Radio emission in Mercury magnetosphere
AAstronomy & Astrophysics manuscript no. RadioEmission c (cid:13)
ESO 2018October 15, 2018
Radio emission in Mercury magnetosphere
J. Varela V. Reville A. S. Brun F. Pantellini and P. Zarka AIM, CEA / CNRS / University of Paris 7, CEA-Saclay, 91191 Gif-sur-Yvette, Francee-mail: [email protected] LESIA, Observatoire de Paris, CNRS, UPMC, Universite Paris-Diderot, Place J. Janssen, 92195 Meudon, France LESIA & USN, Observatoire de Paris, CNRS, PSL / SU / UPMC / UPD / SPC, Place J. Janssen, 92195 Meudon, Franceversion of October 15, 2018
ABSTRACT
Context:
Active stars possess magnetized wind that has a direct impact on planets that can lead to radio emission. Mercury is a goodtest case to study the e ff ect of the solar wind and interplanetary magnetic field on radio emission driven in the planet magnetosphere.Such studies could be used as proxies to characterize the magnetic field topology and intensity of exoplanets. Aims:
The aim of this study is to quantify the radio emission in the Hermean magnetosphere.
Methods:
We use the MHD code PLUTO in spherical coordinates with an axisymmetric multipolar expansion for the Hermeanmagnetic field, to analyze the e ff ect of the interplanetary magnetic field (IMF) orientation and intensity, as well as the hydrodynamicparameters of the solar wind (velocity, density and temperature), on the net power dissipated on the Hermean day and night side. Weapply the formalism derived by Zarka [2001, 2007] to infer the radio emission level from the net dissipated power. We perform a set ofsimulations with di ff erent hydrodynamic parameters of the solar wind, IMF orientations and intensities, that allow us to calculate thedissipated power distribution and infer the existence of radio emission hot spots on the planet day side, and to calculate the integratedradio emission of the Hermean magnetosphere. Results:
The obtained radio emission distribution of dissipated power is determined by the IMF orientation (associated with thereconnection regions in the magnetosphere), although the radio emission strength is dependent on the IMF intensity and solar windhydro parameters. The calculated total radio emission level is in agreement with the one estimated in [Zarka, 2001], between 5 × and 2 × W. Key words.
Mercury’s magnetosphere – Hermean magnetosphere – solar wind – radio emission
Contents ff ect of the interplanetary magnetic field 3 ff ect of the hydro parameters of the solar wind 75 Conclusions and discussion 7
1. Introduction
An obstacle facing a magnetized flow leads to the partial dis-sipation of the flow energy. Part of the energy is dissipated asradiation in di ff erent ranges of the electromagnetic spectrum, de-pending on the incoming flow properties and the intrinsic mag-netic field of the obstacle. This scenario describes the interactionof the stellar wind with the magnetosphere and atmosphere ofplanets or other stars.The power dissipated in the interaction of a magnetized flowwith an obstacle can be sized as the intercepted flux of themagnetic energy ([ P d ] ≈ B v π R obs / µ ), with B the magneticfield intensity perpendicular to the flow velocity in the frame of the obstacle, µ o the magnetic permeability of the vacuum, v the flow velocity and R obs the radius of the obstacle. See Sauret al. (2013); Strugarek et al. (2015) for a description of the sizeand shape of the intersecting region and location of the maximalPoynting flux generation.The planets of the solar system with intrinsic magnetic fieldsare emitters of cyclotron MASER emission at radio wavelengths,generated by energetic electrons (keV) traveling along the mag-netic field lines, particularly in the auroral regions (Wu 1979).The source is the reconnection region between the interplane-tary magnetic field (IMF) and the intrinsic magnetic field of theplanet, although in gaseous planets as Jupiter there are other in-ternal sources like the plasma released from Io’s torus or the fastrotation of the planet. The magnetic energy is transferred as ki-netic and internal energy to the electrons (consequence of the lo-cal balance between Poynting flux, enthalpy and kinetic fluxes).Most of the power transferred is emitted as aurora emission inthe visible electromagnetic range, but a fraction is invested incyclotron radio emission (Zarka 1998).Radiometric Bode’s law links up incident magnetized flowpower and obstacle magnetic field intensity with radio emissionas [ P rad ] = β [ P d ] n , with [ P rad ] the radio emission and β the ef-ficiency of dissipated power to radio emission conversion with n ≈ β values between 3 · − to 10 − (Zarka 1997).The power dissipated in the interaction between solar windand magnetosphere field is strongly variable. Indeed several fac- Article number, page 1 of 10 a r X i v : . [ a s t r o - ph . E P ] A ug & A proofs: manuscript no. RadioEmission tors influence the nature of the interaction. The topology of theplanet magnetic field is a ff ected by the IMF orientation and in-tensity, as well as hydrodynamic parameter of the solar wind(SW) like density, velocity or temperature, leading to di ff er-ent distributions of radio emission hot spots and total emis-sivity. This is the case of Mercury, where the proportion ofIMF and Hermean (Mercury) magnetic field intensity, definedas α = B sw / B M (Baker 2009, 2011), oscillates from 0.3 duringa coronal mass ejection, B sw ≈
65 nT, to 0.04 for a period oflow magnetic activity of the Sun, B sw ≈ ff erent configurations of theHermean magnetosphere (Fujimoto 2007) due to the reconnec-tion with the planet magnetic field (Slavin 1979). At the sametime, SW hydrodynamic parameters predicted by ENLIL (time-dependent 3D MHD model of the heliosphere) + GONG WSA(prediction of background solar wind speed and IMF polarity)cone models show too a large range of possible values: between12 −
180 cm − for density, 200 −
500 km / s for velocity and2 · − · K for temperature (Odstrcil 2003; Pizzo 2011).Consequently, a parameter study is required to analyze the radioemission from Mercury.First measurements of the Hermean magnetic field byMariner 10 identified a dipolar moment of 195 nT ∗ R M ( R M Mer-cury radius) (Slavin 2008), further refined by MESSENGER ob-servations leading to a more precise description as a multipo-lar expansion (Anderson 2008a). Electron cyclotron frequencyin the Hermean magnetosphere is smaller than the plasma fre-quency of the SW, so the radio power in Mercury is expected tobe trapped into the magnetosphere (Zarka 2000).The aim of this study is to calculate the radio emission drivenin the interaction of the solar wind with the Hermean magneto-sphere, analyzing the kinetic and magnetic energy flux distribu-tions as well as the net power dissipated on the planet day andnight side. The analysis is performed for di ff erent orientationsof the IMF and SW hydro parameters. The radio emission fromplanetary magnetospheres is a source of information to foreseenthe topology and intensity of exoplanets magnetospheres.The interaction of the SW with the Hermean magnetosphereis studied using di ff erent numerical frameworks as single (Kabinet al. 2008; Jia et al. 2015), multifluid (Kidder et al. 2008)and hydrid codes (Wang et al. 2010; Müller et al. 2011, 2012;Richer et al. 2012). The simulations show that the Hermean mag-netic field is enhanced or weakened in distinct locations of themagnetosphere according to the IMF orientation, modifying itstopology (Slavin 1979; Kabin et al. 2000; Slavin et al. 2009).To perform this study we use the MHD version of the singlefluid code PLUTO in spherical 3D coordinates (Mignone 2007).The Northward displacement of the Hermean magnetic field isrepresented by a axisymmetric multipolar expansion (Anderson2008b). Present study is based in previous theoretical studiesdevoted to simulate global structures of the Hermean magneto-sphere using MHD numerical models (Varela 2015, 2016a,b).This paper is structured as follows. Section II, description ofthe simulation model, boundary and initial conditions. SectionIII, analysis of the radio emission generation for configurationswith di ff erent IMF orientations and intensities. Section IV, studyof the radio emission generation for configurations with di ff erentSW hydro parameters. Section V, conclusions and discussion.
2. Numerical model
We use the ideal MHD version of the open source code PLUTOin spherical coordinates to simulate a single fluid polytropicplasma in the non resistive and inviscid limit (Mignone 2007).The conservative form of the equations are integrated usinga Harten, Lax, Van Leer approximate Riemann solver (hll) asso-ciated with a di ff usive limiter (minmod). The divergence of themagnetic field is ensured by a mixed hyperbolic / parabolic diver-gence cleaning technique (Dedner 2002).The grid is made of 196 radial points, 48 in the polar angle θ and 96 in the azimuthal angle φ (the grid poles correspond to themagnetic poles). The numerical magnetic Reynolds number ofthe simulations due to the grid resolution is R m = V L /η ≈ V = m / s and L = . · m the characteristic velocityand length of the model, and η ≈ . · m / s the numericalmagnetic di ff usivity of the code. The numerical magnetic di ff u-sivity was evaluated in dedicated numerical experiments using amodel with the same grid resolution but a simpler setup.In order to have a realistic representation of the Hermeanmagnetic field we make use of the current best knowledge of itstopology and amplitude based on MESSENGER data. Ander-son et al. (2012) study provides a multipolar expansion of thefield assuming an axisymmetric model, thus we implement inour setup an axisymmetric multipolar field up to l = m = Ψ is expanded in dipolar, quadrupolar,octupolar and hexadecapolar terms: Ψ ( r , θ ) = R M (cid:88) l = ( R M r ) l + g l P l ( cos θ ) (1)The current free magnetic field is B M = −∇ Ψ . r is the dis-tance to the planet center, θ the polar angle and P l ( x ) the Legen-dre polynomials. The numerical coe ffi cients g l taken from An-derson et al. 2012 are summarized in Table 1.coe ff g (nT) g / g g / g g / g −
182 0 . . . Table 1.
Multipolar coe ffi cients g l for Mercury’s internal field. The simulation frame is such that the z-axis is given by theplanetary magnetic axis pointing to the magnetic North pole andthe Sun is located in the XZ plane with x sun >
0. The y-axiscompletes the right-handed system.The simulation domain is confined within two sphericalshells centered in the planet, representing the inner and outerboundaries of the system. The shells are at 0 . R M and 12 R M .Between the inner shell and the planet surface (at radius unity inthe domain) there is a "soft coupling region" where special con-ditions apply. Adding the soft coupling region improves the de-scription of the plasmas flows towards the planet surface, isolat-ing the simulation domain from spurious numerical e ff ects of theinner boundary conditions (Varela 2016a,b). The outer boundaryis divided in two regions, the upstream part where the solar windparameters are fixed and the downstream part where we considerthe null derivative condition ∂∂ r = ∇ · B = R M the IMF is dominant andconstant). At the inner boundary the value of the intrinsic mag-netic field of Mercury is specified. In the soft coupling regionthe velocity is smoothly reduced to zero when approaching theinner boundary. The magnetic field and the velocity are parallel,and the density is adjusted to keep the Alfven velocity constant Article number, page 2 of 10arela et al.: Radio emission in Mercury magnetosphere v A = B / √ µ ρ =
25 km / s with ρ = nm p the mass density, n theparticle number, m p the proton mass and µ the vacuum magneticpermeability. In the initial conditions we define a paraboloid inthe night side with the vertex at the center of the planet, definedas r < . − sin ( θ ) cos ( φ ) / ( sin ( θ ) sin ( φ ) + cos ( θ )), where thevelocity is null and the density is two order of magnitude smallerthan in the solar wind. The IMF is also cut o ff at 2 R M .We assume a fully ionized proton electron plasma, the soundspeed is defined as v s = (cid:112) γ p /ρ (with p the total electron + proton pressure), the sonic Mach number as M s = v / v s with vthe velocity.The radio emission study for di ff erent IMF intensities is lim-ited to the range of 10 to 30 nT. Lower or higher IMF intensitiescorrespond to a solar magnetic activity below or over the aver-age, not considered in the present communication. In the radioemission study with di ff erent hydro parameter of the SW andfixed IMF orientation and intensity, we adopt the maximum andminimum values expected by ENLIL + GONG WSA cone mod-els for the SW density, temperature and velocity. The radio emis-sion for configurations mimicking CME conditions are out of thescope of this study.
3. Effect of the interplanetary magnetic field
In this section we estimate the radio emission in Mercury fordi ff erent orientations and intensities of the IMF. We calculatethe power dissipated by the interaction of the SW with the Her-mean magnetosphere on the planet day side and the reconnectionregion of the magnetotail on the planet night side. The e ff ectof the reconnections on the day side is fully accounted for thestudy.The energy flux is calculated as a combination of kinetic P k (associated with the solar wind dynamic pressure) and mag-netic terms P B (due to the reconnection between the IMF and theHermean magnetic field): P k = ρ v | v | (2) P B = E ∧ B µ = ( η J − v ∧ B ) ∧ B µ (3)where E is the electric field and J the current density. The e ff ectof the numerical magnetic di ff usivity η is negligible in the cal-culation of the power dissipation on the planet day side, but it isconsidered in the reconnection region.The net power dissipated is calculated as the volume integralof P k and P B :[ P k ] = (cid:90) V ∇ · (cid:32) ρ v | v | (cid:33) dV (4)[ P B ] = (cid:90) V ∇ · E ∧ B µ dV (5)On the day side, the volume integrated extends from the bowshock to the inner magnetosphere (magnetosheath and magne-topause included). On the night side the integrated volume islocalized around the X point of the magnetotail, covering the re-gion where the intensity of the planet magnetic field is at least10% smaller than for a configuration without IMF. We analyze first the e ff ect of the IMF orientation, fixing the hy-drodynamic parameters of the SW and the module of the IMFto 30 nT. The hydrodynamic parameters of the solar wind in thesimulations are summarized in Table 2. Figure 1 shows a 3Dview of the system for a Northward configuration of the IMF,identifying the region of the BS (color scale of the density dis-tribution), field lines of the Hermean magnetic field (red lines),IMF (pink lines) and solar wind stream lines (green lines). Thearrows indicate the orientation of the Hermean and interplane-tary magnetic fields and the dashed white line the beginning ofthe simulation domain. Fig. 1.
3D view of the system. Density distribution (color scale), fieldlines of the Hermean magnetic field (red lines), IMF (pink lines) andsolar wind stream lines (green lines). The arrows indicate the orientationof the Hermean and interplanetary magnetic fields (case Bz). Dashedwhite line shows the beginning of the simulation domain. n (cm − ) T (K) v (km / s) M s
60 58000 250 6 . Table 2.
Hydrodynamic parameters of the SW
In the following we identify the Mercury-Sun orientation asBx simulations, the Sun-Mercury orientation as Bxneg simula-tions, the Northward orientation respect to Mercury’s magneticaxis as Bz simulations (shown in figure 1 example), the South-ward orientation as Bzneg simulations, the orientation perpen-dicular to previous two cases on the planet orbital plane as By(East) and Byneg (West) simulations. The IMF intensity of themodel is denoted by a number attached to the orientation label,for example the simulation Bz3 identifies a Northward orienta-tion of the IMF with module 30 nT. All the simulations and pa-rameters are summarized in appendix A. We include as referencecase a simulation without IMF (B0).
Article number, page 3 of 10 & A proofs: manuscript no. RadioEmission
Fig. 2.
Hermean magnetic field lines with the intensity imprinted on thefield lines by a color scale for the reference case (A) and simulation Bx3(C). Magnetic field intensity at the frontal plane X = . R M . SW streamlines (green). Inflow / outflow regions on the planet surface (blue / red).Polar plot of the density distribution (displaced 0 . R M in Y direction)for the reference case (B) and simulation Bx3 (D). Dashed pink curveindicates the surface plotted in figures 3 and 4. In Figure 2 we illustrate the interaction of the IMF and mag-netospheric field for the reference case and Bx3 simulation. Pan-els A and C show the Hermean magnetic field lines (magneticfield lines are color-coded with the magnetic field amplitude),SW stream lines (green lines), magnetic field intensity at thefrontal plane X = . R M and inflow / outflow (blue / red) regionson the planet surface. Reconnection regions are identified as bluecolors at the frontal plane, not observed in the reference case andlocated in the South of the magnetosphere for the Bx3 simula-tion. Panels B and D show polar plots of the density distributionincluding the magnetic field lines of the planet (red lines) andSW stream lines (green lines), identifying the regions of the bowshock, magnetosheath and magnetopause. The dashed pink lineindicates the surface plotted in figures 3 and 4 for the Bx3 simu-lation.Figure 3 shows a frontal view of the magnetic energy fluxon the planet day side ( P B ( DS )) for di ff erent IMF orientations,observed towards the planet-Sun direction from the planet nightside. There is a strong dependency of P B ( DS ) hot spot distri-bution with the IMF orientation. Local minima of the magneticenergy flux are correlated with a local decrease of the Hermeanmagnetic field intensity, although local maxima are correlatedwith a local enhancement of the Hermean magnetic field. ForBx3 (panel A) and Bxneg3 (panel D) IMF orientations, P B ( DS )hot stops are located close to the planet. There is a North-Southasymmetry due to the presence of a reconnection region, lo-cated in the South (North) of the magnetosphere for the Bx3(Bxneg3) case, identified as a local decrease of P B ( DS ). Bx3 and Bxneg3 orientation weakly a ff ect the Hermean magnetospheretopology at low-middle latitudes, only nearby the poles, reasonwhy both cases appear to be similar. Compared with other IMForientations, the local maximum of P B ( DS ) is almost one orderof magnitude smaller. Models with By3 (panel B) and Byneg3(panel E) IMF orientations have P B ( DS ) hot spots nearby thepoles, showing the same East-West asymmetry than the mag-netosphere, with the reconnection regions located in the planetsides (local minimum of P B ( DS )). Bz3 (panel C) and Bzneg2(panel F) cases show di ff erent distributions of the P B ( DS ) hotspots, along the planet sides for Bz3 orientation (reconnectionregions located near the poles) and a quadripolar structure in theBzneg2 model (reconnection region at the planet equator). Theseresults indicate a large variability of the radio emission distribu-tion on the planet dayside with the IMF orientation. Thus, futureradio emission observation from exoplanets must show a strongdependency with the host star magnetic activity.Figure 4 shows a frontal view of the kinetic energy flux onthe planet day side ( P k ( DS )) for di ff erent IMF orientations, ob-served towards the planet-Sun direction from the planet nightside. There is a local enhancement (decrease) of P k ( DS ) associ-ated with a local decrease (enhancement) of the magnetosphericfield. P k ( DS ) is linked with the dynamic pressure of the SW al-though the local enhancements observed for all the IMF orien-tations is determined by the magnetosphere topology and IMForientation. This statement is valid in case of exoplanets as longas we consider a purely radial outflow of stellar wind betweenthe star and the exoplanet, condition that could not be fulfilledfor exoplanet with eccentric orbits.Figure 5 shows the magnetic energy flux ( P B ( NS )) on theplanet night side. P B ( NS ) distribution shows a local maxima be-tween the reconnection regions of the magnetotail and magne-topause for all IMF orientations. If the magnetotail is slender andstretched, case of By3 (panel B), Byneg3 (panel E) and Bzneg2(panel F) IMF orientations, the magnetic tension is larger lead-ing to a more e ffi cient dissipation of the magnetic energy andlarger P B ( NS ) values. We don’t include the analysis of the ki-netic energy flux ( P k ( NS )), whose local maxima is located inthe magnetotail reconnection region, because the expected radioemission associated with [ P k ] is small compared to [ P B ] (see ta-ble 4). Consequently, we must presume greater radio emissionon the exoplanets night side if the IMF orientation drives slen-der and stretched magnetotail topologies. At the same time, forexoplanets with more intense magnetic field hosted by stars withstronger magnetic activity than the Sun, radio emission on planetnight side should dominate because magnetic and kinetic energyfluxes in the magnetotail reconnection region are enhanced.Table 3 shows the magnetic and kinetic net power dissipatedon the planet day side and the reconnection region of the magne-totail on the planet night side. The net magnetic energy is neg-ative because the IMF interaction with the Hermean magneto-sphere leads in all models to a net erosion of the magnetosphericfield, so the system loses locally magnetic energy. The net kineticenergy is negative too on planet day side because the solar windis decelerated as soon as it reaches the Hermean magnetosphere,losing kinetic energy. The opposite scenario is observed in themagnetotail X point, there is a net gain of kinetic energy by theplasma because it is accelerated in the reconnection region. Bz3orientation is the only case with [ P k ( NS )] <
0, because it is theconfiguration with the magnetotail X point located the furthestfrom the planet, leading to a smaller magnetic energy flux andplasma acceleration in the reconnection region. [ P B ( DS )] and[ P k ( DS )] are larger than [ P B ( NS )] and [ P k ( NS )] for all IMF ori-entations except Bx3 case. [ P B ( DS )] for Bx3 and Bxneg3 IMF Article number, page 4 of 10arela et al.: Radio emission in Mercury magnetosphere
Fig. 3.
Frontal view of the magnetic energy flux on the planet day side for di ff erent IMF orientations. We observe the magnetic energy fluxdistribution towards the planet-Sun direction from the night side. 1st color bar is related to (A) and (D) panels, 2nd color bar to the other 4 cases.The plotted surface is defined between the bow shock and the magnetopause where the magnetic energy flux reaches its maxima (see fig. 2, panelsB and D, pink dashed line). orientations is one order of magnitude smaller than in other mod-els. [ P k ] is larger than [ P B ] on the planet day side although [ P B ]is larger than [ P k ] in the reconnection region of the magnetotailon the night side for the models By3, Byneg3 and Bzneg2. TheIMF orientation that drives the highest net power dissipation isBzneg2 configuration, while Bx3 orientation leads to the small-est. In table 4 we show the expect radio emission calculated fromthe net magnetic and kinetic power dissipated on the planet dayside and the reconnection region at planet night side using radio-metric Bode’s law (Zarka et al. 2001; Farrell 1999):[ P ( DS )] = a [ P k ( DS )] + b [ P B ( DS )] (6)[ P ( NS )] = a [ P k ( NS )] + b [ P B ( NS )] (7)with a and b e ffi ciency ratios assuming a linear dependency of[ P k ] and [ P B ] with [ P ]. Observations of other planets in the solarsystem are explained by two possible combination of parameters( a = − , b =
0) or ( a = b = · − ) (Zarka 2007).[ P B ] is similar to [ P k ] for all IMF orientations (except Bx3and Bxneg3 cases with [ P k ] one order of magnitude larger than[ P B ]), so the combination of e ffi ciency ratios ( a = − , b = a = b = · − ),see table 4. [ P ( NS )] for ( a = b = · − ) combination isalmost 5 times smaller than [ P ( DS )], pointing out that the main source of radio emission in the Hermean magnetosphere shouldbe the strong compression of the planet magnetic field lines bythe SW on the planet dayside, as well as local amplifications ofthe Hermean magnetic field by the IMF. To determine the com-bination of e ffi ciency ratios that better fits radio emission fromMercury, it is required to perform in situ measurements compar-ing radio emission on the planet day and night side. If the radioemission on the planet day side is in average 10 times larger thanthe radio emission at the night side, ( a = b = · −
3) combi-nation is the best description, although if the average di ff erenceis closer to 100 times, ( a = − b =
0) combination is the bestapproach. The ratio between radio emission on the planet dayand night side (DS-NS ratio) must change in exoplanets withmore intense magnetic fields, hosted by stars with stronger mag-netic activity than the Sun. It is mandatory to study the ratio ofDS-NS radio emission in giant planets of the solar system anddetermine which combination of e ffi ciency ratios fits better theobservations. We analyze the influence of the IMF amplitude variation on ra-dio emission. We perform 13 new simulation using the same SWhydro parameters and IMF orientations than in the previous sec-tion (see table 2), varying the IMF intensity from 10 to 30 nT.Figure 6 shows [ P ( DS )] (panel A) and [ P ( NS )] (panel B)( a = b = · − combination) for models with di ff er- Article number, page 5 of 10 & A proofs: manuscript no. RadioEmission
Fig. 4.
Frontal view of the kinetic energy flux on the planet day side for di ff erent IMF orientations. We observe the kinetic energy flux distributiontowards the planet-Sun direction from the night side.Color scale on the left for figures (A) and (D). The plotted surface is defined between the bowshock and the magnetopause where the kinetic energy flux reaches its maxima (see fig. 2, panels B and D, pink dashed line). Fig. 5.
Magnetic energy flux on the planet night side ( P B ( NS )). Blue color indicates the reconnection region (iso-surface with magnetic field valuesbetween 0 − ent IMF orientations and modules from 10 to 30 nT. [ P ( DS )]and [ P ( NS )] increase with the IMF module for all orientations except Bx and Bxneg cases, almost insensitive to the IMF inten-sity variation. The radio emission enhancement is linked with a Article number, page 6 of 10arela et al.: Radio emission in Mercury magnetosphere
Model [ P k ( DS )] (10 W) [ P B ( DS )] (10 W) [ P k ( NS )] (10 W) [ P B ( NS )] (10 W)Bx3 − . − .
13 3 . − . − . − .
25 3 . − . − . − .
81 3 . − . − . − .
83 3 . − . − . − . − . − . − . − .
94 7 . − . Table 3.
Net magnetic and kinetic power dissipated on the planet day side and the reconnection region at planet night side. SW hydrodynamicparameters: ρ =
60 cm − , v =
250 km / s and T = Model [ P ( NS )] (10 W) [ P ( DS )] (10 W) [ P ( NS )] (10 W) [ P ( DS )] (10 W)Bx3 0 .
32 0 .
28 3.11 4.60Bxneg3 0 .
17 0 .
48 3.48 4.71By3 1 .
59 5 .
64 3.30 5.93Byneg3 1 .
61 5 .
68 3.50 5.94Bz3 0 .
86 5 .
92 6.19 5.91Bzneg2 2 .
70 5 .
88 7.40 11.4
Table 4.
Expected radio emission on the planet day side and in the reconnection region of the magnetotail on the planet night side for the e ffi ciencyratios ( a = b = · − , second and third columns, and ( a = · − , b = local increase of the magnetospheric field by the IMF, amplifica-tion not observed in Bx and Bxneg simulations, because in theseconfigurations the Herman magnetic field and IMF are perpen-dicular at low and middle latitudes, with the reconnection regionlocated close to the poles. Bz orientation shows a decrease of[ P ( NS )] in the simulations with IMF module 10 and 20 nT, be-cause the magnetotail is wider and less stretched, leading to adecrease of the magnetic field lines tension. The tendency is in-verted in Bz3 simulation due to the induced North-South stretch-ing of the magnetotail.
4. Effect of the hydro parameters of the solar wind
This section studies the e ff ect of the SW hydrodynamic param-eters on radio emission generation. We perform 6 new simula-tions fixing IMF module and orientation, B S W = (4 , ,
6) nT.We choose a IMF configuration with weak module (7 .
28 nT) tomaximize the e ff ect of the SW hydro parameters, and a mixedorientation to show a more realistic case. SW parameters of ref-erence case are the same than in Table 3. The name of the modelis given by the hydro parameter that is modified respect to refer-ence case (see Table 5).Figure 7 shows a frontal view of the magnetic energy fluxon the planet dayside for di ff erent configurations of SW hydroparameters, observed towards the planet-Sun direction from thenight side. P B ( DS ) distribution is similar for all simulations, pointingout that the location of radio emission hot spots is dictated by theIMF orientation and not by the SW hydro parameters. SW hy-dro parameters can enhance or weaken the local maxima but thedistribution is only slightly modified. P B ( DS ) local maxima areenhanced if the SW dynamic pressure ( q = ρ v /
2) is larger, asin the simulations ρ max and v max , compared to low SW dynamicpressure configurations as ρ min and v min . P B ( DS ) local maximaare almost the same for T max and T min simulations, because thetemperature doesn’t a ff ect the Hermean magnetic field compres-sion, only leads to a decompression of the magnetosheath, in-creasing the SW sound velocity and reducing the sonic Machnumber. In summary, if we follow the evolution of the hot spotdistribution as the SW dynamic pressure increases (panels A, B, C, F, D and E in this order), hot spot intensity increases but thedistribution remains almost the same.Table 5 shows [ P B ( DS )], [ P k ( DS )] and [ P ( DS )] with radioe ffi ciency parameters ( a = b = · − ) and ( a = − , b = ff erent SW hydro parameters. ( a = b = · − ) combination leads to a radio emission two ordersof magnitude larger than ( a = − , b = P ( DS )] are ρ max and v max , more than one or-der of magnitude larger than configurations with lower dynamicpressure as ρ min and v min . T min and T max simulations show sim-ilar [ P ( DS )] values, slightly larger in the simulation with lesscompressed magnetosheath. [ P k ( DS )] is 2 to 5 times larger than[ P B ( DS )] for all cases except ρ max case. These results demon-strate that radio emissions are sensitive to the time variation ofthe SW hydro parameters.
5. Conclusions and discussion
The analysis of the power dissipation in 3D simulations of thesolar wind interaction with the Hermean magnetosphere showsthat hot spot distribution of the radio emission is determined bythe IMF orientation, although the intensity of the local maximais dictated by the IMF intensity and SW hydro parameters. Theorientation of the IMF establishes the location of the reconnec-tion regions in the Hermean magnetosphere. A local enhance-ment of the magnetospheric field on the day side is correlatedwith a maxima of the magnetic energy flux and a minima of thekinetic energy flux.The net dissipated power on the planet day side is larger thanin the reconnection region of the magnetotail on the planet nightside, by almost one order of magnitude larger. This proportioncan be very di ff erent in other planets of the solar system withmore intense magnetic field, facing a SW of lower dynamic pres-sure, as in the case of the Earth of giant gaseous planets, leadingto configurations with stronger radio emission from the recon-nection region of the magnetotail and weaker from the planetdayside.Radio emission on the planet day side is maximized forany IMF orientation di ff erent than Sun-Mercury or Mercury-Sundirections. These two cases show a radio emission more thanone order of magnitude smaller. The magnetic field lines of the Article number, page 7 of 10 & A proofs: manuscript no. RadioEmission
Fig. 6.
Radio emission on the planet day side (A) and in reconnection region of the magnetotail on the planet night side (B) with radio e ffi ciencyparameters ( a = b = · − ) for models with di ff erent IMF orientation and modules from 10 to 30 nT. The reference case without IMF isincluded. Bx orientations (black line), By orientations (red line) and Bz orientation (blue line). Model Mod. Parameter [ P k ( DS )] (10 W) [ P B ( DS )] (10 W) [ P ] (10 W) [ P ] (10 W) ρ min n =
12 cm − -1.03 -0.50 0.10 1.03 ρ max n =
180 cm − -8.24 -10.30 2.06 8.24v min v =
200 km / s -2.42 -0.72 0.14 2.42v max v =
500 km / s -18.1 -9.03 1.80 18.1 T min T = · K -3.66 -0.68 0.14 3.66 T max T = · K -4.78 -0.98 0.20 4.78
Table 5.
Second column indicates the hydrodynamic parameter modified respect to reference case ( n =
60 cm − , v =
250 km / s and T = ffi ciency parameters ( a = b = · − ), fourth column, and ( a = − , b = Fig. 7.
Frontal view of the magnetic energy flux on the planet day side for simulations with di ff erent SW hydro parameters. We observe themagnetic energy flux distribution towards the planet-Sun direction from the night side. The plotted surface is defined between the bow shock andthe magnetopause where the magnetic energy flux reaches its maxima (see fig. 2, panels B and D, pink dashed line). IMF and Hermean magnetosphere are almost perpendicular at low-middle latitudes, avoiding an amplification of the magneto-
Article number, page 8 of 10arela et al.: Radio emission in Mercury magnetosphere spheric field. This result is consistent with the weak dependencyof radio emission and IMF module for these orientations. Theother IMF orientations lead to local enhancements of the mag-netospheric field on the planet dayside, correlated with hot spotsof radio emission.The net dissipated power is dominated by the magnetic com-ponent, pointing out that on the planet night side the main sourceof radio emission is the magnetic tension of the magnetotail fieldlines. The consequence is a stronger radio emission in such mag-netosphere configurations with stretched magnetotail and recon-nection X point located close to the planet, see cases with Bzneg,By and Byneg IMF orientations.The combination of e ffi ciency ratios that lead to larger ra-dio emission is ( a = b = · − ), several order of magni-tude larger than the expected radio emission for the combination( a = − , b = a = b = · − a = − b = ffi ciency ratioscombination.The results obtained are compatible with the predicted valuesby Zarka et al. (2001), expecting a radio emission around 10 W.This is the case for all the simulations expect configurations withthe IMF oriented in Sun-Mercury of Mercury-Sun directions, ormodels with low dynamic pressure and weak IMF intensity. Sim-ulations with large dynamic pressure and IMF intensities largerthan 10 nT not oriented in Sun-Mercury of Mercury-Sun direc-tions, show radio emissions from 1 to 2 · W.Radiometric Bode’s law for Mercury’s magnetosphere con-sidering a stand o ff distance of 1 . R M predicts a net kinetic en-ergy dissipation of 6 · W and a net magnetic energy dissi-pation of 4 − · W (depending on the IMF intensity). Thenet kinetic energy dissipation calculated from the simulations issmaller than the expected value by Bode’s law, consequence ofthe complex flows reproduced in the simulations with regions ofplasma deceleration on the day side and acceleration in the mag-netotail reconnection region. On the other side, the simulationsand Bode’s law lead to similar results for the net magnetic en-ergy dissipation, pointing out that the model is able to provide areasonable guess of the magnetic energy dissipation on the dayside and magnetotail reconnection regions.A systematic study of the conversion e ffi ciency between dis-sipated power and radio emission in the planets of the solar sys-tem is a key study to calibrate the radio emission from exoplan-ets. It is expected that radio emission data brings constrains onthe intensity and topology of exoplanets magnetic fields, infor-mation required to study the potential habitability of exoplan-ets, directly linked with the presence of permanent and strongenough magnetic fields to shield the planet surface and atmo-sphere from the stellar wind erosion. We analyze the e ff ect ofthe IMF orientation and module, as well as SW hydro parame-ters on radio emission generation, showing the large variabilityinduced by these factors on hot spot distribution and intensity. Ageneralization of present study to the specific environment of theexoplanets, stellar wind of host star and expected IMF intensityand orientation at exoplanet orbit, is mandatory to reconstructthe topology and intensity of the intrinsic magnetic field from ra-dio emission data when available (Hess 2011; Zarka et al. 2015). Acknowledgements.
The research leading to these results has received fundingfrom the European Commission’s Seventh Framework Programme (FP7 / / PNST for our grant. We acknowledge GENCI allocation 1623 foraccess to supercomputer where most simulations were run and DIM-ACAV forsupporting ANAIS project and our graphics / post-analysis and storage servers. Article number, page 9 of 10 & A proofs: manuscript no. RadioEmission
Summary of simulations parameters:Model B (nT) n (cm − ) T (10 K) v (km / s)Reference (0, 0, 0) 60 0.58 250Bx (10, 0, 0) 60 0.58 250Bx2 (20, 0, 0) 60 0.58 250Bx3 (30, 0, 0) 60 0.58 250Bxneg (-10, 0, 0) 60 0.58 250Bxneg2 (-20, 0, 0) 60 0.58 250Bxneg3 (-30, 0, 0) 60 0.58 250By (0, 10, 0) 60 0.58 250By2 (0, 20, 0) 60 0.58 250By3 (0, 30, 0) 60 0.58 250Byneg (0, -10, 0) 60 0.58 250Byneg2 (0, -20, 0) 60 0.58 250Byneg3 (0, -30, 0) 60 0.58 250Bz (0, 0, 10) 60 0.58 250Bz2 (0, 0, 20) 60 0.58 250Bz3 (0, 0, 30) 60 0.58 250Bzneg (0, 0, -10) 60 0.58 250Bzneg2 (0, 0, -20) 60 0.58 250 ρ min (4, 1, 6) 12 0.58 250 ρ max (4, 1, 6) 180 0.58 250v min (4, 1, 6) 60 0.58 200v max (4, 1, 6) 60 0.58 500 T min (4, 1, 6) 60 0.20 250 T max (4, 1, 6) 60 1.80 250 Table .1.
Summary of simulations parameters.
Bzneg3 simulation is not included in the text because themagnetopause is located on the planet surface. Present modellacks the Physics required to correctly reproduce that scenario.
References