S. J. Schwartz
Astronomy Unit, Queen Mary and Westfield College, London, United Kingdom
G. E. Paschmann, N. Sckopke, and T. M. Bauer
Max-Planck-Institut für Exterresiche Physik, Garching, Germany
M. W. Dunlop
Space and Atmospheric Physics, Imperial College, London, United Kingdom
A. N. Fazakerley
Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, London, United Kingdom
M. F. Thomsen
Los Alamos National Laboratory, Los Alamos, USA
The discovery in the mid-1980s of regions of hot, highly deflected plasma, often containing intervals of depressed magnetic fields, near the Earth's bow shock [Schwartz et al., 1985; Thomsen et al., 1986] sparked a flurry of research activity. Within several years, these Hot Flow Anomalies (HFAs) were known to be associated with the passage of an interplanetary current sheet, and simulations, both test particle and self-consistent kinetic, confirmed that the injection of particles reflected at the bow shock, when channeled back upstream under appropriate field configurations, replicated most, if not all of the observed features. This state of affairs is reviewed in Schwartz .
With theory and observation in accord, and the small, transient, apparently inconsequential nature of HFAs universally believed, the subject was considered closed. However, recent reports [Sibeck et al., 1998, 1999] of an HFA which resulted in a rapid (~7 min) displacement of the magnetopause by some 5 RE with observable consequences in the ionosphere have renewed interest in HFAs. Sibeck et al.  point out that the underlying interplanetary current sheet which appears to have been responsible for this HFA is itself totally un-remarkable, and thus suggest that such transient but dramatic disturbances of the magnetosphere are common.
The present paper seeks to address precisely the question of how common HFAs are by studying the properties of all known HFAs. Additionally, we draw on multi-mission data where available for supporting information. An enlarged version of this work is under revision for publication in the Journal of Geophysical Research.
Burgess  pursued the relationship of HFAs with an interplanetary current sheet by studying the behavior of solar wind test particles specularly reflected at the bow shock (as observed under quasi-perpendicular shock geometries [Sckopke et al., 1983 and references therein]). When the interplanetary conditions are such that the motional electric field E = - V B points toward the current sheet such particles are channeled back along the current sheet into the upstream region. Fully self-consistent hybrid simulations by Thomas et al.  confirmed this requirement, and showed that the resulting disturbance was attached to the bow shock, advanced upstream, and replicated essentially all the observational features noted above. These simulations also confirmed earlier claims that HFAs form at tangential discontinuities (TDs) and not at rotational discontinuities (RDs). Thomsen et al.  showed that all 9 reported ISEE HFAs also possessed a toward-pointing electric field on at least one side.
The more recent reports by Sibeck et al.  suggest that the IMF current sheet appears to be unremarkable, implying that HFAs should be as common as interplanetary TDs (~0.6 per hour [Lepping and Behannon, 1986]) and represent a perhaps non-negligible perturbation of the magnetosphere. The question we wish to address here is, therefore, whether there other restrictions as to which IMF TDs give rise to HFAs.
Our set of 30 HFAs includes all previously reported events based on AMPTE UKS, AMPTE IRM, ISEE 1/2, and Interball spacecraft, together with a few new AMPTE events. References describing the spacecraft and instrumentation can be found in the comprehensive HFA publications [Paschmann et al., 1988; Schwartz et al., 1988; Sibeck et al., 1999; Thomsen et al., 1988].
We seek here to characterize the interplanetary environment accompanying our set of HFAs in order to determine what special circumstances might be necessary to provoke HFA formation.
Several parameters of the HFA environments may play some role in HFA formation. These include local shock geometry before and after HFA passage and the cone angle of the IMF current sheet with respect to the Sun-Earth line, which in turn provides an estimate of the speed of transit of the current sheet-bow shock intersection along the bow shock.
The presence of the large disturbance associated with the HFA precludes the use of minimum variance analysis to determine the tangential/rotational nature of the underlying interplanetary discontinuity. Following previous practice and guided by the negative simulational results in the case of an RD found by Thomas et al. , we calculate the current sheet normal as the cross-product between pre- and post-HFA fields, as appropriate for a TD.
The determination of whether a discontinuity is a TD or an RD traditionally requires testing the size of the magnetic field normal to the current sheet, Bn, and the jump in field magnitude from pre- to post-current sheet [Neugebauer et al., 1984]. Estimating Bn involves a minimum variance analysis through the current sheet which, as noted above, we cannot do. However, a summary of the jump in field magnitude is presented in Figure 1. Over 2/3rds of all HFAs have jumps less than 0.2, which would have precluded their positive identification as TDs in the historical discontinuity literature [Neugebauer et al., 1984]. Lepping and Behannon  suggest, however, that the full population of discontinuities does indeed include a "mixed'' group which supplies a similar proportion of TDs with small jumps in field magnitude.
Interestingly, there are cases where the RD/TD distinction is already better established. These include the simulations [Thomas et al., 1991] and the Interball HFA with upstream data from WIND [Sibeck et al., 1999]. These all report underlying TDs in which there is little or no change in field magnitude.
Figure 2 presents the local shock geometry before and after the HFA. The figure reveals a slight tendency for pre-HFA bow shocks to be more quasi-parallel and post-HFA shocks more quasi-perpendicular. Interestingly, at least near the local point of observation relatively few HFAs correspond to quasi-perpendicular conditions on both sides, and several HFAs have quasi-parallel shocks on both sides. This may indicate that these HFAs were formed at a quasi-perpendicular environment some distance from the point of observation. Alternatively, intermittent ion reflection under quasi-parallel shock conditions [Gosling et al., 1982] may be sufficient to promote some local HFA development.
The suggestion by Burgess  that toward/away motional electric fields played a key role in HFA formation, confirmed by the simulations of Thomas et al. , received observational support by Thomsen et al. . We repeat that test here in Figure 3. With our convention that ncs Vsw < 0, the angle between a toward electric field and ncs should be < 90 o in the pre-HFA region and > 90 o in the post-HFA region. The figure confirms again the requirement that at least one side of the interplanetary current sheet possesses a toward field.
The HFA normals have a very pronounced distribution in cone angle as shown in Figure 4 by comparison with general TD survey results. This provides the first clear indication that not every interplanetary tangential discontinuity results in HFA formation. Normals with cone angles above 60o account for over 80% of all HFAs but only 30% of all TDs.
Here we investigate the speed of transit Vtr of the current sheet bow shock intersection (line) along the bow shock; the calculation only involves components in the plane containing the normals to the bow shock and the current sheet (both taken as planar). The ratio of Vtr to the gyrospeed Vg of an ion (specularly) reflected at the bow shock determines whether the transit speed is sufficiently slow for the ions to be channeled along the shock. This ratio depends only on geometric factors and can be written
where qbs:sw [ qcs:sw ] is the angle between the bow shock normal [current sheet normal] and solar wind velocity and qcs:bs is the angle between the current sheet and bow shock. If all the angles in (1) are 45o this ratio is ~1.
Figure 5 shows a histogram of the minimum (pre-HFA or post-HFA) normalized transit speed. As expected from Figure 4, this ratio is small ( < 0.5) on at least one side of all but 10% of the HFAs in the present study. Two-thirds of the HFAs have normalized transit speeds less than 0.3.
A partial resolution of the RD/TD/Either dilemma posed in Section 3.1.1. above is to identify the same interplanetary current sheet further upstream of the bow shock, where the HFA disturbance is absent. We have found 4 such cases. The general timing delays and pre/post-HFA IMF conditions are similar to those at the HFA observation location. All 4 cases show discontinuities with small normal components, consistent with identification as TDs, though in most cases the small jump in | B| is also present. However, several of the discontinuities observed upstream away from the HFA location show significant dips in field magnitude in the interior of the current sheet. This property strengthens the TD identification.
We can now estimate the rate of occurrence of HFAs by assuming that all TDs above 60o cone angles with a toward electric field on at least one side result in HFAs. The overall interplanetary directional discontinuity rate at 1 AU is ~1.25 per hour of which a fraction 0.89/1.89 = 47% are TDs [Lepping and Behannon, 1986]. Assuming equal probabilities for positive and negative interplanetary field polarities, 3/4 of these TDs should have a toward-pointing E on at least one side. We estimate the HFA rate of occurrence as: 0.3 1.25 0.47 0.75 = 0.13 per hour or 3.2 HFAs per day. This rate is entirely consistent with the number (20) of HFAs AMPTE IRM observed in its first year of operations when the orbital and operational aspects are taken into account.
Treating the 30 HFAs used in this study as representative, we conclude that HFAs should be relatively common. The conditions for HFA formation include:
- an interplanetary current sheet with a motional electric field which points toward it on at least one side;
- current sheets whose normals make a large cone angle with the sunward direction;
- tangential discontinuities (probably).
Moreover, HFA formation appears to be favored by:
- discontinuities with a relatively small jump in field magnitude from one side to the other;
- quasi-perpendicular bow shock conditions on at least one side, and preferentially the post-HFA side.
The fact that several HFAs locally have quasi-parallel conditions on both sides suggests that they survive well beyond their region of formation.
The above conditions, when compared against known statistics of interplanetary directional discontinuities, suggest that HFAs should occur at a rate of ~3 per day. The degree of disruption of the bow shock/magnetopause observed in association with one HFA [Sibeck et al., 1999] suggests that HFAs are more consequential than originally envisaged in terms of their dynamic impact on the dayside magnetosphere.
There remain several questions which require multi-point measurements. What portion of the bow shock is involved during the lifetime of an HFA? Is it simply related to the criteria listed above when applied to the curved bow shock? What is the shape of the resulting disturbance? This study has also highlighted the need to develop better analysis tools to separate tangential and rotational discontinuities particularly when the jump in field magnitude is small.
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