Ion bulk heating in magnetic reconnection exhaustsat Earth’s magnetopause: Dependence on the inflowAlfvén speed and magnetic shear angleT. D. Phan1, J. F. Drake2, M. A. Shay3, J. T. Gosling4, G. Paschmann5, J. P. Eastwood6, M. Oieroset1,M. Fujimoto7, and V. Angelopoulos8

1University of California, Berkeley, California, USA, 2University of Maryland, College Park, Maryland, USA, 3University ofDelaware, Newark, Delaware, USA, 4University of Colorado Boulder, Boulder, Colorado, USA, 5Max-Planck Institut fürExtraterrestrische Physik, Garching, Germany, 6Imperial College, London, UK, 7ISAS, Kanagawa, Japan, 8University ofCalifornia, Los Angeles, California, USA

Abstract We surveyed 87 magnetopause reconnection exhausts detected by the THEMIS spacecraft toinvestigate how the amount and anisotropy of ion bulk heating depend on the inflow boundary conditions.We find that the heating,ΔTi , is correlated with the asymmetric Alfvén speed,VAL,asym, based on the reconnectingmagnetic field and the plasma number density measured in both inflow regions. Best fit to the dataproduces the empirical relationΔTi = 0.13miVAL,asym

2, wheremi is the protonmass, indicating that the increase inthe ion internal (thermal) energy, 3ΔTi/2, is 20% of the available magnetic energy per proton-electron pair.The observed parallel heating generally exceeds perpendicular heating (by a factor of ~2), and there aresome indications that the heating is reduced in the presence of a strong guide field. Finally, the ratio of ion toelectron bulk heating is ~8 on average.

1. Introduction

Magnetic reconnection converts stored magnetic energy into particle energies. One of the key unresolvedproblems in reconnection research is understanding what controls the degree of ion heating in reconnectionexhausts. In the fluid description slow shocks can form at the exhaust boundaries that compress and heatthe inflowing plasma [Petschek, 1964; Lin and Lee, 1993]. The fluid model, however, does not apply to collisionlessplasmas in which inflowing ions from the two sides of the exhaust can freely interpenetrate. The resultingcounterstreaming ion distributions produce an effective increase in the ion temperature [Cowley, 1982].

While ion heating associated with reconnection has been reported in space and in the laboratory [Yamadaet al., 2010, and references therein], there has been no comprehensive observational study of the factorsthat determine ion heating in reconnection exhausts and that has compared observed ion heating totheoretical predictions. Moreover, the space observations display great variability. For example, at themagnetopause [Gosling et al., 1986] and in the solar wind [Gosling et al., 2005], some reconnectionexhausts show clear evidence for ion heating by tens to hundreds of eV, while others show no heating atall [Gosling et al., 2007; Gosling and Phan, 2013; Gosling, 2012]. In contrast, in the Earth’s magnetotail,substantial ion heating (by up to many keV) is generally observed in fully developed reconnection jets[e.g., Angelopoulos et al., 1992]. Furthermore, many solar wind exhausts where ion heating was not observedwere associated with strong (>>1) normalized guide fields [Gosling and Phan, 2013]. The differing ionheating associated with reconnection in different regions suggests that the degree and characteristics of ionheating depend on plasma regimes as well as the magnetic shear angle (guide field).

In a statistical study of ion heating in solar wind reconnection exhausts observed by Wind and having small(<0.6) normalized guide fields,Drake et al. [2009a] found thatΔTi= 0.13mi Vex

2, whereΔTi is proton heating,Vex isthe exhaust jet speed and mi is the proton mass. However, this is substantially less than miVex

2/3, the heatingpredicted for Alfvénic counterstreaming proton beams in the exhaust. It is also less than miVA,inflow

2/5, thetemperature increase predicted if slow shocks bound the exhausts. Drake et al. [2009a] also found that alphaparticle heating was ~4 times greater than proton heating within small guide field exhausts.

To better understand the nature of ion heating by reconnection we have performed a statistical studybased on 87 magnetopause exhausts having highly asymmetric inflow conditions and a variety of guide

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PUBLICATIONSGeophysical Research Letters

RESEARCH LETTER10.1002/2014GL061547

Key Points:• Factors controlling ionheating in reconnection atmagnetopause revealed

• Ion heating linearly dependent oninflow magnetic energy per particle

• Ion heating is 13% of availablemagnetic energy per particle

Correspondence to:T. D. Phan,phan@ssl.berkeley.edu

Citation:Phan, T. D., J. F. Drake, M. A. Shay, J. T.Gosling, G. Paschmann, J. P. Eastwood,M. Oieroset, M. Fujimoto, andV. Angelopoulos (2014), Ion bulkheating in magnetic reconnectionexhausts at Earth’s magnetopause:Dependence on the inflow Alfvén speedand magnetic shear angle, Geophys. Res.Lett., 41, 7002–7010, doi:10.1002/2014GL061547.

Received 15 AUG 2014Accepted 26 SEP 2014Accepted article online 30 SEP 2014Published online 24 OCT 2014

fields. This study complements and extends the earlier Drake et al. [2009a] study using 22 solar windexhausts which were largely symmetric and having small guide fields.

The concepts of temperature and heating in multiple ion population plasmas. The ion temperatures used inthe present study are obtained from the second moment of the distributions and, at least partiallybecause of intermixing of multiple populations from both inflow regions, do not necessarily represent thetemperature in the thermodynamic sense, as in a single Maxwellian distribution. Nevertheless, suchtemperatures are useful because they provide measures of the average energy in the ion rest frame[Paschmann et al., 1998]. We refer to these temperatures as bulk temperatures and describe the increasein exhaust temperature (relative to the inflow temperatures) as bulk heating.

2. Sample Event

To illustrate our methodology in evaluating the bulk heating of magnetosheath and magnetosphericions entering into the exhaust and in determining the inflow boundary conditions, Figure 1 showsan outbound magnetopause crossing by THEMIS D at low latitude near the subsolar point (11.9 magneticlocal time). The evidence for reconnection in this event was described in more detail in Phan et al. [2013].We describe the event backward in time, going from the magnetosheath to the magnetosphere asmost of the ions in the exhaust originated from the magnetosheath. A reconnection jet directed in the�L direction and having a flow speed of ~400 km/s relative to that in the magnetosheath (Figure 1b)was embedded in the magnetopause current layer (15:12–15:14:30 UT, between the green verticalline and the leftmost red vertical dotted line). The magnetic shear angle across the magnetopausewas ~173°, corresponding to a normalized guide field of 0.06 (Figure 1a). The magnetosheath andmagnetospheric ion β based on the reconnecting field component BL (not shown) were 0.43 and0.038, respectively, and the Alfvén speed based on BL (Figure 1h) was 410 km/s in the magnetosheathand 1407 km/s in the magnetosphere. The asymmetric Alfvén speed VAL,asym, which is the predictedoutflow jet speed in asymmetric reconnection, was 595 km/s, where VAL,asym = [BL,shBL,sph(BL,sh + BL,sph)/μ0(ρshBL,sph + ρsphBL,sh)]

0.5, BL is the reconnecting magnetic field, ρ is the plasma mass density, and thesubscripts sh and sph refer to the magnetosheath and magnetosphere inflow regions, respectively[Cassak and Shay, 2007; Swisdak and Drake, 2007]. The inflowing magnetic energy per proton-electronpair miVAL,asym

2 was 3.7 keV.

Across the magnetosheath edge of the magnetopause, both parallel and perpendicular ion temperaturesincreased abruptly (Figure 1d).ΔTi|| was almost twice as large asΔTi⊥. But because Ti⊥>Ti|| in themagnetosheath,the exhaust temperature was nearly isotropic.

To determine heating associated with a reconnection exhaust one needs to determine the ion temperaturesboth in the inflow regions as well as in the exhaust. For magnetopause reconnection where plasma andfield parameters on the two sides of the exhaust can be quite different, the effective inflow temperature isgiven by

Ti;inflow ¼ NsphTi;sph=BL;sph þ NshTi;sh=BL;sh� �

= Nsph=BL;sph þ Nsh=BL;sh� �

The dependence on the magnetic field has been introduced to account for the differing amounts of plasmaentering the exhaust from the two sides as equal magnetic fluxes are reconnected. The magnetosheathandmagnetospheric temperatures are determined by averaging between the two red vertical dotted lines andthe two black vertical dashed lines, respectively. The effective inflow temperature, Ti,inflow, for this event was422 eV based on magnetosheath and magnetosphere ion temperatures of 379eV and 799 eV.

One way of determining a single exhaust ion temperature is simply to average the ion temperature inthe exhaust. However, because the exhaust temperature is not uniform but instead systematicallyincreases while the density decreases toward the magnetospheric edge, a better measure of the averageexhaust temperature is <Ti,exhaust> = <NTi>/<N>, where < > denotes averages over the entireexhaust interval. In this case we find that <Ti,exhaust> = <NTi>/<N> = 983 eV, which is not very differentfrom what is obtained (1016 eV) from a simple average of the exhaust temperature. Thus, the averageincrease in ion temperature for this exhaust was ΔTi =<Ti,exhaust> � Ti,inflow ~561 eV. Considering parallel

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and perpendicular temperatures separately, we find ΔTi || = 830 eV and ΔTi⊥ = 426 eV. In comparison, anelectron temperature increase of 70 eV was reported by Phan et al. [2013] for this event, so the ratio ofion to electron heating was ~8.

We also examined the ion distributions measured in the exhaust and in the two inflow regions to investigatefactors responsible for the temperature increase in the exhaust. Figure 1i shows a typical ion distribution inthe magnetosheath proper with anisotropic temperature (Ti⊥>Ti ||). Figure 1n shows a representativemagnetospheric distribution that contains both hot and cold (plume) ion components. The total (hot andcold) magnetospheric ion density was 0.68 cm�3. Figures 1j–1m show four distributions sampled in the

Figure 1. (a) The magnetic field in LMN minimum variance coordinates [Sonnerup and Cahill, 1967], (b) ion velocity in LMN, (c) ion number density, (d) paralleland perpendicular ion temperatures, (e) parallel and perpendicular electron temperatures, (f, g) ion and electron spectrograms of energy flux (eV s�1 cm�2

ster�1 eV�1), (h) ion Alfvén velocity based on BL, (i–n) 2-D cuts of 3-D ion distributions in the spacecraft frame through velocity space in the plane thatcontains the magnetic field direction (to the right) and E × B direction (upward), where E was obtained from �v × B. The tip of the black line from the originindicates the overall bulk velocity. Labels “1” to “6” under Figure 1h point to the times of the distributions shown in Figures 1i–1n.

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exhaust. The distribution sampled near the magnetospheric edge of the exhaust (Figure 1m) containscounterstreaming accelerated magnetosheath ions at negative v|| and cold magnetospheric ionsat positive v|| , both of which were heated (especially perpendicular to the magnetic field). Beaminterpenetration produced a high Ti||. At the magnetosheath edge of the exhaust (Figures 1j and 1k), thedistributions consist of relatively cold magnetosheath ions and an additional ion population havingpositive v|| and apparently coming from the direction of the magnetosphere. However, the additional ionpopulation does not appear to be of magnetospheric origin because its phase space density far exceedsthat of the magnetosphere. These ions may be reflected magnetosheath ions [Sonnerup et al., 1981;Gosling et al., 1990a; Fuselier et al., 1991] possibly associated with Speiser orbits in the current sheet[Cowley, 1982; Drake et al., 2009a]. The parallel and perpendicular bulk temperatures of the entiredistributions were significantly higher than in the magnetosheath proper (Figure 1i).

Figure 1l displays a typical distribution sampled deeper in the exhaust that is nearly isotropic and quasi-thermalized, with parallel and perpendicular temperatures comparable to those sampled at the edges ofthe exhaust.

The ion distributions indicate that the higher temperatures in the exhaust result from a combination offactors. There is evidence that both incoming populations (magnetosheath and magnetospheric cold ions)were individually heated, at least perpendicular to the magnetic field. In addition, counterstreaming betweenions of magnetosheath and magnetospheric origin as well as between ions of magnetosheath originand their reflected component led to parallel temperature enhancements. The end result near the center ofthe exhaust was heated ion distributions that were nearly isotropic and quasi-thermalized.

3. Statistical Survey3.1. Data Sets and Selection Criteria

We use 3 s resolution magnetic field [Auster et al., 2008] and plasma [McFadden et al., 2008] measurementsfrom THEMIS. We started with a large set of low-latitude THEMIS-D and THEMIS-E magnetopause crossingsin 2008 and 2009, respectively, that contained reconnection exhausts. In order to investigate the iontemperature change associated with entry into an exhaust, we required that the inflow magnetosheathand magnetospheric conditions be well defined (as in the example in Figure 1). A total of 103 exhaustssatisfied this requirement. Some of the 103 exhausts had substantial numbers of cold (plume) ions in themagnetosphere (in addition to the usual hot magnetospheric ions). These cold ions are not always detectedin the magnetosphere by the plasma instruments because their energies often fall below the low-energythreshold of the instruments. However, these ions are accelerated by the overall reconnection processand often become detectable in the exhaust [Gosling et al., 1990b]. The result of not detecting these ions inthe magnetosphere is that the magnetospheric plasma density is underestimated and the temperature isoverestimated. Consequently, the available magnetic energy per particle in the magnetosphere (miVAL,asym

2)as well as the effective inflow ion temperature (Ti,inflow) would be overestimated such that the heatingrelative to the inflowing magnetic energy would be underestimated. This problem can be severe if theundetected cold ion density is high.

When the cold ion density in the magnetosphere is comparable to the magnetosheath density,reconnection is quasi-symmetric and the exhaust density is enhanced relative to the magnetosheath andmagnetospheric densities. In contrast, for reconnection involving highly asymmetric inflow numberdensities, the exhaust density is expected to be intermediate between the two inflow densities [e.g., Levyet al., 1964]. In order to minimize the effects of undetected cold magnetospheric ions, we exclude eventswith Nexhaust>Nmagnetosheath, reducing the number of events from 103 to 87. In section 3.2 below we showthat, compared to the ion heating in the 87-exhaust data set, the apparent ion heating relative to theinflowing magnetic energy in the 16 excluded events was significantly lower.

For comparison, only 79 of the available exhausts could be used for an earlier [Phan et al., 2013] studyof electron bulk heating because of the requirement that the inflow electron temperatures be well definedin that study; only 65 exhausts were common to both studies.

The range of magnetic shear angles (or equivalently the guide field), magnetosheath and magnetosphericion β, and Alfvén speed based on the reconnecting field in the present data set are 40°< shear< 177°(0<normalized guide field <2.7), 0.19< βiL,sh< 547, and 0.024< βiL,sph< 1.2.

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Figure 2a shows the relationship between the effective inflow ion temperature Ti,inflow and the magnetosheathtemperature, Ti,sh, for the 87 events. Generally, Ti,inflow is close to Ti,sh because the magnetosheath density isgenerally much larger than the magnetospheric density. For this same reason, the effective inflow temperaturedoes not correlate with the magnetospheric temperature (not shown).

3.2. Parameters Controlling the Degree of Ion Bulk Heating

Using the set of 87 reconnection exhausts, we examined how ΔTi depends on plasma and field conditionson the two sides of the magnetopause. We could not find a clear dependence of ΔTi on any purely

Figure 2. (a) Effective inflow ion temperature as a function of magnetosheath ion temperature. Changes in ion tempera-tures from outside to inside exhausts as a function of (b) magnetosheath reconnecting field component, (c) magne-tosheath ion number density, (d) magnetosheath ion temperature, (e) magnetosheath Alfvén speed based on thereconnecting field component, (f ) asymmetric inflow Alfvén speed, (g) inflowing magnetic energy, and (h) inflowingmagnetic energy for events in which the average exhaust density exceeds the magnetosheath density due to the presenceof dense cold magnetospheric ions.

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magnetospheric parameters because the magnetospheric plasma and field parameters do not vary muchfrom one event to the next in our data set. On the other hand, ΔTi depends on a number of magnetosheathparameters, which have a large range of variation. We found that ΔTi tends to increase with increasingmagnetosheath reconnecting field component BL,sh (Figure 2b) and tends to decrease with increasingmagnetosheath number density Nsh (Figure 2c). There also seems to be a trend for ΔTi to increase withincreasing magnetosheath temperature Ti,sh (Figure 2d).

The heating dependence on BL,sh, Nsh, and Ti,sh suggests that ΔTi may depend on combinedparameters such as the magnetosheath ion β and VAL,sh, the Alfvén speed based on BL,sh. An explicitβ dependence would imply that ΔTi correlates with the density and temperature in the samemanner such that the two parameters can be interchanged. However, the observed heating iscorrelated with the temperature but anticorrelated with the density, which is inconsistent with aheating dependence on β. On the other hand, ΔTi is well correlated with VAL,sh (Figure 2e). In fact, thedependence on VAL,sh is clearer than on the reconnecting field and plasma density individually. Todeduce the power of the VAL,sh dependence, we fit the data to the function ΔTi = constantVAL,sh

power.The best fit gives a power of 2.44.

Figure 2f shows, however, that ΔTi correlates equally well with the combined inflow Alfvén speed inasymmetric reconnection, VAL,asym. Fitting the data to the function ΔTi= constantVAL,asym

power produces apower of 1.99 (blue curve in Figure 2f). Refitting the data to VAL,asym

2 gives ΔTi = 1.34 ×10�3 VAL,asym2

(red curve in Figure 2f, nearly undistinguishable from the blue curve), where ΔTi and VAL,asym are in units of eVand km/s, respectively. The significance of the dependence on VAL,asym

2 is that miVAL,asym2 represents the

combined incoming magnetic energy per proton-electron pair from both sides of the current sheet. Theempirical relation can be reexpressed as ΔTi=0.13miVAL,asym

2 where both sides of the relation have the sameunits (e.g., of electron volt) (Figure 2g).

As a check of our decision to remove 16 events with exhaust number density>magnetosheath numberdensity, which are likely associated with dense unmeasured cold (plume) ions in the magnetosphere, weshow in Figure 2h the dependence of ΔTi on miVAL,asym

2 for these events. The much lower best fit slope of0.065 is consistent with the available magnetic energy per particle in the magnetosphere beingoverestimated due to unmeasured dense cold ions.

3.3. Anisotropy of Ion Heating

In addition to examining the total ion heating, we have also investigated parallel and perpendicular ionheating separately. Figures 3a and 3b show that both ΔTi || and ΔTi⊥ are correlated withmiVAL,asym

2 but ΔTi || ison average twice as large as ΔTi⊥. Figure 3c shows that even on an event-by-event basis, with only a fewexceptions, ΔTi || exceeds ΔTi⊥ by about a factor of 2.

We also examined the role of the guide field on ion heating. Figure 3c shows that for eventswith magnetic shear <90° (red dots) ΔTi|| and ΔTi⊥ were small (<100 eV). To investigate furtherwhether this could simply be due to weak reconnecting fields in small magnetic shear angle cases,we examined the dependence of ΔTi on miVAL,asym

2 separately for events with large (>165°) andsmall (<90°) magnetic shears. Figure 3d shows that indeed, the small shear angle cases correspondto lower miVAL,asym

2, but the data also show that ΔTi for the small magnetic shear cases is belowthat of the large shear angle cases (blue dots) even for the same values of miVAL,asym

2. The lattersuggests that both ΔTi|| and ΔTi⊥ are reduced in the presence of a strong guide field. If the dataset is restricted to cases with magnetic shear >165° (blue dots in Figure 3d), we find thatΔTi = 0.14 miVAL,asym

2.

3.4. Ion to Electron Heating Ratio

In their statistical study of electron bulk heating in reconnection exhausts at the magnetopause, Phan et al.[2013] found that ΔTe = 0.017 miVAL,asym

2. From the empirical relation ΔTi= 0.13 miVAL,asym2 for ions, we

deduce that the ratio of ion to electron heating in magnetopause exhausts is 7.6 on average. Figure 3edisplays ΔTi versus ΔTe for the 65 events common to both the electron and ion studies. The ratio isvariable, but the average ratio (the best linear fit slope) is ~8.0, close to the ratio of 7.6 deduced from theseparate ion and electron empirical formulas.

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4. Summary and Discussions

The observed bulk heating, ΔTi, in reconnection exhausts at the magnetopause on average obeys theempirical relation ΔTi = 0.13 miVAL,asym

2, indicating that the increase in the ion internal (thermal) energy,3ΔTi/2, is 20% of the available magnetic energy per proton-electron pair. For the simplified case ofisotropic plasmas, the percentage of the inflowing Poynting flux converted into ion enthalpy flux is givenby [γ/(γ � 1)]ΔTi/miVAL,asym

2 = 0.13 γ/(γ � 1) = 33%, where γ= 5/3 is the ratio of the specific heat. Foranisotropic plasmas with Ti ||> Ti⊥, this percentage is higher. In comparison, using the empirical formulafor electrons [Phan et al., 2013], the increase in the electron enthalpy flux relative to the inflowing magneticenergy, 0.017 γ/(γ � 1), is 4.3% or more.

Our finding should in principle be general and applicable to symmetric reconnection as well withΔTi = 0.13 miVAL,inflow

2, or equivalently 0.13 BL,inflow2/μ0Ninflow, where VAL,inflow, BL,inflow, and Ninflow are

the inflow (upstream) Alfvén speed, reconnecting field, and number density on both sides of the exhaust.The dependence of ΔTi on miVAL,inflow

2 is exactly equivalent to ΔTi/Ti,inflow = 0.26/βiL,inflow, indicatingthat ion heating relative to its initial temperature is substantial in low β plasmas. The dependence on1/βiL,inflow, however, should be viewed with care. For example, the 1/βiL,inflow dependence seems to implystronger heating with smaller Ti,inflow, while, in fact, ΔTi is independent of Ti,inflow in the βiL,inflowdependence expression.

The empirical relation may explain the relatively weak ion heating in solar wind exhausts at 1 AU andstrong ion heating in magnetotail exhausts. At 1 AU, the Alfvén speed of the solar wind is typically ~50 km/s.

Figure 3. (a, b) Parallel and perpendicular ion temperature changes versus miVAL,asym2, (c) perpendicular versus parallel

ion temperature changes for three different magnetic shear angle ranges, (d) ion temperature change versus miVAL,asym2

for low and high magnetic shear angles, and (e) ion versus electron temperature changes. The red lines in Figures 3a–3c, and3e are linear best fits to the data.

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For that value of VAL the predicted ion bulk heating based on our empirical formula is only ~3.4 eV andeven less for the much smaller values of VAL associated with low field shear angle exhausts that aredominant in the solar wind [Gosling et al., 2007]. Extrapolating our finding to the magnetotail plasmaregime, where the typical Alfvén speed in the reconnection inflow (i.e., lobe) region is ~1000–3000 km/s(based on a typical density of 0.05 cm�3 [Svenes et al., 2008] andmagnetic field of 10–30 nT), the expected ionheating would be in the 1.3–12 keV range, roughly consistent with the strong ion heating typically seen inmagnetotail exhausts.

We have found that parallel ion heating almost always exceeds perpendicular heating. This suggests that thedominant heating process is field aligned. However, the fact that both parallel and perpendicular iontemperatures often increase simultaneously and immediately at the exhaust boundary (as in the exampledescribed in section 2) suggests that perpendicular heating does not arise simply by scattering of parallelenergy into perpendicular energy in the weak-field region that may occur near the center of the exhaust. Thus,there must be other scattering processes or separate parallel and perpendicular heating processes.

The results from the limited number of events (seven) in our study associated with magnetic shears <90°suggest that the guide field suppresses both parallel and perpendicular ion heating and thus does not have astrong effect on the temperature anisotropy. This is in contrast to our previous finding that the guidefield suppresses perpendicular electron heating but does not affect parallel electron heating with the effectthat the electron heating is highly anisotropic in the presence of a strong guide field.

The ion to electron heating ratio is found to be ~8 on average. Interestingly, this ratio is close to thetemperature ratio of 7 found for the plasma sheet in the magnetotail [e.g., Baumjohann, 1993]. This maysuggest that reconnection in the magnetotail involving extremely cold (<10 eV) inflow (lobe) ions andelectrons may be the source of the observed plasma sheet temperature ratio.

We now discuss possible mechanisms that could give rise to the scaling of heating with miVAL2 and to the

dependence of heating on the guide field.

The scaling of ΔTi with miVAL2 could arise from interpenetrating beams that originate from the two inflow

regions [Cowley, 1982]. Such beams have been reported at the magnetopause [Gosling et al., 1990b;Fuselier et al., 1991], in the solar wind [Gosling et al., 2005], and in simulations [Krauss-Varban and Omidi, 1995;Hoshino et al., 1998]. These beams lead to parallel heating. Instabilities are expected eventually to disruptthe beams, turning some of the parallel energy into perpendicular energy [Lottermoser et al., 1998].

The ion temperature increase associated with counterstreaming ion beams is expected to be ΔTi=mi Vex2/3

or ~miVAL,inflow2/3 if the outflow jet speed, Vex, is close to VAL as predicted by theory assuming cold ion

beams [Drake et al., 2009a]. Including the thermal spread of the beams would further raise the predictedtemperature increment [Drake and Swisdak, 2014] which is consistent with the trend seen in Figure 2d thatΔTi increases with increasing inflow ion temperature. However, although the scaling with miVAL,inflow

2 isconsistent with observations, the predicted heating fraction (the coefficient of 1/3 in front of miVAL,inflow

2)is almost a factor of 3 higher than the value of 0.13 found in both this magnetopause study and in theDrake et al. [2009a] solar wind study. This indicates that the observed ion heating is less than that predictedby a simple heating model based on counterstreaming particle beams. In contrast, we note that the observedelectron heating in magnetopause exhausts is substantially greater than would be expected from simplecounterstreaming electrons on field lines moving at the ion outflow speed [Phan et al., 2013]. Furthermore, theion distributions shown in section 2 suggest that at the magnetosheath edge of some exhausts, the paralleltemperature enhancement may not be due to mixing of magnetosheath and magnetospheric ions but ratherappears to be associated with an additional population of possibly reflected magnetosheath ions.

A possible reason for the lower than expected increment of heating is that observed exhaust jet velocitiesare often less than VAL,asym. We separated the exhausts into two sets depending upon whether theexhaust outflow velocity was greater than or less than 75% of the predicted Alfvénic jet speed in order to seeif sub-Alfvénic field line convection in the exhaust could explain that observed heating is less than thepredicted ΔTi=miVAL,inflow

2/3. However, both subsets produced essentially the same increment of heating.Thus, sub-Alfvénic outflow jetting does not seem to account for the large discrepancy. This is in agreementwith the Drake et al. [2009a] solar wind study that examined ion heating as a function of the outflowspeed instead of the inflow Alfvén speed.

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It is noted that the scaling of ΔTi withmiVAL2 is also predicted for ion heating across slow shocks [Drake et al.,

2009a]. However, for magnetopause reconnection with highly asymmetric inflow conditions, slow shocksare neither predicted nor observed.

Finally, according to theory, the effect of strong guide fields on ion heating depends on whether theplasma and field parameters are in the ion pickup regime or not [see Drake et al., 2009b, equation (1)]. Thestrong guide field (magnetic shear <90°) events in our data set have magnetosheath βiL > 0.9, which isin the nonpickup regime. In this regime, the guide field is expected to suppress both parallel andperpendicular heating [Drake et al., 2009b], consistent with our observations. In contrast, in the ionpickup regime, the perpendicular heating should be enhanced and the parallel heating reduced (suchthat ΔTi⊥ > ΔTi ||) which would be inconsistent with our finding [Drake et al., 2009a].

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AcknowledgmentsWe thank the THEMIS team for provid-ing well-calibrated plasma and fielddata. This research was funded by NASAgrants NNX08AO83G, NASS02099,NNX10AC01G, NNX08AO84G,NNX11AD69G, and NNX13AD72G andNSF grants ATM-0645271 andAGS1202330. We wish to acknowledgesupport from the International SpaceScience Institute, Bern.

Benoit Lavraud thanks Steven Petrinecand one anonymous reviewer for theirassistance in evaluating this paper.

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