NO EVIDENCE FOR HEATING OF THE SOLAR WIND AT STRONG CURRENT SHEETS

Strong current sheets are ubiquitous in the fast and slow solar-wind plasmas (Siscoe et al. 1968; Burlaga 1969; Borovsky 2008). Depending on the quantitative definition of "strong," about two or three sheets per hour are convected past a spacecraft by the wind (Borovsky & Denton 2010). Since the strong current sheets produce the majority of the magnetic-field Fourier power in the solar wind and dominate correlation functions and Alfvénicity measures (Siscoe et al. 1968; Borovsky 2010a; Borovsky & Denton 2010; Li et al. 2011), accurate interpretation of solar-wind spectra and higher-order moments depends on an understanding of the physics of the current sheets. Hence, it is important to study strong current sheets in the solar wind.

There is no consensus as to the nature of these strong current sheets. Three distinct possibilities are (1) plasma boundaries (tangential discontinuities; Bruno et al. 2001; Li 2007; Borovsky 2008, 2010b), (2) steepened Alfvén waves (rotational discontinuities; Tsurutani & Ho 1999; Vasquez & Hollweg 1999; Tsurutani et al. 2002), or (3) turbulence-generated features (Leamon et al. 2000; Matthaeus et al. 2003; Greco et al., 2010).

It is well observed that the solar-wind protons (Marsch et al. 1982; Schwartz & Marsch 1983; Freeman & Lopez 1985; Richardson et al. 1995) and electrons (Pilipp et al. 1990; Phillips et al. 1995) are heated with distance from the Sun. It has been conjectured that strong currents in the solar wind are the sites of solar-wind heating (Leamon et al. 2000; Matthaeus et al. 2003; Greco et al. 2010; Osman et al. 2011); this conjecture is motivated by observation of dissipation and particle heating at turbulence-generated current sheets in resistive-MHD computer simulations (e.g., Biskamp & Welter 1989; Dmitruk et al. 2004; Lehe et al. 2009).

In this Letter, we will test the heating conjecture by comparing solar-wind temperatures and specific entropies at strong current sheets with temperatures and specific entropies in the adjacent plasmas.

Magnetic-field (Smith et al. 1998) and plasma (McComas et al. 1998) measurements with a 64 s cadence from the ACE spacecraft upstream from the Earth are used to analyze the solar-wind plasma.

Strong current sheets in the solar wind are identified by directional changes Δθ > 45° of the solar-wind magnetic-field vector over a 128 s time interval. At 1 AU, Δθ = 45° is the breakpoint between two populations in a magnetic-field direction-change distribution (Borovsky 2008, 2010a). (See Li 2007, 2008 for an assessment of this current-sheet identification scheme.)

For analysis here the proton temperature T_p and the proton specific entropy S_p = T_p/n^2/3 (Birn & Schindler 1983; Goertz & Baumjohann 1991) are determined from the ACE measurements with 64 s time resolution. During February–October of 1998, electron temperatures T_e are available with 128 s time resolution (Skoug et al. 2000). A total of 194,070 strong current sheets are analyzed.

Evidence of localized proton heating would be a localized increase in the proton temperature T_p. Stronger evidence would be a localized increase in the proton specific entropy S_p, the inverse of which is the number density of adiabatic invariants per unit magnetic flux of the proton population (Borovsky & Cayton 2011). Increases in the proton specific entropy have traditionally been used as a measure of heat added to the solar-wind plasma (e.g., Schwartz & Marsch 1983; Freeman & Lopez 1985; Whang et al. 1989; Goldstein et al. 1995).

In Figure 1(a), the ratio of the proton temperature at the location of a strong current sheet to the proton temperature in the adjacent plasmas is binned for the current sheets. If in the sequence of 64 s resolution temperature measurements the current sheet is located at integer number "i", then the ratio in the purple curve measuring the adjacent plasmas 64 s before and after is formed as T_i/(0.5(T_i−1+T_i+1)) and the ratio in the green curve measuring the adjacent plasmas 128 s before and after is formed as T_i/(0.5(T_i−2+T_i+2)). As noted in the first two rows of Table 1, for both distributions of Figure 1(a) the mean, the median, and the logarithmic mean are all very close to unity meaning that the temperature at the current sheets is statistically the same as the temperature outside of the current sheets. This indicates that there is no significant proton heating at the locations of the strong current sheets.

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In Figure 1(b), the ratio of the proton specific entropy at the location of a strong current sheet to the proton specific entropy in the adjacent plasmas is binned for the current sheets. The ratio S_i/(0.5(S_i−1+S_i+1)) in the purple curve measures the adjacent plasmas 64 s before and after and the ratio S_i/(0.5(S_i−2+S_i+2)) in the green curve measures the adjacent plasmas 128 s before and after. As noted in the third and fourth rows of Table 1, the mean, the median, and the logarithmic mean of both distributions are all very close to unity meaning that the proton specific entropy at the current sheets is statistically the same as the proton specific entropy outside of the current sheets. This indicates that there is no significant proton heating at the locations of the strong current sheets.

In Figure 1(c), the ratio of the electron temperature at the location of a strong current sheet to the electron temperature in the adjacent plasmas is binned for 3884 current sheets in 1998. The ratio T_i/(0.5(T_i−2+T_i+2)) in the green curve measures the adjacent plasmas 128 s before and after. As noted in the last row of Table 1, the mean, the median, and the logarithmic mean of the distribution are all very close to unity meaning that the electron temperature at the current sheets is statistically the same as the electron temperature outside of the current sheets. This indicates that there is no significant electron heating at the locations of the strong current sheets.

Strong current sheets in the solar wind, however, are more prevalent in higher-temperature plasma than in lower-temperature plasma (cf. Miao et al. 2011). This is demonstrated in Figure 2 and Table 2 where the temperatures and specific entropies of the plasma at the location of strong current sheets is compared with the temperatures and specific entropies of the plasma everywhere. In Figure 2(a), the distribution of proton temperatures measured at the locations of the strong current sheets is plotted in red and the distribution of all proton temperatures in the ACE data set is plotted in black. As can be seen (cf. Table 2), the current sheets are found on average in plasma with a higher proton temperature (12.5 eV) than the average solar wind (6.0 eV). In Figure 2(b), the distribution of proton specific entropies measured at the locations of the strong current sheets is plotted in red and the distribution of all proton specific entropies in the ACE data set is plotted in black. As quantified in Table 2, the current sheets are found on average in plasma with a higher proton specific entropy (5.14 eV cm²) than the average solar wind (3.81 eV cm²). In Figure 2(c), the distribution of electron temperatures measured at the locations of the strong current sheets is plotted in red and the distribution of all electron temperatures in the 1998 February–October ACE data set is plotted in black. For the electron temperatures the two distributions are very similar, with the current-sheet distribution only slightly hotter on average (15.4 eV) than the total distribution (14.7 eV). The conclusion drawn from the first three panels of Figure 2 is that strong current sheets in the solar wind are found more often in plasma with a hotter proton temperature and a higher proton specific entropy. This hotter, higher-entropy wind is fast wind (cf. Figure 4 of Borovsky & Denton 2010). In Figure 2(d), the distribution of solar-wind velocities measured at the locations of the strong current sheets is plotted in red and the distribution of all solar-wind velocities in the ACE data set is plotted in black. As can be seen (cf. Table 2), the current sheets are found on average in higher-speed solar wind (492 km s⁻¹) than the average solar wind (441 km s⁻¹).

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Note that the proton-temperature and electron-temperature occurrence distributions in Figures 2(a) and (c) are consistent with the distributions in the lower left and upper right panels of Figure 2 of Osman et al. (2011). The Osman et al. "region-3" events are chosen by the size of their variation ΔB_x in the radial component of B, which chooses the very strongest current sheets since the current sheets in the solar wind tend to have their vector variations ΔB normal to the radial direction. The region-3 events in Figure 2 of Osman et al. have a mean proton temperature of 16.6 eV as opposed to the 5.9 eV temperature of the much-more-prevalent "region-1" events; the strong current sheets of the present study have a mean temperature of 12.5 eV as opposed to the 6.0 eV temperature of all of the solar-wind data. (If the 10% of our current sheets with the largest ΔB_x are selected, the mean temperature is 16.4 eV.) Osman et al. find this region-3 to region-1 temperature difference to be "consistent with the small-scale coherent structures of MHD turbulence being associated with increased heating in the solar wind"; the present authors find this temperature difference consistent with strong current sheets being encountered at a higher rate in hotter (= faster) solar wind.

No evidence for proton or electron heating is found at the locations of strong current sheets in the solar wind. As summarized in Figure 1 and Table 1, the proton temperature, proton specific entropy, and electron temperature at the sites of the strong current sheets are statistically the same as the proton temperature, proton specific entropy, and electron temperature in the adjacent plasmas. This rebuts the conjecture that strong currents in the solar wind are the sites of solar-wind heating (e.g., Leamon et al. 2000; Matthaeus et al. 2003; Greco et al. 2010; Osman et al. 2011).

The statistical results presented in Figure 2 of this Letter are consistent with the statistical results presented in Figure 2 of Osman et al. (2011), with the interpretation here that strong current sheets are more prevalent in the hotter solar wind than in cooler solar wind. Two reasons why strong current sheets should be more prevalent in the fast wind were given in Borovsky (2008): (1) hot solar wind statistically is fast solar wind (Richardson & Cane 1995; Borovsky & Steinberg 2006) and in the fast wind structures are swept past a spacecraft faster, increasing the counting frequency of current sheets, and (2) slow wind (cooler) is expanded more near the Sun than is fast (hot) wind (Wang & Sheeley 1990; Arge & Pizzo 2000; Arge et al. 2003), reducing the spatial density of chromospheric structure seeded into the cooler slow wind.

The motivation for the conjecture that solar-wind heating should occur at current sheets came from observations of reconnection and heating at current sheets in incompressible resistive-MHD simulations of turbulence. Perhaps in the solar wind there is heating at weaker current sheets, which are more likely to be part of an MHD turbulence (e.g., Bruno et al. 2004; Neugebauer & Giacalone 2010; Miao et al. 2011). Note, however, that the collisionless solar-wind plasma is not well described by incompressible resistive MHD (Borovsky & Gary 2009). In collisionless plasmas reconnection can only occur when current sheets are thin, of the order of the ion skin depth c/ω_pi whereas strong current sheets in the solar wind have thicknesses much greater than c/ω_pi (Siscoe et al. 1968; Vasquez et al. 2007): indeed, reconnection of solar-wind strong current sheets is observed to be rare (Gosling 2007, 2010). In incompressible resistive MHD, reconnection tends to be of the diffusive Sweet–Parker type in which Ohmic dissipation is important (Ugai 1995); reconnection in collisionless plasmas is of the Petschek type where Ohmic heating is unimportant and where the plasma specific entropy is conserved (Birn et al. 2006, 2008).

Using similar methodology, a recent study (Borovsky & Steinberg 2011) finds no evidence for heating of the solar-wind plasma at regions of strong velocity shear in the solar wind.

The authors thank Joachim Birn, Michael Hesse, Bill Matthaeus, John Podesta, Aaron Roberts, Ruth Skoug, John Steinberg, and Bernie Vasquez for helpful conversations. This research was supported at Los Alamos by the NSF SHINE Program, the NASA Heliospheric SR&T Program, and the NASA Heliospheric Guest-Investigator Program, and research at Lancaster University was supported by STFC Grant ST/G002401/1.