The dependence of magnetic reconnection on plasma β and magnetic shear: Evidence from magnetopause observations


Corresponding author: T. D. Phan, University of California, Berkeley, CA, USA. (


[1] We have performed a statistical study of THEMIS spacecraft crossings of the asymmetric dayside magnetopause to test the prediction that the diamagnetic drift of the X-line due to a plasma pressure gradient across the magnetopause can suppress magnetic reconnection. The study includes crossings both when reconnection exhausts were present and when they were absent in the current sheet. When we restrict the survey to the subsolar region (10 < MLT < 14), we find that for low Δβ (the difference of plasma β on the two sides of the current sheet) the majority of reconnection events occurred over a large range of magnetic shears, whereas when Δβ was high reconnection events occurred only for high shears. Furthermore, nonreconnection events occurred primarily in the Δβ-shear regime in which reconnection is predicted to be suppressed, in good agreement with theory. The Δβ-shear condition should have general consequences for the occurrence of reconnection in space and laboratory plasmas.

1 Introduction

[2] Magnetic reconnection is a plasma process that converts magnetic energy into particle energy and is important in many space and laboratory contexts. Past observations have provided unambiguous evidence for reconnection at Earth's magnetopause, especially under large magnetic shear conditions [e.g., Paschmann et al., 1979; Gosling et al., 1990]. However, it has also become clear that not all large-shear magnetopause current sheets are prone to reconnection [e.g., Paschmann et al., 1986]. Previous magnetopause observations have suggested that the plasma β in the magnetosheath region adjacent to the magnetopause may be a controlling factor, with reconnection less likely to occur when β > 2 [Paschmann et al., 1986; Scurry et al., 1994]. However, no physical explanations for the dependence of reconnection on β were given in those studies.

[3] Swisdak et al. [2003, 2010] proposed that the occurrence of asymmetric reconnection depends not on β alone, but on a combination of the difference in the β on the two sides of the current sheet and the magnetic shear angle, θ, across the current sheet at the X-line. The underlying physics is the diamagnetic drift of the X-line associated with the plasma pressure gradient across the current sheet. Reconnection is suppressed if the X-line drift speed (along the reconnection outflow direction) exceeds the reconnection outflow speed. For a given θ at the X-line, Swisdak et al. [2010] predicted that reconnection is suppressed if Δβ satisfies the following relation:

display math(1)

where L/λi is the width of the plasma pressure gradient layer across the current sheet in units of the ion skin depth λi. This width is a free parameter but is expected to be comparable to the width of the ion diffusion region which, in turn, is expected to be of the order of λi. According to this prediction, reconnection is allowed for a large range of θ at low Δβ but requires large θ at high Δβ values.

[4] In a recent study Phan et al. [2010] found that reconnection exhausts in the solar wind are consistent with the Δβθ dependence predicted by Swisdak et al. [2010]. For low Δβ reconnection exhausts were observed for a large range of θ, whereas for large Δβ reconnection occurred only when θ was large.

[5] In the present study we test Relation (1) at the Earth's magnetopause where the plasma pressures on the two sides of the current sheet are asymmetric. In contrast to our study of solar wind reconnection events [Phan et al., 2010], this study examines both reconnection and nonreconnection events and extends our earlier results to a much higher plasma β regime, thereby further illustrating the universal nature of Relation (1).

2 Determination of Reconnection Versus Nonreconnection Events

[6] To investigate the Δβθ dependence of reconnection we identify both reconnecting and non-reconnecting magnetopause current sheets and measure the total β (βion + βelectron) in the two inflow regions (i.e., the magnetosheath and the magnetosphere) as well as the total magnetic shear, θ, across the current sheet. Strictly speaking, the comparison between the spacecraft observations of the exhaust and the Swisdak et al. [2010] theoretical prediction (Relation 1) is meaningful only if the boundary conditions at the exhaust are representative of the conditions at the X-line. This issue will be addressed in section 'Statistical Survey'. We now describe the methodology used to determine if any given magnetopause crossing did or did not exhibit reconnection signatures.

2.1 Walen Test

[7] For asymmetric magnetopause reconnection, where the plasma density on the magnetosheath side of the current sheet is much higher than on the magnetosphere side, the largest plasma flow acceleration occurs across the rotational discontinuity (RD) located on the magnetosheath edge of the magnetopause [e.g., Levy et al., 1964]. To check whether the plasma flow in the magnetopause is consistent with the prediction from tangential stress balance across an RD, we compare the observed flow change across the magnetosheath edge of the magnetopause with the Walen relation [Hudson, 1970; Paschmann et al., 1986, equation (7)]:

display math(2)

where v, B, and ρ are the ion bulk velocity, magnetic field, and proton mass density, respectively. α  = (p|| – p)μ0/B2 is the anisotropy factor where p|| and p are the plasma pressures parallel and perpendicular to B. Subscript 1 denotes the magnetosheath (inflow) region, which will be averaged over a 10 s interval immediately adjacent to the magnetopause. Subscript 2 denotes the outflow jet region and will be taken at the point of maximum observed flow change, Δvobs, across the magnetosheath edge of the magnetopause [Phan et al., 1996]. The Walen test should be performed across the RD and should not extend into the slow-mode expansion fan region earthward of the RD [e.g., Levy et al., 1964]. To avoid the slow-mode expansion fan, the Walen test is made only in the interval from the magnetosheath edge of the magnetopause to a location in the current layer just before the density drops below 20% of the magnetosheath density.

[8] The Walen relation predicts a correlated or anticorrelated change of the tangential velocity and magnetic field components across the magnetosheath edge of the magnetopause. To obtain a single, scalar, and dimensionless measure of the agreement between observed and predicted flow acceleration, we compute Δv* = Δvobs • Δvpredicted/|Δvpredicted|2 [Paschmann et al., 1986] where Δvobs is the observed velocity change. A perfect agreement of Δvobs with theory in magnitude as well as direction would give Δv* = 1, while lower values of Δv* would indicate poorer agreement.

2.2 Interpenetrating Ions

[9] A kinetic signature of reconnection is the presence inside the exhaust of mixed ion populations originating from the opposite sides of the current sheet, which implies magnetic connection across the exhaust [e.g., Gosling et al., 2005]. Interpenetrating ions are most evident when the magnetosphere adjacent to the magnetopause contains cold ions that originated in the plasmasphere [e.g., Gosling et al., 1990]. The inclusion of the cold ions in the plasma moment computation leads to an underestimation of the accelerated magnetosheath plasma velocity, which may result in poorer agreement with the Walen relation (see section 'Reconnection Event').

3 Examples of Reconnection and Nonreconnection Events

[10] In this section we illustrate the determination of reconnection and nonreconnection events and their boundary conditions.

3.1 Reconnection Event

[11] Figures 1a–1f show a THEMIS-D inbound crossing of a reconnecting magnetopause current sheet on 30 July 2008 in the 19:33:00–19:33:30 UT interval. The crossing occurred at 13.7 h magnetic local time, MLT, and –17.6° in magnetic latitude, MLAT. The magnetic field (Figure 1a) and ion velocity (Figure 1b) components are displayed in the LMN boundary normal coordinate system obtained from the minimum variance analysis of the magnetic field [Sonnerup and Cahill, 1967], with L along the outflow direction, M along the X-line and N along the current sheet normal. The reconnection exhaust was identified by the presence of a ~95 km/s plasma jet within the region where the magnetic field rotated, with the change in vL (Figure 1b) and BL (Figure 1a) being anticorrelated across the magnetosheath (left) edge of the magnetopause. However, quantitative comparison with the Walen relation (see section 'Walen Test') reveals that the observed flow change |Δvobs| (taken at its peak in the current sheet at the vertical dotted line) was only ~34% of the predicted flow change of 276 km/s, while the angle between the observed and predicted flow change was 12°, resulting in Δv* ~ 0.34. Thus while the jet direction was in reasonable agreement with the prediction, the flow speed was substantially less than predicted by the Walen relation. In this case we use the additional evidence from the ion distributions to classify this event as resulting from reconnection.

Figure 1.

Examples of reconnection (left) and nonreconnection (right) magnetopause crossings. (a, g) The magnetic field in LMN minimum variance coordinates, (b, h) proton velocity in LMN, (c, i) proton density, (d, j), total plasma β, (e, k) ion energy spectrogram in units of eV s–1 cm–2 ster–1 eV–1. The left and right pairs of vertical dashed lines denote the 10 s intervals on the two sides of the current sheet. The vertical dotted line denotes the location of maximum |Δvobs| in the current layer. Figures 1f and 1l show two-dimensional cuts of three-dimensional ion distributions in the spacecraft frame through velocity space that contains the magnetic field direction (to the right) and E × B (upward), where E was obtained from −v × B. The length of the black line from the origin indicates the overall bulk velocity. The big black dot denotes the predicted velocity from the Walen relation.

[12] Examination of the ion distributions in the current sheet shows the presence of interpenetrating magnetosheath ions and cold magnetospheric ions in eight consecutive 3 s distributions. The distribution shown in Figure 1f was taken within the current sheet on a field line with magnetospheric orientation (+BL). At this location, the magnetosheath ion population has gone through the field kink and been accelerated to v|| ~ −200 km/s, while the cold magnetospheric ion population (seen just above the origin) has a smaller positive v|| (of ~ +40 km/s) because it has not gone through the field kink. Both populations have the same E × B velocity (of ~100 km/s) as required. Thus, while the velocity of the magnetosheath population was close (~70%) to the predicted flow velocity (marked by the big black dot), the bulk velocity computed by combining the 2 populations is a lot slower and far off the prediction. This event illustrates the importance of examining particle distributions in addition to performing the Walen test, especially in cases where there is a correlated change in the flow and field across the magnetopause expected from reconnection but the plasma velocity moment is substantially less than predicted.

[13] The β and magnetic shear values were obtained by averaging the data over 10 s intervals between the left and right pairs of vertical dashed lines (in Figure 1a–1e) on the two sides of the current sheet. A fixed 10 s interval has been used in all events studied here to ensure that the averages and standard deviations of β and magnetic shear can be meaningfully compared between events. For this event, the difference in β on the two sides of the current sheet, Δβ, was 5.6 ± 1.4 while the magnetic shear was 148° ± 15°. The relatively large uncertainties in the β and shear values are likely due to the presence of mirror-mode waves in high β magnetosheath. This event illustrates that reconnection can occur at high β when the magnetic shear is large.

3.2 Nonreconnection Event

[14] Figures 1g–1l show an example of a magnetopause crossing in which there were no accelerated flows nor interpenetrating ion beams. THEMIS-D crossed the magnetopause near the subsolar point (11.8 MLT, –11.3° MLAT) on an outbound pass at ~18:37:00–18:37:30 UT on 4 September 2008. We will describe this event backward in time, going from the magnetosheath to the magnetosphere. The absence of accelerated flow expected from reconnection is evident by the lack of any significant vL change associated with the magnetic field BL rotation at the magnetosheath edge of the magnetopause (the left red dashed line). Note that the large spikes in vM and vN at ~18:37:02 UT (at density < 1 cm–3) had no associated changes in the magnetic field and therefore could not have been caused by reconnection.

[15] Quantitative comparison with the Walen relation reveals that the observed flow change |Δvobs| (taken at the dotted line which corresponds to the peak in |Δvobs| within the current sheet sunward of where the density dropped below 20% of magnetosheath density) was only ~16% of the prediction. The angle between the observed and predicted flow change was ~44°, resulting in a Δv* of 0.12. Thus both the magnitude and direction of the flow change across the magnetopause failed the Walen test.

[16] Furthermore, ion distributions in the magnetopause (Figure 1l) taken at similar magnetospheric locations as in the previous example do not show the presence of interpenetrating ions. This further supports the interpretation of this case as a crossing of a non-reconnecting magnetopause current sheet. For this event, Δβ across the magnetopause was 11.3 ± 2.8, while the magnetic shear was 96° ± 14°.

4 Statistical Survey

[17] To test the validity of Relation (1) it is important to select only events where the evidence for reconnection or no reconnection is convincing, and that the boundary conditions are sufficiently well defined.

4.1 Data Set and Selection Criteria

[18] We use 3 s resolution magnetic field and plasma data collected by the THEMIS-D spacecraft in June to October 2008. This spacecraft was chosen because of its dayside magnetopause skimming orbit, resulting in more than 400 complete magnetopause crossings in the 5 month period. Partial magnetopause crossings in which the spacecraft did not fully traverse the magnetopause are not included in this study. We down-selected from this data set crossings for which (1) the magnetic shear across the magnetopause was >45° (below this shear angle the reconnection site is likely to be located at high latitude where the magnetic shear may be substantially different from the shear measured at the spacecraft location), and (2) the spacecraft was in the “Fast Survey” or “Burst” mode in which three-dimensional ion distributions were available at 3 s resolution, and (3) the adjacent magnetosheath condition was sufficiently stable so that the magnetosheath edge of the magnetopause can be identified and the magnetosheath β value and the magnetic shear at the magnetopause can be determined relatively reliably.

[19] The total number of magnetopause crossings that satisfied the above criteria is 91. We then grouped the crossings into three categories: “reconnection”, “nonreconnection”, and “ambiguous”. There were 49 reconnection, 24 non-reconnection, and 18 ambiguous events. The classification is based on (1) the correlation between the flow and field change across the magnetopause, (2) the Walen test, and (3) the presence or absence of interpenetrating ions in the magnetopause. It should be noted that interpenetrating ions are only evident when the magnetospheric plasma next to the magnetopause contains cold ions. These cold ions are observed in the magnetosphere in more than half of all magnetopause crossings in this data set.

[20] A magnetopause crossing is deemed as a nonreconnection event if (a) there is no correlation between the magnetic field rotation and the plasma velocity change across the magnetosheath edge of the magnetopause (i.e., no accelerated flows), and (b) there is no evidence for interpenetrating ions. Although the level of agreement with the Walen relation (Δv*) was not used to determine nonreconnection events the findings in section 'Results' confirm that nonreconnection events tend to have low Δv* and poor angle agreement.

[21] A crossing is deemed as a reconnection event if there is evidence for accelerated or decelerated flows across the magnetosheath edge of the magnetopause, with correlated or anticorrelated changes in the flow and field. In events that show the presence of accelerated flows but the agreement with the Walen relation, Δv*, is less than 0.5, we further require the presence of interpenetrating ions. For events with Δv* > 0.5 we do not impose the interpenetrating ions requirement.

[22] A crossing is deemed as an ambiguous event if there are correlated or anticorrelated changes in the flow and field across the magnetopause, but Δv* < 0.5 and there is no evidence for interpenetrating ions.

[23] Strictly speaking, the comparison between the spacecraft observations at the local magnetopause and the theoretical prediction (Relation 1) is meaningful only if the local conditions are representative of the conditions at the X-line. Because of the curved magnetopause surface, the draping of the magnetosheath field over the magnetopause results in a variety of magnetic shear depending on the location, with values ranging from 0° to 180° along the magnetopause surface at any given time. By choosing a data set of dayside low-latitude magnetopause and with magnetic shear >45°, the expectation or hope is that any X-line present is close to the subsolar region and not too far away from the spacecraft [Trattner et al., 2012].

4.2 Results

4.2.1 Statistics on Reconnection Versus Nonreconnection Events

[24] Figure 2c shows that Δv* of the reconnection events ranges from 0.23 to 1.28, with average and median values (indicated by the vertical dotted and dashed lines in Figure 2c) of 0.66 and 0.6, respectively. Figure 2d shows that the angle between the predicted and observed flow changes is <30°, with an average agreement of 13°. For nonreconnection events, on the other hand, Δv* is less than 0.5 for all cases (Figure 2 h), and the angle between predicted and observed flow changes cover the entire range, from 1.4° to 87° (Figure 2i). Thus although the reconnection events on average have higher Δv* than the nonreconnection events, there is an overlapping Δv* range (mostly between 0.2 and 0.4), which means that one cannot use a single Δv* value to separate cleanly reconnection from nonreconnection events. For example, if we had used the condition of Δv* > 0.5 to define reconnection events, we would have missed 10 of the 49 reconnection events.

Figure 2.

Results of statistical survey of reconnection (left) and nonreconnection (right) events. (a, f) Scatter plot of magnetic shear versus Δβ across the magnetopause for all MLT; (b, g) magnetic shear versus Δβ in the vicinity of the subsolar region (10 < MLT < 14); (c, h) distribution of the quality measure, Δv*, of the agreement between observed and predicted flow acceleration; (d, i) distribution of the angle between observed and predicted flow change; and (e, j) the magnetic latitude and magnetic local time of the magnetopause crossings.

[25] Figures 2e and 2j show that the reconnection events cover a slightly larger range of MLT than nonreconnection events, but there are no appreciable differences in terms of their magnetic latitude locations.

4.2.2 Dependence on the Plasma β and Magnetic Shear

[26] Figures 2a and 2f show scatter plots of magnetic shear (θ) and Δβ for all 49 reconnection (Figure 2a) and 24 nonreconnection (Figure 2f) events. Note that because β in the magnetosphere is generally much smaller than in the magnetosheath, Δβ ~ βmagnetosheath. Thus, the main difference between reconnection and nonreconnection events is their magnetosheath β values. For reconnection events 0.14 < Δβ < 8, whereas 3.2 < Δβ < 93 for the nonreconnection events. Thus, there is an overlapping range of Δβ in which both reconnection and non-reconnection events are detected.

[27] Overlaid on the upper two rows of panels are theoretical curves from Relation (1) for three different values of the pressure gradient scale at the X-line: L = 0.5 λi, 1.0 λi, and 2.0 λi. Below these curves reconnection is expected to be suppressed by the diamagnetic drift effect. In contrast to the finding in the solar wind that essentially all the reconnection events were above the line defined by the L = λi curve [Phan et al., 2010], 5 of the magnetopause reconnection events clearly lie below the L = λi curve. If the pressure gradient scale were 2 λi, on the other hand, then only one reconnection event would fall below the L = λi curve. For the nonreconnection events (Figure 2f), the majority (20 of 24) events lie below the L = λi curve.

[28] When we restrict the data set to 10 < MLT < 14, Figures 2b and 2g show that both the reconnection and non-reconnection events are now much better separated by the L = λi curve, with most of reconnection events lying above the line and most of the nonreconnection events lying below it. A possible reason for this improvement is that near the subsolar region the local magnetic shear and β conditions are likely to be representative of conditions at the X-line because the X-line is probably located nearby.

5 Discussion

[29] In our survey of THEMIS data at the dayside magnetopause we have found a clear separation between the reconnection and nonreconnection events in terms of their β and magnetic shear conditions. In agreement with the prediction of Swisdak et al. [2003, 2010], the majority of reconnection events were found in the regime where reconnection is not predicted to be suppressed by the diamagnetic drift effect while the majority of nonreconnection events were found in the regime where reconnection is predicted to be suppressed by that effect. The agreement with prediction is further improved if the observations are restricted to the region close to the subsolar point (10 < MLT < 14).

[30] While it is not surprising to find few reconnection events in the suppressed zone, it is perhaps surprising that few nonreconnection events are in the zone where the diamagnetic drift effect should not suppress reconnection. One would have expected more non-reconnection events in that zone because other conditions (such as a thick current sheet) can prevent reconnection from occurring. A possible interpretation of our finding is that, due to the compression of the solar wind against the dayside magnetosphere, the subsolar magnetopause is usually sufficiently thin to allow reconnection to occur. If this is true, diamagnetic drift of the X-line may be the main effect that controls the occurrence of reconnection at the subsolar magnetopause. Further down the flanks other effects, such as velocity shears, can suppress reconnection [e.g., Cowley and Owen, 1989].

[31] The suppression of low-shear reconnection at high Δβ should have general consequences for the occurrence of reconnection in space and laboratory plasmas. For example, it is plausible that this effect could explain why most prolonged magnetopause reconnection events have been observed for low magnetosheath β [ Gosling et al., 1982; Phan et al., 2004]. Under such conditions the magnetosheath plasma is stable to the mirror-mode, thus allowing relatively steady β conditions in the magnetosheath, and allowing magnetopause reconnection to be steady. Similarly, bursty reconnection is to be expected (but not yet confirmed) when the underlying magnetosheath β is high and mirror waves are present, producing fluctuating intervals of low and high-β.

[32] Finally, the Δβ-shear effect may have consequences for the occurrence frequency of magnetopause reconnection at inner versus outer planets. Because the solar wind β increases with increasing distance from the Sun, the occurrence rate of magnetopause reconnection at the outer planets is expected to be lower than at the inner planets due to the magnetic shear-Δβ effect. Indeed, Masters et al. [2012] have reported that the magnetic shear and β conditions at the Saturn magnetopause are most often in the regime where reconnection is predicted to be suppressed by the diamagnetic drift effect. It remains to be determined whether reconnection is indeed frequently absent at the Saturn magnetopause.


[33] This research was funded by NASA grant NNX08AO83G and NASA contract NAS5-02099 at UC Berkeley and NASA grants NNX10AC01G and NNX08AO84G at CU Boulder. We acknowledge NASA contract NAS5-02099 for use of data from the THEMIS mission.