Statistical Study of Magnetic Reconnection in the Solar Wind

(1)

Statistical Study of Magnetic Reconnection in the Solar Wind

J. Enˇzl, L. Pˇrech, J. ˇSafr´ankov´a, and Z. Nˇemeˇcek

Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic.

Abstract. Magnetic reconnection is a phenomenon where the energy stored in the magnetic field dissipates into plasma heating and acceleration. It can occur on boundaries connecting plasma with different magnetic field orientations. In spacecraft observations, we can identify magnetic reconnection through its exhaust where the plasma on reconnected field lines leaves the reconnection site.

We present a statistical study of magnetic reconnection in the solar wind based on data from the WIND spacecraft during the period of 1995–2010. We track the signatures of the magnetic reconnection exhaust such as a rotation of the magnetic field or acceleration and heating of the plasma. We found dependence of the heating and plasma acceleration inside reconnection exhaust.

Introduction

Magnetic reconnection is a process where the energy stored in the magnetic field dissipates into plasma heating and acceleration. It can occur on boundaries connecting plasma with different magnetic field topologies [Gosling et al., 2005]. Generally, magnetic reconnection occurs at thin current sheets separating plasmas carrying oppositely oriented magnetic field lines. Due to the kinetic effects, non-ideal terms in a generalized Ohm’s law gain importance in some locations of the current sheet. As a result, the diffusion region where the frozen-in magnetic field condition is no longer satisfied is formed around the X-line.

Magnetic field lines reconnect into a topology with less magnetic energy. The released magnetic field energy is dissipated into heating and acceleration of plasma away from the X- line into the exhaust. The plasma enters the exhaust also on its boundaries where the heating and acceleration take place as well [Petschek, 1964; Shay et al., 2001]. The sketch of the Petschek reconnection model is in Fig. 1. The outflow region is bounded by stationary slow mode shock waves. The diffusion region is located in the center.

At 1 AU, local quasi-stationary reconnection of the Petschek-type forms exhausts char- acterized by a correlated rotation of the magnetic field with local velocity and temperature enhancements [Gosling et al., 2005; Phan et al., 2010]. The reconnection exhaust is bounded by slow shocks and rotational discontinuities at which the changes of flow velocity and magnetic field vectors are correlated on one side and anti-correlated on the other side [Gosling et al., 2007b].

Figure 1. The Petschek model of magnetic reconnection.

WDS'13 Proceedings of Contributed Papers, Part II, 7–12, 2013. ISBN 978-80-7378-251-1 © MATFYZPRESS

(2)

ENZL ET AL.: MAGNETIC RECONNECTION IN THE SOLAR WIND

Figure 2. An example of magnetic reconnection. Vertical dashed lines denote the regions used in the statistics for averaging. The values with subscript “in” were averaged inside the reconnection exhaust, whereas the values with the subscript “out” are used for the averages from the exhaust surroundings.

Reconnection exhausts were observed predominantly in the plasma having a low proton beta (β < 1) [Gosling, 2011]. The magnetic field shears across the exhausts range from about 70^◦ to 180^◦with the most probable value of 135^◦. On the other hand, the reconnection events observed in the pristine solar wind often occur at lower magnetic shears [Gosling et al., 2007a]. Due to the relatively low reconnection rates connected with small shear angles, the corresponding exhausts tend to be quite narrow (< 4 × 10⁴ km) but they can be surprisingly long. For example, we have found an exhaust more than 130 R_E long [Enˇzl et al., 2013]; Phan et al. [2006] reported three-spacecraft observations of the accelerated flow where the reconnection X-line extended at least 390 RE.

Previous statistical surveys [Gosling et al., 2007a; Phan et al., 2010] show that magnetic reconnection with high ∆β (absolute value of the difference of the β parameter in the regions surrounding reconnection) is suppressed for low shear angles. However, ∆β is necessarily small for the low β plasma and reconnection can occur regardless of the β asymmetry. This fact is consistent with a suppression of the reconnection rate by the diamagnetic drift of the X-line associated with the pressure gradients across the current sheet [Swisdak et al., 2003; Swisdak et al., 2010].

In this study, our concern is to determine how magnetic reconnection depends on the

(3)

Figure 3. The dependence of the speed of the accelerated flow on the Alfv´en speed. The dashed straight line means equality of both speeds.

shear angle and to quantify transformation of the magnetic energy into plasma acceleration and heating. We expect that the released energy should depend on the shear angle because the released energy is limited by the magnetic stress energy.

Statistical results

The data from the WIND spacecraft during a period of 1995–2010 were used to track magnetic reconnection in the solar wind. The automated event identification was based on correlated and anti-correlated changes of the velocity and magnetic field. The identified events were then checked by visual inspection of the plots and 381 reconnection events were found as a result. We computed the parameters of the exhaust such as the plasma acceleration, temperature enhancement or shear angle in order to provide basic characteristics of magnetic reconnection events.

Table 1. Mean values of magnetic reconnection in the solar wind.

Shear Angle Brec Vacc Tenh Nenh Exhaust width [^◦] [nT] [km/s] [eV] [cm⁻³] [km]

104 4.2 23.9 1.2 1.5 16 · 10³

In Fig. 2, we present an example of magnetic reconnection observations. The region labeled as “in” represents the magnetic reconnection exhaust. The proton density and temperature are enhanced and the magnetic field depressed in this region. The velocity of the solar wind is accelerated up to the Alfv´en speed in the direction of the exhaust. The magnetic field rotates as the spacecraft moves across the exhaust. The rotation of the magnetic field in this particular example is not smooth but it takes place only at the exhaust boundaries.

Average parameters of 381 reconnection events were computed as a first step. Table 1 presents mean values of the following parameters: The shear angle, reconnection magnetic field Brec (guide field was subtracted), speed of the accelerated flow (Vacc) which was obtained as a mean magnitude of the velocity deviation inside the exhaust from the average solar wind velocity, temperature enhancement inside the reconnection exhaust (T_enh), density enhancement inside the exhaust (Nenh), and exhaust width computed from the event duration and the solar wind speed. The Alfv´en speed was computed using Brec and the density within the reconnection exhaust.

(4)

Figure 4. In the upper panel: The dependence of the reconnection magnetic field B_rec on the shear angle. In the bottom panel: The dependence of the decrease of the magnetic field (B_dec= Bout− B_in) normalized to the reconnection magnetic field on the shear angle.

Figure 5. In the upper panel: The dependence of the accelerated flow speed Vacc on the reconnection field B_rec. In the bottom panel: The dependence of the accelerated flow speed V_acc on the shear angle.

(5)

Figure 6. A connection between the energy stored in the accelerated flow V_{acc energy} (i.e., normalized kinetic energy of the accelerated flow in the frame moving with discontinuity) and the n ∗ dT – energy of the temperature enhancement. The dashed curve denotes a linear fit y = a · x. The fit coefficients are in the table inside the plot.

Discussion and conclusion

We have searched for magnetic reconnection exhausts in the solar wind and identified 381 events in the period of 1995–2010. Their mean parameters are summarized in Table 1. The mean shear angle of the reconnection is 100^◦ but we should consider that our automated event identification cuts all shear angles below 30^◦ and that the event identification is not equally efficient for all shear angles because it depends on variations of the magnetic field direction. It could lead to overestimation of the mean shear angle. The determined exhaust width is in an agreement with previous studies [Gosling et al., 2007b].

Our results are plotted in a series of Figs. 3–6. Statistically, B_rec grows with the shear angle due to the guide field subtraction (Fig. 4). As a result, we can observe the increasing dependence of the accelerated flow inside the reconnection exhaust on the shear angle (Fig. 5).

According to Figure 3, the accelerated flow velocity seems to be limited to the Alfv´en speed V_alf. The accelerated flow velocity is also dependent on the magnetic field magnitude Brec (Fig. 5) because the Alfv´en speed is dependent on the magnetic field magnitude; therefore the larger magnetic field implies faster flow inside the exhaust.

The dependence of the magnetic field depression and the reconnection magnetic field B_rec on the shear angle is in Fig. 4. The depression of the magnetic field is more distinctive for shear angles larger than ≈ 130^◦. For such shear angles the reconnection magnetic field almost vanished in some cases.

Together with the accelerated flow, the plasma heating takes place. The energy released via magnetic reconnection is transformed into heating and plasma acceleration. The mean ratio of the energy stored in the accelerated flow to the energy stored in temperature enhancements is ≈ 4.5 (Fig. 6). It means that a more energy released via reconnection is transformed into the plasma acceleration than into heating. The enhancement of the proton temperature is thus a minor signature of magnetic reconnection. Actually, the decreased proton temperature can be observed on a number of events from our dataset. It is necessary to measure the dependence of the temperature enhancement on the X-line distance to provide information where the observed

(6)

heating exactly takes place, if it is a consequence of the reconnection process or a part of the dissipation process of the accelerated plasma flow. Finally, we should note that our plots exhibit a large spread of data points. We believe that the reason for this should be the unknown distance from the X-line, which cannot be estimated from single spacecraft measurements. The velocity of the accelerated plasma flow inside the exhaust, V_acc decreases with the distance from the X-line due to dissipation processes as we demonstrated in Enˇzl et al. [2013].

Acknowledgments. We thank to the WIND spacecraft working team and CDAWeb data center for providing data and images. The work was supported by the Grant Agency of Charles University under contract 1096213.

References

Enˇzl, J., Pˇrech, L., ˇSafr´ankov´a, J., and Nˇemeˇcek, Z., Multi-spacecraft observations of magnetic reconnection in the solar wind, AIP Conference Proceedings, 1539 , 159–162, URL http://link.aip.org/link/?APC/1539/159/1, 2013.

Gosling, J. T., Magnetic Reconnection in the Solar Wind, Space Sci. Rev., p. 104, 2011.

Gosling, J. T., Skoug, R. M., McComas, D. J., and Smith, C. W., Direct evidence for magnetic reconnection in the solar wind near 1 AU, J. Geophys. Res., 110 , 1107, 2005.

Gosling, J. T., Eriksson, S., McComas, D. J., Phan, T. D., and Skoug, R. M., Multiple magnetic reconnection sites associated with a coronal mass ejection in the solar wind, J. Geophys. Res., 112 , A08 106, 2007a.

Gosling, J. T., Phan, T. D., Lin, R. P., and Szabo, A., Prevalence of magnetic reconnection at small field shear angles in the solar wind, Geophys. Res. Lett., 34 , URL http://dx.doi.org/10.1029/2007GL030706, 2007b.

Petschek, H. E., Magnetic field annihilation, NASA Special Publications, 50 , 425–439, 1964.

Phan, T. D., Gosling, J. T., Davis, M. S., Skoug, R. M., Øieroset, M., Lin, R. P., Lepping, R. P., McComas, D. J., Smith, C. W., Reme, H., and Balogh, A., A magnetic reconnection X-line extending more than 390 Earth radii in the solar wind, Nature, 439 , 175–178, 2006.

Phan, T. D., Gosling, J. T., Paschmann, G., Pasma, C., Drake, J. F., Øieroset, M., Larson, D., Lin, R. P., and Davis, M. S., The dependence of magnetic reconnection on plasma beta and magnetic shear:

evidence from solar wind observations, ApJL, 719 , 199–203, 2010.

Shay, M. A., Drake, J. F., Rogers, B. N., and Denton, R. E., Alfvenic collisionless magnetic reconnection and the Hall terme, J. Geophys. Res., 106 , 3759–3772, 2001.

Swisdak, M., Rogers, B. N., Drake, J. F., and Shay, M. A., Diamagnetic Suppression of Component Magnetic Reconnection at the Magnetopause, J. Geophys. Res., 108 , 2003.

Swisdak, M., Opher, M., Drake, J. F., and Bibi, F. A., The vector direction of the in- terstellar magnetic field outside the heliosphere, The Astrophysical Journal , 710 , 1769, URL http://stacks.iop.org/0004-637X/710/i=2/a=1769, 2010.