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Flux transfer events: Motion and signatures
Journal of Atmospheric and Solar-Terrestrial Physics 87–88 (2012) 20–24
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Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
Flux transfer events: Motion and signatures D.G. Sibeck a,n, N. Omidi b a b
Code 674, NASA/GSFC, Greenbelt Road, Greenbelt, MD 20723, United States Solana Scientific, Solana Beach, CA 92075, United States
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2011 Received in revised form 25 July 2011 Accepted 27 July 2011 Available online 5 August 2011
We present results from a 2.5 dimensional hybrid code simulation for the evolution of flux transfer events (FTEs) during intervals of due southward interplanetary magnetic field (IMF) orientation. The structures invariably form between pairs of reconnection lines, often remaining nearly stationary on the subsolar magnetopause before their motion begins. Although a few structures move sunward, ultimately coalescing with others, most eventually accelerate antisunward, reaching velocities many times greater than the sound speed in the magnetosheath but only about one Alfve´n speed greater than the ambient magnetosheath flow. At these velocities, slow mode wakes (but not shocks) marked by density enhancements and magnetic field strength decreases extend outward from the structures into the magnetosheath. Upon encountering the cusps, the structures decelerate, undergo reconnection, and are destroyed. Published by Elsevier Ltd.
Keywords: Flux transfer events Magnetopause Reconnection
1. Introduction Transient ( 1–2 min) events are common in the immediate vicinity of the Earth’s dayside magnetopause. Those exhibiting magnetic field strength enhancements and symmetric bipolar magnetic field signatures normal to the nominal magnetopause are termed flux transfer events or FTEs (Russell and Elphic, 1978). However, FTEs can also display depressed or crater-like magnetic field strength variations (Labelle et al., 1987) and/or asymmetric bipolar magnetic field signatures normal to the nominal magnetopause (Fear et al., 2010). Because they tend to occur for southward interplanetary magnetic field orientations and strongly sheared magnetosheath and magnetospheric magnetic field configurations (Berchem and Russell, 1984; Rijnbeek et al., 1984) and frequently exhibit accelerated mixtures of streaming magnetosheath and magnetospheric plasmas with densities intermediate between those of either region (Paschmann et al., 1982; Daly et al., 1984), FTEs observed near local noon are generally interpreted in terms of bursty reconnection. If FTEs contribute significantly to (Lockwood et al., 1990) or dominate (Lockwood et al., 1995) the overall solar wind–magnetosphere interaction, then studies of FTEs may tell us much about when, where, and how reconnection occurs as a function of solar wind conditions. For example, case and statistical studies of observed (Korotova et al., 2009), calculated (Dunlop et al., 2005), or inferred (Rijnbeek
n
Corresponding author. Tel.: þ1 301 286 5998; fax: þ1 301 286 1648. E-mail addresses: [email protected] (D.G. Sibeck), [email protected] (N. Omidi). 1364-6826/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jastp.2011.07.010
et al., 1984; Berchem and Russell, 1984) structure velocities can reveal the location(s) of the reconnection line. In the absence of readily available high spatial and temporal resolution results from global numerical simulations, several researchers have used the analytical Cooling et al. (2001) model for the motion of reconnected magnetosheath and magnetospheric magnetic field lines to demonstrate that the locations where FTEs are observed are consistent with their formation along postulated subsolar reconnection lines (e.g., Dunlop et al., 2005; Fear et al., 2005; Wild et al., 2005, 2007). In this model, FTEs move at the sum of the local magnetosheath plasma and Alfve´n velocities throughout their existence, i.e. they always move at the Alfve´n velocity through the ambient magnetosheath flow. The model predicts structure speeds within a factor of 2 and directions to within 301 of those inferred from multispacecraft timing in 78% of cases in which structure dimensions exceed 5000 km (Fear et al., 2007). The speed at which structures move through the ambient media is also an important factor in determining the signatures that they produce. Farrugia et al. (1988) showed that an extended cylinder moving through an incompressible magnetohydrodynamic plasma generates transient magnetic field strength enhancements and bipolar magnetic field signatures normal to the nominal magnetopause, as frequently observed. However, when Mach numbers approach or exceed unity compressible solutions must be employed. Fig. 1 illustrates the solution regimes predicted for a cylindrical structure moving through a compressible plasma when the ambient magnetic field lies perpendicular to the structure axis (Sonnerup et al., 1992). Supersonic and superAlfve´nic structures generate fast mode shocks marked by magnetic field strength and density enhancements, while subsonic and subAlfve´nic structures
D.G. Sibeck, N. Omidi / Journal of Atmospheric and Solar-Terrestrial Physics 87–88 (2012) 20–24
Fig. 1. Shock regimes predicted for single-adiabatic field-aligned flows as a function of the Alfve´nic and sonic Mach numbers (Sonnerup et al., 1992). N. S. indicates no shock, while S. S. indicates slow shock. Circles indicate Mach numbers for the relative motion of the largest FTE in the simulation through the ambient magnetosheath plasma. Crosses indicate Mach numbers at the times when other structures generated notable density enhancements in the magnetosheath. As predicted by the Cooling et al. (2001) model, the structures eventually move through the magnetosheath at the Alfve´n velocity (M2A 1).
moving faster than the slow mode speed generate slow mode shocks marked by density enhancements but magnetic field strength decreases. Structures moving at velocities much slower than the slow mode velocity, superAlfve´nic but subsonic velocities, or supersonic but subAlfve´nic velocities generate magnetic field strength and density perturbations, but no shocks. When the sum of the pressure gradient and magnetic curvature forces acting upon structures is finite, they accelerate. With the advent of multispacecraft missions, it has become possible to calculate this rate of acceleration. Fear et al. (2009) demonstrated that the rate of acceleration was negligible in a case study of multipoint THEMIS observations near the flanks of the magnetosphere. As space plasma physics transitions towards an environment in which results from global simulations based on first-principle physics become increasingly available, there is a need to compare the predictions of numerical simulations with those of the analytical models. Omidi and Sibeck (2007) presented results from a 2.5 dimensional global hybrid code simulation for the interaction of the solar wind with the magnetosphere indicating the frequent occurrence of FTEs on the dayside magnetopause. They identified one large structure that generated a slow mode bow wave as it accelerated towards the northern cusp and reached a speed approaching one Alfve´n velocity faster than the ambient magnetosheath flow. This paper presents more detailed observations of the same structure and examines the predictions of the hybrid code model for more structures in the same run, addressing the locations where they are generated, their velocity and acceleration, and the slow mode bow waves that they generate. It places the new simulation results within the context of previously reported observations, simulations, and theoretical models.
2. Model We examine output from the model originally presented by Omidi and Sibeck (2007). Solar wind plasmas and electromagnetic
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fields enter the noon–midnight meridional plane domain of the model through its dayside boundary and exit freely through the three remaining boundaries. As noted by Omidi and Sibeck (2007), the ratio of the standoff distance of the magnetopause to the proton skin depth in the solar wind is 85, resulting in a magnetosphere 7.5 times smaller than that of the Earth. Nevertheless, the resulting magnetosphere has characteristics similar to that of Earth’s. The simulation retains all three components of the electromagnetic fields and plasma flows, the solar wind Mach number is set to 5, ion and electron betas are set to 0.5, resistivity is spatially uniform, and the IMF points due southward. Given the 2.5D nature of the model, simulation results are appropriate to studies of flux transfer events with the large dawn/dusk extents expected during intervals of strongly southward IMF orientation moving northward or southward along the noon meridian in response to combined pressure gradient and magnetic curvature forces (e.g., Fedder et al., 2002; Pinnock et al., 2003; Raeder, 2006). Results from the simulation are presented in the X–Y coordinate system, where X points antisunward and Y points northward. The Earth lies at (X, Y)¼(450, 500). Distances are measured in units of ion skin depth or c/opi, where opi is the ion plasma frequency. For a solar wind density of 6 cm 3, 1 c/opi ¼93 km. Time is measured in units of Oi 1, where Oi is the ion gyrofrequency. For an IMF strength of 5 nT, Oi 1 is 2 s. We set Oi 1 ¼0 at the time when the first FTE appears, which corresponds to Oi 1 ¼122.25 in the paper of Omidi and Sibeck (2007). Velocities are measured in units of the solar wind Alfve´n speed, VA. For a southward-pointing IMF strength of 5 nT, VA ¼41 km s 1. Cell sizes in the simulation are 1 c/opi, resistive scale lengths are 0.3 c/opi. Densities and magnetic field strengths presented in this paper are normalized to solar wind values.
3. Simulation results Figs. 2 and 3 present snapshots of densities, magnetic field strengths, and magnetic field directions at three times late in the simulation run: Oi 1 ¼67.95, 72.6, and 79.35. The dayside magnetosphere is readily identifiable as a region of extremely low (0.05) normalized densities and high ( 412) normalized magnetic field strengths. Dayside magnetospheric magnetic fields point northward ( þY). By comparison, magnetosheath densities are much higher ( 3) and magnetic field strengths are much lower ( 4). Dayside magnetosheath magnetic fields point southward. Mantle and lobe densities lie between those in the magnetosheath and dayside magnetosphere, ranging from 0.5 to 3. Mantle and lobe magnetic field strengths are also intermediate, ranging from 4 to 16. Mantle and lobe magnetic fields have strong southward components. As noted by Omidi and Sibeck (2007), the most prominent transient feature in the simulation is the large FTE that moves northward along the magnetopause from a position near (X, Y) ¼(375, 544) at Oi 1 ¼67.95 to (X, Y) ¼(407, 574) at Oi 1 ¼79.35. Depressed ( 2) densities, enhanced ( 8) magnetic field strengths, and a closed loop structure bound the enhanced ( 6) densities and depressed ( 1) magnetic field strengths within the core region of this crater FTE. As the FTE moves away from its point of origin near the subsolar magnetopause, it generates a slow mode bow wave marked by enhanced densities and depressed magnetic field strengths. By Oi 1 ¼67.95, a region of enhanced densities (and slightly depressed magnetic field strengths) stretches outward from the magnetopause and preceeds the arrival of the FTE. The density enhancement increases with time, becoming more prominent at Oi 1 ¼72.6, and stretching outward into the magnetosheath from (rather than preceding)
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D.G. Sibeck, N. Omidi / Journal of Atmospheric and Solar-Terrestrial Physics 87–88 (2012) 20–24
Fig. 2. Results from the 2.5D hybrid code for densities in the noon–midnight meridional plane at three times during the simulation. A large FTE marked by normalized densities of 6 moves northward from the subsolar point towards the northern cusp. The structure generates an increasingly prominent density wake that extends far into the magnetosheath.
Fig. 3. Results from the 2.5D hybrid code for magnetic field strengths and field lines in the noon–midnight meridional plane at three times during the simulation. A large FTE marked by a closed loop structure moves northward from the subsolar point towards the northern cusp. A region of slightly depressed magnetic field strengths and field lines that bow earthward precedes the structure.
the structure at Oi 1 ¼79.35. The region of enhanced densities within the wake corresponds to slightly depressed magnetic field strengths on kinked magnetosheath magnetic field lines that bow outward towards the magnetosheath. None of the other FTEs that occurred in this run reached the size of this structure. A small FTE that was present on the subsolar magnetopause near (X, Y)¼ (365, 490) at Oi 1 ¼ 67.95 moved southward to (370, 470) at Oi 1 ¼79.35. A larger structure near (X, Y)¼ (370, 470) at Oi 1 ¼67.95 moved southward to (375, 460) at Oi 1 ¼72.6 and (390, 445) at Oi 1 ¼79.35. The latter structure generated a bow wave, which became detectable at Oi 1 ¼76.5 (not shown) and prominent by Oi 1 ¼79.35. As in the case of the much larger northern hemisphere structure in the northern hemisphere, this bow wave also lay on kinked magnetosheath magnetic field lines that bowed outward towards the magnetosheath. The FTEs shown in Figs. 2 and 3 were only three of many that occurred throughout the entire run. From Oi 1 ¼0 to the end of the run at 87.75, 10 FTEs were identified, giving an average recurrence time of 8.8 Oi 1. Curves in Fig. 4a and b track the X and Y positions of the centers of all 10 FTEs as a function of time, respectively. As indicated by the histograms in Fig. 5, the FTEs originated within 301 of the equatorial plane. For most of the interval shown, they were precluded from originating precisely at the equator due to the presence of the large and slowly growing structure, whose subsequent northward motion was discussed within the context of Figs. 2 and 3. Most structures moved
antisunward (positive X direction) and towards the nearest pole (positive Y direction for structures at Y greater than 500, negative Y direction for structures at Y less than 500). However, two structures moved sunward and equatorward from Oi 1 ¼35 to 40 under the influence of greater reconnection rates and outflows at the reconnection line on their poleward edges than those on their equatorward edges Marked by blue curves in Fig. 4, these structures coalesced with the large equatorial structure during the prolonged interval that it spent nearly at rest on the subsolar magnetopause. Note that the simulation does not predict the production of pairs of bubble-like FTEs at single reconnection lines (Southwood et al., 1988; Scholer, 1988). Nor does it generate pairs of bubblelike FTEs bounding flux ropes, as is the case of two-dimensional MHD simulations of reconnection on a planar magnetopause (Ding et al., 1991). Instead, the simulation routinely generates single flux rope FTEs between pairs of reconnection lines (Lee and Fu, 1985; Raeder, 2006). One such FTE, marked by high densities and low magnetic field strengths, was in the process of being generated near (X, Y)¼(365, 490) at Oi 1 ¼67.95. The curves in Fig. 4c show structure velocities as a function of time. These velocities were determined by taking the first derivative of structure positions as a function of time. Structures with long durations typically exhibit three phases: an initial small decrease in velocity, a long steady rise, and an abrupt final decrease. The first phase occurs as a newly formed FTE moves
D.G. Sibeck, N. Omidi / Journal of Atmospheric and Solar-Terrestrial Physics 87–88 (2012) 20–24
X (c/ωp)
410.0
Antisunward
370.0 Sunward
Y(c/ωp)
580.0
North
500.0
V (SW VA)
420.0
South
5.0
A (SW VAΩι)
1.0 0.8 0.0 -0.8 0
20
40 T (1/Ωi)
60
80
Fig. 4. The locations (X, Y), velocity (V), and acceleration (A) of FTEs seen in the hybrid code simulation. Black curves indicate structures moving northward, red those moving southward, and blue those moving sunward and equatorward. Black, red, and blue curves for the velocity and acceleration are time derivatives of the structure X and Y positions. For comparison, black circles in the third panel show the velocities observed at the center of the largest northward-moving structure. Black crosses in the same panel indicate the times when density enhancements appear in the magnetosheath outside six structures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
5.0 # Events
Initial
1.0
Cusp Coalescence Destruction
1.0 -90
Final
Cusp Destruction
# Events
5.0
-70
-50
-30
-10 10 Latitude
30
50
70
90
Fig. 5. Histograms for the latitudes at which structures first appear and those to which they ultimately move. Most structures move to and are destroyed by reconnection in the cusp. A few structures move sunward and coalesce.
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encounters the obstacle posed by the mantle and lobe. The velocities of structures with shorter durations simply increase as they move poleward. Velocities peak at 3.5–5.5 solar wind Alfve´n velocities. Fig. 4d shows structure acceleration as a function of time. These accelerations were determined by taking the first derivatives of structure velocities as a function of time. Structures with long durations typically decelerate briefly, accelerate over a much longer period of time as they move poleward, and then abruptly decelerate as they enter the cusp and encounter the mantle and lobe. If the FTEs move as solid bodies, then the velocities observed at their cores should correspond to those determined by taking the first derivatives of structure positions as a function of time. Black circles in the Fig. 4c present the velocities observed within the core region of the large northward-moving FTE as a function of time. These velocities agree very well with those determined by taking the first derivative of the structure positions as a function of time (longest black curve in Fig. 4c), confirming that the structures move as solid bodies. For comparison with the predictions of the analytical model presented by Sonnerup et al. (1992) and shown in Fig. 1, we must calculate the sonic and Alfve´nic Mach numbers for structure motion relative to the background flow. Circles in Fig. 1 show these values for the large northward-moving structure. We calculate the Mach numbers by subtracting ambient magnetosheath flow velocities from those observed within the core of the structure (the circles in Fig. 4c) and dividing the result by the ambient magnetosheath sonic and Alfve´nic speeds. The structure initially moves very slowly, with sonic and Alfve´nic Mach numbers much lower than unity. As the structure accelerates, sonic Mach numbers increase to values much greater than unity, whereas Alfve´nic Mach numbers increase to values in the vicinity of unity. Once the structure encounters the cusp, the slowdown in structure motion causes Alfve´nic Mach numbers to diminish to values much less than unity. Given the errors inherent in reading structure and ambient flow velocities, the peak Alfve´nic Mach numbers are essentially equivalent to unity. Thus, rather than moving through the magnetosheath flow at the Alfve´n velocity throughout its existence, the structure gradually accelerates up to the Alfve´n velocity, only reaching this speed as it departs the dayside magnetopause and just before it encounters the cusp. Since the values for the Alfve´nic and sonic Mach numbers do not lie in the regions of parameter space where either slow or fast mode shocks are expected, the density enhancement and magnetic field strength decrease extending into the magnetosheath from the flank of the largest structure is a slow mode wave and not a shock. Similar density and magnetic field strength perturbations accompany five other FTEs. Black crosses in Fig. 4c mark the times and event velocities when these perturbations first appear, generally just before or after FTEs encounter the cusps and disintegrate. The perturbations often appear at or just after event disintegration, i.e. at times when event velocities cannot be obtained by differencing the positions of their centers. Crosses in Fig. 1 indicate the sonic and Alfve´nic Mach numbers for structure motion relative to the background flow at these times, calculated in a manner similar to that described above for the largest structure. As in the case of this structure, sonic Mach numbers greatly exceed unity, but Alfve´nic Mach numbers lie in the vicinity of unity. By the ends of their lifetimes, as they encounter the cusps, the structures have accelerated to velocities about one Alfve´n speed faster than the background magnetosheath flow.
4. Discussion and conclusions towards a location where it can grow steadily. The second phase occurs as the structure moves poleward towards the cusps. The final phase occurs when the structure enters the cusps and
This paper presented results from a 2.5 dimensional hybrid code model for the evolution of FTEs during intervals of due
24
D.G. Sibeck, N. Omidi / Journal of Atmospheric and Solar-Terrestrial Physics 87–88 (2012) 20–24
southward IMF orientation. The structures invariably form between pairs of reconnection lines, often remaining nearly stationary on the subsolar magnetopause before their motion begins. Although a few structures move sunward, ultimately coalescing with other structures, most eventually accelerate antisunward, reaching velocities about one Alfve´n speed greater than the ambient magnetosheath flow. At these velocities, slow mode wakes (but not shocks) marked by density enhancements and magnetic field strength decreases extend outward from the structures into the magnetosheath. As previously discussed by Omidi and Sibeck (2007), the structures ultimately decelerate and disintegrate upon encountering the cusps. Observations are needed to confirm model predictions. The model predicts the gradual growth and acceleration of structures to speeds one Alfve´n velocity greater than the background magnetosheath flow. Consequently larger structures and those observed near the terminator are more likely to move at the predicted velocities than smaller structures and those observed on the subsolar magnetopause. Fear et al. (2007) compared structure velocities derived from multipoint Cluster observations with the predictions of the Cooling et al. model, which predicts steady structure motion at speeds one Alfve´n velocity greater than the background magnetosheath flow. They found that 73% of observed structures move at speeds within a factor of 2 and directions to within 301 of those predicted by the model. By contrast 78% of larger structures (those with dimensions greater than 5000 km) satisfy these conditions. Although they did not report the distribution of observed to predicted speeds, the acceleration predicted by the model presented in this paper provides a natural explanation for events moving at velocities less than or equal to those predicted. Although both common and prominent in the predictions of the numerical simulation, the wake density enhancements predicted by the model have yet to be reported. Since the perturbations are generated by strong flow shears between FTEs and the background magnetosheath, they should be most prominent at times and locations where FTEs move rapidly through slowly moving magnetosheath plasmas. The perturbations should therefore be most prominent for strongly southward IMF orientations, when the curvature forces that accelerate the structures relative to the magnetosheath flow lie perpendicular to east–west oriented structure axes. Further, the perturbations should intensify with distance from the subsolar point as structures accelerate, but diminish once the structures encounter the cusps and decelerate. They should therefore be most readily observed at latitudes at and just equatorward of the cusps. Finally, the perturbations should be most prominent during intervals when solar wind flow speeds are low, since these are also intervals when magnetosheath velocities are small.
Acknowledgments Research at GSFC was funding by NASA’s Heliophysics Guest Investigator Program. Research at Solana Scientific was funded by NSF grants ATM-0502992 and AGS-1007449. References Berchem, J., Russell, C.T., 1984. Flux transfer events on the magnetopause: spatial distribution and controlling factors. J. Geophys. Res. 89, 6689–6703.
Cooling, B.M.A., Owen, C.J., Schwartz, S.J., 2001. Role of the magnetosheath flow in determining the motion of open flux tubes. J. Geophys. Res. 106, 18763–18775. Daly, P.W., Rijnbeek, R.P., Sckopke, N., Russell, C.T., Saunders, M.A., 1984. The distribution of reconnection geometry in flux transfer events using energetic ion, plasma and magnetic data. J. Geophys. Res. 89, 3843–3854. Ding, D.Q., Lee, L.C., Ma, Z.W., 1991. Different FTE signatures generated by the bursty single X line reconnection and the multiple X line reconnection at the dayside magnetopause. J. Geophys. Res 96, 57–66. Dunlop, M.W., Taylor, M.G.G.T., Davies, J.A., Owen, C.J., Pitout, F., Fazakerley, A.N., Pu, Z.-Y., Bogdanova, Y.V., Zong, Q.-Z., Shen, C., Nykyri, K., Lavraud, B., Milan, S.E., Phan, T.-D., Reme, H., Carr, C.M., Cargill, P., Lockwood, M., Sonnerup, B., 2005. Coordinated Cluster/Double Star observations of dayside reconnection signatures. Ann. Geophys. 23, 2867–2875. Farrugia, C.J., Elphic, R.C., Southwood, D.J., Cowley, S.W.H., 1988. Field and flow perturbations outside the reconnected field line region in flux transfer events: theory. Planet. Space Sci. 35, 227–240. Fear, R.C., Fazakerley, A.N., Owen, C.J., Lucek, E.A., 2005. A survey of flux transfer events observed by Cluster during strongly northward IMF. Geophys. Res. Lett., 32. doi:10,1029/2005GL023811. Fear, R.C., Milan, S.E., Fazakerley, A.N., Owen, C.J., Asikainen, T., Taylor, M.G.G.T., Lucek, E.A., Re´me, H., Dandouras, I., Daly, P.W., 2007. Motion of flux transfer events: a test of the Cooling model. Ann. Geophys. 25, 1669–1690. Fear, R.C., Milan, S.E., Fazakerley, A.N., Fornacon, K.-H., Carr, C.M., Dandouras, I., 2009. Simultaneous observations of flux transfer events by THEMIS, Cluster, Double Star, and SuperDARN: acceleration of FTEs. J. Geophys. Res., 114. doi:10.1029/2009JA0143310. Fear, R.C., Milan, S.E., Raeder, J., Sibeck, D.G., 2010. Asymmetry in the bipolar signatures of flux transfer events. J. Geophys. Res., 115. doi:10.1029/ 2010JA015363. Fedder, J.A., Slinker, S.P., Lyon, J.G., Russell, C.T., 2002. Flux transfer events in global numerical simulations of the magnetosphere. J. Geophys. Res., 107. doi:10.1029/2001JA000025. Korotova, G.I., Sibeck, D.G., Rosenberg, T., 2009. Geotail observations of FTE velocities. Ann. Geophys. 27, 83–92. Labelle, J., Treumann, R.A., Haerendel, G., Bauer, O.H., Paschmann, G., 1987. AMPTE IRM observations of waves associated with flux transfer events in the magnetosphere. J. Geophys. Res. 92, 5827–5843. Lee, L.-C., Fu, Z.-F., 1985. A theory of magnetic flux transfer at the Earth’s magnetopause. Geophys. Res. Lett. 12, 105–108. Lockwood, M., Cowley, S.W.H., Sandholt, P.E., Lepping, R.P., 1990. Signatures of flux transfer events and solar wind dynamic pressure changes. J. Geophys. Res. 95, 17113–17135. Lockwood, M., Cowley, S.W.H., Smith, M.F., Rijnbeek, R.P., Elphic, R.C., 1995. The contribution of flux transfer events to convection. Geophys. Res. Lett. 22, 1185–1188. Omidi, N., Sibeck, D.G., 2007. Flux transfer events in the cusp. Geophys. Res. Lett. 34, L04106. doi:10.1029/2006GL028698. Paschmann, G., Haerendel, G., Papamastorakis, I., Sckopke, N., Bame, S.J., Gosling, J.T., Russell, C.T., 1982. Plasma and magnetic field characteristics of magnetic flux transfer events. J. Geophys. Res. 87, 2159–2168. Pinnock, M., Chisham, G., Coleman, I.J., Freeman, M.P., Hairston, M., Villain, J.-P., 2003. The location and rate of dayside reconnection during an interval of southward interplanetary magnetic field. Ann. Geophys. 21, 1467–1482. Raeder, J., 2006. Flux transfer events: 1. Generation mechanism for strong southward IMF. Ann. Geophys. 24, 381–392. Rijnbeek, R.P., Cowley, S.W.H., Southwood, D.J., Russell, C.T., 1984. A survey of dayside flux transfer events observed by ISEE 1 and 2 magnetometer. J. Geophys. Res. 89, 786–800. Russell, C.T., Elphic, R.C., 1978. Initial ISEE magnetometer results: magnetopause observations. Space Sci. Rev. 22, 681–715. Scholer, M., 1988. Magnetic flux transfer at the magnetopause based on single X line bursty reconnection. Geophys. Res. Lett 15, 291–294. Sonnerup, B.U.O., Hau, L.N., Walthour, D.W., 1992. On steady field-aligned doubleadiabatic flow. J. Geophys. Res. 97, 12015–12028. Southwood, D.J., Farrugia, C.J., Saunders, M.A., 1988. What are flux transfer events? Planet. Space Sci. 36, 503–508. Wild, J.A., Milan, S.E., Cowley, S.W.H., Bosqued, J.M., Reme, H., Nagai, T., Kokubun, S., Saito, Y., Mukai, T., Davies, J.A., Cooling, B.M.A., Balogh, A., Daly, P.W., 2005. Simultaneous in-situ observations of the signatures of dayside reconnection at the high- and low-latitude magnetopause. Ann. Geophys. 23, 445–460. Wild, J.A., Milan, S.E., Davies, J.A., Dunlop, M.W., Wright, D.M., Carr, C.M., Balogh, A., Reme, H., Fazakerley, A.N., Marchaudon, H., 2007. On the location of dayside magnetic reconnection during an interval of duskward oriented IMF. Ann. Geophys. 25, 219–238.
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Journal of Atmospheric and Solar-Terrestrial Physics journal homepage: www.elsevier.com/locate/jastp
Flux transfer events: Motion and signatures D.G. Sibeck a,n, N. Omidi b a b
Code 674, NASA/GSFC, Greenbelt Road, Greenbelt, MD 20723, United States Solana Scientific, Solana Beach, CA 92075, United States
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 March 2011 Received in revised form 25 July 2011 Accepted 27 July 2011 Available online 5 August 2011
We present results from a 2.5 dimensional hybrid code simulation for the evolution of flux transfer events (FTEs) during intervals of due southward interplanetary magnetic field (IMF) orientation. The structures invariably form between pairs of reconnection lines, often remaining nearly stationary on the subsolar magnetopause before their motion begins. Although a few structures move sunward, ultimately coalescing with others, most eventually accelerate antisunward, reaching velocities many times greater than the sound speed in the magnetosheath but only about one Alfve´n speed greater than the ambient magnetosheath flow. At these velocities, slow mode wakes (but not shocks) marked by density enhancements and magnetic field strength decreases extend outward from the structures into the magnetosheath. Upon encountering the cusps, the structures decelerate, undergo reconnection, and are destroyed. Published by Elsevier Ltd.
Keywords: Flux transfer events Magnetopause Reconnection
1. Introduction Transient ( 1–2 min) events are common in the immediate vicinity of the Earth’s dayside magnetopause. Those exhibiting magnetic field strength enhancements and symmetric bipolar magnetic field signatures normal to the nominal magnetopause are termed flux transfer events or FTEs (Russell and Elphic, 1978). However, FTEs can also display depressed or crater-like magnetic field strength variations (Labelle et al., 1987) and/or asymmetric bipolar magnetic field signatures normal to the nominal magnetopause (Fear et al., 2010). Because they tend to occur for southward interplanetary magnetic field orientations and strongly sheared magnetosheath and magnetospheric magnetic field configurations (Berchem and Russell, 1984; Rijnbeek et al., 1984) and frequently exhibit accelerated mixtures of streaming magnetosheath and magnetospheric plasmas with densities intermediate between those of either region (Paschmann et al., 1982; Daly et al., 1984), FTEs observed near local noon are generally interpreted in terms of bursty reconnection. If FTEs contribute significantly to (Lockwood et al., 1990) or dominate (Lockwood et al., 1995) the overall solar wind–magnetosphere interaction, then studies of FTEs may tell us much about when, where, and how reconnection occurs as a function of solar wind conditions. For example, case and statistical studies of observed (Korotova et al., 2009), calculated (Dunlop et al., 2005), or inferred (Rijnbeek
n
Corresponding author. Tel.: þ1 301 286 5998; fax: þ1 301 286 1648. E-mail addresses: [email protected] (D.G. Sibeck), [email protected] (N. Omidi). 1364-6826/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.jastp.2011.07.010
et al., 1984; Berchem and Russell, 1984) structure velocities can reveal the location(s) of the reconnection line. In the absence of readily available high spatial and temporal resolution results from global numerical simulations, several researchers have used the analytical Cooling et al. (2001) model for the motion of reconnected magnetosheath and magnetospheric magnetic field lines to demonstrate that the locations where FTEs are observed are consistent with their formation along postulated subsolar reconnection lines (e.g., Dunlop et al., 2005; Fear et al., 2005; Wild et al., 2005, 2007). In this model, FTEs move at the sum of the local magnetosheath plasma and Alfve´n velocities throughout their existence, i.e. they always move at the Alfve´n velocity through the ambient magnetosheath flow. The model predicts structure speeds within a factor of 2 and directions to within 301 of those inferred from multispacecraft timing in 78% of cases in which structure dimensions exceed 5000 km (Fear et al., 2007). The speed at which structures move through the ambient media is also an important factor in determining the signatures that they produce. Farrugia et al. (1988) showed that an extended cylinder moving through an incompressible magnetohydrodynamic plasma generates transient magnetic field strength enhancements and bipolar magnetic field signatures normal to the nominal magnetopause, as frequently observed. However, when Mach numbers approach or exceed unity compressible solutions must be employed. Fig. 1 illustrates the solution regimes predicted for a cylindrical structure moving through a compressible plasma when the ambient magnetic field lies perpendicular to the structure axis (Sonnerup et al., 1992). Supersonic and superAlfve´nic structures generate fast mode shocks marked by magnetic field strength and density enhancements, while subsonic and subAlfve´nic structures
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Fig. 1. Shock regimes predicted for single-adiabatic field-aligned flows as a function of the Alfve´nic and sonic Mach numbers (Sonnerup et al., 1992). N. S. indicates no shock, while S. S. indicates slow shock. Circles indicate Mach numbers for the relative motion of the largest FTE in the simulation through the ambient magnetosheath plasma. Crosses indicate Mach numbers at the times when other structures generated notable density enhancements in the magnetosheath. As predicted by the Cooling et al. (2001) model, the structures eventually move through the magnetosheath at the Alfve´n velocity (M2A 1).
moving faster than the slow mode speed generate slow mode shocks marked by density enhancements but magnetic field strength decreases. Structures moving at velocities much slower than the slow mode velocity, superAlfve´nic but subsonic velocities, or supersonic but subAlfve´nic velocities generate magnetic field strength and density perturbations, but no shocks. When the sum of the pressure gradient and magnetic curvature forces acting upon structures is finite, they accelerate. With the advent of multispacecraft missions, it has become possible to calculate this rate of acceleration. Fear et al. (2009) demonstrated that the rate of acceleration was negligible in a case study of multipoint THEMIS observations near the flanks of the magnetosphere. As space plasma physics transitions towards an environment in which results from global simulations based on first-principle physics become increasingly available, there is a need to compare the predictions of numerical simulations with those of the analytical models. Omidi and Sibeck (2007) presented results from a 2.5 dimensional global hybrid code simulation for the interaction of the solar wind with the magnetosphere indicating the frequent occurrence of FTEs on the dayside magnetopause. They identified one large structure that generated a slow mode bow wave as it accelerated towards the northern cusp and reached a speed approaching one Alfve´n velocity faster than the ambient magnetosheath flow. This paper presents more detailed observations of the same structure and examines the predictions of the hybrid code model for more structures in the same run, addressing the locations where they are generated, their velocity and acceleration, and the slow mode bow waves that they generate. It places the new simulation results within the context of previously reported observations, simulations, and theoretical models.
2. Model We examine output from the model originally presented by Omidi and Sibeck (2007). Solar wind plasmas and electromagnetic
21
fields enter the noon–midnight meridional plane domain of the model through its dayside boundary and exit freely through the three remaining boundaries. As noted by Omidi and Sibeck (2007), the ratio of the standoff distance of the magnetopause to the proton skin depth in the solar wind is 85, resulting in a magnetosphere 7.5 times smaller than that of the Earth. Nevertheless, the resulting magnetosphere has characteristics similar to that of Earth’s. The simulation retains all three components of the electromagnetic fields and plasma flows, the solar wind Mach number is set to 5, ion and electron betas are set to 0.5, resistivity is spatially uniform, and the IMF points due southward. Given the 2.5D nature of the model, simulation results are appropriate to studies of flux transfer events with the large dawn/dusk extents expected during intervals of strongly southward IMF orientation moving northward or southward along the noon meridian in response to combined pressure gradient and magnetic curvature forces (e.g., Fedder et al., 2002; Pinnock et al., 2003; Raeder, 2006). Results from the simulation are presented in the X–Y coordinate system, where X points antisunward and Y points northward. The Earth lies at (X, Y)¼(450, 500). Distances are measured in units of ion skin depth or c/opi, where opi is the ion plasma frequency. For a solar wind density of 6 cm 3, 1 c/opi ¼93 km. Time is measured in units of Oi 1, where Oi is the ion gyrofrequency. For an IMF strength of 5 nT, Oi 1 is 2 s. We set Oi 1 ¼0 at the time when the first FTE appears, which corresponds to Oi 1 ¼122.25 in the paper of Omidi and Sibeck (2007). Velocities are measured in units of the solar wind Alfve´n speed, VA. For a southward-pointing IMF strength of 5 nT, VA ¼41 km s 1. Cell sizes in the simulation are 1 c/opi, resistive scale lengths are 0.3 c/opi. Densities and magnetic field strengths presented in this paper are normalized to solar wind values.
3. Simulation results Figs. 2 and 3 present snapshots of densities, magnetic field strengths, and magnetic field directions at three times late in the simulation run: Oi 1 ¼67.95, 72.6, and 79.35. The dayside magnetosphere is readily identifiable as a region of extremely low (0.05) normalized densities and high ( 412) normalized magnetic field strengths. Dayside magnetospheric magnetic fields point northward ( þY). By comparison, magnetosheath densities are much higher ( 3) and magnetic field strengths are much lower ( 4). Dayside magnetosheath magnetic fields point southward. Mantle and lobe densities lie between those in the magnetosheath and dayside magnetosphere, ranging from 0.5 to 3. Mantle and lobe magnetic field strengths are also intermediate, ranging from 4 to 16. Mantle and lobe magnetic fields have strong southward components. As noted by Omidi and Sibeck (2007), the most prominent transient feature in the simulation is the large FTE that moves northward along the magnetopause from a position near (X, Y) ¼(375, 544) at Oi 1 ¼67.95 to (X, Y) ¼(407, 574) at Oi 1 ¼79.35. Depressed ( 2) densities, enhanced ( 8) magnetic field strengths, and a closed loop structure bound the enhanced ( 6) densities and depressed ( 1) magnetic field strengths within the core region of this crater FTE. As the FTE moves away from its point of origin near the subsolar magnetopause, it generates a slow mode bow wave marked by enhanced densities and depressed magnetic field strengths. By Oi 1 ¼67.95, a region of enhanced densities (and slightly depressed magnetic field strengths) stretches outward from the magnetopause and preceeds the arrival of the FTE. The density enhancement increases with time, becoming more prominent at Oi 1 ¼72.6, and stretching outward into the magnetosheath from (rather than preceding)
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Fig. 2. Results from the 2.5D hybrid code for densities in the noon–midnight meridional plane at three times during the simulation. A large FTE marked by normalized densities of 6 moves northward from the subsolar point towards the northern cusp. The structure generates an increasingly prominent density wake that extends far into the magnetosheath.
Fig. 3. Results from the 2.5D hybrid code for magnetic field strengths and field lines in the noon–midnight meridional plane at three times during the simulation. A large FTE marked by a closed loop structure moves northward from the subsolar point towards the northern cusp. A region of slightly depressed magnetic field strengths and field lines that bow earthward precedes the structure.
the structure at Oi 1 ¼79.35. The region of enhanced densities within the wake corresponds to slightly depressed magnetic field strengths on kinked magnetosheath magnetic field lines that bow outward towards the magnetosheath. None of the other FTEs that occurred in this run reached the size of this structure. A small FTE that was present on the subsolar magnetopause near (X, Y)¼ (365, 490) at Oi 1 ¼ 67.95 moved southward to (370, 470) at Oi 1 ¼79.35. A larger structure near (X, Y)¼ (370, 470) at Oi 1 ¼67.95 moved southward to (375, 460) at Oi 1 ¼72.6 and (390, 445) at Oi 1 ¼79.35. The latter structure generated a bow wave, which became detectable at Oi 1 ¼76.5 (not shown) and prominent by Oi 1 ¼79.35. As in the case of the much larger northern hemisphere structure in the northern hemisphere, this bow wave also lay on kinked magnetosheath magnetic field lines that bowed outward towards the magnetosheath. The FTEs shown in Figs. 2 and 3 were only three of many that occurred throughout the entire run. From Oi 1 ¼0 to the end of the run at 87.75, 10 FTEs were identified, giving an average recurrence time of 8.8 Oi 1. Curves in Fig. 4a and b track the X and Y positions of the centers of all 10 FTEs as a function of time, respectively. As indicated by the histograms in Fig. 5, the FTEs originated within 301 of the equatorial plane. For most of the interval shown, they were precluded from originating precisely at the equator due to the presence of the large and slowly growing structure, whose subsequent northward motion was discussed within the context of Figs. 2 and 3. Most structures moved
antisunward (positive X direction) and towards the nearest pole (positive Y direction for structures at Y greater than 500, negative Y direction for structures at Y less than 500). However, two structures moved sunward and equatorward from Oi 1 ¼35 to 40 under the influence of greater reconnection rates and outflows at the reconnection line on their poleward edges than those on their equatorward edges Marked by blue curves in Fig. 4, these structures coalesced with the large equatorial structure during the prolonged interval that it spent nearly at rest on the subsolar magnetopause. Note that the simulation does not predict the production of pairs of bubble-like FTEs at single reconnection lines (Southwood et al., 1988; Scholer, 1988). Nor does it generate pairs of bubblelike FTEs bounding flux ropes, as is the case of two-dimensional MHD simulations of reconnection on a planar magnetopause (Ding et al., 1991). Instead, the simulation routinely generates single flux rope FTEs between pairs of reconnection lines (Lee and Fu, 1985; Raeder, 2006). One such FTE, marked by high densities and low magnetic field strengths, was in the process of being generated near (X, Y)¼(365, 490) at Oi 1 ¼67.95. The curves in Fig. 4c show structure velocities as a function of time. These velocities were determined by taking the first derivative of structure positions as a function of time. Structures with long durations typically exhibit three phases: an initial small decrease in velocity, a long steady rise, and an abrupt final decrease. The first phase occurs as a newly formed FTE moves
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X (c/ωp)
410.0
Antisunward
370.0 Sunward
Y(c/ωp)
580.0
North
500.0
V (SW VA)
420.0
South
5.0
A (SW VAΩι)
1.0 0.8 0.0 -0.8 0
20
40 T (1/Ωi)
60
80
Fig. 4. The locations (X, Y), velocity (V), and acceleration (A) of FTEs seen in the hybrid code simulation. Black curves indicate structures moving northward, red those moving southward, and blue those moving sunward and equatorward. Black, red, and blue curves for the velocity and acceleration are time derivatives of the structure X and Y positions. For comparison, black circles in the third panel show the velocities observed at the center of the largest northward-moving structure. Black crosses in the same panel indicate the times when density enhancements appear in the magnetosheath outside six structures. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
5.0 # Events
Initial
1.0
Cusp Coalescence Destruction
1.0 -90
Final
Cusp Destruction
# Events
5.0
-70
-50
-30
-10 10 Latitude
30
50
70
90
Fig. 5. Histograms for the latitudes at which structures first appear and those to which they ultimately move. Most structures move to and are destroyed by reconnection in the cusp. A few structures move sunward and coalesce.
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encounters the obstacle posed by the mantle and lobe. The velocities of structures with shorter durations simply increase as they move poleward. Velocities peak at 3.5–5.5 solar wind Alfve´n velocities. Fig. 4d shows structure acceleration as a function of time. These accelerations were determined by taking the first derivatives of structure velocities as a function of time. Structures with long durations typically decelerate briefly, accelerate over a much longer period of time as they move poleward, and then abruptly decelerate as they enter the cusp and encounter the mantle and lobe. If the FTEs move as solid bodies, then the velocities observed at their cores should correspond to those determined by taking the first derivatives of structure positions as a function of time. Black circles in the Fig. 4c present the velocities observed within the core region of the large northward-moving FTE as a function of time. These velocities agree very well with those determined by taking the first derivative of the structure positions as a function of time (longest black curve in Fig. 4c), confirming that the structures move as solid bodies. For comparison with the predictions of the analytical model presented by Sonnerup et al. (1992) and shown in Fig. 1, we must calculate the sonic and Alfve´nic Mach numbers for structure motion relative to the background flow. Circles in Fig. 1 show these values for the large northward-moving structure. We calculate the Mach numbers by subtracting ambient magnetosheath flow velocities from those observed within the core of the structure (the circles in Fig. 4c) and dividing the result by the ambient magnetosheath sonic and Alfve´nic speeds. The structure initially moves very slowly, with sonic and Alfve´nic Mach numbers much lower than unity. As the structure accelerates, sonic Mach numbers increase to values much greater than unity, whereas Alfve´nic Mach numbers increase to values in the vicinity of unity. Once the structure encounters the cusp, the slowdown in structure motion causes Alfve´nic Mach numbers to diminish to values much less than unity. Given the errors inherent in reading structure and ambient flow velocities, the peak Alfve´nic Mach numbers are essentially equivalent to unity. Thus, rather than moving through the magnetosheath flow at the Alfve´n velocity throughout its existence, the structure gradually accelerates up to the Alfve´n velocity, only reaching this speed as it departs the dayside magnetopause and just before it encounters the cusp. Since the values for the Alfve´nic and sonic Mach numbers do not lie in the regions of parameter space where either slow or fast mode shocks are expected, the density enhancement and magnetic field strength decrease extending into the magnetosheath from the flank of the largest structure is a slow mode wave and not a shock. Similar density and magnetic field strength perturbations accompany five other FTEs. Black crosses in Fig. 4c mark the times and event velocities when these perturbations first appear, generally just before or after FTEs encounter the cusps and disintegrate. The perturbations often appear at or just after event disintegration, i.e. at times when event velocities cannot be obtained by differencing the positions of their centers. Crosses in Fig. 1 indicate the sonic and Alfve´nic Mach numbers for structure motion relative to the background flow at these times, calculated in a manner similar to that described above for the largest structure. As in the case of this structure, sonic Mach numbers greatly exceed unity, but Alfve´nic Mach numbers lie in the vicinity of unity. By the ends of their lifetimes, as they encounter the cusps, the structures have accelerated to velocities about one Alfve´n speed faster than the background magnetosheath flow.
4. Discussion and conclusions towards a location where it can grow steadily. The second phase occurs as the structure moves poleward towards the cusps. The final phase occurs when the structure enters the cusps and
This paper presented results from a 2.5 dimensional hybrid code model for the evolution of FTEs during intervals of due
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southward IMF orientation. The structures invariably form between pairs of reconnection lines, often remaining nearly stationary on the subsolar magnetopause before their motion begins. Although a few structures move sunward, ultimately coalescing with other structures, most eventually accelerate antisunward, reaching velocities about one Alfve´n speed greater than the ambient magnetosheath flow. At these velocities, slow mode wakes (but not shocks) marked by density enhancements and magnetic field strength decreases extend outward from the structures into the magnetosheath. As previously discussed by Omidi and Sibeck (2007), the structures ultimately decelerate and disintegrate upon encountering the cusps. Observations are needed to confirm model predictions. The model predicts the gradual growth and acceleration of structures to speeds one Alfve´n velocity greater than the background magnetosheath flow. Consequently larger structures and those observed near the terminator are more likely to move at the predicted velocities than smaller structures and those observed on the subsolar magnetopause. Fear et al. (2007) compared structure velocities derived from multipoint Cluster observations with the predictions of the Cooling et al. model, which predicts steady structure motion at speeds one Alfve´n velocity greater than the background magnetosheath flow. They found that 73% of observed structures move at speeds within a factor of 2 and directions to within 301 of those predicted by the model. By contrast 78% of larger structures (those with dimensions greater than 5000 km) satisfy these conditions. Although they did not report the distribution of observed to predicted speeds, the acceleration predicted by the model presented in this paper provides a natural explanation for events moving at velocities less than or equal to those predicted. Although both common and prominent in the predictions of the numerical simulation, the wake density enhancements predicted by the model have yet to be reported. Since the perturbations are generated by strong flow shears between FTEs and the background magnetosheath, they should be most prominent at times and locations where FTEs move rapidly through slowly moving magnetosheath plasmas. The perturbations should therefore be most prominent for strongly southward IMF orientations, when the curvature forces that accelerate the structures relative to the magnetosheath flow lie perpendicular to east–west oriented structure axes. Further, the perturbations should intensify with distance from the subsolar point as structures accelerate, but diminish once the structures encounter the cusps and decelerate. They should therefore be most readily observed at latitudes at and just equatorward of the cusps. Finally, the perturbations should be most prominent during intervals when solar wind flow speeds are low, since these are also intervals when magnetosheath velocities are small.
Acknowledgments Research at GSFC was funding by NASA’s Heliophysics Guest Investigator Program. Research at Solana Scientific was funded by NSF grants ATM-0502992 and AGS-1007449. References Berchem, J., Russell, C.T., 1984. Flux transfer events on the magnetopause: spatial distribution and controlling factors. J. Geophys. Res. 89, 6689–6703.
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