A Case Study of the Plasma in the Magneto-Sheath Using The

MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017

A case study of the plasma in the magnetosheath using the numerical magnetosheathmagnetosphere model and THEMIS measurements

Polya Dobreva1,*, Olga Nitcheva1, Monio Kartalev1 1 Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., block 4, Sofia, Bulgaria

Abstract. This paper presents a case study of the plasma parameters in the magnetosheath, based on THEMIS measurements. As a theoretical tool we apply the self-consistent magnetosheath-magnetosphere model. A specific aspect of the model is that the positions of the bow shock and the magnetopause are self-consistently determined. In the magnetosheath the distribution of the velocity, density and temperature is calculated, based on the gas-dynamic theory. The magnetosphere module allows for the calculation of the magnetopause currents, confining the magnetic field into an arbitrary non-axisymmetric magnetopause. The variant of the Tsyganenko magnetic field model is applied as an internal magnetic field model. As solar wind monitor we use measurements from the WIND spacecraft. The results show that the model quite well reproduces the values of the ion density and velocity in the magnetosheath. The simlicity of the model allows calulations to be perforemed on a personal computer, which is one of the mean advantages of our model.

1 Introduction The magnetosheath plays very important role in the solar wind–magnetosphere-ionosphere interaction. In the magnetosheath the solar wind slows down, as its density and temperature increase. The Earth’s magnetosheath is a transitional region, through which energy is transferred from the Sun to the Earth’s atmosphere. Therefore, understanding the mechanism of energy transfer requires the creation of adequate magnetosheath models. The pioneering work in description the magnetosheath dynamics was the model of Spreiter [1]. For given input parameters – the Mach number and polytropic index, and a given magnetopause shape, the model calculates the plasma parameters in the magnetosheath - density, velocity and temperature. The bow shock position is also calculated as a part of the solution. Later, the model was further developed including the distribution of the magnetic field in the magnetosheath [2]. As the solution (and in particular the velocity distribution) is known, the magnetic field in the magnetosheath can

* Corresponding author: [email protected]

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017

easily e calculated from the magnetic induction euation. oweer, the model has some limitations, such as the assumption of aisymmetric ow shoc shape and a gien prescried shape of the magnetopause . Eecution of large gloal simulations in the domains of the solar wind to the atmosphere reuires significant computing resources. n recent decades, the adances of computer technology made possile the creation of codes, that sole the magnetohydrodynamics euations. Eamples of these simulations are the gino model , S model rand nified agnetosphere–onosphere oupling Simulation . ther well nown codes include pen pen eneral eospace irculation odel , model yon–edder–oarry , S Space eather odelling ramewor which is ased on TSS code . The numerical magnetosheathmagnetosphere model was deeloped ased on a simpler gasdynamic approach, that is capale of descriing the main characteristics of the megnetosheath without the need for etreme computational resources. The model is ale to reproduce the real geometry of the magnetosheath oundaries ow shoc S and magnetopause , including indentations around the cusp at the magnetopause. The model also accounts for the downdus asymmetries in the tail magnetopause and north south displacement, induced y the dipole tilt ariations. The accuracy and relatie simplicity of our model mae it an accessile instrument to descrie the largescale magnetosheath properties. The model was preiously applied to study the ion flu distriution in the magnetosheath, using the nterall measurements mainly – , . The aim of this paper is to test the model capailities on recent data from the TES mission. arameters to e interpreted are the ion elocity and ion density in a case of TES passage through the magnetosheath. n une the satellite crosses the euatorial magnetosheath close to the terminator plane. rief description of the model will e gien in Section . n Section we will present the solar wind data, the magnetosheath data and a comparison etween the model calculations and the eperiment.

2 MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017 easily e calculated from the magnetic induction euation. oweer, the model has some The st inde ased on the oto e page and the dipole tilt are also set at the limitations, such as the assumption of aisymmetric ow shoc shape and a gien eginning of a simlation more detailed description of the nmerical algorithm sed in prescried shape of the magnetopause . the calclations can e fond in preios papers Eecution of large gloal simulations in the domains of the solar wind to the atmosphere reuires significant computing resources. n recent decades, the adances of computer technology made possile the creation of codes, that sole the 3 Numerical results magnetohydrodynamics euations. Eamples of these simulations are the gino model , S model rand nified agnetosphere–onosphere oupling Simulation . 3.1 Input data ther well nown codes include pen pen eneral eospace irculation odel , model yon–edder–oarry , S Space eather odelling n ne the E spacecraft is in orit arond agrange point ince ramewor which is ased on TSS code . dring this interal the E densit measrements are not aailale we will se The numerical magnetosheathmagnetosphere model was deeloped ased on a simpler measrements from the spacecraft as inpt data The spacecraft is also gasdynamic approach, that is capale of descriing the main characteristics of the megnetosheath without the need for etreme computational resources. The model is ale to reproduce the real geometry of the magnetosheath oundaries ow shoc S and magnetopause , including indentations around the cusp at the magnetopause. The model also accounts for the downdus asymmetries in the tail magnetopause and north south displacement, induced y the dipole tilt ariations. The accuracy and relatie simplicity of our model mae it an accessile instrument to descrie the largescale magnetosheath properties. The model was preiously applied to study the ion flu distriution in the magnetosheath, using the nterall measurements mainly – , . The aim of this paper is to test the model capailities on recent data from the TES mission. arameters to e interpreted are the ion elocity and ion density in a case of TES passage through the magnetosheath. n une the satellite crosses the euatorial magnetosheath close to the terminator plane. rief description of the model will e gien in Section . n Section we will present the solar wind data, the magnetosheath data and a comparison etween the model calculations and the eperiment.

2 Short description of the model ere, we will present only in general outline the numerical scheme that has een applied. The interaction of the solar wind with the Earth’s magnetosphere is descried y the self consistent magnetosheathmagnetosphere model. singlefluid model is implemented in the magnetosheath, while in the magnetosphere we employ a magnetic field model. The flow in the magnetosheath is descried y the compressile Euler euations of a perfect gas. The system of euations is soled y a ariant of the gridcharacteristic methods , Fig. 1. Input solar wind data on 10-11 June 2009 : a) ion number density; b) Vx component of the ion which are often used in gasdynamics. The magnetic field is represented as a ariant of the velocity; c) ion temperature Ti (green) and electron temperature Te (gray); d) Bx, e) By and f) Bz GSM magnetosphere model of Tsyganeno T or T , . The Tsyganeno model is (Geocentric Solar Magnetospheric) components of the interplanetary magnetic field. The data are not shifted in time. modified to allow for a particular, nonaisymmetric shape of the oundary. The magnetopause is approimated as a surface of a tangential discontinuity. in the pristine solar wind located at aot E Earth radii from the Earth The The imposed oundary conditions are the anineugoniot relations. They are reduced propagation time from to the Earth aries etween min at T and to the pressure alance euation at the magnetopause. The euation allows us to otain min at T on ne The plasma and magnetic field measrements condcted specific magnetopause geometry, including indentations at the cusp, northsouth and dawn the satellite on ne are presented in ig ring this interal the solar dus asymmetries. Thus, there is no need of rescaling the satellite traectories or the wind conditions are iet as the plasma parameters ar in a narrow range The ion magnetosheath thicness in order to achiee a coincidence with the oundary positions. densit is almost constant – aot sm similarl to the electron temperatre that is nput data are plasma and magnetic field properties of the incoming flow, including the aot ºK. The elocit aries in the range ms the ion dynamic pressure d, sonic ach numer , y and components of the nterplanetary temperatre is ºK at the beginning of the interval, drops to about ºK at agnetic ield , polytropic coefficient γ. the interal T on ne and rises to ºK after 2:00 UT on ne

3 MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017

The input densit, veloit and eletron teperature are based on olar ind perient devie , the ion teperature – on lasa analer 20. The nterplanetar agneti field is deterined b agneti ield nvestigation 2. The tie resolution is . in for the densit, the veloit and the ion teperature, in for the agneti field and 2s for the eletron teperature.

3.2 Magnetosheath measurements

Fig. 2. Projection of the TH B orbit on the (X,Y) and (Y,Z) GSE (Geocentric Solar Ecliptic) coordinate planes, during the interval [12:00-06:00] UT on 10-11 June 2009. The point denotes the beginning of the interval. The inner curve represents the magnetopause from the Shue 97 model [24], calculated with average solar wind parameters of Pd=2 nPa, and Bz=0 nT, while the outer curve is the bow shock, calculated by our model for the above mentioned magnetopause boundary. ro pril to une 200 the ere on radiation belt ission and oved in stritl ellipti orbits ith apogees on the dus side. The outer probes T and 2 T have an apogee of 0 and 20 respetivel. The inner three probes T , T and T oved lose to eah other ith an apogee of 2 .

4 MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017

3.2 Magnetosheath measurements

T Tie istor of events and arosale nteration during ubstors is a onstellation of five probes, hih priar obetive is to stud the energ release during the substors in the agnetosphere 22, 2. aunhed on ebruar 200, the arried idential instruentation aboard. or the first onths of the ission, the operated in so alled oast phase, oving as a tight luster in elliptial orbit ith an apogee of . . fter the preliinar phase, that ontinued until epteber 200, the ere separated fro eah other and their baseline ission of sientifi observations began. Fig. 3. Plasma measurements, conducted onboard THEMIS B satellite on 10-11 June 2009: a) ion number density; b) Vx (blue) ,Vy (gray) and Vz (red) GSM component of the measured ion velocity. The vertical dashed lines denote the moments of the BS and MP crossings. On 10-11 June 2009 all five satellites moved on the dusk side, as the inner three probes P3, P4 and P5 stayed in the magnetosphere. The outer P2 probe only partially crossed the magnetosheath. We will use data from the outermost P1 probe, which on 10-11 June crossed the magnetosheath entirely. In this paper we use TH B notation to refer to THEMIS P1 probe, which is most commonly used in the literature. Fig. 2. shows the orbit of TH B on two perpendicular GSE planes, corresponding to the interval [12:00 – 06:00 UT] on 10-11 June 2009. For clarity, exemplary shapes of the bow shock and magnetopause are also shown. The magnetopause shape is the form of Shue 1997 [24], corresponding to mean values of dynamic pressure Pd=2. nPa and IMF Bz = 0.nT. The bow shock is that calculated by out model for the given magnetopause shape and given input parameters of Mach=8 and polytropic index γ =2. Most of the time TH B stayed close to equatorial GSE plane, meanwhile moving earthward and slowly northward. Fig. 2. Projection of the TH B orbit on the (X,Y) and (Y,Z) GSE (Geocentric Solar Ecliptic) The ion density and velocity, based on TH B on 10-11 June 2009 are visualized in Fig. coordinate planes, during the interval [12:00-06:00] UT on 10-11 June 2009. The point denotes the 3. The jump of the density and velocity shows, that the satellite crosses the BS at 16:03 UT beginning of the interval. The inner curve represents the magnetopause from the Shue 97 model [24], and after 2:50 UT (11 June) it stayed entirely in the magnetosphere. The density drop at the calculated with average solar wind parameters of Pd=2 nPa, and Bz=0 nT, while the outer curve is the bow shock, calculated by our model for the above mentioned magnetopause boundary. short interval [16:20-16:40 UT] is associated with the satellite’s re-entering in the solar wind. After 16:40UT the spacecraft remained entirely in the magnetosheath. Since our ro pril to une 200 the ere on radiation belt ission and oved in purpose is not the investigation of multiple crossings we will consider the magnetosheath stritl ellipti orbits ith apogees on the dus side. The outer probes T and 2 passage from the moment of the first BS crossing at 16:03 UT. During the interval [2:20- T have an apogee of 0 and 20 respetivel. The inner three probes T , 2:50 UT] on 11 June the satellite encountered both magnetosheath and magnetospheric T and T oved lose to eah other ith an apogee of 2 . plasma, as after 2:50UT TH B remained in the magnetosphere. The data, shown on the plot are based on TH B/ESA (Electrostatic Analyzer) instrument [25] and have a time resolution of 6.5 min.

3.3 Model results Our purpose is to calculate the values of the plasma parameters along the satellite trajectory in the magnetosheath and to compare them with the measurements. Here we apply the algorithm, that was already used in our previous papers, considering satellite data interpretation [10, 11, 16]. We divide the whole interval into three subintervals [16:03-18:30 UT], [18:30-22:30 UT], [22:30-2:50 UT] and make the calculations with sets of input parameters, corresponding to the time moments 16:45UT, 22:00UT (on 10 June) and 2:30 UT (on 11

5 MATEC Web of Conferences 145, 03004 (2018) https://doi.org/10.1051/matecconf/201814503004 NCTAM 2017

e he ales i each idiidal iteral are cocateated to ie the soltio i the etire iteral araeters alied i the silatios are ie i ale the ratio o seciic heats is γ

Table 1.

UT Pd M By Bz Dst tilt º 24.7º º

i resets distritios o the desit a ad elocit i the aetosheath calclated at the oet o crossi he lai that asses throh the satellite locatio at the oet o the crossi is show he satellite orit is also added he le oit deotes the satellite ositio whe it iall eters ito the aetoshere at e see that the osered oet o crossi is i ood coicidece with the odelcalclated odar

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e he ales i each idiidal iteral are cocateated to ie the soltio i the solar wind ig. 4a. The density reaches its maimum at the ow shock, which is aout 1.7 etire iteral araeters alied i the silatios are ie i ale the ratio o times higher than that at the magnetopause – ig. 4a, ig . seciic heats is γ

Table 1.

UT Pd M By Bz Dst tilt º 24.7º º

Fig. 5. omparison etween the measured plasma parameters lue and those, calculated y the model green. rom top to ottom , y , components and of the ion velocity.

Fig. 4. istritio o the io desit let ad the elocit riht i the aetosheath he araeters are reseted i o diesioal its he thic lac lie deicts the orit roectio o ro o e he coariso o the reslts o the calclatio o the lasa elocities with the oes easred ooard is show i i he directioal cooets i coordiates ad the asolte ale o the elocit are show s the traector is close to omparison etween the measured lue and the numerically calculated green ion density. the eatorial lae the low has stro ad cooets the cooet is Fig. 6. sall ad aries i rae 50 ÷ 50 km/s. The computed values of the directional cooets ad coicide well with the reistered oes – i a he odel 4 Summary cooets diers ore siiicatl ro the osered ales t this cooet i itsel is less tha other cooets eore the crossi at is i the This is a test of the model capailities in the description of the ehaviour of the plasma solar wind and measures the velocity of the solar wind. At the satellite’s position, close to parameters in the magnetosheath. ere, data from the most recent space mission of the teriator lae the elocit i the aetosheath is aot ro the solar wid T spacecraft were used. The model presented here is capale of descriing the elocit – i d measured plasma parameters in the magnetosheath with great accuracy and may e used to i resets the osered ad ericall calclated io desit at the oits o the interpret the phenomena, oserved in the terrestrial magnetosheath. satellite’s trajectory in the magnetosheath on 10 e e osere a ood coicidece o the odelcalclated ad easred ales o the desit e see i the lgarian National Council “Scientific Research” under Project aetosheath a icrease o the desit a actor o coared to the shoced

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