Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters
N. V. Erkaev, P. Odert, H. Lammer, K. G. Kislyakova, L. Fossati, A. V. Mezentsev, C. P. Johnstone, D. I. Kubyshkina, I. F. Shaikhislamov, M. L. Khodachenko
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Effect of stellar wind induced magnetic fields on planetaryobstacles of non-magnetized hot Jupiters
N. V. Erkaev , , P. Odert , H. Lammer , K. G. Kislyakova , , L. Fossati ,A. V. Mezentsev , C. P. Johnstone , D. I. Kubyshkina , I. F. Shaikhislamov ,M. L. Khodachenko Institute of Computational Modelling SB RAS, 660036 Krasnoyarsk, Russia Siberian Federal University, 660041 Krasnoyarsk, Russia Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042, Graz, Austria Institute for Astronomy, University of Vienna, T¨urkenschanzstrasse 17, A-1180 Vienna, Austria Institute of Laser Physics SB RAS, 630090 Novosibirsk, Russia
ABSTRACT
We investigate the interaction between the magnetized stellar wind plasma and thepartially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphereof non- or weakly magnetized hot Jupiters. We use the well-studied hot JupiterHD 209458b as an example for similar exoplanets, assuming a negligible intrinsic mag-netic moment. For this planet, the stellar wind plasma interaction forms an obstaclein the planet’s upper atmosphere, in which the position of the magnetopause is deter-mined by the condition of pressure balance between the stellar wind and the expandedatmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show thatthe neutral atmospheric atoms penetrate into the region dominated by the stellar wind,where they are ionized by photo-ionization and charge exchange, and then mixed withthe stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show thatan induced magnetic field forms in front of the planetary obstacle, which appears to bemuch stronger compared to those produced by the solar wind interaction with Venusand Mars. Depending on the stellar wind parameters, because of the induced mag-netic field, the planetary obstacle can move up to ≈ Key words: hydrodynamics – MHD – planets and satellites: atmospheres – ultravi-olet: planetary systems
As shown by several studies, the upper atmosphereof hydrogen-dominated exoplanets can develop hydrody-namic outflow conditions if the planet orbits close tothe host star and is exposed to sufficiently large ex-treme ultraviolet (EUV) fluxes (Yelle 2004; Tian et al. 2005;Garcia Munoz 2007; Penz et al. 2008; Murray-Clay et al.2009; Guo 2011; Koskinen et al. 2010, 2013a,b; Lavvas et al.2014; Shaikhislamov et al. 2014; Khodachenko et al. 2015;Chadney et al. 2015, 2016; Salz et al. 2016; Erkaev et al.2016). These studies neglected the interaction of the plan-etary atmosphere with the stellar wind, though in realitythe escaping atmospheric particles penetrate into the stel- lar wind and may exert a strong influence on the windplasma flow in the vicinity of the planet. None of thesestudies included also the magnetized stellar wind plasmaflow that may interact with the upper atmosphere if theplanet has no, or only a weak, intrinsic magnetic moment.The main effect of an intrinsic planetary magnetic field onatmospheric escape is to suppress the outflow and to make ithighly anisotropic (Adams 2011; Trammell et al. 2011, 2014;Owen & Adams 2014; Khodachenko et al. 2015). However,several studies addressed the interaction between a close-in planet with the host star’s wind, but some of them ne-glected magnetic fields and all just considered a purely hy-drodynamic interaction (Stone & Proga 2009; Bisikalo et al.2013; Tremblin & Chiang 2013; Christie et al. 2016). Other c (cid:13) N. V. Erkaev et al. studies, instead, applied MHD models (Cohen et al. 2011;Matsakos et al. 2015; Tilley et al. 2016), but employingmostly simplified descriptions of the planetary wind.Recently, Shaikhislamov et al. (2016) used a multi-fluidcode to study the interaction of a non-magnetized hotJupiter with the stellar wind, taking into account heatingby the stellar extreme ultraviolet (XUV) flux and hydro-gen photochemistry to self-consistently model the planetaryoutflow. However, they did not include the interplanetarymagnetic field (IMF) and its effect on the formation of theplanetary obstacle, which is the topic of the present study.Sophisticated MHD simulations have been applied byCohen et al. (2014) to study the magnetospheric structureof habitable zone planets for different conditions of the stel-lar wind. Using a multi-species MHD model, Cohen et al.(2015) investigated the stellar wind interaction with aVenus-like demagnetized planet. In addition, a multi-speciesMHD model, developed previously for Venus, was adaptedby Dong et al. (2017) for the calculation of the ion escapeprocess from Proxima Centauri b.There are many physical processes, thermal and non-thermal, which are responsible for the escape of heavy ionsand neutral particles and the importance of accounting fornon-thermal escape processes for the solar system planets,and Earth in particular, has been shown for example byWelling & Liemohn (2016). However, the ion escape causedby the interaction with the stellar wind (Kislyakova et al.2013, 2014a; Erkaev et al. 2016) and the loss of photochemi-cally produced suprathermal hydrogen atoms (Shematovich2010) from a non- or weakly magnetized HD 209458b-likehot Jupiter are about an order of magnitude smaller thanthe thermal escape caused by the absorption of the high-energy stellar flux.Kislyakova et al. (2014b, hereafter KIS14) employed anupper atmosphere-stellar wind interaction particle code thatincludes acceleration by the stellar radiation pressure, nat-ural and Doppler spectral line broadening, and charge ex-change with the stellar wind to reproduce the Hubble SpaceTelescope (HST) Ly- α transit observations of HD 209458b(Vidal-Madjar et al. 2003; Ben-Jaffel 2007). The best fit tothe observed Ly- α absorption was obtained for a planetarymagnetic field smaller than 0.4 G. The results of KIS14 donot support a magnetic moment much larger than about10% of Jupiter’s, in agreement with previous studies re-lated to the non-detection of exoplanetary radio emissionfrom hot Jupiters, which suggested that because of tidallocking, hot Jupiters may have weak magnetic moments(Grießmeier et al. 2004, 2007; Weber et al. 2017). As shownby Khodachenko et al. (2015), such weak intrinsic magneticfields do not significantly influence the atmospheric outflow.Following the indirect evidence that HD 209458b mayhave a weak intrinsic magnetic field, we investigate thebuild-up of a planetary obstacle produced by the interac-tion of the partially ionized planetary wind with the plasmaflow of a magnetized stellar wind. In Sect. 2, we describethe input parameters and the adopted modeling scheme. InSect. 3, we present our results and discuss the influence ofthe assumed stellar wind plasma parameters on the obstacleformation and the possible implications for UV observations.Finally, we gather our conclusions in Sect. 4. We use a 3D MHD flow model, based on the scheme ofFarrugia et al. (2008, 2009), to compute the plasma flowaround a non-magnetized HD 209458b-like planet and tocalculate the steady-state plasma parameters and magneticfield in the environment surrounding the planet, consideringdifferent stellar wind conditions. This model allows us tocalculate the induced electric currents due to the ionizationand charge-exchange processes acting on the hydrodynami-cally expanding upper planetary atmosphere. Such currentsproduce an induced magnetic field, which can strongly affectthe location of the boundary of the planetary obstacle.The model solves the following equations ∂ ( ρ V ) ∂t + ∇ · (cid:20) ρ VV + I (cid:18) P + B π (cid:19) − BB π (cid:21) == Q i V h − Q ex ( V − V h ) , (1) ∇ · B = 0 , (2) ∂ρ∂t + ∇ · ( ρ V ) = Q i , (3) ∂ B ∂t − ∇ × ( V × B ) = 0 , (4) ∂W∂t + ∇ · (cid:18) ρV V + γγ − P V + 14 π B × ( V × B ) (cid:19) =( Q i + Q ex ) (cid:18) V h + 3 kT h m p (cid:19) − Q ex (cid:18) V + 3 kT m p (cid:19) , (5) W = ρ V + 1 γ − P + 18 π B , (6)where ρ , V , P , and B are the mass density, velocity, plasmapressure, and magnetic field of the stellar wind, respectively.The parameter γ is the polytropic index (assumed to beequal to 5/3), while V h and T h are the velocity and temper-ature of the escaping atmospheric neutral hydrogen atoms.The mass conservation equation includes an interactionsource term, which is related to photoionization Q i = α i N hn m p (7)and charge exchange ionization Q ex = ρ < V rel > N hn σ ex (8)of the hydrogen atoms. Here, N hn is the number densityof the neutral planetary hydrogen atoms, m p the particlemass, σ ex ( ∼ − cm ) the charge exchange cross section, < V rel > the average relative speed of the stellar wind andatmospheric particles, and α is the ionization rate propor-tional to the EUV flux α = 5.9 × − I EUV s − .We apply a Godunov-type finite difference method forthe numerical calculations of the non-stationary MHD flowaround the planetary obstacle, which can briefly be de-scribed by rewriting the system of equations in a compactvector form as ∂U∂t + 1 r ∂ ( r Γ) ∂r + 1 r sin( θ ) ∂ (sin( θ )Ψ) ∂θ + 1 r sin( θ ) ∂ Φ ∂φ = G, (9)where the vector quantity U consists of the mass, momen-tum, energy densities, and magnetic field components. Thequantities Γ, Ψ, and Φ denote instead the correspondingfluxes in the radial, meridional, and azimuthal directions, c (cid:13) , 1–8 ffect of stellar wind magnetic fields respectively, and the vector G consists of the correspondingsource terms.We employ a finite difference approximation of theMHD equations, which is based on a conservative Godunov-type scheme, (cid:0) U n +1 i,j,k − U ni,j,k (cid:1) ∆ t + 1 r i (cid:16) r i +1 / Γ n +1 / i +1 / ,j,k − r i − / Γ n +1 / i − / ,j,k (cid:17) ∆ r + 1 r i sin( θ j ) (cid:16) sin( θ j +1 / )Ψ n +1 / i,j +1 / ,k − sin( θ j − / )Ψ n +1 / i,j − / ,k (cid:17) ∆ θ + 1 r i sin( θ j ) (cid:16) Φ n +1 / i,j,k +1 / − Φ n +1 / i,j,k − / (cid:17) ∆ φ = G ni,j,k , (10)where the quantities with half-integer numbers correspondto intermediate time steps. These quantities are determinedon the basis of the approximate Riemann solver. A small re-gion around the polar axis ( θ = 0) is treated separately in alocal Cartesian coordinate system in order to avoid singular-ities. The condition ∇ · B = 0 is maintained employing themethod proposed by Powell (1994) and Powell et al. (1999),with the modifications of Janhunen (2000).The stellar wind flow is loaded by newly born planetaryions generated by charge exchange with the exoplanet’s neu-tral exosphere. The mass loading process results in a strongdeceleration of the stellar wind plasma and in an enhance-ment of the magnetic field in front of the obstacle, whichcorresponds to the formation of an induced magnetosphere.We approximate the streamlined obstacle by a semi-sphere.The distance between the planet and the stagnation point ofthe stellar wind ( R s ) is determined by the pressure balancecondition. This means that the total pressure of the externalmagnetized stellar wind flow at the stagnation point has tobe equal to the sum of the thermal and dynamic pressuresof the internal atmospheric flow.We note that we shift the planetary center by somedistance d towards the star. We do this to avoid the viola-tion of the pressure balance at the flanks, where the stellarwind pressure at the obstacle boundary decreases substan-tially. We assume a d/R s distance ratio of 0.3. The calcu-lation domain for the MHD stellar wind flow is bound bythe external semi-sphere related to the undisturbed stellarwind region and the internal semi-sphere corresponding tothe streamlined obstacle. At the outer boundary, we set theundisturbed stellar wind parameters: density, velocity, tem-perature, and magnetic field. At the obstacle boundary, weset zero conditions for the normal components of the stel-lar wind velocity and magnetic field. We obtain a steady-state solution as a result of time relaxation of the non-steady MHD solution. As initial conditions, we apply theundisturbed stellar wind parameters in the computationaldomain. To study the EUV heating and expansion and to inferthe mass-loss rates of the hydrogen-dominated upper atmo-sphere of the planet, we apply a time-dependent 1D hydro-dynamic model described in detail by Erkaev et al. (2016).The model solves the absorption of the stellar EUV fluxby the thermosphere, the hydrodynamic equations for mass, momentum, and energy conservation, and the continuityequations for neutrals and ions (both atoms and molecules).The code also accounts for dissociation, ionization, recom-bination, and Ly- α cooling. The quasi-neutrality conditiondetermines the electron density.The model does not self-consistently calculate the ratioof the net local heating rate to the rate of the stellar radiativeenergy absorption. In general, this ratio, also called heat-ing efficiency, is not constant with altitude. Studies solvingthe kinetic Boltzmann equation applying a direct-simulationMonte Carlo model to calculate the heating efficiency indi-cate values between 10 and 20% (Shematovich et al. 2014).We therefore adopt a heating efficiency of 15%, which isin good agreement with what obtained by Owen & Jackson(2012), Shematovich et al. (2014), and Salz et al. (2016).As in Murray-Clay et al. (2009), we assume a singlewavelength for all EUV photons ( hν = 20 eV) and use anaverage EUV photoabsorption cross section for hydrogenatoms and molecules of 2 × − cm and 1.2 × − cm ,respectively, which are in agreement with experimental dataand theoretical calculations (e.g. Cook & Metzger 1964).In the framework of our spherically symmetric hydro-dynamic model for the planetary atmosphere, we can de-scribe only radial variations of the atmospheric density, pres-sure, velocity, and temperature. Since we are not capable todescribe angular variations of the atmospheric parameters(which requires a 2D model), we can fulfill the pressure bal-ance condition just at the central stagnation point, wherethe stellar wind velocity goes to zero. By applying this con-dition, we determine the radial distance between the stagna-tion point and the planetary center. In particular, we use theprofiles for the atmospheric parameters and find the pointwhere the sum of atmospheric thermal and dynamic pres-sures is equal to the stellar wind total pressure. The latteris the sum of the magnetic and plasma pressures, which de-pend on the stellar wind upstream input parameters. For the stellar and planetary system parameters (i.e., plan-etary mass M p , planetary radius R p , equilibrium temper-ature T eq , orbital separation a , stellar mass M star , andstellar radius R star ) we adopt the values of HD 209458and HD 209458b from Southworth (2010). Following the re-sults of Lammer et al. (2016), Cubillos et al. (2017), andFossati et al. (2017), we fix the lower boundary for the hy-drodynamic model of the planetary upper atmosphere atthe optical transit radius. Here, we assume that the pres-sure ( P ) is equal to 100 mbar and the temperature is equalto the equilibrium temperature ( T eq ). For the stellar EUVflux at the planet’s orbit ( I EUV ), we adopt the value givenby Guo & Ben-Jaffel (2016).In this work we consider both a slow and a fast stel-lar wind. The host star HD 209458 is similar to the Sun,both in terms of mass and age. Since observations cannotdirectly constrain the stellar wind parameters, we considertwo sets of parameters obtained from the solar wind mod-els presented by Johnstone et al. (2015), plus those inferredby KIS14 derived from fitting the HST Ly- α transit obser-vations. For the latter scenario, we study cases with andwithout a stellar magnetic field. The stellar magnetic fieldvalue was estimated by rescaling the solar interplanetary c (cid:13) , 1–8 N. V. Erkaev et al.
Table 1.
Input parameters of the simulations. The stellar windparameters, denoted by the index w , correspond to the values atthe planetary orbit of 0.047 AU. Case 1 corresponds to a slowand Case 2 to a fast stellar wind with the inclination angle be-tween the IMF and plasma velocity directions in the undisturbedstellar wind of θ B = 90 ◦ . Case 3 corresponds to the slow wind,but assumes a θ B = 45 ◦ . Cases 4 and 5 correspond to the stellarwind parameters obtained by KIS14, where the former neglects B w and the latter assumes B w = 0.014 G. Stellar Case 1 Case 2 Case3 Case 4 Case 5wind N w [cm − ] 4045 1371 4045 5000 5000 V w [km s − ] 236 532 236 400 400 T w [10 K] 1.3 2.9 1.3 1.1 1.1 B w [G] 0.014 0.014 0.014 0.0 0.014 θ B [ ◦ ] 90 90 45 — 90Planetaryparameters M p [ M Jup ] 0.714 R p [ R Jup ] 1.380 T eq [K] 1459 P [bar] 0.1 a [AU] 0.047Stellarparameters M star [ M ⊙ ] 1.148 R star [ R ⊙ ] 1.162 I EUV [erg s − cm − ] 1086 Note.
The parameters M p and R p are the planetary mass andradius, respectively, while M star and R star are those of the hoststar, and a is the orbital semi-major axis. magnetic field at the Earth’s orbit. The full set of adoptedinput parameters is given in Table 1. Assuming that HD 209458b has a negligible intrinsic mag-netic field, and by considering the input parameters givenin Table 1, we employ our 1D and 3D models to obtain theinduced magnetic field strength and the stellar wind plasmaparameters of the flow around HD 209458b’s planetary ob-stacle.Figure 1 shows the spatial distribution of the magneticfield strength obtained from the numerical MHD model em-ploying the Case 1 stellar wind parameters (slow wind).Here, the magnetic field is given in units of the stellar windmagnetic field, B w , which is equal to 0.014 G. The origin ofthe coordinate system is at planet center and the star is lo-cated along the X -axis, while the Z -axis is directed along thedirection of B w (the arrow in Fig. 1), which is assumed to beperpendicular to the undisturbed wind velocity (in the refer-ence frame of the planet). The white area close to the originof the Z -axis indicates a region filled just by atmosphericparticles, while the dark blue semi-circle indicates the plan-etary surface. The magnetic field has strong pile up in frontof the stagnation point. In this region of strong induced mag-netic field the magnetic pressure exceeds the local thermalgas pressure of the stellar wind loaded by the outflowingatmospheric atoms. To estimate the influence of the IMFrotation angle, we consider in Case 3 an inclination angle of θ B = 45 ◦ between the IMF and plasma velocity directions inthe undisturbed stellar wind. The calculated distribution of −6 −4 −2 0 2 4 60123456 Z / R p X / R p B B / B w Figure 1.
Cut at Y = 0 of the simulation showing the distributionof the magnetic field strength around HD 209458b normalized tothe IMF of 0.014 G for a slow stellar wind (Case 1). The white areaclose to the origin of the Z -axis indicates the atmospheric regionaround the planet, while the half-circle indicates the planetaryoptical radius. The star is located along the X -axis. The arrowshows the direction of the interplanetary magnetic field. −6 −4 −2 0 2 4 61234567 Z / R p X / R p B B / B w Figure 2.
Same as Fig. 1, but for an IMF inclined by 45 ◦ (Case 3). the magnetic field intensity is shown in Fig. 2. One can seethat the inclination angle of the magnetic field leads to anasymmetry of the flow structure and of the magnetopauseposition with respect to the planet. The maximum of thetotal pressure is also shifted away from the X -axis.By solving the non-steady MHD equations, a stationaryflow pattern is formed after some relaxation period. Initially,we assume that the uniform stellar wind flow is suddenly X / R p P t o t / P d w t = 1,7 R p / V w t = 2,1 R p / V w t = 2,5 R p / V w t = 2,9 R p / V w t = 3,4 R p / V w t = 4,0 R p / V w Figure 3.
Radial profiles along the line connecting the planetarycenter and the stagnation point for the total pressure (sum ofthe magnetic and thermal pressures) at six different calculationtimes. c (cid:13) , 1–8 ffect of stellar wind magnetic fields Figure 4.
From top to bottom: radial profiles along the stagna-tion line for the magnetic field strength, total pressure (sum of themagnetic and thermal pressures), and thermal pressure. The solidand dashed lines correspond to the Cases 1 and 2, respectively.The planet center is located at r = 0. stopped at the planetary obstacle. This results in the ap-pearance of a shock-like front close to the obstacle and whichpropagates outwards from it. Since we have a sub-Alfvenicstellar wind flow, this shock propagates far away towardsthe star. The time dependent propagation of the shock isindicated in Fig. 3, which shows the behaviour of the totalpressure along the line connecting the planetary center andthe stagnation point (hereafter stagnation line) at differentcalculation times. We reach a stationary profile after a timecorresponding to about 4 × R p /V w .Figure 4 shows the magnetic field strength, the totalstellar wind pressure (sum of magnetic and thermal pres-sures), and the thermal stellar wind pressure as a functionof the radial distance along the stagnation line for the stellarwind parameters of Case 1 (solid line) and Case 2 (dashedline). The magnetic field is given in units of IMF in theundisturbed stellar wind. The magnetic field and total pres-sure experience a substantial enhancement along the stag-nation line from the star towards the planet and reaches itsmaximum at the stagnation point. The magnetic field at thestagnation point is increased by a factor of . × cm − atthe stagnation point. This is due to the loading of the stel-lar wind plasma by newly ionized particles penetrating intothe flow from the planet’s upper atmosphere. The strongdeceleration of the stellar wind plasma near the stagnationpoint is caused by the appearance of the newly ionized slowparticles from the upper planetary atmosphere, which arecreated via charge exchange and immediately mixed intothe plasma flow environment.Figure 6 shows HD 209458b’s radial profiles of the up-per atmosphere’s hydrodynamic parameters. The top panelshows the radial profiles of the planetary upper atmospheric Figure 5.
Stellar wind velocity and number density as a functionof the radial distance along the stagnation line for Case 1 (solidline) and Case 2 (dashed line). The planet is located at r = 0. Figure 6.
Top: radial profiles of the planetary atmospheric num-ber densities of molecular hydrogen (H ; solid line), atomic hydro-gen (neutral plus ions; dashed line), and electrons (dash-dottedline). Middle: temperature and velocity of the escaping atmo-spheric particles as a function of distance from the planetary cen-ter. Bottom: sum of the dynamic and thermal pressures (Π) in theatmospheric hydrodynamic flow as a function of the radial dis-tance. The diamonds and the corresponding vertical dotted linesindicate the position of the stagnation points for the stellar windcases 1 to 5 . number densities of molecular hydrogen, total atomic hy-drogen (neutrals and ions), and electrons. The middle panelshows the temperature and velocity of the escaping atmo-spheric particles as a function of the radial distance. Thebottom panel presents the sum of the dynamic and thermalpressures (Π) in the atmospheric hydrodynamic flow as afunction of the radial distance. The diamonds and verticaldotted lines indicate pressure balance distances between thestellar wind plasma and the planetary outflow, correspond-ing to the stellar wind parameters of cases 1 to 5 (Table 1).One can see, that in cases 1 (slow wind) and 2 (fast wind)with θ B = 90 ◦ the pressure balance distances are rather closeto each other. Comparing the slow wind cases, Case 1 (withIMF and θ B = 90 ◦ ) with Case 3 (with IMF and θ B = 45 ◦ ),one can conclude that the angular difference of 90 ◦ → ◦ increases the obstacle distance from about 1.6 R p to 1.7 R p .The pressure balance for the slow wind (Case 1) isreached at the distance of about 1.6 R p . At this point thehydrogen number density N h (neutrals and ions) is equal to c (cid:13) , 1–8 N. V. Erkaev et al. × cm − . In case of an inclined magnetic field (Case 3; θ B = 45 ◦ ), the minimal stand-off distance increases slightlyto 1.7 R p .The pressure balance for the fast wind (Case 2) cor-responds to a smaller distance of about 1.53 R p , wherethe hydrogen number density is about 1.3 × cm − . InCase 4, the pressure balance distance is located at about1.9 R p with a total hydrogen number density of about4.5 × cm − . In Case 5, the pressure balance occurs atabout 1.47 R p , where the hydrogen number density is about1.6 × cm − . The pressure balance distances are muchcloser to the planet than those estimated in previous studies( & R p , i.e. outside the Roche lobe; e.g. Khodachenko et al.(2015); Shaikhislamov et al. (2016)), which neglect the in-duced magnetic field.In addition to the pressure balance, we consider alsothe penetration of the neutral atmospheric particles into thestellar wind. For these particles, we take into account radia-tive ionization and charge exchange processes. The newlyborn ions are captured by the IMF and move away togetherwith the magnetized stellar wind flow. From our simulations,we estimate that about 7 . × g s − H atoms are ion-ized and removed by the stellar wind flow. The correspond-ing loss of neutral H atoms is about 3 . × g s − , whichis in agreement with studies by Murray-Clay et al. (2009);Khodachenko et al. (2015); Shaikhislamov et al. (2016). Al-though the H + loss rates are about 4.6 times lower thanthe thermal escape of neutral H atoms, one should still con-sider that the H + loss rate is about twice higher than thatof suprathermal H atoms, which is about 3 . × g s − (Shematovich 2010).We remark that for all five stellar wind cases consideredin our study we obtained obstacle boundaries closer to theplanet than that yielding the best-fit to the Ly- α transit ob-servations (2.9 R p ; KIS14). By comparing the results of thepresent study with the parameters that have been obtainedby KIS14 to reproduce the observed Ly- α transit absorp-tion, one can expect that our resulting planetary obstaclesand the related stellar wind parameters most likely wouldnot reproduce the observations. If a planetary obstacle witha stand-off distance like that assumed by KIS14 at about3 R p is indeed necessary for fitting the Ly- α transit observa-tions, then HD 209458b should likely have a weak intrinsicmagnetic field.Table 2 shows the estimated strength of the planetarymagnetic moments M necessary to push the planetary ob-stacle to a distance of about 3 R p for the stellar wind cases 1to 5. The effect of the intrinsic planetary magnetic field wasestimated just by adding the planetary magnetic pressureterm to the pressure balance equation. Because the windof HD 209458 has likely a non-zero B w , HD 209458b mostlikely has an intrinsic magnetic moment with a strength ofabout 13–22% that of Jupiter’s. Our study also shows thataccurate modeling of Ly- α transit observations should notneglect intrinsic and induced magnetic fields, as well as theplasma environment in the planet’s vicinity. We apply a 3D MHD model to the stellar wind flow aroundthe planetary obstacle of the hot Jupiter HD 209458b, in
Table 2.
Planetary magnetic moments needed to push the ob-stacle to about 3 R p , necessary for the reproduction of the HSTLy- α transit observations for the five stellar wind cases consideredhere.Parameter cases M [A m − ] M [ M Jup ]Case 1: slow wind 2 . × . × . × . × w . × combination with a hydrodynamic upper atmosphere model.We model the hydrodynamically expanding hydrogen atmo-sphere due to the absorption of the EUV flux from its hoststar. In this system, the EUV flux has a rather high in-tensity, which is more than 200 times larger than that forpresent Earth. Such EUV flux provides sufficient heating ofthe upper atmosphere to drive the hydrodynamic outflow ofthe hydrogen atoms. In addition to EUV heating, we accountfor dissociation, ionization, and recombination processes andfocus only on the aspect of the interaction between the es-caping neutral hydrogen atoms and the magnetized stellarwind plasma flow. In particular, we analyzed the effect ofa strong enhancement of the stellar wind magnetic field infront of the planetary obstacle and its influence on the totalpressure and position of the boundary.Numerical solutions of the stellar wind interaction withan assumed non-magnetic HD 209458b-like planet are ob-tained for five sets of stellar wind parameters. The results ofthe MHD simulations indicate that a strong magnetic fieldpiles up in front of the planetary obstacle, where the mag-netic pressure dominates the gas pressure of the stellar windloaded by the ionized planetary particles. An important fea-ture is that the maximum of the total pressure at the stag-nation point is much larger than the dynamic pressure of theundisturbed stellar wind. This is due to the strong influenceof the induced magnetic field, which can move the plane-tary obstacle stand-off distance closer towards the planet,as compared to cases where the induced magnetic field isneglected.This indicates that Ly- α transit observations can giveimportant clues to understand how an exoplanet’s upperatmosphere reacts to the stellar wind. Another importanteffect of the interaction between the stellar wind and theexpanding planetary upper atmosphere is the pile-up ofions near the stagnation point due to charge exchangeprocesses. By comparing our results of an assumed non-magnetic HD 209458b-like exoplanet to the stellar wind pa-rameters and planetary obstacle obtained by KIS14 fromthe fit to the observed Ly- α transit observations, we findthat HD 209458b should likely have an intrinsic magneticmoment of about 13–22% that of Jupiter’s. This value islarger than that predicted by KIS14.An inclination of the IMF relative to the stellar windflow leads to a strong asymmetry of the flow structure, aswell as of the magnetopause position. The total pressuremaximum is shifted away from the X -axis, and the min-imum distance between the planet and the magnetopausebecomes a bit larger. Taking an inclination angle of 45 ◦ , c (cid:13) , 1–8 ffect of stellar wind magnetic fields we estimate that an intrinsic planetary magnetic momentof about 2 . × A m − is necessary to shift the magne-topause to the distance of about 3 R p , in order to agree withthe Ly- α transit observations.Finally, our results show that the atmospheric loss rateof a weakly magnetized HD 209458b-like hot Jupiter is dom-inated by the EUV-driven hydrodynamic escape of H atoms,which is of the order of about 3 . × g s − , which is about4.6 times and about 10 times larger than the loss rates ofH + ions and suprathermal H atoms, respectively. ACKNOWLEDGMENTS
The authors thank the anonymous referee for their use-ful comments. HL, PO and NVE acknowledge supportfrom the Austrian Science Fund (FWF) project P25256-N27 “Characterizing Stellar and Exoplanetary Environ-ments via Modeling of Lyman- α Transit Observationsof Hot Jupiters”. The authors acknowledge the supportby the FWF NFN project S11601-N16 “Pathways toHabitability: From Disks to Active Stars, Planets andLife”, and the related FWF NFN subprojects, S11604-N16 “Radiation & Wind Evolution from T Tauri Phaseto ZAMS and Beyond” (CJ), S11606-N16 “MagnetosphericElectrodynamics of Exoplanets” (MLK) and S11607-N16“Particle/Radiative Interactions with Upper Atmospheresof Planetary Bodies Under Extreme Stellar Conditions”(KK, HL, NVE). DK, LF, and NVE acknowledge alsothe Austrian Forschungsf¨orderungsgesellschaft FFG project“TAPAS4CHEOPS” P853993. The authors further acknowl-edge support by the Russian Foundation of Basic Researchgrants No 15-05-00879-a (NVE, AVM) and No 16-52-14006(NVE, AVM, IFS). MLK also acknowledges support byFWF projects I2939-N27, P25587-N27, P25640-N27, andthe Leverhulme Trust Grant IN-2014-016.
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