Magnetospheric electrodynamics of exoplanets (II)
Summary
Investigation of key factors and physical mechanisms which determine the structure, topology and dynamics of exoplanetary magnetospheres and their role in the evolution of planetary atmospheric environments and habitability, formed the focus of project. This goal is connected with the study of the whole complex of stellar-planetary interactions, as well as additional factors, e.g. stellar radiation and wind, circumplanetary dust, planetary magnetic field, considered over the planet history time scales. Special attention was paid to development of theoretical approaches and modelling tools for simulation of exoplanetary magnetized environments and understanding of their observational manifestation.
The work in SP06 comprised simultaneous research in two basic directions. First direction includes the investigation of structure and large-scale features of exoplanetary magnetospheres, taking into account the effects of escaping planetary upper atmospheric material and its interaction with the stellar winds. This work involved application of the paraboloid magnetosphere model (PMM) of an exoplanet (Khodachenko et al. 2012) complimented with a dedicated study of upper atmosphere aeronomy related with the expansion and mass loss. The latter was based on hydrodynamic and magnetohydrodynamic (HD/MHD) models of the expanding exoplanetary atmospheres in the presence planetary magnetic field and stellar wind flow. Second direction deals with development of deep insight into physics and fine structure of the magnetospheric current system, e.g., thin current sheets of magnetodisk and magnetotail, using the methods of plasma kinetic theory. This required elaboration of special approaches (Sasunov et al., 2015a,b,c), which go beyond the traditional MHD used for the description of escaping magnetized planetary winds. As result, a way for analytic self-consistent description of charged particles motion in key regions of exoplanetary magnetosphere current systems has been elaborated (Sasunov et al. 2015b, 2017, 2018).
Regarding possible observational manifestations of the dynamical processes in exoplanetary magnetospheres and near-by plasma environments, the transit spectral absorption features (e.g., Khodachenko et al. 2017) and the efficiency of the electron cyclotron maser instability (ECMI) mechanism of radio emission, as well as the conditions for its escape, were investigated (Weber et al. 2017). The need to quantify the stellar XUV impact on exoplanetary environments lead to development of a proxy approach for the stellar X-ray/EUV luminosity (Arkhypov et al. 2018), whereas complex dynamical multicomponent media around exoplanets and especially the circumplanetary dust contaminations were probed by the analysis of anomalous features and asymmetries in the optical transit light-curves. This project work was done jointly with other NFN subprojects (e.g., SP04, SP07) and collaborating FWF projects (P25587-N27, I2939-N27).
Scientific background and aims of research
The close location of giant exoplanets, so-called hot Jupiters (HJs), to host stars leads to intensive heating and ionization of their upper atmospheres by the stellar X-ray/EUV (XUV) radiation, resulting sometimes in hydrodynamic (HD) escape of the ionized atmospheric material in the form of expanding planetary wind (PW), which contributes to the so-called thermal mass loss of the planetary atmosphere. In the region of interaction of the expanding PW with the stellar wind (SW) the escaping particles are picked up by the SW, resulting in a non-thermal mass loss. In fact, both kinds of the mass loss operate together and have to be treated simultaneously in a unified manner, taking into account the self-consistent generation of the escaping PW and its interaction with the incoming SW, including the effects of the planetary and stellar magnetic fields and gravitational force. This constitutes the global problem, which was tacked within SP06. The expanded atmospheres and escaping PW have been studied by means of HD models in Yelle (2004), Tian et al. (2005), García Muñoz (2007), Erkaev et al. (2005, 2007), Murray-Clay et al. (2009), Guo (2011, 2013), and Koskinen et al. (2010, 2013).. The work of SP06 in that respect was aimed at development of a set of fully self-consistent 1D, 2D and 3D multi-fluid HD models, which include the hydrogen and helium plasma photo-chemistry, self-consistent XUV radiation energy input to the upper atmosphere of planets, effects of gravity, and the SW plasma flow.
The present day extensive study of the Solar system planetary magnetospheres provides important background for investigation of exoplanetary magnetospheres. However, the ‘solar’-‘extrasolar’ analogy still remains very limited and must be applied with caution. The influence of magnetic field has two major aspects. First, the large-scale fields and related electric currents form the planetary magnetosphere which acts as a barrier for SW and protects the ionosphere and upper atmosphere of planet against direct impact of SW plasma (Khodachenko et al. 2007a,b; Khodachenko et al. 2012). Second, the magnetic field in inner part of planetary magnetosphere affects the expanding PW plasma and its further interaction with SW, being at the same time influenced by the moving plasma (Trammell et al. 2011; Owen and Adams 2014; Khodachenko et al. 2015). Detailed investigation of these processes in the context of escaping planetary atmospheres and mass loss was among the strategic goals, aimed in SP06. Particular attention was paid to evaluation of the role of the magnetosphere scaling and the equatorial magnetodisk, as well as the associated “dead-“ / “wind-“ zones (Mestel 1968; Trammel et al. 2014; Owen and Adams 2014; Khodachenko et al. 2015) in the planetary mass loss. The treatment of magnetic field effects in the context of interacting PW and SW requires development of a global self-consistent multi-fluid 3D MHD model of the stellar-planetary system, hitherto not existing. The work performed in SP06 (jointly with FWF project I2939-N27) on development of such kind 3D HD model (Shaikhislamov et al. 2018a), as well as the combined modelling approach based on 3D hybrid and PMM numerical concepts (Parunakian et al. 2017; Alexeev et al. 2018), together with the 2D MHD model by Khodachenko et al. (2015) appear a crucial step on this way.
The development of a consistent approach to the description and modelling of exoplanetary magnetospheres with inclusion of an appropriate physics requires an account of multi-scale specifics of the problem. HD/MHD models give only a global large-scale picture of the stellar-planetary interaction and roughly indicate the location and topology of major elements of the planetary magnetospheric current system (e.g., magnetotail, magnetopause, magnetodisk), not being able to resolve their real fine structure. The kinetic effects of magnetized charged particles motion appear of crucial importance for the structuring, scaling and energetics of these fundamental magnetospheric components. The particular goal of SP06 in that respect was to understand the macro- and micro- scalings in exoplanetary magnetospheres in their mutual relation. The research scope included comparative study of the magnetosphere sizes (macro-scale) under different stellar activity and SW conditions, to conclude on magnetospheric protection and possible evolution scenarios for the terrestrial planets’ atmospheres, as a crucial factor of planetary habitability. This approach was applied to ancient Terrestrial and Martian magnetospheres under the conditions of young Sun to shed light on the atmospheres’ evolutional pathways. Complimentary to that, a novel approach, based on the analysis of charged particles trajectories in the self-consistent magnetic field (Sasunov et al. 2015a,b, 2017, 2018) has been elaborated in SP06, to investigate physical backgrounds and fine structure (micro-scale) of current sheets of exopanetary magnetotails, and magnetodisks, confirmed with laboratory experiments and MHD models (Antonov et al. 2013; Khodachenko et al. 2015).
Another challenge concerns a possibility of observational characterization of exoplanetary magnetospheric phenomena. In that respect the task for scientists consists in further identification and investigation of the potential observables, among which planetary radio emission (e.g., Zarka 2007) and in-transit spectral absorption (e.g., Linsky et al. 2010; Vidal-Madjar et al. 2013) are considered. SP06, jointly with SP04, SP07 and the partner FWF project I2939-N27, studied the efficiency of ECMI mechanism of radio emission on HJs and the conditions for the radiation escape (Weber et al. 2017). Another direction was the model-based characterization the in-transit spectral absorption (Kislyakova et al. 2014; Khodachenko et al. 2017; Shaikhislamov et al. 2018b; Dwivedi et al., 2019)
Results and discussion of results
The work in SP06 went in two basic directions: First, investigation and modelling of the dynamics and large-scale structuring of exoplanetary near-by multicomponent plasma environments taking account of magnetic field effects, stellar radiation and SW; Second, the development of deep insight in fine structure and electrodynamics of the magnetospheric current system elements. In both cases, special attention was paid to identifying and characterization of the potentially observable phenomena.
Within the scope of first direction, primary goal was to gain better understanding of the large-scale structure of close-orbit exoplanetary magnetospheres affected by the expanding PWs.
Magnetodisk-dominated magnetospheres of HJs and their macro-scaling. A more complete view of magnetosphere of a close-orbit giant exoplanet, based on the Paraboloid Magnetospheric Model (PMM), was proposed (Khodachenko et al. 2012). Besides of intrinsic planetary magnetic dipole, PMM includes the electric current systems of magnetotail, magnetopause, and wagnetodisk. The key novel element of the considered model consists in the account of effects of HJ’s expanding upper atmosphere heated by stellar XUV radiation. The escaping atmospheric material is ionized and builds an extended magnetodisk around the planet which determines the magnetosphere size. A slower, than dipole-type decrease of the magnetic field with distance constitutes an essential specifics of the magnetodisk-dominated magnetospheres of HJs, which are 40 - 70 % larger, as compared to the traditionally considered dipole-type magnetospheres. Such larger magnetospheres provide better protection of close-orbit planets against extreme SWs. Additionally, the scaling of inner edges of different types of astrophysical disks, incl. exoplanetary magnetodisks, was studied to conclude on their common features caused by magnetic field of disk hosting object (Belenkaya & Khodachenko 2012, Belenkaya et al. 2012, 2015).
Laboratory simulations of HJ’s magnetodisk formation. To verify the idea of an inflated magnetodisk-dominated magnetosphere of HJ, formed under conditions of an expanding PW in the background planetary dipole magnetic field, a dedicated laboratory experiment has been performed (Antonov et al. 2013). The vacuum chamber KI-1 at the collaborating partner Institute of Laser Physics of the Russian Academy of Sciences was used for this study. The measured magnetic field, electric current, and plasma density (Fig.SP06-1) indicate formation of a thin current disk extending beyond the Alfvénic point. At the edge of disk, the induced magnetic field was found to be several times larger than the field of dipole source. This experiment confirms the theoretically expected (Mestel 1968, Kodachenko et al. 2012) specific distortion of the dipole field topology in the magnetosphere of HJ under the conditions of expanding PW.
Self-consistent HD/MHD modelling of the HJs’ PW and plasma environments. A series of numerical self-consistent models has been developed in SP06 to simulate the processes of XUV heating, ionization and expansion of exoplanetary upper atmospheres including the consequent interaction of escaping PW with the magnetic field of planetary dipole and SW. Besides of revealing of details of exoplanetary magnetosphere structure, the goal was to simulate the dynamics of complex multicomponent environments of close-orbit exoplanets and their mass loss. To investigate the role of different physical effects and conditions, potentially affecting the process of atmospheric escape, formation of inner magnetosphere, and mass loss, SP06 started with 1D HD multi-fluid model of an expanding upper atmosphere (Shaikhislamov et al. 2014). The focus was on self-consistent inclusion of the XUV radiative heating and ionization of the atmospheric gas with its consequent escape in the outer space with the inclusion of H3+ cooling, adiabatic and Lyα cooling, Lyα reabsorption and radiation pressure effects.
As a next step, the HD model of expanding exoplanetary atmosphere was generalized to the case of a magnetized planet, to study the topology of inner magnetosphere, escaping PW, and mass loss. This self-consistent axisymmetric 2D MHD model, besides of the above mentioned features of 1D model, includes the basic hydrogen chemistry, realistic solar-type XUV spectrum, as well as the gravitational and rotational forces acting in the tidally locked planet-star systems (Khodachenko et al. 2015). The formation of a current-carrying magnetodisk and its cyclic behavior were discovered and investigated (Fig. SP06-2). The mass loss rate of a typical HJ, analogous to HD209458b, but was found to be strongly affected by m.field exceeding 0.3 Gauss.
To investigate the effect of incoming SW on the escape regimes of expanding PW for sufficiently close star-planet systems, the self-consistent multi-fluid 1D HD model was upgraded to the 2D one with the inclusion of SW plasma flow (Shakhislamov et al. 2016, Khodachenko et al. 2017, Dwivedi et al., 2019). This work, as well as further development of a global 3D HD model of the whole star-planet system with self-consistent aeronomy and SW modelling blocks (Shakhislamov et al. 2018a, Berezutsky et al., 2018, Khodachenko et al. 2019) has been done in collaboration with FWF-RFBR project I2939-N27. It has been shown for the first time that the ENAs, crucial for the interpretation of Lyα in-transit absorption of HJs and warm Neptunes, produced due to charge exchange between PW atoms and SW protons, are generated in the region between the ionopause and bow-shock (Fig.SP06-3) where high densities of the interacting components are provided (Khodachenko et al. 2017).
Terrestrial-type PMM – implications to atmospheric evolution. The PMM of Terrestrial paleo-magnetosphere for the late Hadean eon (~4.1 Gyr ago) was developed. The model runs were performed with different measured ancient Terrestrial dipole field varying between 12% and 100% of the present day value (Tarduno et al. 2010) with account of ancient SW data. The simulations show that Terrestrial magnetopause stand-off distance, RsE, was significantly smaller (as compared to the present-day value), varying from 3.43RE for the most extreme Hadean conditions (i.e., small dipole field, fast and dense SW) to 9.17RE for the least extreme case. The modelling also reveals that the polar caps were significantly broader than at present day and they affected the ion outflow via the poles. The latter was in the range from 20 to 500 times of the present day value for the slow rotating Sun and present day dipole and fast rotating Sun and 12% of the present day dipole, respectively. The PMM was also adapted to perform analogous simulations of the ancient Martian magnetosphere for 4.1-3.6 Gyr ago, depending on rotation rate of the early Sun and the strength of the ancient dipole field. The obtained results are relevant to the terrestrial type exoplanets in the habitable zones of Sun-like stars.
Combined 3D PMM-Hybrid model of planetary magnetospheres. A novel approach to 3D modelling of planetary magnetospheres that involves a combination of the hybrid modelling concept (kinetics - for ions and heavy particles, fluid approximation - for electrons) and the PMM model has been elaborated jointly with the international cooperating partners from Moscow State University (Russia) and Aalto University (Finland). While both of the individual models have been applied in the past, their combination enabled overcoming of the known difficulty of hybrid models in revealing of self-consistent magnetic field and compensated the lack of plasma simulation in PMM. The combined model has been shown to reproduce the magnetosphere and magnetosheath of Mercury (as a prototype of a moderately close-orbit magnetized rocky exoplanet) controlled by the interplanetary medium conditions (Parunakian et al. 2017, Alexeev et al. 2018). The locations of bowshock and magnetopause determined in the simulations (Fig.SP06-4) were compared with measurements of the MESSENGER on-board magnetometers. The combined PMM-hybrid model was further applied to study plasma environment of ancient Mars and its magnetosphere under the conditions of slow rotating Sun for ~4.3 Gyr and ~3.8 Gyr ago, with 20 and 10 times higher EUV flux than that of the present day, respectively. The losses of C and O from the ancient Martian atmosphere were shown to increase with the increasing solar EUV flux.
Within the scope of second research direction, the motion of particles inside a symmetric current sheet (CS) has been investigated.
Particle trajectory method for self-consistent thin current sheets. Based on particle trajectories analysis, analytic solutions for the electric current density and plasma parameters in a thin current sheet (TCS) were obtained and compared with the results of numerical simulations. The particle trajectories have been initially calculated for a cold plasma assumption, i.e. neglecting the effects of the velocity thermal dispersion, and later were extended to the case of hot plasma (Sasunov et al. 2015a). It was shown that the TCS structure strongly depends on particle pitch-angle distribution and is determined by the competing diamagnetic and paramagnetic currents. The obtained analytic expression for TCS scaling agreed in the limiting cases with known estimates derived under more general assumptions. The proposed model describes well the observed characteristics of plasma layer in case when its current is created by contrstreaming particles with the same pitch-angle (Sasunov et al. 2015b). Based on conservation of particle magnetic moment, an analytic relation between the incoming particles flow velocity and plasma density in a TCS was obtained. This relation was confirmed with a dedicated PIC modeling (Sasunov et al. 2017). Further on, the particles motion in a strong gradient of magnetic field has been investigated. By inclusion of the effects of velocity thermal dispersion in the self-consistent description it was possible to generalize the TCS models to the case of arbitrary particle distribution functions.
Self-consistent description of particle kinetics in CS. A new system of differential equations for the particle pitch-angle and rotation phase was derived from the analysis of particle trajectory in a given magnetic field (Sasunov et al. 2018). These equations provide an opportunity for analytic study of particle motion in arbitrary magnetic field, enabling an easy description of planetary magnetosphere CSs. The obtained self-consistent solutions for tangential CS reveal strong bifurcated profiles for the electric current and plasma density, with the bifurcation, controlled by the particle pitch-angle φ0 value (see Fig. SP06-5). This fact has been confirmed with modeling of an ensemble of non-interacting moving particles. The performed analysis gives a relation between two characteristic scales of the problem, thermal Larmor radius and inertial length. This relation, together with conservation of total pressure across TCS, allows predicting of TCS macro parameters, e.g., particle density and magnetic field. The obtained solutions for a self-consistent CS allow the reconstructing of particle distribution function on the basis of the corresponding electric current profile. This opens a way to probe particle distribution function and the related moments in the CS, using just the measured electric current distribution. The proposed methodology reveals also that in case of a down-dusk electric field the particle motion conserves the magnetic moment on specific segments of trajectory. It was shown that the current sheet can play a role of a lens, which focuses particles to specific pitch-angle values. The gained energy of accelerated particles in a TCS was found to depend linearly on the module of their TCS entry speed.
Starspot variability as an X-ray radiation proxy. Stellar X-ray emission plays important role in the study of exoplanets as a proxy for stellar winds and as a basis for the prediction of EUV flux, unavailable for direct measurements, which in their turn are important factors for the mass-loss of planetary atmospheres. In spite of detection thresholds, limiting the number of stars with the directly measured X-ray fluxes, the known connection between sunspots and X-ray sources allows using of the starspot variability as an accessible proxy for the stellar X-ray emission. To realize this approach, the light curves of 1729 main-sequence stars with rotation periods 0.5d<P<30d and effective temperatures 3236K<Teff<7166K observed by Kepler mission were analyzed. It was found that the squared amplitude of the 1st rotational harmonic of stellar light-curve may be used as an activity index. This index reveals practically the same relation with the Rossby number as the ratio, Rx, of X-ray to bolometric luminosity. Thus, the regressions for the stellar X-ray luminosity Lx(P, Teff) and its related EUV analogue LEUV were obtained for the main-sequence stars (Fig. SP06-6).
Cooperation within and outside of the NFN
The national and international cooperation in SP06 included regular communication and exchange visits with world leading experts from the project topical area for the experience exchange and expert support. In some cases, short-term subcontracts for performing of project related tasks (e.g., computational model runs, codes development and expert support) were issued. The circle of national collaboration of SP06 involved SP04, SP07, SP08 teams of NFN consortium.
The modelling of interaction of the expanding PW with the intrinsic planetary magnetic dipole field, and the aeronomy studies under different conditions of stellar XUV radiation and SW, as well as laboratory simulation of HJ’s magnetodisk were performed in cooperation with scientists from the Institute of Laser Physics (ILP) of the Russian Academy of Sciences (RAS) in Novosibirsk, Russia. Elaboration of the generalized PMM for exoplanets with a magnetodisk, and the model study (jointly with SP7) of planetary magnetospheric protection with diagnostics of SW parameters and planetary magnetic fields, as well as development of a self-consistent plasma kinetic theory of magnetospheric current sheets, involved cooperation with colleagues from Skobeltsyn Institute of Nuclear Physics (SINP) of the Moscow State University (MSU) in Moscow, Russia. The work on combining of the PMM model, with the hybrid numerical platform MULTI from the Aalto University and Finnish Meteorological Institute (FMI) involved cooperating scientists from these organizations.
References
Alexeev, I.I., Parunakian, D., Dyadechkin, S., Khodachenko, M.L., et al., Cosmic Research, 2018, 56, No. 2, 108–114 (in Russian published in Kosmicheskie Issledovaniya, 2018, Vol. 56, No. 2, pp. 119–127) (DOI: 10.1134/S0010952518020028).
Antonov, V. M., Boyarinsev, E. L., Boyko, A. A., et al., ApJ, 2013, 769, 28 (DOI:10.1088/0004-637X/769/1/28).
Arkhypov, O.V., Khodachenko, M.L., Lammer, H., et al., MNRAS, 2018, 476, 1224 (Open Access: https://academic.oup.com/mnras/article/476/1/1224/4839014).
Belenkaya, E.S., Khodachenko, M.L., Int. Journ. of Astron. and Astrophys., 2012, 2, 81-96 (doi:10.4236/ijaa.2012.22012; On-line www.SciRP.org journal/ijaa).
Belenkaya, E. S., Alexeev, I. I., Khodachenko, M. L., 2012, Astrophysics and Space Science Proceedings, 33, 217, (DOI:10.1007/978-3-642-30442-2 24)
Belenkaya, E.S., M.L. Khodachenko, I.I. Alexeev, 2015, Section 12 In: Characterizing Stellar and Exoplanetary Environments, Eds. Lammer, H., M.L. Khodachenko, Springer, Berlin, 239-246, (DOI: 10.1007/978-3-319-09749-7_12)
Berezutsky, A. G., Shaikhislamov, I. F., Miroshnichenko, I. B., et al., Solar System Research, 2019, 53, 138, DOI:10.1134/S0038094619020011 (Green OA)
Dwivedi, N. K., Khodachenko, M. L., Shaikhislamov, I. F., et al., MNRAS, 2019, 487, 4208, (DOI:10.1093/mnras/stz1345)
Erkaev, N. V., Penz, T., Lammer, H., et al., ApJS, 2005, 157, 396 (DOI: doi.org/10.1086/427904).
Erkaev, N. V., Kulikov, Yu. N., Lammer, H., et al., A&A, 2007, 472, 329 (DOI: doi.org/10.1051/0004-6361:20066929).
García Muñoz, A. P&SS, 2007, 55, 1426 (DOI: doi.org/10.1016/j.pss.2007.03.007).
Guo, J. H., ApJ, 2011, 733, 98 (DOI: doi.org/10.1088/0004-637X/733/2/98).
Guo, J. H., ApJ, 2013, 766, 102 (DOI: doi.org/10.1088/0004-637X/766/2/102).
Hünsch M., Schmitt J. H. M. M., Sterzik M. F., Voges W., A&AS, 1999, 135, 319 (DOI: 10.1051/aas:1999169)
Khodachenko, M.L., Ribas, I., Lammer, H., et al., Astrobiology, 2007a, 7, No.1, 167 (DOI: doi.org/10.1089/ast.2006.0127).
Khodachenko, M.L., Lammer, H., Lichtenegger, H.I.M., et al., P&SS, 2007b, 55, 631 (DOI: doi.org/10.1016/j.pss.2006.07.010).
Khodachenko, M.L., Alexeev, I.I., Belenkaya, E., et al., ApJ, 2012, 744, 70 (DOI: 10.1088/0004-637X/744/1/70).
Khodachenko, M.L., Shaykhislamov, I., Lammer, H., et al., ApJ, 2015, 813:50 (DOI: 10.1088/0004-637X/813/1/50).
Khodachenko, M.L., Shaikhislamov, I.F., Lammer, H., et al., ApJ, 2017, 847:126 (Open Access: doi.org/10.3847/1538-4357/aa88ad).
Khodachenko, M.L., Shaikhislamov, I.F., Lammer, H., et al., Global 3D hydrodynamic modeling of in-transit Lyα absorption of GJ436b, ApJ, 2019 (submitted).
Kislyakova, G. K., Holmström, M., Lammer, H., et al., Science, 2014, 346, 981 (DOI: 10.1126/science.1257829).
Koskinen, T. T., Yelle, R. V., Lavvas, P., Lewis, N. K. 2010, ApJ, 723, 116 (DOI: doi.org/10.1088/0004-637X/723/1/116).
Koskinen, T. T., Harris, M. J., Yelle, R. V., Lavvas, P., 2013, Icarus, 226, 1678 (DOI: doi.org/10.1016/j.icarus.2012.09.027).
Linsky, J. L., Yang, H., France, K., et al., ApJ, 2010, 717, 1291 (DOI: doi.org/10.1088/0004-637X/717/2/1291)
Mestel, L., MNRAS, 1968, 138, 359 (DOI: doi.org/10.1093/mnras/138.3.359).
Murray-Clay, R. A., Chiang, E. I., Murray, N., ApJ, 2009, 693, 23 (DOI: doi.org/10.1088/0004-637X/693/1/23).
Owen, J. E., Adams, F. C., MNRAS, 2014, 444, 3761 (DOI: doi.org/10.1093/mnras/stu1684).
Parunakian, D., Dyadechkin, S., Alexeev, I.I., Khodachenko, M.L., et al., J. Geophys. Res. Space Physics, 2017, 122, 8310, (DOI: 10.1002/2017JA024105).
Sasunov, Yu. L., Khodachenko, M. L., Alexeev, I. I., et al., 2015a, J. Geophys. Res. Space Physics, 120, 1633 (DOI:10.1002/2014JA020486).
Sasunov, Yu.L., Khodachenko, M.L., Alexeev, I.I., et al., Geophys. Res. Lett., 2015b, 42, 9609 (DOI: 10.1002/2015GL066189).
Sasunov, Yu. L., Semenov, V. S., Heyn, M. F., et al., J. Geophys. Res. Space Physics, 2015c, 120, 8194-8209 (DOI:10.1002/2015JA021504)
Sasunov, Yu.L., Khodachenko, M.L., Alexeev, I.I., et al., J. Geophys. Res. Space Physics, 2017, 122, 493 (DOI: 10.1002/2016JA023162).
Sasunov, Yu.L., Khodachenko, M.L., Alexeev, I.I., et al., Phys. Plasmas, 2018, 25, 092110, (DOI: 10.1063/1.5044720).
Shaikhislamov, I. F., Khodachenko, M. L., Sasunov, Yu. L., et al., ApJ, 2014, 795:132 (DOI:10.1088/0004-637X/795/2/132).
Shaikhislamov, I. F., Khodachenko, M. L., Lammer, H., et al., ApJ, 2016, 832:173 (DOI: dx.doi.org/10.3847/0004-637X/832/2/173).
Shaikhislamov, I.F., Khodachenko, M.L., Lammer, H., et al., MNRAS, 2018a, 481, 5315 (DOI: 10.1093/mnras/sty2652).
Shaikhislamov, I. F., Khodachenko, M. L., Lammer, H., et al., ApJ, 2018b, 866:47 (Open access: doi.org/10.3847/1538-4357/aadf39).
Tarduno,J.A., Cottrell, R.D., Watkeys, M.K., et al., Science, 2010, 327, 1238 (DOI: 10.1126/science.1183445).
Tian, F., Toon, O. B., Pavlov, A. A., De Sterck, H., ApJ, 2005, 621, 1049 (DOI: doi.org/10.1086/427204).
Trammell, G. B., Arras, P., Li, Z.-Y., ApJ, 2011, 728, 152 (DOI: doi.org/10.1088/0004-637X/728/2/152)
Trammell, G. B., Li, Z. Y., Arras, P., ApJ, 2014, 788, 161 (DOI: doi.org/10.1088/0004-637X/788/2/161).
Vidal-Madjar, A., Huitson, C. M., Bourrier, V., et al., A&A, 2013, 560, A54 (DOI: doi.org/10.1051/0004-6361/201322234)
Weber, C., Lammer, H., Shaikhislamov, I. F., Khodachenko, M. L., et al., MNRAS, 2017, 469, 3505 (DOI: 10.1093/mnras/stx1099).
Yelle, R. V., Icarus, 2004, 170, 167 (DOI: doi.org/10.1016/j.icarus.2004.02.008).
Zarka, P., Planet. & Space Sci., 2007, 55, 598 (DOI: 10.1016/j.pss.2006.05.045).