which can pick up planetary ions. We model the stellar wind interaction of the short-periodic exoplanets OGLE-TR-56b and HD 209458b at their orbital distances of approximate to 0.023 AU and approximate to 0.045 AU, by calculating the Alfven Mach number and the magnetosonic Mach number in the stellar wind plasma flow. We then analyze the different plasma interaction regimes around the planetary obstacles, which appear for different stellar wind parameters. Our study shows that the stellar wind plasma parameters like temperature, interplanetary magnetic field, particle density, and velocity near planetary obstacles at orbital distances closer than 0.1-0.2 AU have conditions such that no bow shocks evolve. Our study shows also that these close-in exoplanets are in a submagnetosonic regime comparable to the magnetospheric plasma interaction of the inner satellites of Jupiter and Saturn. Furthermore, we compare the results achieved for both exoplanets with the Jupiter-class exoplanet HD 28185b at its orbital distance of approximate to 1.03 AU. Finally, we also discuss the behavior of the stellar wind plasma flow close to the planetary obstacles of two highly eccentric gas giants, namely, HD 108147b and HD 162020b. Because of their eccentric orbits, these two exoplanets periodically experience both regimes with and without a bow shock. Finally, we simulate the neutral gas density of HD 209458b with a Monte Carlo model. By using the plasma parameters obtained in our study we calculate the ion production and loss rate of H+ with a test particle model. Our simulations yield H+ loss rates for HD 209458b or similar giant exoplanets in orders of about 10(8)-10(9) g s(-1). These ion loss rates are at least 1 order of magnitude lower than the observed loss rate of evaporating neutral H atoms. Our study indicates, that similar gas giants at larger orbital distances have lower ion loss rates. Thus, the dominating component of particle loss of short-periodic Jupiter-class exoplanets will be neutral hydrogen.


Доп.точки доступа:
Erkaev, N.V.; Еркаев, Николай Васильевич; Penz, T.; Lammer, H.; Lichtenegger, H.I.M.; Biernat, H.K.; Wurz, P.; Griessmeier, J.M.; Weiss, W.W.

[Text] / H. Lammer [et al.] // Celest. Mech. Dyn. Astron. - 2005. - Vol. 92, Is. 01.03.2013. - P273-285, DOI 10.1007/s10569-005-0004-4. - Cited References: 27 . - ISSN 0923-2958РУБ Astronomy & Astrophysics + Mathematics, Interdisciplinary Applications

Аннотация: The region around a star where a life-supporting biosphere can evolve is the so-called Habitable Zone (HZ). The current definition of the HZ is based only on the mass-luminosity relation of the star and climatological and meteorological considerations of Earth-like planets, but neglects atmospheric loss processes due to the interaction with the stellar radiation and particle environment. From the knowledge of the planets in the Solar System, we know that planets can only evolve into a habitable world if they have a stable orbit around its host star and if they keep the atmosphere and water inventory during: (i) the period of heavy bombardment by asteroids and comets and (ii) during the host stars' active X-ray and extreme ultraviolet (XUV) and stellar wind periods. Impacts play a minor role for planets with the size and mass like Earth, while high XUV fluxes and strong stellar winds during the active periods of the young host star can destroy the atmospheres and water inventories. We show that XUV produced temperatures in the upper atmospheres of Earth-like planets can lead to hydrodynamic "blow off", resulting in the total loss of the planets water inventory and atmosphere, even if their orbits lie inside the HZ. Further, our study indicates that Earth-like planets inside the HZ of low mass stars may not develop an atmosphere, because at orbital distances closer than 0.3 AU, their atmospheres are highly affected by strong stellar winds and coronal mass ejections (CME's). Our study suggests that planetary magnetospheres will not protect the atmosphere of such planets, because the strong stellar wind of the young star can compress the magnetopause to the atmospheric obstacle. Moreover, planets inside close-in HZ's are tidally locked, therefore, their magnetic moments are weaker than those of an Earth-like planet at 1 AU. Our results indicate that Earth-like planets in orbits of low mass stars may not develop stable biospheres. From this point of view, a HZ, where higher life forms like on Earth may evolve is possibly restricted to higher mass K stars and G stars.


Доп.точки доступа:
Lammer, H.; Kulikov, Y.N.; Penz, T.; Leitner, M.; Biernat, H.K.; Erkaev, N.V.; Еркаев, Николай Васильевич

[Text] / T. Penz [et al.] ; ed.: O. Witasse // PLANETARY ATMOSPHERES, IONOSPHERES, AND MAGNETOSPHERES. Ser. ADVANCES IN SPACE RESEARCH : ELSEVIER SCIENCE LTD, 2005. - Vol. 36: 35th COSPAR Scientific Assembly (JUL 18-25, 2004, Paris, FRANCE), Is. 11. - P2049-2056, DOI 10.1016/j.asr.2004.11.039. - Cited References: 20 . - ISBN 0273-1177РУБ Engineering, Aerospace + Astronomy & Astrophysics + Geosciences, Multidisciplinary + Meteorology & Atmospheric Sciences

Аннотация: It is known from Pioneer Venus measurements that at the Venusian ionopause wave-like structures develop, which can detach in the form of ionospheric plasma clouds. This phenomenon is assumed to occur due to the Kelvin-Helmholtz instability, which can appear in large regions of the Venusian ionopause. Recent studies of Mars Global Surveyor measurements indicate that wave-like structures and plasma clouds also detach from the Martian ionopause. Therefore, these features seem to be common for the solar wind interaction of non-magnetized planets. We study the conditions at the Martian ionopause with respect to the occurrence of several MHD instabilities. The conditions in the magnetosheath are modeled by a semi-analytical MHD simulation that includes mass loading. The ionospheric parameter needed for the model calculations are taken from a global hybrid model. The stability of the Martian ionopause against the Kelvin-Helmholtz, the Rayleigh-Taylor, and the interchange instability is analyzed. Further, we suggest that including the Hall term in the description of the Kelvin-Helmholtz instability gives a current in the planetary boundary layer resulting in a shear flow compared with the ionospheric plasma, which can lead to an unstable boundary layer near the subsolar point. Since the interchange instability depends on the curvature of the magnetic field lines, we additionally study the influence of the strong curvature of the Martian ionopause due to the localized, remnant, crustal magnetism appearing mainly in the southern hemisphere of Mars. (c) 2004 COSPAR. Published by Elsevier Ltd. All rights reserved.


Доп.точки доступа:
Penz, T.; Arshukova, I.L.; Terada, N.; Shinagawa, H.; Erkaev, N.V.; Еркаев, Николай Васильевич; Biernat, H.K.; Lammer, H.; Witasse, O. \ed.\

[Text] / M. Blanc, R. Kallenbach, N. V. Erkaev // Space Sci. Rev. - 2005. - Vol. 116: Workshop on Comparative Study of the Outer Planets before the Exploration of Saturn (JAN 12-14, 2004, Bern, SWITZERLAND), Is. 01.02.2013. - P227-298, DOI 10.1007/s11214-005-1958-y. - Cited References: 202 . - ISSN 0038-6308РУБ Astronomy & Astrophysics

Аннотация: This article proposes a short review of our present knowledge of solar system magnetospheres, with the purpose of placing the study of Saturn's inagnetosphere in the context of a comparative approach. We describe the diversity of solar system magnetospheres and the underlying causes of this diversity: nature and magnetization state of the planetary obstacle, presence or not of a dense atmosphere, rotation state of the planet, existence of a system of satellites, rings and neutral gas populations in orbit around the planet. We follow the "russian doll" hierarchy of solar system magnetospheres to briefly describe the different objects of this family: the heliosphere, which is the Sun's magnetosphere; the "elementary" magnetospheres of the inner planets, Earth and Mercury; the "complex" magnetospheres of the giant planets, dominated by planetary rotation and the presence of interacting objects within their magnetospheric cavities, some of which, like Ganymede, to or Titan, produce small intrinsic or induced magnetospheres inside the large one. We finally describe the main original features of Saturn's magnetosphere as we see them after the Voyager fly-bys and before the arrival of Cassini at Saturn, and list some of the key questions which Cassini will have to address during its four-year orbital tour.


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Blanc, M.; Kallenbach, R.; Erkaev, N.V.; Еркаев, Николай Васильевич

[Text] / I. L. Arshukova [et al.] ; ed. E. Kallio // PLANETARY ATMOSPHERES, IONOSPHERES AND PLASMA INTERACTIONS. Ser. ADVANCES IN SPACE RESEARCH : PERGAMON-ELSEVIER SCIENCE LTD, 2004. - Vol. 33: 2nd World Space Congress/34th COSPAR Scientific Assembly (OCT 10-19, 2002, HOUSTON, TEXAS), Is. 2. - P182-186, DOI 10.1016/j.asr.2003.04.015. - Cited References: 12 . - ISBN 0273-1177РУБ Engineering, Aerospace + Astronomy & Astrophysics + Geosciences, Multidisciplinary + Meteorology & Atmospheric Sciences

Аннотация: Within the magnetohydrodynamic (MHD) approach, the interchange instability is studied for the subsolar magnetosheath of Venus. The instability analysis considers the profiles of magnetic field and plasma parameters between the bow shock and the ionopause which are obtained from the numerical MHD solution of the solar wind flow around the ionosphere. With the Fourier transformations, the linearized MILD equations are reduced to a second-order differential equation for the total pressure perturbation as a function of the normal distance from the ionopause. This equation is integrated numerically, and the interchange instability growth rate is obtained as a function of the wave number. The instability growth time is found to be smaller than the time scale of magnetic barrier formation. (C) 2003 COSPAR. Published by Elsevier Ltd. All rights reserved.


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Arshukova, I.L.; Erkaev, N.V.; Еркаев, Николай Васильевич; Biernat, H.K.; Vogl, D.F.; Kallio, E. \ed.\

[Text] / H. K. Biernat [et al.] // Nonlinear Process Geophys. - 2000. - Vol. 7: 24th General Assembly of the European-Geophysical-Society (APR 19-23, 1999, THE HAGUE, NETHERLANDS), Is. 03.04.2013. - P201-209. - Cited References: 34 . - ISSN 1023-5809РУБ Geochemistry & Geophysics + Meteorology & Atmospheric Sciences

Аннотация: The study of the interaction of the solar wind with magnetized and unmagnetized planets forms a central topic of space research. Focussing on planetary magnetosheaths, we review some major developments in this field. Magnetosheath structures depend crucially on the orientation of the interplanetary magnetic field, the solar wind Alfven Mach number, the shape of the obstacle (axisymmetric/non-axisymmetric, etc.), the boundary conditions at the magnetopause (low/high magnetic shear), and the degree of thermal anisotropy of the plasma. We illustrate the cases of Earth, Jupiter and Venus. The terrestrial magnetosphere is axisymmetric and has been probed in situ by many spacecraft. Jupiter's magnetosphere is highly non-axisymmetric. Furthermore, we study magnetohydrodynamic effects in the Venus magnetosheath.


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Biernat, H.K.; Erkaev, N.V.; Еркаев, Николай Васильевич; Farrugia, C.J.; Vogl, D.F.; Schaffenberger, W.

[Text] / C. J. Farrugia, H. K. Biernat, N. V. Erkaev // Planet Space Sci. - 1998. - Vol. 46, Is. 5. - P507-514, DOI 10.1016/S0032-0633(97)00225-0. - Cited References: 20 . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: The solar wind flow past nonaxisymmetric magnetospheres exhibits features which are absent in the case of axisymmetric magnetospheres such as that of Earth. We discuss results obtained by a numerical integration of the dissipationless MHD equations, under simplifying assumptions, and apply them to the two outer planets Jupiter and Saturn, both of whose magnetospheres depart substantially from axisymmetry. We model these magnetospheres as paraboloids with two different radii of curvature at the subsolar point, L-0 and L-1, where L-0 and L-1 refer to a magnetopause cut containing the rotational axis, and to the rotational equator, respectively (L-0 L-1). The degree of flattening is expressed by a parameter q :


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Farrugia, C.J.; Biernat, H.K.; Erkaev, N.V.; Еркаев, Николай Васильевич

[Text] / C. J. Farrugia, H. K. Biernat, N. V. Erkaev // PLANETARY IONOSPHERES AND MAGNETOSPHERES. Ser. ADVANCES IN SPACE RESEARCH-SERIES : PERGAMON PRESS LTD, 1997. - Vol. 20: C3.2 Symposium of COSPAR Scientific Commission C on Planetary Ionospheres and Magnetospheres, at the 31st COSPAR Scientific Assembly (JUL 14-21, 1996, BIRMINGHAM, ENGLAND), Is. 2. - P209-213, DOI 10.1016/S0273-1177(97)00535-8. - Cited References: 15 . - ISBN 0273-1177. - ISBN 0-08-043297-2РУБ Engineering, Aerospace + Astronomy & Astrophysics + Geosciences, Multidisciplinary + Meteorology & Atmospheric Sciences

Аннотация: We discuss results on the solar wind flow past the non-axisymmetric magnetospheres of planets Jupiter and Saturn obtained by integrating numerically the dissipationless MHD equations under simplifying assumptions. We model these equatorially broadened magnetospheres as paraboloids with two different radii of curvature at the subsolar point. The thickness of the magnetosheath and the width and structure of the plasma depletion layer are found to be strong functions of the orientation of the interplanetary magnetic field (IMF). The effect of the IMF on the magnetosheath is strongest (weakest) when the IMF is directed perpendicular (parallel) to the rotational equator. For any intermediate IMF orientation, a smooth rotation of the magnetosheath magnetic field towards the direction of the planet's rotational axis is superimposed on the field strength enhancement (and the density reduction) as the respective magnetopauses are approached. These effects are more pronounced at Jupiter than at Saturn. (C) 1997 COSPAR. Published by Elsevier Science Ltd.


Доп.точки доступа:
Farrugia, C.J.; Biernat, H.K.; Erkaev, N.V.; Еркаев, Николай Васильевич

[Text] / H. . Lammer [et al.] // Astron. Astrophys. - 2009. - Vol. 506, Is. 1. - P399-410, DOI 10.1051/0004-6361/200911922. - Cited References: 46. - The authors thank the anonymous referee for constructive comments and suggestions which helped to improve the paper. H. Lammer, P. Odert, M. Leitzinger, M. L. Khodachenko and A. Hanslmeier gratefully acknowledge the Austrian Fonds zur Forderung der wissenschaftlichen Forschung (FWF grant P19446) for supporting this project. M. Panchenko and M. L. Khodachenko acknowledge also the Austrian Fonds zur Forderung der wissenschaftlichen Forschung (project P20680-N16). H. Lammer, H. I. M. Lichtenegger, H. K. Biernat, Yu. N. Kulikov and N. V. Erkaev thank the AAS "Verwaltungsstelle fur Auslandsbeziehungen" and the RAS. H. Lammer, H. I. M. Lichtenegger, M. L. Khodachenko and Yu. N. Kulikov acknowledge support from the Helmholtz-Gemeinschaft as this research has been supported by the Helmholtz Association through the research alliance "Planetary Evolution and Life". H. Lammer, M. L. Khodachenko, T. Penz, and Yu. N. Kulikov also acknowledge the International Space Science Institute (ISSI; Bern, Switzerland) and the ISSI teams "Evolution of Habitable Planets" and "Evolution of Exoplanet Atmospheres and their Characterization". H. K. Biernat acknowledges additional support due to the Austrian Science Fund under project P20145-N16. The authors also acknowledge fruitful discussions during various meetings related to the Europlanet N2 activities as well as within the N2 Exoplanet discipline working group DWG 7. T. Penz and G. Micela acknowledge support by the Marie Curie Fellowship Contract No. MTKD-CT-2004-002769 of the project "The influence of stellar high radiation on planetary atmospheres". The authors also thank the Austrian Ministry bm:bwk and ASA for funding the CoRoT project. . - ISSN 0004-6361РУБ Astronomy & Astrophysics

Аннотация: Aims. We study the possible atmospheric mass loss from 57 known transiting exoplanets around F, G, K, and M-type stars over evolutionary timescales. For stellar wind induced mass loss studies, we estimate the position of the pressure balance boundary between Coronal Mass Ejection (CME) and stellar wind ram pressures and the planetary ionosphere pressure for non- or weakly magnetized gas giants at close orbits. Methods. The thermal mass loss of atomic hydrogen is calculated by a mass loss equation where we consider a realistic heating efficiency, a radius-scaling law and a mass loss enhancement factor due to stellar tidal forces. The model takes into account the temporal evolution of the stellar EUV flux by applying power laws for F, G, K, and M-type stars. The planetary ionopause obstacle, which is an important factor for ion pick-up escape from non- or weakly magnetized gas giants is estimated by applying empirical power-laws. Results. By assuming a realistic heating efficiency of about 10-25% we found that WASP-12b may have lost about 6-12% of its mass during its lifetime. A few transiting low density gas giants at similar orbital location, like WASP-13b, WASP-15b, CoRoT-1b or CoRoT-5b may have lost up to 1-4% of their initial mass. All other transiting exoplanets in our sample experience negligible thermal loss (<= 1%) during their lifetime. We found that the ionospheric pressure can balance the impinging dense stellar wind and average CME plasma flows at distances which are above the visual radius of "Hot Jupiters", resulting in mass losses <2% over evolutionary timescales. The ram pressure of fast CMEs cannot be balanced by the ionospheric plasma pressure for orbital distances between 0.02-0.1 AU. Therefore, collisions of fast CMEs with hot gas giants should result in large atmospheric losses which may influence the mass evolution of gas giants with masses
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Доп.точки доступа:
Lammer, H.; Odert, P.; Leitzinger, M.; Khodachenko, M.L.; Panchenko, M.; Kulikov, Y.N.; Zhang, T.L.; Lichtenegger, H.I.M.; Erkaev, N.V.; Еркаев, Николай Васильевич; Wuchterl, G.; Micela, G.; Penz, T.; Biernat, H.K.; Weingrill, J.; Steller, M.; Ottacher, H.; Hasiba, J.; Hanslmeier, A.; Austrian Fonds zur Forderung der wissenschaftlichen Forschung [P19446, P20680-N16]; Helmholtz Association; Austrian Science Fund [P20145-N16]; "The influence of stellar high radiation on planetary atmospheres" [MTKD-CT-2004-002769]

[Text] / K. G. Kislyakova [et al.] // Astron. Astrophys. - 2014. - Vol. 562. - Ст. A116, DOI 10.1051/0004-6361/201322933. - Cited References: 45. - K.G. Kislyakova, C.P. Johnstone, M.L. Khodachenko, H. Lammer, T. Luftinger and M. Gudel acknowledge the support by the FWF NFN project S116601-N16 "Pathways to Habitability: From Disks to Active Stars, Planets and Life", and the related EWE NFN subprojects, S116 604-N16 "Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond". 5116 606-N16 "Magnetospheric Electrodynamics of Exoplanets", and S116607-N16 "Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions". T. Luftinger acknowledges also the support by the FWF project P19962-N16. K. G. Kislyakova, H. Lammer, and P. Odert thank also the Helmholtz Alliance project "Planetary Evolution and Life". P. Odert acknowledges support from the EWE project P22950-N16. The authors also acknowledge support from the EU FP7 project IMPEx (No.262863) and the EUROPLANET-RI projects, JRA3/EMDAF and the Na2 science WG5. N. V. Erkaev acknowledges support by the RFBR grant No 12-05-00152-a. Finally, the authors thank the International Space Science Institute (ISSI) in Bern, and the ISSI team "Characterizing stellar- and exoplanetary environments". This research was conducted using resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North (HPC2N). The authors thank also the anonymous referee for his useful comments. . - ISSN 0004-6361. - ISSN 1432-0746РУБ Astronomy & Astrophysics

Аннотация: Aims. We study the interactions between stellar winds and the extended hydrogen-dominated upper atmospheres of planets. We estimate the resulting escape of planetary pick-up ions from the five "super-Earths" in the compact Kepler-11 system and compare the escape rates with the efficiency of the thermal escape of neutral hydrogen atoms. Methods. Assuming the stellar wind of Kepler-11 is similar to the solar wind, we use a polytropic ID hydrodynamic wind model to estimate the wind properties at the planetary orbits. We apply a direct simulation Monte Carlo model to model the hydrogen coronae and the stellar wind plasma interaction around Kepler-11b-f within a realistic expected heating efficiency range of 15-40%. The same model is used to estimate the ion pick-up escape from the XUV heated and hydrodynamically extended upper atmospheres of Kepler-11b-f. From the interaction model, we study the influence of possible magnetic moments, calculate the charge exchange and photoionization production rates of planetary ions, and estimate the loss rates of pick-up H+ ions for all five planets. We compare the results between the five "super-Earths" and the thermal escape rates of the neutral planetary hydrogen atoms. Results. Our results show that a huge neutral hydrogen corona is formed around the planet for all Kepler-11b-f exoplanets. The non-symmetric form of the corona changes from planet to planet and is defined mostly by radiation pressure and gravitational effects. Non-thermal escape rates of pick-up ionized hydrogen atoms for Kepler-11 "super-Earths" vary between similar to.6.4x10(30) s(-1) and similar to 4.1 x10(31) s(-1), depending on the planet's orbital location and assumed heating efficiency. These values correspond to non-thermal mass loss rates of similar to 1.07 x 10(7) g s(-1) and similar to 6.8 x 10(2) g s(-1) respectively, which is a few percent of the thermal escape rates.

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Доп.точки доступа:
Kislyakova, K.G.; Johnstone, C.P.; Odert, P.; Erkaev, N.V.; Еркаев, Николай Васильевич; Lammer, H.; Luftinger, T.; Holmstrom, M.; Khodachenko, M.L.; Guedel, M.; FWF NFN project [S116601-N16]; EWE NFN subprojects T Tauri Phase [S116 604-N16]; "Magnetospheric Electrodynamics of Exoplanets" [5116 606-N16]; "Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions" [S116607-N16]; FWF project [P19962-N16]; EWE project [P22950-N16]; EU [262863]; EUROPLANET-RI projects [JRA3/EMDAF, Na2 science WG5]; RFBR [12-05-00152-a]

[Text] / N. V. Erkaev [et al.] // Planet Space Sci. - 2014. - Vol. 98. - P. 106-119, DOI 10.1016/j.pss.2013.09.008. - Cited References: 94. - P. Odert, H. Lammer, K. G. Kislyakova and Yu. N. Kulikov acknowledge support from the Helmholtz Alliance project "Planetary Evolution and Life". E. Dorfi, M. Gudel, K. G. Kislyakova, H. Lammer, A. Stokl and E. A. Dorfi acknowledge the Austrian Science Fund (FWF) for supporting this study via the FWF NFN project S116 "Pathways to Habitability: From Disks to Active Stars, Planets and Life", and the related FWF NFN subprojects, S 116 02-N1 "Hydrodynamics in Young Star-Disk Systems", S116 604-N16 "Radiation & Wind Evolution from T Tauri Phase to ZAMS and Beyond", and S11607-N16 "Particle/Radiative Interactions with Upper Atmospheres of Planetary Bodies Under Extreme Stellar Conditions". M. Leitzinger and P. Odert also acknowledge the support from the FWF project P22950-N16. N. V. Erkaev acknowledges support by the RFBR Grant no 12-05-00152-a. Finally, H. Lammer thanks M. lkoma from the Department of Earth and Planetary Science, of the University of Tokyo, Japan, for discussions related to the accumulation of nebular-based hydrogen envelopes around Mars-mass bodies. Finally the authors thank an anonymous referee for the interesting and important suggestions and recommendations that helped to improve the results of our study. . - ISSN 0032-0633РУБ Astronomy & Astrophysics

Аннотация: Latest research in planet formation indicates that Mars formed within a few million years (Myr) and remained as a planetary embryo that never grew to a more massive planet. It can also be expected from dynamical models that most of Mars' building blocks consisted of material that formed in orbital locations just beyond the ice line which could have contained similar to 0.1-0.2 wt.% of H2O. By using these constraints, we estimate the nebula-captured and catastrophically outgassed volatile contents during the solidification of Mars' magma ocean and apply a hydrodynamic upper atmosphere model for the study of the soft X-ray and extreme ultraviolet (XUV) driven thermal escape of the martian protoatmosphere during the early active epoch of the young Sun. The amount of gas that has been captured from the protoplanetary disk into the planetary atmosphere is calculated by solving the hydrostatic structure equations in the protoplanetary nebula. Depending on nebular properties such as the dust grain depletion factor, planetesimal accretion rates and luminosities, hydrogen envelopes with masses >= 3 x 10(19) g to <= 6.5 x 10(22) g could have been captured from the nebula around early Mars. Depending on the before mentioned parameters, due to the planets low gravity and a solar XUV flux that was similar to 100 times stronger compared to the present value, our results indicate that early Mars would have lost its nebular captured hydrogen envelope after the nebula gas evaporated, during a fast period of similar to 0.1-7.5 Myr. After the solidification of early Mars' magma ocean, catastrophically outgassed volatiles with the amount of similar to 50-250 bar H2O and similar to 10-55 bar CO2 could have been lost during similar to 0.4-12 Myr, if the impact related energy flux of large planetesimals and small embryos to the planet's surface lasted long enough, that the steam atmosphere could have been prevented from condensing. If this was not the case, then our results suggest that the timescales for H2O condensation and ocean formation may have been shorter compared to the atmosphere evaporation timescale, so that one can speculate that sporadically periods, where some amount of liquid water may have been present on the planet's surface. However, depending on the amount of the outgassed volatiles, because of impacts and the high XUV-driven atmospheric escape rates, such sporadically wet surface conditions may have also not lasted much longer than similar to 0.4-12 Myr. After the loss of the captured hydrogen envelope and outgassed volatiles during the first 100 Myr period of the young Sun, a warmer and probably wetter period may have evolved by a combination of volcanic outgassing and impact delivered volatiles similar to 4.0 +/- 0.2 Gyr ago, when the solar XUV flux decreased to values that have been <10 times that of today's Sun. (C) 2013 Elsevier Ltd. All rights reserved.

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Erkaev, N.V.; Еркаев, Николай Васильевич; Lammer, H.; Elkins-Tanton, L.T.; Stokl, A.; Odert, P.; Marcq, E.; Dorfi, E.A.; Kislyakova, K.G.; Kulikov, Y.N.; Leitzinger, M.; Gudel, M.; Helmholtz Alliance project "Planetary Evolution and Life"; Austrian Science Fund (FWF); Austrian Science Fund (FWF) via the FWF NFN project [S116]; FWF NFN subprojects [S 116 02-N1, S116 604-N16, S11607-N16]; FWF project [P22950-N16]; RFBR [12-05-00152-a]