How the asymmetry is induced

As described in the previous section, it is clear that aBycomponent in the IMF leads to aBycomponent with the same sign inside the closed magnetosphere. The manifestation of this asymmetry has been described extensively in the three previous sections. The next step is then to address how this asymmetry arises. The observedBy component inside the closed magnetosphere was first considered as a superposition of the terrestrial field and the IMF, leading to a (partial) “penetration” of theBy in the IMF. This view can explain the basic direction of the observed field, but it does not address how theBy

enters the magnetosphere, why there are large spatial variations in the “penetrated” field and why there are certain time delays between changes in the IMFByand changes inside the magnetosphere. A more physical description was put forward byCowley[1981a].

When aBycomponent is present in the IMF, the field lines are not added symmetrically to the magnetotail. IfBy > 0, the tension force acting on the newly reconnected field lines pulls them toward dawn in the northern hemisphere and toward dusk in the southern hemisphere. This leads to a pileup of magnetic flux in these regions, increasing the magnetic pressure. It is also possible that lobe reconnection contributes to this pileup of flux, as the tension force exerted by the IMF acts in the same direction for field lines that have undergone high-latitude reconnection. The increased pressure leads to convection; the plasma and field lines in the northern hemisphere convect toward dusk

and the plasma and field lines in the southern hemisphere convect toward dawn. This also moves the footpoints of the field lines, towards dusk and dawn at the northern and southern footpoint, respectively. Cowley [1981a] proposed that the asymmetry then enters the closed magnetosphere when these field lines reconnect in the magnetotail.

Later, Moses et al.[1985] interpreted the IMF By induced asymmetries in the closed magnetosphere in terms of zonal polar cap convection created by field tension moving the ionospheric ends of the field lines in the IMFBydirection. The sense of convection is opposite in the northern and southern hemispheres, which tilts the closed field lines and creates aBycomponent in the plasma sheet.

Another explanation was put forward byKhurana et al.[1996]. They argued that the asymmetric pressure distribution resulting from asymmetric loading of flux influence the closed magnetosphere more directly though fast-mode MHD pressure waves. This induces flows towards dusk in the northern hemisphere and towards dusk in the southern hemisphere in the closed magnetosphere, as observed in the magnetotail, which in turn induce the observed By component. A key difference between this description and the description put forward by Cowley [1981a], is the timescales on which the magnetospheric system can respond and reconfigure to the IMF conditions since the travel time of pressure waves exceed the convection velocity. Tenfjord et al.[2018] used the Lyon-Fedder-Mobarry (LFM) global MHD to simulate how the magnetosphere responds to changes in the IMF By component. They found a rapid response when the IMFBy component was introduced in the simulation, consistent with asymmetries being introduced by pressure gradients directly. Using magnetometer data from the Geostationary Operational Environmental Satellite (GOES) probes in superposed epoch studies, the closed magnetosphere was found to respond to IMF By reversals at the magnetopause in less than 10 minutes and completely reconfigure within 50 minutes, both at the dayside and the nightside for both northward and southward IMF [Tenfjord et al., 2017, 2018]. Simulations efforts byTenfjord et al.[2018] show that all the major MHD models produce similar response and reconfiguration times at geosynchronous orbit. These results strongly suggest that lobe pressure plays a major role in inducing asymmetries in the closed magnetosphere.

Several studies have also reported timescales that have been assumed to be more consistent with asymmetries being induced through convection, as suggested byCowley [1981a]. Motoba et al.[2011] reported a 51-minute delay between changes in the IMF and theBycomponent measured by Cluster, but the observed signature in this event is most likely a bursty bulk flow [Tenfjord et al., 2017]. A 1–1.5-hours delay was reported by Rong et al. [2015], but alternative interpretations exist, as the events occurred at the same time as a solar wind dynamic pressure pulse [Tenfjord et al., 2017]. Support for longer response time was put forward by Browett et al. [2017], who statistically studied the time scale for introducing a Bycomponent into the closed magnetosphere using Cluster data. They reported a delay between the IMF By and the magnetotail observations of about 1 and 3 hours for southward and northward IMF. In Paper I, we outline several sources that could explain the discrepancy between these time scales and the time scales reported byTenfjord et al.[2015, 2017, 2018]. For example, the results are based on data obtained from further downtail than the GOES observation, a linear correlation is assumed and rather long time-averages have been used in the IMF, which could mask faster signatures. There are also several studies of the response between variations of the IMFByand observations in the ionosphere. As noted in section 3.1.2,

Figure 3.4: Cross-section of the magnetotail [Liou and Newell, 2010]. Thin black lines indicate magnetic field lines and thick lines indicate plasma flow. Plasma sheet is rotated around the magnetotail axis in the clockwise direction, while the field lines in the closed magnetosphere are rotated in the opposite direction, giving rise to a positiveBycomponent. The plasma flow is also oppositely directed in the two hemispheres.

Motoba et al. [2010] reported a 1-hour delay between the IMF By and the auroral displacement. The response time in the field-aligned currents was studied by Milan et al.[2018], who found that the currents reconfigured within 30 minutes at the dayside and between 40–120 minutes at the nightside for IMFBz <0. The reconfiguration time was found to be similar at the dayside for IMFBz > 0, but with reconfiguration at the nightside between 60–95 minutes.

Several studies finding a delay between the IMF and observations in the mag-netosphere of about 1–1.5 hours have been taken into account for the model where asymmetries are introduced into the closed magnetosphere y convection. This is some-what in agreement with the cross polar cap transit time of 1–2 hours found byZhang et al.[2015] during an event with southward IMF conditions, but shorter than the av-erage convection of field lines across the polar cap estimated to be in the region of 2–5 hours by e.g.Browett et al.[2017]. This means that although the observed changes in some studies are slower than the timescales observed at geosynchronous orbit, they could still be faster than the response time that should be expected by the convection model. An explanation of the longer time delay in the ionospheric current and convec-tion pattern could be that the changes will not be observed here before the plasma moves sufficiently to give rise to an observable signal, but it seems clear that further studies are needed to resolve the apparent discrepancy of time-scales derived from observations in the magnetosphere and the ionosphere.

As a positive IMFBycomponent leads to a positive magnetosphericBycomponent, it implies that the magnetic field lines in the magnetotail are bent counter-clockwise when seen from the tail. An important, but perhaps not so obvious feature of the magnetotail, is that the plasma sheet rotates in the opposite direction [Fairfield, 1979;Cowley, 1981a].

This is illustrated in Figure 3.4, showing a cross-section of the magnetotail when IMF By >0, and is referred to as magnetotail twisting.Cowley[1981a] speculated that this twisting around the magnetotail axis was due to the torque exerted on the magnetosphere by the open IMF field lines, but the same rotation could be expected also from just considering the asymmetric pressure distribution. If treated as an independent process, the magnetotail twisting should reduce theByinduced by pressure gradients, estimated

byPetrukovich[2011] to be about 10% in an empirical model based on Geotail data.

Interestingly,Petrukovich[2011] found that model quality did not change if the term explicitly describing magnetotail twisting was omitted from the model, which could imply that only a single mechanism related to the IMF By is needed to explain the inducedBy. Case et al.[2018] studied the response time of the magnetotail twisting to reversals of the IMFBy, and found a median response time of 17 minutes, a time scale that again is consistent with pressure gradients inducing asymmetries.

Grocott and Milan[2014] studied the ionospheric convection in the northern hemi-sphere parametrized by 1) the IMF clock angle and 2) the length of time that the IMF clock angle had been maintained. They found that the convection pattern, after∼30 min-utes of stable IMF, were similar to the time-averaged convection patterns seen by e.g.

Ruohoniemi and Greenwald[1995]. In addition, they observed that the convection pat-tern for northward andBydominated IMF continually became more asymmetric, even after several hours of stable clock angle. The same change was not observed for south-ward and By dominated IMF, which remained at the asymmetric state reached after

∼30 min.Grocott and Milan[2014] speculated that this longer time frame reconfigura-tion was due to an addireconfigura-tional mechanism associated with IMFBy. Whether this longer time scale asymmetries are introduced by an additional mechanism or if also this is a manifestation of the asymmetric pressure distribution, is currently unresolved.