Cluster Hot Flow Anomaly Observations During Solar Cycle Minimum
Gabor Facsko, Mariella Tatrallyay, Geza Erdos, Iannis Dandouras
aa r X i v : . [ phy s i c s . s p ace - ph ] J u l Cluster hot flow anomaly observations duringsolar cycle minimum
G. Facsk´o ∗ , M. T´atrallyay , G. Erd˝os , and I. Dandouras KFKI Research Institute for Particle and Nuclear Physics, H-1525 Budapest,P.O.Box 49, Hungary, [email protected] CESR, 9, Avenue du Colonel ROCHE, 31028 TOULOUSE CEDEX 4, France
Summary.
Hot flow anomalies (HFAs) are studied using observations of the FGMmagnetometer and the CIS plasma detector aboard the four Cluster spacecraft. Pre-viously we studied several specific features of tangential discontinuities on the basisof Cluster measurements in February-April 2003 and discovered a new condition forforming HFAs that is the solar wind speed is higher than the average. However dur-ing the whole spring season of 2003, the solar wind speed was higher than average.In this study we analyse HFAs detected in 2007, the year of solar cycle minimum.Our earlier result was confirmed: the higher solar wind speed is a real condition forHFA formation; furthermore this constraint is independent of Schwartz et al.’s [9]condition for HFA formation.
Hot flow anomalies were discovered in the 1980s [8, 14]. It is commonly agreedthat HFAs are generated by the interaction of a tangential discontinuity andthe bow shock. They are explosive events, particle acceleration, magnetic de-pletion take place at their center and the magnitude of the magnetic fieldincreases at the rim. The plasma temperature increases whereas the densitydrops within the affected region, but the most interesting phenomenon is thedirectional change of the solar wind flow. The flow turns away from the anti-sunward direction and might even be directed backward [10, 11, 13, 14]. Boththe previous global investigation [9] and our earlier studies also indicated thatHFAs are not rare phenomena [3]. Cluster multispacecraft measurements helpnot only to understand the microphysics of HFA formation [5] but also todetect much more events than before because the spacecraft stay close to thebow shock for a long time; furthermore Cluster satellites have all necessaryinstruments to detect HFAs. ∗ Now at LPCE, 3A, Avenue de la Recherche Scientifique, 45071 ORL´EANSCEDEX 2, France Facsk´o et al.
We checked observationally a previous HFA simulation [4] determining thedifferent angles using Cluster FGM and CIS HIA together with ACE MAGand SWEPAM measurements in the solar wind. In doing so, we discovered anew condition of HFA formation which was not predicted by the simulations;namely that the solar wind velocity is [2]. Although a previous investigation in the magnetosheath[15] supports our result, however we want to check this condition in anotheryear closer to the solar cycle minimum because during the whole spring seasonof 2003, the solar wind speed was higher than average. We chose 2007 becausethis is close to the solar minimum and the average solar wind velocity wasexpected to be lower than in 2003 when solar wind velocity was higher than theaverage value in the whole February-April season. We searched and analysedCluster measurements in 2007 using the same methods like in [2] and comparedthem with previous results.The structure of this paper is the following: in Section 2 we discuss theprocessed and analysed measurements and in Section 3 we give the summaryof our results.
We set the same criteria for the selection of HFA events as in our previouspapers [2, 3]. Using these criteria we found more then 50 HFA events inJanuary-April 2007 and in all cases we could determine the discontinuitynormal from Cluster FGM and ACE MAG measurements.We identified the tangential discontinuities which generated HFA eventsbetween January 1 and April 30, 2007 using Cluster-1 and -3 FGM 1s averagemagnetic field and CIS 4s average solar wind speed measurements as well asMAG magnetic (16s) and SWEPAM (64s) plasma data from ACE. We appliedboth the minimum variance techniques [12] and the cross product method [7]to determine their normal vectors. We checked whether the normal componentof the magnetic field disappears at the discontinuity. If its value approacheszero then the discontinuity was identified as tangential and we could use thecross product method to determine its normal vector. We accepted the resultof minimum variance method if the angle between the minimum varianceand the crossproduct vector was less then 15 o . We plotted all discontinuitynormal determined using Cluster FGM and ACE MAG measurements. If aHFA was observed and its TD normal was calculated from more than oneCluster and the ACE spacecraft, the average vector was also plotted and thelargest deviation from its direction was considered as the error and it wasdrawn by dashed-dotted line on Fig. 1. Normal belonging to the same eventwas connected by dashed line.Almost all the cone angles of the TD normals are larger than 45 o as pre-dicted theoretically [4] and confirmed observationally [2, 9]. We could not findTD-s neither in ACE nor in Cluster in the second part of March and in April luster hot flow anomaly observations during solar cycle minimum 3 Fig. 1.
Polar plot of the direction of the normal vectors of TDs. The azimuthalangle is measured between the GSE y direction and the projection of the normalvector onto the GSE yz plane. The distance from the center is the cone angle asdetermined by the cross-product method. The regions surrounded by dashed dottedlines are the projection of error cones around the average normal vector marked by“X”. Circles and squares symbolize ACE and Cluster data, respectively. (See: Fig. 3). We found many embedded HFAs in SLAMS in this interval andwe could not determine the TD of those events. solar wind speed ( km/s ) 2003 2007 Figduring HFA formation by C1 680 ±
86 613 ±
80 2aby C3 671 ±
92 613 ± ±
84 634 ± M f numbers by ACE 8 . ± . . ± . ±
97 512 ±
102 2cbetween 1998-2003/2008 by ACE 492 ±
102 498 ±
101 2c M f numbers by ACE 5 . ± . . ± . ∆M f . . Table 1.
Solar wind speed and fast magnetosonic Mach numbers mean values andtheir deviation measured by Cluster CIS and ACE SWEPAM. The last column givesthe figure numbers on Fig. 2. Facsk´o et al.
Fig. 2.
Upstream solar wind speed distribution measured by Cluster and ACE space-craft. (a) Solar wind speed distribution measured by Cluster-1 (shifted grey dashdotted line) and Cluster-3 CIS HIA (shifted grey dash dotted line) ACE SWEPAM(solid line) upstream of HFA formation. (b) Fast magnetosonic Mach number distri-bution calculated using ACE MAG and SWEPAM data during HFA formation. (c)Solar wind speed distribution measured by ACE SWEPAM from January to April,2007 (grey line) and from 1998 to 2008 (solid line). (d) Same as (c) but measuredin M f units. We determined the solar wind velocity and fast-magnetosonic Mach-number distributions upstream of HFA formation and compared them to thesame distributions in spring 2007 and for about 10 years (Fig. 2, Tab. 1). Theaverage velocities seem to be lower than in 2003 but with error it is not so sig-nificant. Although Mach number average values seem to be higher in 2007 butits error is too high and makes this difference not so significant. This meansthat the solar wind velocity is higher when HFA develops but the difference isonly 120 km/s in 2007. The difference measured in Mach numbers is greater[2], but the difference is within the error limit. In Fig. 2c the typical doublepeak distribution of solar wind velocity [1] can be seen for spring 2007. Ithelps us to understand why the solar wind distribution is anomalous duringHFA formation on Fig. 2a. After comparing the positions of the maximum onFig. 2b and Fig. 2d the difference in Mach numbers can be seen.We also plotted the 1 h averaged solar wind speed time series from Januaryto April, 2007 (Fig. 3). The last HFA event, on April 30, 2007 was not plotted,but it is evident that HFA events are coupled to high solar wind velocityintervals like in spring 2003. luster hot flow anomaly observations during solar cycle minimum 5 Fig. 3.
The measured SW speed at the L1 point for 4 solar rotations. ACE 1-hraverages are from ACE Science Center. The times of the observed HFAs are markedby vertical lines.
Our final conclusions based on measurements in spring 2007 are the following:1. The solar wind velocity is about 120 km/s or ∆M f = 3 . o like in 2003.4. Approximately another 40-50 HFA events were embedded in SLAMS, butthe TD raising them could not be identified.Based on observations it is hard to say whether the higher solar wind velocityor Mach number is more important. Further independent theoretical consider-ations [6] suggest that both higher Mach number and higher solar wind speedare important in HFA formation. This theoretical work studied the orbit ofparticles accelerated by the bow-shock and led back to the shock by the con-vective electric field ( − v × B ) on both side of the tangential discontinuity. Facsk´o et al.
Fig. 4.
The distribution of the value of Schwartz el al.’s formula [9] by Cluster-1and -3 measurements. The values are mostly less than 1.0.
The particles are accelerated – and form a HFA - if the angle between thesolar wind direction and the TD normal is less than the calculated critical an-gle. This critical angle depends on the ratio of the upstream and downstreammagnetic field (which is a function of Mach number) and the solar wind speed.Furthermore this critical angle is 41 . o calculated for typical Mach numbersand high solar wind speed so the theory confirms our observational resultsand the prediction of Lin’s computational work [4].The above discussed analysis of HFA events in the spring 2007 seasonconfirmed and extended our earlier results based on the study of HFA eventsin spring 2003 that higher solar wind speed is an important condition of HFAformation. This feature restricts Schwartz et al.’s formula [9] but these eventsalso confirm their result: (cid:12)(cid:12)(cid:12)(cid:12) V tr V g (cid:12)(cid:12)(cid:12)(cid:12) = cos θ cs : sw θ bs : sw sin θ B n sin θ cs : bs , where V tr is the transit velocity of the current sheet along the bow-shock, V g is the gyration speed, θ cs : sw , θ bs : sw and θ cs : bs are the angles between the dis-continuity normal, solar wind velocity and the bow-shock; furthermore θ B n is the angle between the magnetic field and bow-shock normal. The neces-sary vectors were calculated and we got that the transition speed is as low asexpected by Schwartz et al.’s formula [9] (Fig. 4). So, in addition to demon-strating that HFA formation depends on solar wind speed, this study confirmsprevious work predicting that HFA formation also depends on the geometryof the shock relative to the solar wind. luster hot flow anomaly observations during solar cycle minimum 7 Acknowledgements
The authors thank the OTKA grant K75640 of the Hungarian Scientific Re-search Fund for support and the Cluster FGM, CIS and ACE MAG, SWEPAMteams for providing data for this study.
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