Final Report

Investigation of key factors and physical mechanisms which determine the structure, topology and dynamics of exoplanetary magnetospheres at close orbits, formed the primary focus of the project. This topic is connected with the study of the whole complex of stellar-planetary interactions, as well as internal processes, including consideration of stellar radiation, plasma flows (e.g., stellar wind, coronal mass ejections), and radiative energy deposition at the upper atmospheric layers, as well as planetary and stellar winds interaction. Special attention was paid to the development of a set of modelling tools and approaches for the description and simulation of exoplanetary magnetospheres and their basic elements, taking into account the specifics of exoplanetary conditions at close to host star orbits, such as the expanding upper atmospheric material (escaping planetary wind) heated and ionized by the stellar XUV, and formation in some cases under the conditions of planetary intrinsic magnetic dipole field, of an equatorial current-carrying plasma disk (Khodachenko et al. 2012). The work within SP6 was based on the inputs regarding the stellar radiation and wind conditions from SP4, whereas the resulting exoplanetary magnetosphere estimations were used jointly with SP7 for the modelling of exoplanetary ENA coronas (Holmström et al. 2008, Ekenbäck et al. 2010) and related diagnostics of stellar winds and planetary magnetic fields (Kislyakova et al. 2014a). The approach of the first four years of the project, consisted in simultaneous research in two basic directions: 1) the investigation of inner structure and large-scale features of the exoplanetary magnetospheres, taking into account the effects of expanding and escaping planetary upper atmospheric material, and interaction of such magnetospheres with the stellar winds; 2) the development of deep insight into fine structure and fundamental physics of the global magnetospheric current systems, e.g., thin current sheets of magnetodisk and magnetotail, with the methods of plasma kinetic theory. Besides of that, the experimental (laboratory) simulation of magnetodisk formation during the plasma outflow from the region with the central magnetic dipole was performed (Antonov et al. 2013). The facility used for this study was the vacuum chamber KI-1 at the Institute of Laser Physics of the Russian Academy of Sciences. The typical disk-type distribution of the electric current magnetic field and plasma dynamics were measured in the experiment. Altogether the experimental results confirmed the theoretical and numerical modelling predictions regarding the inner structure and topology of exoplanetary magnetosphere under the conditions of escaping planetary plasma wind. All the obtained results were published in refereed scientific media and reported on specialized national and international meetings. 

The constantly growing number of discovered exoplanets and accumulation of data regarding their physical and orbital characteristics provide an empirical platform for a more detailed study of general principles and major trends of the formation and evolution of planets and planetary systems (including the potential habitability aspect). More than a half of known exoplanets have orbits around their host stars shorter than 0.6 AU. By this, an evident maximum in the orbital distribution of exoplanets takes place in the vicinity of 0.05 AU, with two well pronounced major populations there, corresponding to the giant type planets (0,2M_J < M_p < 8M_J ), so called Hot Jupiters (HJs), which comprise about 30% of the total number of known exoplanets, and less massive (0,008M_J < M_p < 0,08M_J ) Neptune- and Earth- type planets. Here M_J stays for the mass of Jupiter.

The fact of presence of exoplanets (especially HJs) at close orbital distances opens questions regarding their mass loss, evolution, and related to that, upper atmosphere structure, its interaction with extreme stellar wind plasma flows (Yelle 2004, Holmström et al. 2008, Ekenbäck et al. 2010) and stability against escape of atmospheric gas (e.g., Guillot et al. 1996). The stellar X-ray/EUV (XUV) radiation energy deposition results in heating ionization and consequent expansion of the planetary atmosphere which contributes to the so-called atmosphere thermal escape and related mass loss (Lammer et al. 2003, 2013, Yelle 2004, García Muñoz 2007, Guo 2011, 2013, Koskinen et al. 2010, 2013). Above the exobase and the magnetopause (if it exists), i.e. in the regions of direct interaction of the expanding atmosphere with the stellar wind, the escaping particles are picked up by the stellar wind plasma flow resulting in a non-thermal mass loss. The planetary magnetic field appears a crucial factor which influences both, thermal and non-thermal types of the mass loss of close-orbit exoplanets. In general, this influence has two major aspects. First, the related with the planetary magnetism, large-scale magnetic field and electric currents, form in the surrounding space plasma the planetary magnetosphere which acts as a barrier for the upcoming stellar wind and protects the ionosphere and upper atmosphere of a planet against direct impact of stellar plasmas and energetic particles, which constitute the major factors of the non-thermal mass loss (Khodachenko et al. 2007a, Khodachenko et al. 2007b). Second, the internal magnetic field of the planetary magnetosphere strongly affects the thermal mass loss by influencing the outflow of the expanding planetary plasma and its further interaction with the stellar wind (Adams 2011, Trammell et al. 2011, 2014, Owen and Adams 2014, Khodachenko et al. 2015). Therefore, the processes of material escape and planetary magnetosphere formation have to be considered jointly in a self-consistent way in their mutual relation and influence. The expanding planetary wind interacts with intrinsic magnetic dipole field and appears a strong driver in formation of exoplanetary magnetosphere, which in its turn influences the overall mass loss of a planet.

For the efficient magnetospheric protection of a planet, the size of magnetosphere should be sufficiently large to prevent direct erosion of the atmosphere by stellar wind (Grießmeier et al. 2004). However, early the estimates showed that an intrinsic magnetic dipole moment of a tidally locked close-orbit exoplanet is very likely too weak to build alone a sufficiently large magnetosphere which could protect the planetary upper atmosphere against erosion by the stellar wind (Khodachenko et al. 2007b). To explain the survival of HJs in extreme conditions near their host stars, Khodachenko et al. (2012) proposed a more generic view of an exoplanetary magnetosphere which takes into account the expanding upper atmospheric gas heated and ionized by the stellar XUV radiation. The interaction of outflowing partially ionized planetary plasma wind with the rotating planetary magnetic dipole field leads to the development of a current-carrying magnetodisk. By this, two major regions with different topology of the magnetic field (Mestel, 1968, Trammell et al. 2011) can be distinguished in the magnetosphere driven by the escaping plasma flow. In the so-called “dead-zone” the magnetic force is strong enough to lock plasma with the planet and to keep the field lines closed. In the “wind-zone” the expanding plasma drags and opens the magnetic field lines, leading to appearance of a thin current-carrying magnetodisk. The field of magnetodisk under typical conditions of a close-orbit HJ’s, by far exceeds the dipole field. Altogether, this leads to the development of a new type of magnetodisk-dominated magnetosphere (Khodachenko et al., 2012). Such expanded magnetospheres of HJs have been shown to be up to 40-70% larger, as compared to the traditionally estimated dipole-type ones (Griemeier et al., 2004; Khodachenko et al., 2007a,b). That enabled to resolve a problem of better magnetospheric protection of close-orbit HJs against of the non-thermal erosive action of the stellar winds (Khodachenko et al., 2012). Note, that the specifics and even existence of magnetodisks by lower mass exoplanets (e.g., Neptune- or Terrestrial type), under different stellar wind and radiation conditions, is still a subject for further investigation.

Two basic processes, acting simultaneously, are responsible for the formation of exoplanetary magnetodisk and related structuring of the whole magnetosphere: 1) thermal expansion of the escaping planetary plasma wind, heated by the stellar radiation, and 2) centrifugal acceleration of plasma by rotating planetary magnetic field in the co-rotation region, with subsequent release of material in the vicinity of a centrifugal Alfvénic surface (a so-called “sling” mechanism) (Alekseev et al. 1982, Khodachenko et al., 2012). A simultaneous self-consistent description of both mechanisms represents an important and complex physical problem, and so far these processes are treated separately. That is possible in the case of close-orbit tidally locked planets which are subject to strong radiative energy deposition whereas rotational effects are usually much weaker, as the planetary rotation is synchronized with the orbital revolution (Antonov et al. 2013, Shaikhislamov et al. 2014). In this case, the radial expansion of the hot planetary plasma dominates the corotation in the inner magnetosphere. Besides of a qualitative as well as numerical treatment of the inner (dipole-dominated) and outer (magnetodisk-dominated) parts of an exoplanetary magnetosphere (Adams 2011, Trammell et al. 2011, 2014, Khodachenko et al. 2012, 2015,  Shaikhislamov et al. 2014), the formation of magnetodisk by plasma outflow in a dipole field was demonstrated in laboratory experiment (Antonov et al. 2013).

The development of a self-consistent model of an exoplanetary magnetosphere which properly includes all the basic physical effects and conditions still remains a challenging task. Self-consistent treatment based on 2D MHD codes has been recently performed by (Trammell et al. 2014, Owen and Adams 2014) in which “dead-” and “wind-zones” have been shown to form in the expanding planetary wind. However, the thermosphere heating and the hydrodynamic flow initiated close to the planetary surface were simulated with rather simplified models, assuming a mono-energetic XUV flux, homogenous (e.g., Trammell et al. 2014), or empirically estimated gas temperature, and variable boundary conditions at the planet surface. Note, that the last are known to influence the expanding planetary wind solution (Adams 2011, Trammell et al. 2011, Shaikhislamov et al. 2014). As a result, the obtained estimations for the magnetic field, at which the planetary wind of HD209458b is significantly suppressed, vary in different papers by more than an order of magnitude. Moreover, despite of the recognition of importance of the “dead-” and “wind-zones” in the context of the planetary magnetosphere topology and related atmospheric mass loss, another important structure – magnetodisk – which is closely associated with these regions and influences the global size of the magnetosphere (Khodachenko et al. 2012), has not been sufficiently modelled and investigated so far.

A special group of unsolved questions relates the macro- and micro- scaling of exoplanetary magnetospheric current systems, including those of the magnetodisk, magnetotail and magneopause regions. Their global configuration and topology depend significantly on the conditions of incoming stellar wind (Grießmeier et al. 2004, Khodachenko et al. 2012), whereas the internal scaling and fine structure are defined by the specifics of particle kinetics in self-consistent field of a current sheet. Their detailed study requires a separate treatment with development of special methods and approaches (Alexeev and Malova 1990, Zelenyi et al. 2011, Sasunov et al., 2015a,b,c), which go beyond the traditional MHD used for the description of escaping magnetized planetary winds.

The work during the first four project years (PYs) was performed in line with the proposed research plan. It comprised simultaneous research in two basic directions: First, the investigation of inner structure and large-scale features of the exoplanetary magnetospheres, taking into account the effects of expanding and escaping planetary upper atmospheric material heated by stellar radiation, and interaction of such magnetospheres with the stellar winds; Second, the development of deep insight into fine structure and fundamental physics of the global magnetospheric current systems, e.g., thin current sheets of magnetodisk and magnetotail, mainly with the methods of plasma kinetic theory.

Within the scope of the first direction, the primary goal was to gain better understanding of the physics of the exoplanetary magnetodisk formation. At the time of the project begin, only a simplified semi-qualitative treatment of the case (Kodachenko et al. 2012) has been done, and the whole idea of the disk appearance around a close-orbit giant planet needed its check. In that respect, assuming a close-orbit tidally locked slowly rotating exoplanet with the dominating thermal expansion mechanism of the escaping planetary wind (as compared to the centrifugal one) (Antonov et al. 2013, Shaikhislamov et al. 2014) two research approaches were undertaken during the PY1. (A) To consider a pure case of interaction between the planetary magnetic dipole field and outflowing plasma, a numerical MHD modelling of a simple case of the expanding isothermal plasma in the presence of the background dipole field, without inclusion of planetary and stellar effects (e.g., gravity, radiation, stellar wind, atmospheric composition, etc.) has been performed.

(B) Along with MHD modelling, also the experimental (laboratory) simulation of magnetodisk formation during the plasma outflow from the region occupied by the magnetic dipole field was done (Antonov et al. 2013). The experimental facility used for this study was the vacuum chamber KI-1 at the Institute of Laser Physics of the Russian Academy of Sciences. Both, experimental and simple MHD simulations confirmed the theoretically expected (Mestel 1968, Alexeev 1982, Kodachenko et al. 2012) specific distortion of the dipole field topology by the expanding plasma with the appearance of a thin equatorial current-carrying disk, which begins beyond the Alfvénic distance (where the flow becomes super-Alfvénic).

However, the obtained results of the experimental and numerical modelling, due to some oversimplifications imposed, which ignore several crucial effects, in spite of giving a general picture of the exoplanetary magnetosphere structure, could not be directly applied for the quantitative characterization of real exoplanets. To make a step forward on that way, SP6 developed in the PYs 2 and 3 an advanced numerical model which simulates in a self-consistent way the processes of XUV heating, ionization and expansion of the exoplanetary upper atmosphere including the consequent interaction of the escaping planetary plasma  wind with the magnetic field of planetary dipole. The primary goal of this modelling work, besides of the revealing the details of exoplanetary magnetosphere structure, was to simulate and to quantify the process of thermal mass loss of a close-orbit exoplanet and to conclude about the role of planetary intrinsic magnetic field in that respect. The investigation of exoplanetary magnetospheres by means of numerical simulations requires an efficient and well organized model capable to support a comparative study of different physical effects and processes which contribute to the formation and shaping of the magnetosphere. To investigate all the relevant physical effects and the role of planetary intrinsic magnetic field in the process of atmospheric material escape and mass loss, as well as formation and structuring of planetary inner magnetosphere in a self-consistent way, we adopt a two-step modeling strategy, starting (as a first step) with a hydrodynamic (HD) model of atmosphere expansion driven by the stellar XUV (Shaikhislamov et al. 2014). After having developed a comprehensive model for an expanding upper atmosphere of an exoplanet, we performed, as a next step, the magnetohydrodynamic (MHD) modeling (Khodachenko et al. 2015), with the inclusion of planetary intrinsic magnetic dipole field and studied its role in formation of the inner magnetosphere and atmospheric thermal mass loss.

Therefore, in PY2 we started with a 1D non-isothermal HD model of an upper atmosphere expansion driven by the stellar XUV (Shaikhislamov et al. 2014). While considering a simple hydrogen atmosphere model of a close-orbit HJ, we focused on self-consistent inclusion of the effects of radiative heating and ionization of the atmospheric gas with its consequent expansion in the outer space. Primary attention was paid to investigation of the role of specific conditions at the inner and outer boundaries of the simulation domain, under which different regimes of material escape (free- and restricted- flow) are formed. Comparative study of different processes, such as XUV heating, material ionization and recombination,  cooling, adiabatic and Lyman-alpha cooling, Lyman-alpha reabsorption was performed. The basic consistence of the outcomes of our HD modeling with the results of other similar models of expanding planetary atmospheres was confirmed (see Fig.4.5.1). We obtained that under the typical conditions of an orbital distance 0.05 AU around a Sun-type star a HJ’s plasma envelope may reach maximum temperatures up to ~9000K with a hydrodynamic escape speed ~ 9 km/s resulting in the mass loss rates ~  . In the range of considered stellar-planetary parameters and XUV fluxes that is close to mass loss in the energy limited case.

During the PYs 2 and 3 our “first-step” 1D HD model (Shaikhislamov et al. 2014) was further improved and extended to the 2D geometry case, which is needed (at least) for MHD simulation of the magnetized planetary wind (Khodachenko et al. 2015). Besides of the geometry, the model improvement comprised the inclusion of a realistic solar-type XUV spectrum for calculation of intensity and column density distribution of radiative energy input, account of the one-side illumination of a planet by its host star, incorporation of basic hydrogen chemistry for the appropriate calculation of major gas species in HJ’s upper atmosphere and related radiative energy deposition, as well as H₃⁺ and Lyα cooling processes. The improved model also takes into account gravitational and rotational forces acting in a tidally locked planet-star system. As a next step, in-line with the adopted two-step model development approach, the improved 2D HD model of the HJ’s expanding hydrogen atmosphere was generalized in the PY3 to include the effects of intrinsic planetary magnetic field (Khodachenko et al. 2015). This axisymmetric 2D MHD model, which due to self-consistent inclusion of the major effects and processes, appears the most advanced model of that kind nowadays, was used to demonstrate that the interaction between the expanding atmospheric plasma and the intrinsic planetary magnetic dipole field leads to the formation of a current-carrying magnetodisk and the specific regions inside the magnetosphere, e.g., “dead-zone” and “wind-zone” (Fig.4.5.2a) which all play an important role for topology and scaling of the whole exoplanetary magnetosphere. As an essentially new feature, a cyclic character of the magnetodisk behaviour, comprised of consequent phases of the disk formation and following magnetic reconnection with ejection of a ring-type plasmoid has

been discovered and investigated. It has been found that the mass loss rate of an analog of HD209458b planet is only slightly affected by equatorial surface field of 0.3 G, but is suppressed by order of magnitude at a field of 1 G with the consequent decrease for higher surface field values (Fig.4.5.2b). The advanced 2D MHD model enabled for the first time the detailed investigation of fine structure, as well as plasma dynamics and force balance in the “dead-“ and “wind-zone”, which appear of special importance as a source of potentially observable effects and phenomena.

Another set of investigations within the first research direction of the SP6 concerned the characterization of planetary global magnetospheric obstacle under different planetary and stellar wind conditions. This in particular includes the study of paleo-terrestrial magnetosphere with the generalized paraboloid magnetosphere model (PMM) elaborated in Khodachenko et al. (2012) under different conditions of the young solar wind, taking into account the recently reported paleo-geological data regarding terrestrial magnetism, which estimate the terrestrial magnetic field as ~50 to 70% that of the present-day field (Tarduno et al. 2010). The goal of this investigation which will be performed during the PY4 jointly with SP4 and SP7, is to conclude about the role of paleo-terrestrial magnetosphere in the long-term evolution of the terrestrial atmosphere and formation of its present-day conditions. Besides of that, since the end of the PY3 (according to proposed plan) the development of a combined PMM and hybrid HYB model for the describtion of planetary magnetosphere interaction with a stellar wind has been started. As a test object for the development of such a synthetic model and a prototype of a moderately close-orbit exoplanet, the solar system planet Mercury has been taken. The preliminary result of the synthetic model run (low resolution) is shown in Fig. 4.5.3. The new model appears a unique tool for the investigation of planetary magnetosphere large-scale shaping which combines the advantages of its basic components, PMM and hybrid modelling platform HYB.

Within the scope of the second research direction, the scaling of inner edges of different types of astrophysical disks, including exoplanetary magnetodisks, was studied during the PY1 with a purpose to detect their common features caused by magnetic field of the disk hosting object (Belenkaya & Khodachenko 2012). After that, during PY2, the motion of particles in the region of a symmetric thin current sheet (TCS) has been investigated within a cold plasma assumption, i.e. neglecting the effects of the velocity thermal dispersion. The analytical solutions for the electric current density and plasma parameters in the TCS were obtained. Further on, in PY3, the analysis of particle motion has been extended to the case of a non-monochromatic particle population (Sasunov et al. 2015a). Based on the analysis of particle trajectories, the distributions of the electric current density and plasma parameters in the TCS were calculated analytically and numerically. A set of theoretical approaches for the self-consistent description of a TCS and surrounding plasma has been suggested.  A crucial point here is that the initial current and magnetic field configuration are created by a special population of electrons or suprathermal ions, whereas the majority of partcles then are self-consistently distributed to support the initial configuration. The analysis of amplitude of the current and particle number density in a TCS for different distribution functions of pitch-angle enabled estimation of its characteristic scale, as a function of particle pitch angle. It was shown that the structure of the current sheet depends strongly on pitch-angle distribution function and is determined by two competing currents: diamagnetic and paramagnetic ones. The obtained analytic expression for the TCS scaling has been shown to agree in the limiting cases with known estimates derived under more general assumptions. The comparison of scaling of the observed natural current sheets and the results of analytical calculation was made in Sasunov et al. (2015b). Along with that, as a proxy of reconnection processes in exoplanetary magnetospheres and stellar winds, a detailed analysis of reconnection layers in the solar wind has been performed. The process of reconnection was studied by solving Riemann problem. To compare the obtained analytical solutions with real data, 51 cases of reconnection in solar wind (satellite Wind 1995 - 2005) were analyzed. The results show good qualitative and quantitative agreement (Sasunov et al. 2015c). The whole methodology developed in that regard, will be further used for the investigation of the current structure in a HJ’s magnetodisk.

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