Magnetospheric Structure and Atmospheric Joule Heating of Habitable Planets Orbiting M-dwarf Stars
O. Cohen, J.J. Drake, A. Glocer, C. Garraffo, K. Poppenhaeger, J.M. Bell, A.J. Ridley, T.I. Gombosi
DDraft version August 4, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
MAGNETOSPHERIC STRUCTURE AND ATMOSPHERIC JOULE HEATING OF HABITABLE PLANETSORBITING M-DWARF STARS
O. Cohen , J.J. Drake , A. Glocer , C. Garraffo , K. Poppenhaeger , J.M. Bell , A.J. Ridley , and T.I.Gombosi Draft version August 4, 2018
ABSTRACTWe study the magnetospheric structure and the ionospheric Joule Heating of planets orbiting M-dwarf stars in the habitable zone using a set of magnetohydrodynamic (MHD) models. The stellar windsolution is used to drive a model for the planetary magnetosphere, which is coupled with a model forthe planetary ionosphere. Our simulations reveal that the space environment around close-in habitableplanets is extreme, and the stellar wind plasma conditions change from sub- to super-Alfv´enic alongthe planetary orbit. As a result, the magnetospheric structure changes dramatically with a bowshock forming in the super-Alfv´enic sectors, while no bow shock forms in the sub-Alfv´enic sectors.The planets reside most of the time in the sub-Alfv´enic sectors with poor atmospheric protection.A significant amount of Joule Heating is provided at the top of the atmosphere as a result of theplanetary interaction with the stellar wind. For the steady-state solution, the heating is about 0.1-3% of the total incoming stellar irradiation, and it is enhanced by 50% for the time-dependent case.The significant Joule Heating obtained here should be considered in models for the atmospheres ofhabitable planets in terms of the thickness of the atmosphere, the top-side temperature and density,the boundary conditions for the atmospheric pressure, and particle radiation and transport.
Subject headings: planets and satellites: atmospheres - planets and satellites: magnetic fields - planetsand satellites: terrestrial planets - magnetohydrodynamics (MHD) INTRODUCTIONThe simple definition of planet habitability (the abilityof a planet to sustain life) is whether the surface temper-ature of the planet allows water to exist in a liquid form(Kasting et al. 1993). The corresponding ”HabitableZone” (HZ hereafter) is the range of possible distancesfrom the star at which a planet can have liquid surfacewater. This range depends primarily on the luminosity ofthe host star, but it can also depend on atmospheric andplanetary processes that can affect the planetary surfacetemperature (e.g., Tian et al. 2005; Cowan & Agol 2011;Heller et al. 2011; van Summeren et al. 2011; Wordsworth& Pierrehumbert 2013). While this intuitive definition ofhabitability is based on our familiarity with common lifeon Earth, there is growing evidence that life can arisein places and in forms we do not expect. Examples ofsuch life forms or ”Extremophiles” have been found onEarth under very cold and hot temperatures, very highpressure, high salinity, high and low pH levels, high radi-ation levels, and in oxygen-poor environments (e.g., seeRothschild & Mancinelli 2001).The above definition of habitability means that thesearch for habitable planets is focused on Earth-like,rocky planets inside the HZ. These planets are most likelyto be found around M-dwarf stars, which have low lumi-nosity so that the HZ is very close to the star, and closeenough so that planets can be detected with current ob- Harvard-Smithsonian Center for Astrophysics, 60 Garden St.Cambridge, MA 02138, USA NASA/GSFC, Code 673 Greenbelt, MD 20771, USA. Center for Planetary Atmospheres and Flight Sciences, Na-tional Institute of Aerospace, Hampton, VA 23666, USA Center for Space Environment Modeling, University ofMichigan, 2455 Hayward St., Ann Arbor, MI 48109, USA servational techniques. Recent surveys using the
Kepler database have identified potential Earth-like planets inthe HZ , taking into account the stellar luminosity, aswell as atmospheric effects such as green house gassesand cloud coverage (e.g., Dressing & Charbonneau 2013;Gaidos 2013; Kopparapu et al. 2013; Kopparapu 2013;Petigura et al. 2013; Zsom et al. 2013).M-dwarf stars may be the most feasible targets fordetecting planets in the HZ. However, these stars aretypically highly active magnetically, and as a fractionof their bolometric luminosity they emit more stronglyat UV, EUV and X-ray wavelengths than stars of ear-lier spectra types (Preibisch & Feigelson 2005). If theplanets are located very close to the star (as the HZ def-inition requires), these close-in planets can suffer fromatmospheric evaporation due to the extreme EUV andX-ray radiation (e.g. Lammer et al. 2003; Baraffe et al.2004, 2006; Tian et al. 2005; Garcia Mu˜noz 2007; Penzet al. 2008; Yelle et al. 2008; Murray-Clay et al. 2009), aswell as from atmospheric stripping by the extreme stellarwind and Coronal Mass Ejections (CMEs) (Khodachenkoet al. 2007; Lammer et al. 2007). In order to sustain itsatmosphere, a close-in planet must have a strong internalpressure that opposes the stripping. Such a pressure canbe provided by either a very thick atmosphere, similar tothat of Venus, or a strong intrinsic magnetic field suchas that of the Earth.The dynamics and energetics of planetary upper atmo-spheres are dominated by the interaction of the planetarymagnetic field and magnetosphere with the stellar wind,in the case of a strong planetary magnetic field, or bythe direct interaction of the atmosphere with the stellarwind, in the case of a weak field. The pressure balancebetween the planetary atmosphere and the wind depends a r X i v : . [ a s t r o - ph . E P ] M a y on the dynamic and magnetic pressure of the wind, andon the atmospheric thermal and magnetic pressure. Inaddition, the orientation of the magnetic field of the windcompared to that of the planetary field dictates the en-ergy transfer from the wind to the planet, as it drivesmagnetic reconnection which leads to particle accelera-tion and particle precipitation at the top of the atmo-sphere (e.g., Kivelson & Russell 1995; Gombosi 1999).Fields that drive the ions against the neutrals result inJoule Heating. The particle precipitation can impactthe local ionization and alter Joule Heating processes(see e.g., Roemer 1969; Hays et al. 1973; Deng et al.2011, with references therein) and atmospheric line exci-tation (i.e., auroral excitation Chamberlain 1961; Aka-sofu & Kan 1981; Kivelson & Russell 1995; Gombosi1999; Paschmann et al. 2002; Schunk & Nagy 2004).We emphasize that this ionospheric Ohmic dissipationis different to the Ohmic dissipation used to explain theinflation of hot jupiters (see e.g., Batygin & Stevenson2010). The latter occurs deeper in the atmosphere andis driven by the planetary magnetic field and the strongzonal winds observed in hot jupiters (Showman et al.2008, 2009)Cohen et al. (2011a) investigated the plasma environ-ment and the star-planet magnetic interaction using aglobal magnetohydrodynamic (MHD) model for the stel-lar corona and the stellar wind. In their simulation, theplanet was imposed as an additional boundary condi-tion that mimics the planetary density, temperature, andmagnetic field. In a similar manner, Cohen et al. (2011b)studied the impact of a CME on the atmosphere of aclose-in planet. However, in these simulations, the de-tailed magnetospheric structure and the energy input into the upper atmosphere as a result of the direct inter-action between the planet and the stellar wind could notbe investigated.In this paper, we present a detailed study of the mag-netospheric structure and the energy deposition into theupper atmosphere in close-in Earth-like planets orbitingan M-dwarf star. We use the upstream stellar wind con-ditions, extracted along the planetary orbit from a modelfor the stellar wind, to drive an MHD model for the globalplanetary magnetosphere and the ionosphere. We studyhow the dynamics and energetics of the planetary magne-tosphere and ionosphere changes as a function of the stel-lar wind parameters, dynamic pressure, magnetic fieldtopology, planetary field strength, and ionospheric con-ductance. In addition, we investigate how the transitionalong the planetary orbit between sub- to super-Alfv´enicregime affects the magnetosphere and the energy deposi-tion onto the planet. The Alfv´enic point is defined by theAlfv´enic Mach number, M A = u sw /v A , which is the ratiobetween the stellar wind speed, u sw , to the local Alfv´enspeed, v A = B/ √ πρ , with B being the local magneticfield strength and ρ being the local mass density. Such atransition is unique for close-in exoplanets and does notexist in the solar system, where all the planets are almostalways located in a super-Alfv´enic solar wind flow.In Section 2, we describe the particular systems westudy and in Section 3 we describe our numerical ap-proach. We describe the results in Section 4 and discusstheir implications in Section 5. We conclude our findingsin Section 6. SELECTED PLANETARY AND STELLARSYSTEMSIn principle, the study presented in this paper is rathergeneric and examines the fundamental response of Earth-like planets orbiting M-dwarf stars to the energy inputfrom the stellar wind. Recently, Dressing & Charbon-neau (2013) identified three candidate Earth-like plan-ets inside the HZ of M-dwarf stars: 1) Kepler Objectof Interest (KOI) 2626.01; 2) KOI 1422.02; and 3) KOI854.01. We choose to use the known parameters of theseplanet candidates (shown in Table 1) to represent threetypical Earth-like planets orbiting an M-dwarf star. Themagnetic fields of these planets are unknown so we as-sume an Earth-like magnetic field of 0.3G for all planets(with the exception of modifying the field of Planet A asdescribed in Section 4.3). From this point, we refer toour planet cases as “Planet A” (using the parameters ofKOI 2626.01), “Planet B” (with the parameters of KOI1422.02), and “Planet C” (with the parameters of KOI854.01), where the planets are ordered according to theirdistance from the star (Planet A being the closest).The stellar wind model (described in Section 3.1) isdriven by data describing the photospheric radial mag-netic field (magnetograms). Such data are not availablefor any of the above systems. However, several obser-vations of stars with similar parameters to those we areinterested in have been made using the Zeeman-Dopplerimaging (ZDI) method (Donati & Semel 1990). Theseobservations enable construction of surface maps of thelarge-scale stellar magnetic field, which can be used todrive our model for the stellar wind. It is important tomention that the validity of ZDI data has been ques-tioned, since this reconstruction process does not takeinto account the Stokes components that cannot be mea-sured, and they do not account for the small-scale mag-netic field that may be significant (Reiners & Basri 2009).Garraffo et al. (2013) have shown that missing small-scaleflux can have a significant effect on the predicted X-rayemission, but that the wind solutions, that are the pri-mary interested here, are much less sensitive to this andinstead depend more strongly on the large-scale field.Morin et al. (2008) have constructed ZDI maps for anumber of mid M-dwarf stars. We have identified thestar EV Lac, a mid-age M3.5 class star, as a star with themost similar parameters to the systems we are interestedhere (in particular, the effective temperature, T eff , whilethe rotation periods of these systems are currently un-known). We have constructed a magnetic map based onthat of Morin et al. (2008), assuming it does not containmuch small-scale structure and it represents essentiallya tilted dipole with a polar field strength of 1.5-2 kG.We stress that we choose this approach in order to gen-erate a solution with azimuthally varying plasma condi-tions along the planetary orbit based on typical param-eters of M-dwarf stars. This could not be achieved byusing an aligned dipole, which would yield a symmetricand constant solution. Here we assume that the stellarwind parameters for EV Lac are similar to those of ourplanets, and that these parameters can be used to studythe effects of the stellar wind on the planetary magneto-sphere and ionosphere. We are interested in the tentativeeffects on the planet due to the close proximity of theplanet to the star , the high dynamic pressure, and thestrong field of the stellar wind. The use of the parame-ters of an active M dwarf such as EV Lac (instead of theunknown parameters or idealized parameters) representsa reasonable and tractable approach. NUMERICAL SIMULATIONSFor our simulations, we use the generic
BATS-R-US magnetohydrodynamic (MHD) code (Powell et al. 1999)and the Space Weather Modeling Framework (SWMF,T´oth et al. 2005, 2012), which were developed at the Cen-ter for Space Environment Modeling at the University ofMichigan. The SWMF provides a set of models for dif-ferent domains in space physics, such as the solar corona,the inner and outer heliosphere (i.e., the interplanetaryenvironment and the solar wind), planetary magneto-sphere, planetary ionospheres, and planetary upper at-mospheres. These codes are generally speaking based onsolving the extended MHD or electrodynamic equations.In addition, the SWMF includes codes for the planetaryradiation environment, which are particle codes. All ofthese models (or part of them) can be coupled togetherto provide solutions for the space environment that aremuch more detailed and physics-based than any solutionprovided by each of these models independently. Ourmodeling approach is based on a large number of stud-ies of planets in the solar system carried out with theSWMF in a similar manner (see publications list at the http://csem.engin.umich.edu ).In this work, we use the Stellar Corona (SC) MHDcode to obtain the solution for the interplanetary envi-ronment of the three planet candidates. We then usethese solutions to drive a Global Magnetosphere (GM)MHD model for these planets. In order to obtain a morerealistic magnetospheric solution, as well as calculatingthe energy input at the top of the upper atmosphere,we couple the GM model with a model for the planetaryIonospheric Electrodynamics (IE). In the next sections,we describe in detail each model and the coupling proce-dure. 3.1.
STELLAR WIND MODEL
In order to obtain a solution for the stellar wind, weuse the SC version of
BATS-R-US (Oran et al. 2013;Sokolov et al. 2013; van der Holst et al. 2014). Themodel is driven by the photospheric radial magnetic field(see Section 2), which is used to calculate the three-dimensional potential magnetic field above the stellarsurface (Altschuler & Newkirk 1969). The potential fieldsolution is in turn used as the initial condition for themagnetic field in the simulation domain. Once the ini-tial potential field is determined, the model calculatesself-consistently the coronal heating and the stellar windacceleration due to Alfv´en wave turbulence dissipation,taking into account radiative cooling and the electronheat conduction. Unlike most MHD models for the so-lar corona, the lower boundary of this model is set atthe chromosphere, so that it does not initially assume ahot corona at its base. Instead, the heating is calculatedself-consistently.While the model works very well for the Sun, applyingthis model to M-dwarf stars is not so trivial. Our refer-ence star, EV Lac, has stronger magnetic fields than theSun, and there is a general lack of observations of the winds of other stars (see, e.g., Wood et al. 2004; G¨udel2007, and references therein). Our basic assumption isthat the winds of M-dwarfs are accelerated in a similarmanner to the Sun, with a combination of thermal accel-eration (taken into account in the model) and dissipationof magnetic energy. An example of a different mechanismthat the model cannot account for is stellar winds fromhighly evolved giants, which are likely driven by radia-tion pressure on dust grains (e.g. Lamers & Cassinelli1999) or by radial pulsations (e.g. Willson 2000). Basedon our assumption, several studies of Sun-like stars havebeen made using the SC model. Cohen et al. (2010) haveapplied the model to the active star AB Doradus, wherethey argued for the validity of the model for solar analogs.Similarly, Cohen et al. (2011a) performed simulation ofHD 189733 driven by ZDI observations reproduced fromFares et al. (2010). The model has been used recently byCohen & Drake (2014) to perform a parametric study onthe stellar wind dependence on magnetic field strength,base density, and rotation period.As stated above, we use the ZDI observation of EVLac, as well as its stellar parameters of R (cid:63) = 0 . R (cid:12) , M (cid:63) = 0 . M (cid:12) , and rotation period, P (cid:63) = 4 . L bol = 4 . · W from Morinet al. (2008), which corresponds to an effective tempera-ture of 3400 K . We use a spherical grid that extends upto 100 R (cid:63) so as to include the orbits of all three planets.Once a steady-state solution is obtained, we extract thestellar wind parameters of number density, n , velocity, u , magnetic field, B , and plasma temperature, T , at agiven point along the orbit of one of the planets.The SC solution is provided in the frame of referencerotating with the star (HelioGraphic Rotating coordi-nates or HGR). In this coordinate system, the ˆ Z axis isaligned with the rotation axis of the star, the ˆ X axis isaligned with the initial time of the ZDI observation (lon-gitude ”0”), and the ˆ Y axis completes the right-hand sys-tem. The GM model uses the Geocentric Solar Magne-tospheric (GSM) coordinate system, which is identical tothe Geocentric Solar Ecliptic (GSE) system for the caseof a planetary dipole perpendicular to the ecliptic plane.In this special case, the planetary GSE/GSM coordinatesystem is defined with ˆ X pointing from the planet tothe star (negative radial direction in the stellar frame ofreference assuming a circular planetary orbit), ˆ Z is point-ing to the north pole of the planet (perpendicular to theecliptic plane and the plane of orbit), and ˆ Y completesthe right-hand system. With a circular planetary orbitand an aligned planetary dipole, the conversion betweenthe coordinate systems is: X GSE = − r HGR (1) Y GSE = φ HGR Z GSE = θ HGR . The orbital speed of the planet, U orb , could be easilyconsidered as a constant addition to U GSEy . However, itis hard to estimate what would be the change in B GSEy ,which has a strong effect on the magnetospheric currentsystem. After carefully confirming that the Alfv´en Machnumber with and without the addition of U orb is essen-tially the same for all cases, we have decided to excludethis motion from our simulation.3.2. GLOBAL MAGNETOSPHERE ANDIONOSPHERE MODELS
The Global Magnetosphere (GM) model solves theMHD equations on a Cartesian grid for the physical do-main that includes the planet as the inner boundary, andthe extent of the planetary magnetosphere. The model isdriven from the outer boundary that is facing the star bythe upstream stellar wind conditions, which can be fixedor time-dependent. This boundary is defined with in-flow boundary conditions for all the MHD parametersfor the case of super-Alfv´enic stellar wind conditions.In the case of sub-Alfv´enic stellar wind conditions, theboundary conditions for the pressure are changed to floatin order to diminish numerical effects on the boundaryfrom the inner domain (this does not happen for super-Alfv´enic boundary conditions). For the same reason, wealso set the upstream boundary very far from the planet.The boundary conditions for all the other boundaries areset to float for all the MHD parameters.The inner boundary in GM is defined by the planetaryparameters of radius, mass, magnetic field, and density(as described in Powell et al. 1999). In order to bet-ter constrain the velocities at the inner boundary, theGM model is coupled with a model for the IonosphericElectrodynamics (IE), which is a completely separatemodel that solves for the electric potential in the iono-sphere. The IE model provides the convection electricfield, which is then used to calculate the velocities at theinner boundary of GM, along with the rotational velocityof the planet.The coupling procedure, which is described in detail inRidley et al. (2004) and in T´oth et al. (2005), begins bycalculating the field-aligned currents, J (cid:107) = ( ∇× B ) · b , at3 R p in the GM model. The currents are then mapped as-suming a dipole planetary field to the ionospheric heightof 120 km, using a scaling of B I /B , where B I and B are the field strengths at the ionosphere and at the pointof origin at 3 R p . Using the electric conductance tensor,Σ, an electric potential is solved with: J r ( r I ) = [ ∇ ⊥ · (Σ · ∇ Ψ) ⊥ ] r = r I , (2)and this potential is mapped to the inner boundary of theGM at 2 R p (for numerical efficiency, the inner boundaryis set higher than 1 R p to reduce the planetary dipolestrength and increase the numerical time step). At thefinal stage, the electric field, E = −∇ Ψ, and the bulkconvection velocity, V = E × B /B are calculated. Thevelocity field (along with the rotational velocity) is ap-plied at the GM inner boundary.The coupling of GM and IE models enables us to tospecify more realistic inner boundary conditions for theGM. This improved boundary specification allows us toestimate the energy input at the top of the planetaryatmosphere due to its interaction with the stellar windand the precipitating particles. Assuming the currentsand the (scalar) conductance, σ , are known in the IEmodel, it is trivial to calculate the Joule Heating: Q = J · E = J /σ, (3) from the generalized Ohm’s law with J = σ E .We note that, in a way, the electric conductance cap-tures all the atmospheric parameters in it (chemistry,photoionization etc.). For the case of the Earth, a morecomplex conductance can be used. The conductance de-pends significantly on the solar EUV flux (and correlateswith the radio flux in the F10.7 centimeter wavelength,see e.g., Moen & Brekke 1993), auroral particle precipi-tation (e.g., Robinson et al. 1987; Fuller-Rowell & Evans1987), and other processes that are quite dependent onunderstanding the environment near the planet. Globalmodels of the upper atmosphere, such as the one de-scribed by Ridley et al. (2002) can also be used, but theyare driven by the observed solar luminosity and auroralprecipitation, so it is difficult to drive them properly forother planets to determine the conductance patterns. Inorder to avoid further uncertainties, here we choose to usea constant Pedersen conductance, σ p , of the order of theone used for the Earth (e.g., Ridley et al. 2004). The Ped-ersen conductance allows the magnetospheric currents toclose through the ionosphere, and it depends on the col-lision frequency between electrons and ions, ν e,i , and theelectron plasma frequency, Ω e = n e e /ε m e : σ p = ν e,i ν e,i + Ω e σ , (4)with σ = n e e /ν e,i m e , where n e is the electron density, m e is the electron mass, e is the electric charge, and ε is the permittivity in free space. The extreme EUV irra-diation of close-in planets around M-dwarf stars shouldreduce the altitude of their ionospheres to regions withhigher electron density. It is not trivial to predict howthe Pedersen conductance will change as a result of theincreased EUV radiation, as it has a complicated depen-dence on the density variations of ions electrons and neu-trals, ionization rates, atmospheric chemistry, and per-haps other factors. In the results section, we probe thesensitivity of our calculations to this by showing how asimple increase in the Pedersen conductance affects theJoule Heating for a given set of parameters. RESULTS4.1.
STELLAR WIND AND CORONALSTRUCTURE
The model wind solution for EV Lac shows an averagespeed of about 300 km s − and total mass loss rate of isabout 3 × − M (cid:12) yr − . While these values are closeto those of the solar wind, the mass loss rate per unitstellar surface area from this diminutive M dwarf is anorder of magnitude higher.Figure 1 shows the steady-sate coronal and stellar windsolution for EV Lac. It shows the orbits of the threeplanets, selected coronal magnetic field lines, and colorcontours of the ratio between the dynamic pressure in thesolution to that of a typical solar wind conditions at 1 AU(see background solar wind conditions in Table 1). Thedynamic pressure of the ambient stellar wind at theseclose-in orbits is 10 to 1000 times larger than that nearEarth. In addition, the magnetic field strength rangesbetween 500–2000 nT along the orbit of Planet A, be-tween 200–800 nT along the orbit of Planet B, and be-tween 100–200 nT along the orbit of Planet C. This isin contrast to a field strength of the order of 1–10 nTfor typical solar wind conditions at 1 AU. Finally, thetemperature of the ambient stellar wind along the orbitsof the planets ranges between 300,000 K to over 2 MK.The typical solar wind temperature is about 10 K.As seen in Figure 1, the stellar wind conditions changefrom sub- to super-Alfv´enic along the orbits of all threeplanets. For Planet A and Planet B, we drive the GMsimulation using both sub- and super-Alfv´enic upstreamconditions. For Planet C, we perform three GM simula-tions using sub-Alfv´enic conditions, super-Alfv´enic con-ditions with slow (more dense) stellar wind, and super-Alfv´enic conditions with fast (less dense) stellar wind.Table 1 summarizes the upstream conditions used todrive the GM model for the different Planets.4.2.
STEADY STATE MAGNETOSPHERICSTRUCTURE
Figure 2 shows the magnetospheric structures of PlanetA and Planet B (the magnetospheric structure of PlanetC is qualitatively similar). The most notable result is thedramatic change in the magnetospheric topology whenthe stellar wind upstream conditions change from sub-to super-Alfv´enic. For sub-Alfv´enic conditions the plan-etary field lines simply merge with the stellar wind fieldlines in an Alfv´en-wings topology (Neubauer 1980, 1998).An Alfv´en-wings configuration arises when a conductingobstacle moves in a plasma with a sub-Alfv´enic speedand it is the result of the configuration of the currentsystem that connects the external plasma with the cur-rents flowing inside the body, along low flow cavities. Ithas been well observed and studied for the Jovian moonsIo (Neubauer 1980; Combi et al. 1998; Linker et al. 1998;Jacobsen et al. 2007) and Ganymede (Ip & Kopp 2002;Kopp & Ip 2002; Jia et al. 2008). Some studies suggestthat this configuration can be obtained at Earth duringperiods when the solar wind has a weak Alfv´enic Machnumber (Ridley 2007; Kivelson & Ridley 2008).For super-Alfv´enic upstream conditions, an Earth-likemagnetospheric configuration forms with the planetaryfield lines being draped over by the stellar wind, and amagnetopause bow shock being forming in front of theplanet along with a magnetotail behind.The transitioning between sub- to super-Alfv´enic con-ditions occurs twice per orbit and within a short time.This has implications for the energy input into the upperatmosphere, which are discussed in Section 4.4.4.3.
STEADY STATE JOULE HEATING
Figure 3 shows the distribution of the height integratedionospheric Joule Heating, Q l , (in units of W m − ) ina format of polar plots. Each pair of panels shows theJoule Heating for one of the three planets extracted froma steady-state GM-IE simulation. The heating is clearlystronger for the closer orbit of Planet A than the moredistant orbit of Planet C, for which the color scale ofthe plot has been extended to lower values of heating forclarity. The figure also shows that the heating is strongerfor Super-Alfv´enic stellar wind conditions than for Sub-Alfv´enic conditions, and that the distribution is asym-metric, as expected, due to the asymmetric stellar windmagnetic field and magnetospheric field-aligned currents.For comparison with the case of the Earth, we ran themodel using the planetary parameters of the Earth, and upstream conditions of a typical quiet solar wind, as wellas with upstream conditions of a strong CME event. Theupstream parameters of these reference runs are summa-rized in Table 1. Figure 4 shows the ionospheric JouleHeating for Planet A and for these reference Earth cases.It shows that the heating by the ambient stellar windconditions at close-in orbits is about four orders of mag-nitude higher than the case of the ambient solar windconditions at Earth, and is even higher than the heatingduring a strong space weather event on Earth.The top panel in Figure 5 shows the total area inte-grated power, P = (cid:82) Q l da , for all the solutions, where da is the surface element of the 2D ionospheric sphere.It is consistent with the trend which is usually seenin Figure 3, with the power being the greatest for theclosest planet. For the Planet A, the power reaches10 − W , which is 0.01-0.1% of the total incident ra-diation of the M-dwarf star, assuming L bol = 4 . · W , a = 0 . AU (36 R (cid:63) ), and P ≈ L bol ( R p /a ) ≈ W .Since the planetary albedo is likely not zero, much ofthis radiative will be reflected, and the significance ofthe Joule Heating can be even greater. For all cases, theheating in the super-Alfv´enic regime is higher than thesub-Alfv´enic one, and for the case of Planet C, the heat-ing is greater for the super-Alfv´enic regime with a slowstellar wind than for the super-Alfvenic upstream condi-tions with a fast stellar wind. This is due to the order ofmagnitude density variation of the stellar wind upstreamconditions, which increases the wind’s dynamic pressure(i.e., ρu sw ). Moreover, the super-Alfv´enic sectors are lo-cated near the helmet streamers, where the velocity com-ponent which is not parallel to the magnetic field (i.,e.,the non-radial component) is greater. As a result, andthe upstream electric field, E = − u × B , which dictatesthe ionospheric electric potential and the coupling be-tween the stellar wind and the planetary magnetosphere,is larger as well.In the middle panel of Figure 5, we show the JouleHeating power for different planetary magnetic fieldstrengths for the sub- and super-Alfv´enic upstream con-ditions in Planet A, along with the reference Earth cases.The power is greater for the weaker planetary fields dueto the strong penetration by the stellar wind. As the fieldincreases to 1G, the wind is pushed back and the energyinput to the upper atmosphere is reduced. In addition,the total size of the heated polar cup is reduced too. Dueto the uncertainties about the planetary magnetic field,here we assume a planetary dipole field aligned with thestellar rotation axis. We omit the effect of different dipoleorientation, which could affect the energy input as a re-sult of magnetic reconnection between the stellar windand the planetary magnetosphere (e.g., a geomagneticstorm).The bottom panel of Figure 5 shows the Joule Heatingpower for an ionospheric conductance of 0.25 (the valueused for all simulations), 5, and 50 Siemens for the sub-Alfv´enic case of Planet A, along with the reference Earthcases. As mentioned in Section 3.2, the actual iono-spheric conductance depends on the atmospheric den-sity, composition, the level of ionization, and the level ofphotoionization (the stellar EUV and X-ray flux). Thepower varies inversely with the value of the conductance.As the conductance represents the mobility of the ions,a lower value means that the ions are less mobile andcollide more frequently with neutrals. As a result, theenergy dissipation (or Joule Heating) increases.4.4. TIME-DEPENDENT SOLUTION FORPLANET A
The results presented in Sections 4.2 and 4.3 are thesteady-state solutions for the different planets, which aredriven by the upstream stellar wind conditions extractedfrom the SC solution at particular locations along theirorbit. As stated in Section 4.2, the magnetospheric struc-ture undergoes significant change as the planets movefrom the sub- to super-Alfv´enic plasma sectors along theorbit. In order to obtain the dynamic effect of such atransition, we performed a time-dependent simulation ofPlanet A starting at a sub-Alfv´enic sector and ending ina super-Alfv´enic sector. In this time-dependent simula-tion, the upstream conditions in GM are updated every2:52 hours (10 degrees of the orbit of 4.3 days) so that thechange in the driving stellar wind conditions is captured(in contrast to the single set of stellar wind conditionsfor the steady-state).Figure 6 shows the magnetospheric structure, as wellas the Joule Heating in the ionosphere at after 2:52h,22:52h, 25:44h, and 26:36h. The planet moves to thesuper-Alfv´enic sector around 25:00h, with the white linein the lower two panels representing the M A = u sw /v a =1 line. This line also helps to identify the magnetopausebow shock built in front of the planetary magnetosphereas the planet transitions to a super-Alfv´enic sector. Itcan be clearly seen from the top four panels in Figure 6that there is a significant heating of the upper atmo-sphere as the planet transitions between the sectors.Figure 7 shows the temporal change in the total poweras a result of the planetary motion along the orbit. Thetotal power increases by 50% as the planet moving fromthe sub- to super-Alfv´enic sector. The heating in thesub-Alfv´enic sector is 10 times higher in the dynamicsimulation compared to the steady-state obtained at thesame point, and the heating in the super-Alfv´enic sec-tor is 50% higher in the dynamic simulation comparedto the steady-state obtained at the same point (in thiscase, the heating is almost 1% of the incident stellarradiative power). This is due to the fact that the dy-namic simulation captures the temporal change in themagnetic field, which drives stronger field-aligned cur-rents (the time derivative of the magnetic field is zerofor the steady state, but can and does vary in the time-dependent case). DISCUSSIONThe results of our simulations reveal a number of in-teresting findings regarding close-in planets orbiting M-dwarf stars. These findings relate to the extreme spaceenvironment surrounding these planets and planetaryshielding and protection, the change in the magneto-spheric structure as a result of the planetary orbital mo-tion, and the Joule Heating of the upper atmospheres asa result of the interaction with the stellar winds. Belowwe discuss in details each one of these findings.5.1.
EXTREME SPACE ENVIRONMENT ANDPLANETARY PROTECTION
Our results show in detail that the space environmentof close-in exoplanets is much more extreme in terms of the stellar wind dynamic pressure, magnetic field, andtemperature. Each of these parameters is about 1–3 or-ders of magnitude higher than the typical solar wind con-ditions near the Earth. The ultimate consequence of suchan extreme environment, in the context of this paper, isthe potential for stripping of the planetary atmosphere(in addition to atmospheric evaporation by the enhancedEUV/X-ray stellar radiation, Lammer et al. 2003). Theprocess of atmospheric erosion due to the impact of anionized wind is complex, and here we simply examinethe degree to which the planetary magnetosphere is pen-etrated by the wind.On this basis, a planetary magnetic field similar to thatof the Earth seems to be strong enough to largely resistthe stellar wind in the super-Alfv´enic sectors. However,in the case of the sub-Alfv´enic sectors there is no bowshock at all, and many field lines are connected directlyfrom the stellar wind to the planet, resulting in pooratmospheric protection. In a manner of fact, Planet Ais located most of its orbit in a sub-Alfv´enic plasma andthe assumption of the existence of a bow shock (e.g.,Grießmeier et al. 2004; Khodachenko et al. 2007; Lammeret al. 2007; Vidotto et al. 2011) may not be relevant forplanets of this kind.Grießmeier et al. (2004) have studied the atmosphericprotection for hot-jupiter planets using scaling laws forthe stellar mass loss and the planetary magnetic moment,and by estimating the atmospheric loss of neutral hydro-gen. They concluded that hot-jupiters may have beensignificantly eroded during the early stages of the stel-lar system when stellar magnetic activity was high, andassuming that the mass-loss rate of young stars is com-paratively high (about 100 times the current solar value,Wood et al. 2002). Other estimates of the mass loss ratesof young stars suggest that the winds might not be sostrong (only about 10 time the current Sun, Holzwarth& Jardine 2007; Sterenborg et al. 2011). In the case ofthe planets studied here, we do not include any atmo-spheric outflow. However, our simulations demonstratethat in order to estimate such an outflow and the degreeof planetary protection afforded by a magnetic field, oneshould consider not only the magnitude of the stellar windpressure, but also whether the surrounding space plasmais sub- or super-Alfv´enic and the orientation of the stel-lar magnetic field, as it may allow stellar wind particlesto flow directly into the planetary atmosphere.5.2.
CHANGE IN MAGNETOSPHERICSTRUCTURE ALONG THE ORBIT
The time-dependent results show that the magneto-spheres of the planets under study experience significantchanges in their topology and nature on timescales of afew hours, due only to their transition through differentplasma conditions along their orbit. While the magneto-spheres have an Earth-like structure during times whenthe planet passes through super-Alfv´enic sectors, theyhave an Io-like Alfv´en wing shape during times when theplanet passes through sub-Alfv´enic sectors. Planet Aand Planet B reside in the sub-Alfv´enic sectors for mostof their orbits. Surprisingly, the super-Alfv´enic sectorsare associated with slower wind speed. These sectors aresuper-Alfv´enic due to the order of magnitude increase inthe plasma density, which reduces the Alfv´en speed inthe wind.On the Earth, the Cross Polar Cap Potential (CPCP)is the difference between the maximum and minimumionospheric electric potential. It is associated with thesolar wind driver and it becomes saturated during majorCME events (e.g., Reiff et al. 1981; Siscoe et al. 2002).In the case of the planets studied here, the strong drivingstellar wind is reflected in a saturated CPCP, where themagnitude of the CPCP is 10 − kV—much greaterthan a potential of about 50 kV for the ambient so-lar wind conditions and 1000 kV for CME conditions.Ridley (2007) and Kivelson & Ridley (2008) have dis-cussed the dependence of the CPCP on the solar windconditions. They showed that for larger v A (and likelysub-Alfv´enic flow), the solar/stellar wind conductance,Σ A = ( µ v A ) − ( µ is the permeability of free space),is smaller than the ionospheric conductance, Σ p , and asa result, the reflected fraction of the stellar wind elec-tric field becomes larger than the incident one and theCPCP becomes saturated. In the case of our hypotheti-cal planets, the stellar wind is always extremely strong.Therefore, it seems likely the CPCP in these planets isalways saturated, unless Σ p is reduced even further dueto the space environment conditions so it is again smallerthan Σ A . This can prevent from the stellar wind electricfield to reflect and the CPCP is again in a non-saturatedstate. As mentioned in Section 3.2, we leave the detailedcalculation of the ionospheric conductance in close-in ex-oplanets to future study.5.3. JOULE HEATING OF THE UPPERATMOSPHERE
Our results show that there is a significant Joule Heat-ing at the upper atmospheres of the planets as a result ofinteraction with the extreme stellar wind. Overall, theheating is 2-5 orders of magnitude higher than that ofthe Earth during quiet solar wind conditions. The quiet-time heating for close-in exoplanets is even higher thanthose obtained on Earth during a strong CME event.It is most likely that the heating is even greater duringCME events on these close-in planets as the energy de-posited in such events can be 3 orders of magnitude largerthan a typical CME on Earth (Cohen et al. 2011b). Thetime-dependent simulation of Planet A shows that addi-tional heating is available to the sharp and quick changesin the magnetospheric topology as the planet passes be-tween the sub- to the super-Alfv´enic sectors. In a way,these changes can be viewed as if a CME hits the planettwice in an orbit, leading to sharp and fast changes inthe conditions of the driving stellar wind.As expected, the heating decreases with the increaseof the planetary field strength as the planetary magneticpressure reduces the stellar wind forcing. Of course, thiscan be modified by the particular orientation of the plan-etary and stellar magnetic fields as further heating canbe driven by magnetic reconnection, which acceleratesthe precipitating electrons to higher energies (Kivelson& Russell 1995; Gombosi 1999). Our simulations alsoshow that the heating increases with the decrease of thePedersen conductance in the ionosphere. This is impor-tant because the conductance captures the role of theupper atmosphere in the energy input from the stellarwind. In reality, the conductance is defined by the atmo-spheric parameters and conditions. By estimating theseparameters using a more detailed modeling (e.g., Ridley et al. 2002, 2004), one can obtain a good estimation ofthe conductance and the overall heating of the top-sideatmosphere by the interaction with the stellar wind.While the Joule Heating of the upper atmosphere is farsmaller than the planetary core Joule Heating necessaryto explain the inflation of hot jupiter planets (Batygin &Stevenson 2010; Perna et al. 2010; Huang & Cumming2012; Menou 2012; Rauscher & Menou 2013; Spiegel &Burrows 2013; Rogers & Showman 2014), it is still signif-icant in terms of the energy balance of the atmosphere.For the ambient stellar wind conditions, the heating of10 − W m − can reach 0.1-3% of the total stellar irra-diating input shown in Table 1. As stated above, it canbe even greater for periods of CMEs, as we expect theCME rate in M-dwarf stars to be high (G¨udel 2007). Theadditional heating at the top of the atmosphere is impor-tant for modelling the atmospheres of habitable planets(e.g., Kasting et al. 1993; Spiegel et al. 2008; Heng & Vogt2011; Tian et al. 2014) as they affect the atmospherictemperature. Therefore, these models should take in toaccount the atmospheric Joule Heating in the context oftheir pressure boundary conditions. In addition, JouleHeating at the top of the upper atmosphere transfersthe energy to the thermosphere below, driving changesin the temperature, density, and pressure in the form ofacoustic and gravity waves. As the changes in the mag-netosphere and Joule Heating repeat along the orbit, itwould be interesting to study the time-scale of the changein the driving force (i.e., the stellar wind conditions alongthe orbit), to the propagation time-scale of the planetaryperturbations. However, this study is beyond the scopeof this paper. SUMMARY AND CONCLUSIONSIn this paper, we study the magnetospheric structureand the ionospheric Joule Heating of habitable planetsorbiting M-dwarf stars using a set of magnetohydrody-namic (MHD) models. The stellar wind solution is ob-tained using an MHD model for the stellar corona, whichis driven by the magnetic field observations and the stel-lar parameters of EV Lac - a mid-age M-dwarf star. Weinvestigate how the Joule Heating affects the upper at-mospheres of three hypothetical planets located at theorbits of the three KOIs around EV Lac. We use thestellar wind conditions extracted at particular locationsalong the planetary orbit to drive an MHD model forthe planetary magnetosphere, which is coupled with amodel for the planetary ionosphere. The solutions fromthese simulations provide the magnetospheric structureand the Joule Heating of the upper atmosphere as a re-sult of the interaction with the stellar wind.Our simulations reveal the following major results: • The space environment around close-in exoplanetscan be very extreme, with the stellar wind dynamicpressure, magnetic field, and temperature being 1-3 orders of magnitude stronger than that at 1 AU.The stellar wind conditions along the planetary or-bit change from sub- to super-Alfv´enic. • The magnetosphere structure changes dramaticallyas the planet passes between sectors of sub- tosuper-Alfv´enic plasma. While a bow shock isformed in the super-Alfv´enic sectors, the planets reside in a sub-Alfv´enic plasma most of the orbit,where no bow shock is formed and the stellar windis directed towards the planetary surface. In thiscase, the protection of the planetary atmosphere ispoor. • A significant amount of Joule Heating is providedat the top of the atmosphere as a result of theplanetary interaction with the stellar wind. Theheating is enhanced in the time-dependent calcu-lation as a result of the additional current due tothe temporal changes in the magnetic field. For thesteady-state, the heating is about 0.1-3% of the to-tal incoming stellar irradiation, and it is enhancedby 50% for the time-dependent case. • The transitioning between the plasma sectors alongthe planetary orbit has quantitive similarities to anexoplanet interacting with a CME. • The significant Joule Heating obtained here shouldbe considered in models for the atmospheres of HZplanets in terms of the top-side temperature, den-sity, and boundary conditions for the atmosphericpressure.In this work, we have studied the interaction of magne- tized habitable planets with the stellar wind. However,it is not clear whether the planetary magnetic fields ofthese planets are strong or weak. Alternatively, planetscan have a thick enough, Venus-like atmosphere that cansustain the extreme stellar wind. We leave the investiga-tion of such an interaction for future study.We thank an unknown referee for her/his commentsand suggestions. The work presented here was fundedby the Smithsonian Institution Consortium for Unlock-ing the Mysteries of the Universe grant ’Lessons fromMars: Are Habitable Atmospheres on Planets around MDwarfs Viable?’, and by the Smithsonian Institute Com-petitive Grants Program for Science (CGPS) grant ’CanExoplanets Around Red Dwarfs Maintain Habitable At-mospheres?’. Simulation results were obtained using theSpace Weather Modeling Framework, developed by theCenter for Space Environment Modeling, at the Univer-sity of Michigan with funding support from NASA ESS,NASA ESTO-CT, NSF KDI, and DoD MURI. The sim-ulations were performed on the NASA HEC Pleiades sys-tem under award SMD-13-4076. JJD was supported byNASA contract NAS8–03060 to the
Chandra X-ray Cen-ter during the course of this research and thanks theDirector, H. Tananbaum, for continuing support and en-couragement.
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Planet R (cid:63) [ R (cid:12) ] Stellar T eff [ K ] Semi-major Axis [ R (cid:63) ] R p [ R ⊕ ] Assumed B p [ G ] F [ W m − ]A 0.35 3482 36 1.37 0.3 1500B 0.22 3424 51.98 0.92 0.3 820C 0.4 3562 90 1.69 0.3 255 TABLE 2Stellar Wind Parameters used to drive GM
Parameter Planet A Planet A Planet B Planet B Planet C Planet C Planet Csub-Alfv´enic super-Alfv´enic sub-Alfv´enic super-Alfv´enic sub-Alfv´enic super-Alfv´enic super-Alfv´enicslow fast n [ cm − ] 1100 34250 433 12895 46 3200 123 T [10 K ] 5 .
13 8 .
37 3 .
42 4 .
77 4 .
98 2 .
22 1 . u [ km s − ] (-609,-14,39) (-140,101,13) (-630,-1,30) (-202,102,22) (-728,-50,-17) (-278,92,26) (-660,8,14) B [ nT ] (-1950,-377,170) (-171,438,167) (-804,-173,63) (-57,223,92) (240,88,17) (-14,95,42) (-244,74,18)5 M A TABLE 3Solar Wind Parameters
Parameter Background Solar Wind CME Conditions n [ cm − ] 5 50 T [ K ] 10 · u [ km s − ] (-500,0,0) (-1500,0,0) B [ nT ] (0,0,-5) (0,0,-100) Fig. 1.—
The coronal solution for EV Lac. Left: color contours of the photospheric radial magnetic field used in the simulation (basedon the ZDI map from Morin et al. (2008)) is shown on a sphere representing r = 1 R (cid:63) . Selected coronal magnetic field lines are shown ingrey. Right: selected coronal magnetic field lines are shown in grey with the equatorial plain colored with contours of the ratio betweenthe stellar wind dynamic pressure and the dynamic pressure of the ambient solar wind base on the parameters from Table 1. Also shownare the circular orbits of the three planets, and the Alfv´en surface crossing of the equatorial plain (represented by the solid white line).The locations where the upstream conditions were extracted are marked in black circles for the sub-Alfv´enic regions, and in white circlesfor the super-Alfv´enic regions. The letters ’F’ and ’S’ shows the location of the fast and slow super-Alfv´enic conditions for planet C. Fig. 2.—
The magnetospheres of Planet A (top) and Planet B (bottom) for sub-Alfv´enic (left) and super-Alfv´enic (right) stellar windconditions. Color contours show the number density (note the different scales in the panels) and selected magnetic field lines are shownin grey. The direction of the star (the direction from which the stellar wind is coming) is marked by the small yellow Sun shape. Thestructures and trends are similar for Planet C. Fig. 3.—
Height-integrated Joule Heating (in
W m − ) of the ionospheres of Planet A (top), Planet B (middle), and Planet C (bottom)for sub-Alfv´enic (left) and super-Alfv´enic (right) stellar wind conditions displayed in polar plots of the planetary Northern hemisphere.The sub-stellar point (day side) is marked by the small Sun shape. Note that the heating of Planet C is displayed on a reduced colorscale (marked with *). The distribution of the Joule Heating in the Southern hemisphere is similar, but is mirrored towards the night sideinstead of the day side. Fig. 4.—
Height-integrated Joule Heating (in
W m − ) of the ionospheres of Planet A (top), and for ambient solar wind (bottom-left)and CME (bottom-right) conditions at Earth taken from Table 1. The display is similar to that of Figure 3. Fig. 5.—
Top: the total power (in W ) of the integrated Joule Heating for all the planets and reference Earth cases. Middle: the totalJoule Heating power for Planet A as a function of planetary magnetic field strength shown for the sub-Alfv´enic (red) and super-Alfv´enic(green) cases. Also shown are the reference Earth cases (blue). Bottom: the total Joule Heating power for Planet A for sub-Alfv´enic (red)conditions as a function of the ionospheric conductance. Also shown are the reference Earth cases (blue). Fig. 6.—