JOURNALOFGEOPHYSICALRESEARCH,VOL.117,A00M02,doi:10.1029/2012JA017829,2012 Solar wind alpha particles and heavy ions in the inner heliosphere observed with MESSENGER Daniel J. Gershman,1 Thomas H. Zurbuchen,1 Lennard A. Fisk,1 Jason A. Gilbert,1 Jim M. Raines,1 Brian J. Anderson,2 Charles W. Smith,3 Haje Korth,2 and Sean C. Solomon4,5 Received12April2012;revised28June2012;accepted10July2012;published15September2012. [1] The Fast Imaging Plasma Spectrometer (FIPS) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has made the first insitumeasurementsofsolarwindplasmaintheinnerheliospheresincetheHelios1and2 spacecraft in the 1980s. Although the core of the solar wind velocity distribution is obstructed by the spacecraft sunshade, a data analysis technique has been developed that recoversbothbulkandthermalspeedsto10%accuracyandprovidesthefirstmeasurements of solar wind heavy ions (mass per charge >2 amu/e) at heliocentric distances within 0.5 AU. Solar wind alpha particles and heavy ions appear to have similar mean flow speeds at values greater than that of the protons by approximately 70% of the Alfvén speed. From an examination of the thermal properties of alpha particles and heavier solar wind ions, we find a ratio of the temperature of alpha particles to that of protons nearly twice that of previously reported Helios observations, though still within the limits of excessiveheating ofheavy ionsobserved spectroscopically closeto theSun.Furthermore, examination of typical magnetic power spectra at the orbits of MESSENGER and at 1 AU reveals the lack of a strong signature of local resonant ion heating, implying that a majority ofheavy ionheatingcould occurcloseto theSun.Theseresults demonstrate that the solar wind at (cid:1)0.3 AU is a blend of the effects of wave–particle interactions occurring in both the solar corona and the heliosphere. Citation: Gershman,D.J.,T.H.Zurbuchen,L.A.Fisk,J.A.Gilbert,J.M.Raines,B.J.Anderson,C.W.Smith,H.Korth, andS.C.Solomon(2012),SolarwindalphaparticlesandheavyionsintheinnerheliosphereobservedwithMESSENGER, J.Geophys.Res.,117,A00M02,doi:10.1029/2012JA017829. 1. Introduction ultravioletobservationsofneutralhydrogencoupledtosolar wind plasmas near the Sun through charge exchange and [2] The solar wind is the manifestation of the ubiquitous from direct observations of heavy ions (mass > 4 amu) that expansion of the hot solar corona into space. Although the the ions are preferentially heated, and that this heating is origin, heating, and acceleration of the solar wind are still necessary to attain the observed solar wind speeds [Kohl muchdebated,thereisconsensusonanumberofkeyissues. et al., 1997, 1998]. At about 2 solar radii, solar wind ions Initial models of the solar wind were based on the assump- associatedwithcoronalholeshaverelativetemperaturesthat tionofanisothermalplasma,withelectronsandionshaving strongly depend on the ratio of their mass to their charge equaltemperatures[Parker,1958].However,weknowfrom (m/q); for instance, ratios of the temperatures of Mg9+ and O5+ to that of neutral hydrogen, T /T and T /T , are Mg9+ H O5+ H approximatelyequalto64at1.7and2.2solarradii,respec- 1DepartmentofAtmospheric,OceanicandSpaceSciences,University tively[Kohletal.,1997].Similarly,thederivedflowspeeds ofMichigan,AnnArbor,Michigan,USA. near 2 solar radii are also higher for heavy ions, with v / 2The Johns Hopkins University Applied Physics Laboratory, Laurel, O5+ v (cid:1) 2[Kohletal.,1998]. Maryland,USA. H 3Physics Department, Space Science Center, University of New [3] Theseremotesensingdataelucidatetheimportantrole Hampshire,Durham,NewHampshire,USA. ofwave–particleinteractionsinmostpartsoftheclosedand 4Department of Terrestrial Magnetism, Carnegie Institution of open corona, even though the precise physical processes Washington,Washington,D.C.,USA. 5Lamont-Doherty Earth Observatory, Columbia University, Palisades, involvedintheseinteractionsisstilldebated[e.g.,Fisketal., NewYork,USA. 1999; Verdiniand Velli, 2007; Cranmer etal., 2007]. Most importantly,thesedatashowthatthecollisionalcouplingof Correspondingauthor:D.J.Gershman,DepartmentofAtmospheric, heavy ions to solar wind protons is not as dominant as ini- OceanicandSpaceSciences,UniversityofMichigan,AnnArbor, MI48105,USA.([email protected]) tially assumed in the first comprehensive model of heavy ions by Geiss et al. [1970]. In these collision-dominated ©2012.AmericanGeophysicalUnion.AllRightsReserved. models, heavy ions are coupled to the accelerating protons 0148-0227/12/2012JA017829 A00M02 1of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 through Coulomb collisions, and thus their velocity is typi- speed, temperature, and temperature anisotropies of alpha callysmallerthanthatofprotons.Similarly,duetothedomi- particles and protons. They also argued that there is local nanceofthesecollisions,heavyionswerepredictedtohave heatingthroughthelocaldissipationofkineticAlfvénwaves. thermal speeds smaller than those of protons, again in con- [7] The differential heating of heavy ions with respect to tradictionwithkeyresultsfromtheUltravioletCoronograph the protons is expected to occur near the transition of two Spectrometer (UVCS) [Kohl et al., 1995] on the Solar and subintervals of the magnetic field spectra: the inertial range HeliosphericObservatory(SOHO). andthedissipationrange[Coleman,1968;Bavassanoetal., [4] In situ observations of solar wind heavy ions to date 1982; Frisch, 1996]. The inertial range as it is expected to have been limited to heliocentric distances of 1 AU and existintheplasmaframeoccursatfrequenciessubstantially beyond. These measurements were performed mostly by lower than the gyrofrequency of heavy ions, obscured by solar wind composition instruments such as those on the Doppler shifts that are a consequence of measuring the AdvancedCompositionExplorer(ACE),Ulysses,andSolar magnetic field B in the spacecraft frame. Here, the energy TErrestrial RElations Observatory (STEREO) spacecraft transportoccursinanapproximatelyscale-invariantcascade [Gloeckleretal.,1992,1998;Galvinetal.,2008].Through process, carrying energy to successively smaller spatial their filtering of ions by energy per charge (E/q) and the scales and higher values of frequency (f) without any dis- measurement, after post-acceleration, of time of flight and sipation. The spectral slope of this transport varies as f(cid:3)5/3 total energy, the velocity (v), mass (m), and charge (q) of or f(cid:3)3/2 for dominant fluid dynamics (Kolmogorov) or heavy ions are determined. There are some observational magnetic transport effects (Kraichnan), respectively. At limitations that are worth mentioning: the Solar Wind Ion sufficiently high frequencies, dissipation sets in [Leamon Composition Spectrometer (SWICS) instruments on ACE etal.,1998].Thisdissipationstronglydependsonthekinetic and Ulysses measure only thespeed of eachion and do not properties of the plasma. The importance of various dis- have sufficient angular resolution to recover the full three- sipation processes is a subject of current debate [Leamon dimensional orientation of the velocity vector, prohibiting et al., 1998, 1999; Bale et al., 2005; Hamilton et al., 2008; the analysis of full distribution functions [see von Steiger Smith et al., 2012]. In order to test the predictions of such and Zurbuchen, 2006]. The Plasma and Suprathermal Ion turbulence models, a combined dataset of heavy ions and Composition(PLASTIC)instrumentonSTEREO,however, magnetic field measurements is required at multiple helio- has the ability to resolve incident direction [Bochsler et al., centricdistances. 2010]. [8] The only comprehensive analysis of solar wind ions [5] Generally, these observations near 1 AU show a in the inner heliosphere was made by the Helios spacecraft streamingofheavyionsthatisfasterthanprotonsalongthe inthelate1970sandearly1980s.Helios1andHelios2had magnetic field at differential velocities that are of the same highlyeccentricheliosphericorbitswithperiheliaof0.29AU order, but typically less than the Alfvén speed [Asbridge and0.3AU,respectively.Themission,payload,andplasma et al., 1976; Zurbuchen et al., 2000; Berger et al., 2011]. instrument were described by Schwenn et al. [1975] and The actual amount of differential streaming depends on the Rosenbaueretal.[1977].Thedistribution functionsofpro- massandchargeofionsinawaythatisnotfullyunderstood tons[Marschetal.,1982b]andalphaparticles[Marschetal., [Hefti et al., 1998; von Steiger and Zurbuchen, 2006], 1982a] were characterized in detail, including examinations although there seems to be an ordering of the data by q2/m, of the temperatures and differential flow speeds between indicating a role of collisional effects. Heavy ions observed alpha particles and protons as functions of heliocentric dis- near1AUalsotendtohavethermalspeedsthatareapprox- tance and solar wind speed. However, the Helios payload imately equal, indicating a mass-proportional temperature. included no heavy ion instruments, and there have been no From a comparison of data gathered near 1 AU with data newinsitumeasurementsintheinnerheliosphereforthepast fromUlyssesthatspanupto5.4AU,itisevidentthat,with 30years. increasing heliocentric distance, the solar wind becomes [9] Here, we focus on the dynamic properties of heavy increasinglylesscollisional. ions measured with a mass-resolving instrument that is part [6] Simple electrostatic analysis can be used for the mea- oftheMErcurySurface,SpaceENvironment,GEochemistry, surement of the kinetic properties of alpha particles relative and Ranging (MESSENGER) spacecraft that is currently in toprotonsduringtimeperiodswhenthesolarwindisnottoo orbitaboutMercury[Solomonetal.,2001].Weprovidethe hot[Neugebauer,1976;Marschetal.,1982a].Suchanalyses first combined measurements of solar wind protons, alpha areusedaspartoftheSolarWindElectron,ProtonandAlpha particles, and a group of heavy ions, and we place these Monitor (SWEPAM) [McComas et al., 1998a] or Faraday data into context with previous observations by Helios and cup [e.g., Ogilvie et al., 1995] experiments. These works those more recently obtained near 1 AU. Specifically, we provideanintriguingpictureoftheimportanceofcollisional address the nonthermal behavior of alpha particles and processes, wave–particle interactions, and plasma instabil- heavy ions, including a discussion of the typical solar ities.Ininterpretingthesedata,itiscriticaltorecognizethat wind turbulent environment inferred from high-resolution the alpha particles carry (cid:1)20% of the internal pressure of a magnetic field measurements from both MESSENGER solarwindplasma[McKenzieetal.,1995]andarethereforea and ACE. In Section 2, we provide an introduction of the majorcontributortoplasmadynamics,suchasthedispersion methodology for deriving the relevant kinetic parameters propertiesofwavesandinstabilities[e.g.,Garyetal.,2001]. from partially obscured measurements and show the recov- Following a long-duration analysis of alpha particle and ered solar wind parameters for the inner heliosphere as protondatanear1AU,Kasperetal.[2008]demonstratedthe measured by MESSENGER. In Section 3, we detail obser- importance of collisional processes that shape the relative vations related to the thermal and kinetic properties of 2of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 [11] Fortunately, due to nonradial particle velocities from magneticturbulence,increasedplasmatemperaturescloseto theSun,andaberrationfromasubstantialspacecraftvelocity in the tangential direction, a portion of the solar wind dis- tribution function can often be sampled by the instrument and analyzed. After deriving the moments of a partial Maxwell-Boltzmanndistributionfunction(AppendixA),we find that whereas it is difficult to calculate accurately the plasma density without additional constraints on the three- dimensional solar wind bulk velocity, the solar wind speed and thermal velocity should be readily recoverable. Con- vected isotropic Maxwell-Boltzmann velocity distributions were used in these derivations to enable near-analytical integrations,inrecognitionofthefactthattheseareidealized distributions.Thederivedmomentsarethenappliedtomore realistic distributions such as those that include a strong suprathermal tail and temperature anisotropy. This section describes a methodology for recovering estimates of solar wind speed and thermal velocities of diverse ion species from such partial distributions, as well as an analysis of the corresponding recovery errors. Figure 1. Top view of a portion of the MESSENGER 2.1. Distribution Functionsfor Instrument spacecraftdepictingtheFIPSfieldofviewandtheobstruction Observations ofthe solardirection bythespacecraftsunshade. Becauseof substantialaberrationofvswfromthespacecraftvelocityvs/c, [12] A coordinate system in the FIPS instrument frame radially traveling particles are measured with an effective with respect to a partially observed solar wind plasma is velocityv =v (cid:3)v bythespacecraft,allowing,under defined in Figure 2. This coordinate system will enable the obs sw s/c some conditions, a fraction of the solar wind distribution to derivation of a distribution function for FIPS observations be sampled by FIPS. The coordinate R is radial to the Sun, that can be used to recover solar wind bulk and thermal T is formed by the cross product of the solar rotation axis speeds.Thespacecraftsunshadeblocksallincidentparticles and R and lies in the equatorial plane, and N completes the angles within about 12(cid:4) of the radial direction. The edge of right-handedsystem. thesunshadeinthespacecraftramdirection,withintheFIPS (cid:1)1.4psrfieldofview(FOV),definesaplaneononesideof alpha particles and heavy ions with respect to the protons. whichsolarwindparticlesmayentertheinstrumentaperture Finally, a concluding discussion of our results appears in andontheothersideofwhichtheyareobstructed(Figure1). Section 4. The z-axis is defined to be perpendicular to this plane, such that the +z direction points away from the obstruction. The x–y plane, therefore, is the plane through the end of this 2. Solar Wind Observations by MESSENGER obstruction. The average velocity of the solar wind is [10] The Fast Imaging Plasma Spectrometer (FIPS), one denoted v , and its direction is defined such that the center of two charged particle sensors on MESSENGER’s Ener- of the disotribution lies in the x–z plane with coordinates getic Particle and Plasma Spectrometer (EPPS) instrument [Andrews et al., 2007], was designed to measure magneto- sphericionsaroundMercurywithm/qratiosupto40amu/e andE/qratiosrangingfrom40eV/eto10keV/e,withenergy scantimesof64sor8sdependingoninstrumentoperating mode. FIPS has a near hemispherical instantaneous field of view, with 1.4p sr imaged during each scan at an angular resolutionofapproximately10(cid:4).Typicalsolarwindplasmas fall well within these mass and energy ranges, such that FIPS is fully capable of resolving the solar wind, including several of its less abundant ion species and pickup ions. However,asaconsequenceofthemission’sthermaldesign, the direct line of sight of FIPS in the solar direction is obstructed by the MESSENGER spacecraft sunshade, as illustrated in Figure 1. This obstruction nominally prevents Figure2. CoordinatesystemcenteredintheMESSENGER theinstrumentfromsamplingthemajorityofthesolarwind FIPS frame. Here, the +z-axis points away from the distribution. The time period of the observations presented obstructiondefinedbytheedgeofthesunshadeintheFIPS here is during the first year of MESSENGER’s primary FOV, and the solar wind core is centered at [v sin (q ), 0, o o orbitalmission,from26March2011to19December2011. v cos (q )]. Only the portion of the solar wind distribution During this period, MESSENGER’s heliocentric distance o o in the unshaded area is measured by FIPS. variedbetween0.3AUand0.5AU. 3of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 [v sin(q ), 0, v cos(q )], i.e. f = 0. The angle |p/2 (cid:3) q | n , v , and v can be recovered through manipulations of o o o o o o obs o th represents the minimum angular distance from the distri- these moments, bution center that lies within the instrument’s FOV. Given the sunshade blockage noted above and an aberration n ¼F ; provided by the spacecraft velocity up to 7(cid:4), q ⪆ 5(cid:4) for a obs 0 o F purely radially flowing solar wind. This angle can be v ¼ 0;and o F further reduced via the turbulent motions of thesolarwind r1ffiffiffiffiffi plasmas. Following standard spherical coordinate system F v ¼ 2: ð4Þ definitions, qistheanglefromthez-axisandfistheclock th F 1 angle in the x–y plane. [13] We assume that any other obstructions to the instru- mentFOVarenegligible,sothatthesolarwinddistribution [17] These relations apply to any measured ion species, is visible over the ranges q = [0, p/2] and f = [0, 2p]. The providingthattheproperconversionfrominstrumentenergy to ion velocity is determined. Similar moments are used to highly supersonic solar wind is confined to a small angular derive solar wind parameters for observations from ACE/ widthintheinstrumentFOV,sootherobstructions,suchas SWICS andUlysses/SWICS [von Steiger etal., 2000]. solararraypanelsorsmallprotrusionsofthespacecraftbody 2.1.2. Kappa Distributions intotheFOV,shouldnotmarkedlyaffectthefractionofthe distribution observed. [18] To first order, an isotropic Maxwell-Boltzmann dis- tributionisagooddescriptionofthesolarwind.However,a 2.1.1. Isotropic Maxwell-Boltzmann Distributions moregeneraldistributionfunctionforsolarwindplasmasis [14] With the newly defined coordinate system from a kappadistribution [Vasyliunas, 1968], above,amodelforthesolarwinddistributionfunctiontakes the form of an isotropic drifting Maxwell-Boltzmann distri- ! butioninspherical coordinates: 1 ðv(cid:3)v Þ2 (cid:3)ðkþ1Þ fðv;q;fÞ¼n (cid:1)1(cid:3)3=2 1 fkðvÞ(cid:1) 1þk 2vt2ho : ð5Þ o 2p v3 (cid:1) th (cid:3) (cid:5)exp (cid:3)v2þv2o(cid:3)2vvoðsinqsinqocosfþcosqcosqoÞ ; ð1Þ [19] The parameter k, defined for 1.5 < k < ∞, describes 2v2 the shape of the velocity distribution away from a quasi- th Maxwelliancore.Avaluek≈1.5givesav(cid:3)5powerlawtail, whereno istheplasmpaffiffidffiffieffiffinffiffiffisffiffiiffitffiffiy andvth isrelated tothe tem- i.e., a strong suprathermal particle population commonly perature T by v ≡ k T=m where k is the Boltzmann observed in the solar wind. This particular distribution will th B B constant. place an upper bound on that population, as the measured [15] A FIPS energy scan implicitly integrates over the tail typically begins at several times the solar wind speed instrument FOV to give an observed distribution as a func- [Fisk andGloeckler, 2006;Fisk et al., 2010]. tion of measured speed, fobs(v). This integration can be [20] Higher k values describe distributions with weaker explicitly written as tails, and k → ∞ reduces the distribution to a tailless Maxwellian. However, for a low-k distribution, the results Zp=2 Z2p from Section 2.1.1 may not necessarily apply. The effect f ðvÞ¼ sinqdq df(cid:5)fðv;q;fÞ: ð2Þ of these tails on the recovery of solar wind parameters will obs be to decrease velocity estimates and increase temperature o o estimates,duetoanincreaseinmeasuredeventsatanglesfar [16] Equation (2) can be integrated analytically under the from the core that, in the instrument frame, are necessarily assumption of supersonic flow and a center of the distribu- measured with a lower and wider energy range than for the tion near the edge of the sunshade (see Appendix B). From core. Although indices can be created to characterize the thissolution,themeasuredquantitiesF ,F ,andF maybe strength of the suprathermal population, larger time accu- 0 1 2 calculatedandmanipulatedtoproducetheobserveddensity mulationsforinstrumentmeasuredeventsthanthoseusedin n < n and estimates of v and v directly from FIPS this work would be needed to obtain the required counting obs o o th measurements: statisticsforsuchananalysis.Therefore,asdiscussedbelow, validrecoverycriteriaaredevelopedthatareindependentof Z∞ anyestimateofthesizeofthesuprathermalpopulation. 2.1.3. Bi-Maxwellian Distributions F ¼ f ðvÞ(cid:5)v2dv≈n ; 0 obs obs [21] In addition to a suprathermal tail, solar wind dis- (cid:5)o (cid:6) Z∞ tributions can exhibit structure with respect to the direction F ¼ 1 ¼ 1(cid:5)f (cid:5)v2dv≈ nobs;and ð3Þ of the local magnetic field [Wolfe et al., 1966]. A simple 1 v v obs v model of these distributions is a bi-Maxwellian, with char- o * o + Z∞ acteristic temperatures Tk and T? (and corresponding vth,k F ¼ ðv(cid:3)voÞ2 ¼ ðv(cid:3)voÞ2(cid:5)f (cid:5)v2dv≈ nobs(cid:5)v2th: and vth,?) related to the overall plasma temperature by the 2 v v obs vo relationshipT=1/3(cid:6)(Tk+2T?)[Hundhausenetal.,1970]. o Here we assume that the magnetic field in the inner helio- sphere is nearly radial to the Sun, such that the parallel 4of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 [24] For a given M and qo, the distribution was sampled over q = [0, p/2] and f = [0, 2p] at 1(cid:4) resolution and accu- mulatedtoformf (v).Thisf (v)wasintegratedfollowing obs obs equation (2) to find F , F , F and subsequently estimates 0 1 2 for v and v . These estimates were com- o,recovered th,recovered pared with the known input values of v and v , and the o th relative error between themwas calculated from (cid:9) (cid:9) (cid:9)v (cid:3)v ðM;q Þ(cid:9) E ðM;q Þ¼ o o;recovered o ð7Þ vo o v o and (cid:9) (cid:9) (cid:9)v =M(cid:3)v ðM;q Þ(cid:9) E ðM;q Þ¼ o th;recovered o : ð8Þ vth o v =M o [25] The recoveries tested here are applicable to multiple ion species in the same plasma. Although different species may have different bulk and/or thermal velocities, only Figure3. Relativeerrorinrecoveredvelocityfor(a)isotro- motion of the distribution core with respect to the plane of picMaxwell-Boltzmann,(b)kappadistributionwithk=1.6, the sunshade results in changes to q , i.e., only one dimen- o (c) bi-Maxwellian with Tk/T? = 2, and (d) bi-Maxwellian sion of ion motion can affect qo. Ion species with different with Tk/T? = 0.5. A decreasing M ≡ vo/vth indicates hotter, solar wind speeds, for example, can still have the same qo less supersonic plasma. (90(cid:4) (cid:3) q ) = 0 indicates that 50% values, and consequently their errors are expected to scale o ofthedistribution isvisible, with a lower fraction visible at withoneanother,allowingfordetailedcomparisonbetween increasing angular distance from the core. For all distribu- them.Inaddition,includedintheconversionfrommeasured tions, when the core is within 20(cid:4) of the sunshade obstruc- events to phase space density is a v4 dependent factor that, tion,thevelocity isrecovered towithin10%accuracy. for lower density plasmas, can limit the recovered f (v) obs valuesatlowermeasuredenergies[vonSteigeretal.,2000]. Thiseffectwasnotincludedaspartofthisanalysisbecause directioncorrespondstothesolarwindflowdirection,giving it isdensity dependentand asecond order effect. adistributionoftheform 2.2.1. BulkVelocities (cid:7) (cid:8) ! [26] Foralmostalldistributionsvisibletowithin20(cid:4)ofthe v (cid:3)v 2 ðv Þ2 core, regardless of the suprathermal population, the error in fðvÞ(cid:1)exp (cid:3) k o (cid:3) ? ; ð6Þ recovered velocity is less than 10%, as demonstrated in 2v2 2v2 th;k th;? Figure 3, which shows the relative error in recovered bulk velocities for all sets of analyzed distributions. Small-scale where vk and v? are the components of the velocity in the structure in these images is because multiple pairs of M directions parallel and perpendicular to the local magnetic and q values produce similar distributions. Because of the o field. finite sensitivity of FIPS and typical solar wind plasma [22] Previous studies of inner heliospheric plasmas yield densitiesintheinnerheliosphere[Marschetal.,1982b],itis Tk/T? in the range 10(cid:3)1 to 101 that can vary with different unlikely that any distribution centered more than 20(cid:4) away ion species [Marsch et al., 1982a, 1982b]. Although not from the sunshade obstruction will generate any noticeable modeled in detail here, a substantial heat flux component measuredeventswithinthedetector.Itisthereforeexpected will add an asymmetry into the distribution, usually along that, under the stated assumptions, FIPS can produce accu- the parallel direction [Li, 1999], resulting in a shift of the rate estimates of solar wind speeds for any measured solar mean velocity and an enhanced thermal velocity due to a winddistribution. widening of the distribution. These heat flux contributions, 2.2.2. ThermalVelocities like temperature anisotropy, often exhibit structure with [27] As expected from Appendix A, and shown in respect tothemagnetic field. Figure 4a, the error in recovered thermal velocity is very small for the isotropic Maxwell-Boltzmann distribution and 2.2. Recovery ErrorEstimates is relatively independent of the visible fraction of the dis- [23] Toquantifytherecoveryerrorsinvoandvth,datafrom tribution function. A strong suprathermal tail, however synthetic distributions were analyzed with the methodology (Figure 4b), creates substantial errors in recovered thermal of theprevious section.Four sets of distributions weregen- velocity except for either very hot (M ≈ 3) distributions or erated: (1) an isotropic Maxwell-Boltzmann distribution, when almost half of the distribution function is visible. For (2) a kappa distribution with k = 1.6, (3) a bi-Maxwellian the bi-Maxwellian cases, the recovered thermal velocity is with Tk/T? = 2, and (4) a bi-Maxwellian with Tk/T? = 0.5. dominatedbythevth,kcomponent,specificallyforTk/T?>1, EachsetconsistsofdistributionswithvaryingvaluesofM≡ since the integration is most sensitive to contributions from v /v and q values. Avalue ofv = 450 km/s was selected the flow/magnetic field direction. A substantial temperature o th o o withMvaryingfrom3to12andq varyingfrom90(cid:4)to120(cid:4). anisotropy,therefore,canleadtoabiasinrecoveredthermal o 5of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 the plasma population that is being measured by the instru- ment mustbedetermined. [30] The highest count rates in the instrument correspond to proton events. Therefore, a set of filters that examine the plasma properties of the measured protons were used to determine whether the solar wind distribution was being observed. Less abundant species such as He2+ and other heavy ions were recovered only during these times. H+ velocities were recovered for each instrument energy scan, averaged over approximately 1 min or 10 s depending on instrumentoperatingmode.Longertime-averagedvelocities of H+ are averages of these individual scans. Heavy ion measurements, due to limited statistics, were summed over several scans before recovering their velocities. The thresh- olds below which velocities were not recovered due to insufficientstatisticswereselectedasn <5(cid:6)10(cid:3)3cm(cid:3)3 obs for bulk velocity and n < 1.5 (cid:6) 10(cid:3)2 cm(cid:3)3 for thermal obs velocities. [31] Because of the limitations of mass resolution for FIPS,heavyionchargestatessuchasO6+andC5+cannotbe Figure4. Relativeerrorinrecoveredthermalvelocitiesfor easily separated. Consequently, events from all ions with (a) isotropic Maxwell-Boltzmann, (b) kappa distribution m/q between (cid:1)2 and 3 amu/e were accumulated together. with k = 1.6,(c) bi-Maxwellian with Tk/T?= 2, and (d) bi- These events, however, will typically be dominated by O6+ Maxwellian with Tk/T? = 0.5. For the Maxwell-Boltzmann and C5+, the most abundant heavy ion species in the solar case,therecoveredthermalvelocityiswithin10%indepen- wind[vonSteiger etal.,2000]. Forthisreason,theaverage dent of the fraction of the distribution function that is visi- heavy ions will be denoted as 〈OC〉. Since the conversion ble to FIPS. For the k = 1.6 case, however, the strong from energy-per-charge to velocity depends on m/q, an suprathermaltailcreateslargechangesinrecoveredv with th average solar wind m/q of 2.5 was assumed on the basis of angulardistancefromthecore.Therecoveredthermalveloc- abundances reported by von Steiger et al. [2000]. This ities for the bi-Maxwellian cases are most sensitive to vth,k, factor may introduce additional errors ontheorderof about especiallyforTk/T?>1. 5%tothedeterminationoftheaverageheavyionvelocities. [32] Bulk velocities were recovered from FIPS measure- mentsif:(1)sufficientnumbersofH+eventsweremeasured velocity independent of the fraction of the distribution to obtain 10% peak widths, (2) MESSENGER was outside visible. of Mercury’s bow shock as determined by data from mag- [28] Although the errors for the k = 1.6 case may be dis- netic field measurements (R. M. Winslow et al., Mercury’s couraging, they can nonetheless be used to aid in identifi- magnetopause and bow shock from MESSENGER obser- cationofperiodsofrecoverablethermalvelocities.Consider vations, submitted to Journal of Geophysical Research, theturbulentsolarwindmovinginandoutoftheFIPSFOV. 2012), (3) the measured H+ energy distribution was singly As this movement occurs, the instantaneous q value chan- o peaked, (4) the mean incident location of events was calcu- ges. Following the results in Figure 4b, such movement in lated to be within 30(cid:4) of the radial direction, and (5) more thepresenceofastrongsuprathermalpopulationwillcreate than two consecutive energy scans met criteria (1–4). Ther- sharp changes in the recovered v value as a function of th malvelocitieswererecoveredifcriteria(1–5)weremetwith time. Therefore, despite a lack of knowledge of the precise the added restriction that there must be recoverable thermal values of q or k, if the recovery of thermal velocity is o velocities from at least five consecutive energy scans and restricted to time periods where there is a stably recovered thatthestandarddeviationofthosevelocitiesstayedbelow5 v withtime,itislikelythateitherFIPSisobservinganear- th km/s, indicating a stable recovery. Heavy ion parameters Maxwellian distribution or that it is close to the solar wind wererecoveredwhentheabovecriteriaweremetforH+and core such that theeffects ofthe suprathermal particle popu- when sufficient numbers of heavy ion events were lationwillnotaffecttherecovery.Duringthesetimeperiods, measured. and with the given assumptions, it is estimated that the recoveryofthermalvelocitywillbeaccuratetowithin10%. [33] Asanexample,Figure5showsaperiodofrecovered bulk and thermal velocities for H+, He2+, and 〈OC〉 for the 2.3. Recovery Criteria periodfrom21Juneto1July2011.Thestreamstructureof the solar wind [McComas et al., 1998b] as well as plasma [29] FromSection2.2,bulkandthermalvelocitiesofsolar temperatures consistent with previous observations of inner wind ions can be recovered to within 10% accuracy. How- heliospheric solar wind from Helios 1 and 2 [Freeman, ever, thesolar windis nottheonly plasma populationmea- 1988; Marsch et al., 1982b] were recovered from the fil- sured by FIPS as MESSENGER orbits Mercury, passing throughtheplanet’smagnetospheretwiceperdayduringthe tered dataset. The solar wind parameters derived here were also compared with those generated by the Wang-Sheeley- primary orbital mission. Not only are criteria needed to Arge ENLIL model (D. N. Baker et al., Solar wind forcing determine whether or not we can expect accurately recov- at Mercury: WSA-ENLIL model results, submitted to ered solar wind parameters for a particular ion species, but 6of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 measurements, the local Alfvén speed cannot be reliably determined. However, from the correlation between dv and dB,theeffectivewavespeedfrom(11)isreadilycalculable. [37] For large-amplitude nonlinear Alfvénic fluctuations, correlationsinvandBarepresentinallvectorcomponents, not just those transverse to the direction of propagation [Belcher and Davis, 1971]. However, any analysis of FIPS observationsisrestrictedtothedirectionradialtotheSun,as the recovered speed is approximately equal to the radial component of the solar wind velocity. Therefore, Alfvénic fluctuation events will be identified as time periods during which the measured v correlates with the radial (with H+ Figure 5. Recovered (a) bulk velocities and (b) thermal respecttotheSun)componentofthemagneticfield,BR,and velocitiesofH+,He2+,and〈OC〉fortheperiodfrom21June the magnetic field magnitude |B| is nearly constant. The constant of proportionality between dv and dB has been to 1 July 2011. These filtered datasets show typical solar H+ R wind structure, with speeds and temperatures characteristic usedtoderivetheradialpropagationspeedofthefluctuation of inner heliospheric plasma. Time accumulations for each from equation (11). data productareindicated. 3.2. Differential Streaming ofHeavy Ions [38] Two periods of propagating Alfvénic fluctuations Journal of Geophysical Research, 2012), and they were identified in the FIPS dataset on 19 April 2011, from foundtobeingoodagreementduringquietsolarconditions. 00:00:00 to 02:40:00 UTC, and 28 August 2011, from 14:00:00 to 15:00:00 UTC, are shown in Figures 6 and 7, 3. Heavy Ion Measurements in the Inner respectively,withprotonandheavyionvelocitiesfromFIPS Heliosphere andcorrespondingmagneticfieldvectormeasurementsfrom MAG.Ineachcase,thereisanearlyconstant|B|,consistent [34] Withbulkandthermalvelocitiesrecoverableforboth with incompressible turbulence. There are also observable solar wind protons and heavy ion species, the effects of correlationsbetweenv andB withcorrelationcoefficients H+ R propagating Alfvénic fluctuations and average heavy ion r2=0.62and0.73forthe19April2011and28August2011 kinetic properties can be characterized in the inner helio- events, respectively. The time resolution of the data from sphere (solar distance R < 0.5 AU) with data from both the each event varies because of different FIPS instrument FIPSandtheMagnetometer(MAG)[Andersonetal.,2007] operatingmodes.Foreachcase,themaximumavailabletime onMESSENGER. 3.1. Identification ofAlfvénicTurbulence [35] Alfvénic fluctuations are ubiquitous structures in the solar wind [Coleman, 1968; Belcher and Davis, 1971], particularly in fast streams associated with coronal holes [Smith et al., 1995]. These fluctuations have been observed in situ as close as R = 0.3 AU by Helios [Grappin et al., 1990]. They are identified as periods of nearly constant magnetic field magnitude |B| and plasma density n (mass density r), with correlations between changes in the mea- suredsolarwindvelocityandmagneticfieldvector,suchthat dv≡v(cid:3)hvi ð9Þ and dB≡B(cid:3)hBi: ð10Þ withdvproportionaltodB,wherevisthesolarwindvelocity vectorandBisthemagneticfieldvector.Theproportionality constant (dv/dB) is related to the wave velocity v of the w propagatingfluctuationbytherelation[B.E.Goldsteinetal., 1995] Figure 6. Alfvénic fluctuation event for 19 April 2011, from00:00:00to02:40:00UTC,ininstrumentsurveymode. v ¼ dvB: ð11Þ (a)FIPS-measuredbulkspeedsofH+,He2+,and〈OC〉show w dB differential streaming of heavy ions with respect to solar pffiffiffiffiffiffiffiffi wind protons. Time accumulations for each data product [36] ForanidealAlfvénwave,dv=(cid:7)dB/ 4pr,leadingto are indicated. (b) Magnetic field measurements from MAG a wave propagating with the Alfvén speed along the direc- (1-min averages) indicate strong correlations of B and v tionofB.BecauseofthelargeuncertaintiesinrfromFIPS with a nearlyconstant |B|. R H+ 7of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 fraction of the propagating wave speed. Some weak corre- lation between the He2+ speed and B in Figures 6 and 7 is R further evidence of this incomplete scattering process, as only particles not traveling in the frame of the wave could be susceptible to such interactions. The constant of pro- portionalities between dv and dB for the events in H+ R Figures 6 and 7 are (cid:3)9.2 km/s⋅nT and (cid:3)2 km/s⋅nT, respectively, leading to maximum calculated wave speeds of 175 km/s and 80 km/s. The He2+ bulk radial velocities appear to stream ahead of the protons at a fraction of this speed, approximately 70%, for both the 19 April and 28Augustevents,consistentwiththeresultsofMarschetal. [1982a]. The 〈OC〉 bulk velocities also appear to lead the protons by similar factors, though with the longer required accumulation time and consequently fewer available data pointsforheavyions,thisrelationshipislessclear. [41] For the 28 August event, the heavy ion thermal velocities also lead that of the proton velocity, indicating substantialheatingforeachspecieswhencomparedwithH+. Theaveragethermalvelocityofheavyionsduringtheevent isapproximately90km/s,consistentwithparticlesscattered intotheframeofthepropagatingwave.Ionswithmarkedly different thermal speedscould resultinbiasesintheirrecov- eredbulkvelocities,followingthederivationinAppendixA. However, the effect of this bias would be to decrease the recovered speed of the heavy ions, such that their relative streamingspeedwouldbeslightlyunderestimated. [42] Although the full time interval of eachevent appears Figure7. (a and b) Same as Figures 6a and 6b but for tohaveastrongv (cid:3)B correlation,thereareshortperiods 28August2011,from14:00:00to15:00:00UTC.(c)Corre- H+ R within each period with no observed differential streaming, sponding thermal velocities. During this time period, FIPS i.e.,v =v .Theseperiodscanbeunderstoodasmarking was in its “burst” scanning mode. Time accumulations for H+ heavy changes in the propagation direction of the fluctuations. eachdataproductareindicated.Themagneticfielddatawere Nominally, Alfvén waves are transverse perturbations that averaged over 10-s intervals in order to observe the fine travel parallel to the mean field. However, for nonlinear structureoftheB (cid:3)v correlation. R H+ high-amplitude waves, the propagation direction may be altered by large fluctuations. During these events, although thewavespeed|v |muststayconstant, theindividual com- w resolutionwasusedtoderivevH+inordertoresolvethefine ponents can change to accommodate an evolving direction structureofthefluctuations.Thethermalvelocitiesforthe19 of propagation. The periods in Figures 6 and 7 at which April event did not meet the stability criteria for a reliable v = v correspond to times when the magnetic field H+ heavy recovery and are, as a consequence, not included in this became notably nonradial, i.e., |B |, |B | > |B |, in agree- analysis. However, for the 28 August event, the H+, He2+, mentwiththeanalysisofBergeretTal.[2N011]atR1AU.With and 〈OC〉 thermal velocities are available and are shown in the direction of propagation no longer in the radial direc- Figure7. tion, the differential speed of heavy ions and H+ measured [39] From previous observations [von Steiger and by FIPS should be small. These observations indicate that Zurbuchen, 2006], it is expected that the timescale of inter- Alfvénic fluctuations travel along the local magnetic field actions between solar wind ions and propagating waves direction. High time-cadence measurements are vital for scales as (q/m)a, where a is related to the spectral slope of resolving this phenomenon, as average heavy ion velocities the magnetic field fluctuations. Heavier ions should there- overthetimescaleofthefluctuationscanwashoutthiseffect. fore scatter quickly into the frame of the waves or of the Alfvénicturbulence,leadingtoamotionrelativetoprotons, 3.3. AverageHeavy IonKinetic Properties andalsoexcessiveheating.Inaddition,theseionsareheated [43] Because of the limited solar wind dataset of FIPS, it such that their thermal velocities approach that of the wave is not possible to identify all potential Alfvénic fluctuation speed.Thisprocessresultsindifferentialstreamingofheavy events from instrument observations. Consequently, wave ions with respect to the protons in the direction of the speeds can be identified only for a handful of events for magneticfield [Asbridgeetal., 1976; Marschetal.,1982a; whichtherearelargesegmentsofcontinuousmeasurements. Zurbuchen et al., 2000; Berger et al., 2011]. Since waves Nonetheless, it is possible to investigate average trends of tend to propagate outward from the Sun [Roberts et al., heavy ion dynamics. Such data for the inner heliosphere 1987; Gosling et al., 2009], such streaming results in an (R < 0.5 AU) from FIPS can be compared with previous increased measured solarwind speed ofheavyions. observations at 1 AU. For the full time range available in [40] Thiswave–particlescatteringisincomplete,however, 2011, average bulk and thermal velocities were recovered and particles have been observed to stream with only a from FIPS measurements. 8of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 Figure 8. v as a function of (a) H+ bulk velocities and (b) 〈OC〉 bulk velocities measured by FIPS. He2+ Forlowersolarwindspeeds(v<450km/s),heliumandhydrogentraveltogether.Forhigherspeedwinds (v>450km/s),atwhichAlfvénicturbulencebecomesmoreprevalent,theheliumionsstreamaheadofthe protons. Helium and〈OC〉flow together for all measured solarwind speeds. 3.3.1. Bulk Flow at 3.5 solar radii [Kohl et al., 1998] observed close to the [44] The average bulk velocity of He2+ compared with Sun by UVCS are included in the figure. Although UVCS thoseofH+and〈OC〉areshowninFigure8.Atlowersolar observed temperatures only of neutral hydrogen, similar wind speeds (v < 450 km/s), v ≈ v , indicating the trends are expected to hold for that of H+. Here it is also H+ He2+ absence of substantial differential streaming. However, for assumed that the observations of O5+ are representative of higher speeds (v > 450 km/s), the helium ions consistently coronalHe2+,sincenocorrespondingspectroscopicdataare streamaheadoftheprotons,atrendingoodagreementwith available. Heavy ions seen by MESSENGER are observed increasedAlfvénicwaveactivityincoronal-holewinds.For to be substantially hotter than protons, with few observed all measured solar wind speeds, however, there does not alpha particles in thermal equilibrium with the protons, in appear to be any average streaming between alpha particles contrast to analogous observations at 1 AU. The maximum (m = 4 amu) and heavier ions (m = 12–16 amu). Such v /v from FIPS, however, stayed within the bounds th,He2+ th,H+ behavior is consistent with an m/q-dependent physical pro- of UVCS observations, indicating that a substantial addi- cesses,inwhichhigher-m/qionsallflowwiththeprotonsin tional heating source outside the solar wind acceleration the slower solar wind and all stream ahead of the protons region may not be required to explain FIPS observations. with similar velocities during times of increased Alfvénic Further, Figure 9b indicates that the thermal velocities for waveactivity inthefast wind. He2+ and 〈OC〉, like their bulk velocities, are nearly 3.3.2. Thermal Properties identical. [45] The thermal velocities are compared between He2+ [46] For Parker spiral geometry and a solar wind density and H+ and between He2+ and 〈OC〉 in Figure 9. Lines thatscalesas1/R2,theAlfvénspeed(v )increasesbyabout A indicating thermal equilibrium, equal thermal speeds, and a factor of 2 from 1 AU to 0.4 AU, the average distance of themaximumdifferentialthermalspeeds(v /v ≈2.33 MESSENGER from the Sun during the time period of this th,O5+ th,H Figure9. v asafunctionof(a)H+thermalvelocitiesand(b)〈OC〉thermalvelocitiesmeasuredby th,He2+ FIPS.Heliumissubstantiallyheatedwithrespecttotheprotons;onaverageT /T ≈9.BothHe2+and He2+ H+ 〈OC〉havesimilar thermal speeds, indicating substantial heatingof theheavierions aswell. 9of14 A00M02 GERSHMANETAL.:HEAVYIONSINTHEINNERHELIOSPHERE A00M02 similarthermalvelocities.Fromthisanalysis,measurements ofT /T intheinnerheliosphere appeartobe orderedby ion H+ the solar wind regime, consistent with similar analysis at 1AUbyKasper et al.[2008],butwith substantially higher observedalphaparticletemperatures. [48] As discussed in Appendix A, the recovery of the thermal velocities of ion species relies on the assumption of an isotropic plasma. Although there may be biases in the recovered of thermal velocities from partially observed solar wind plasmas, any bias in the T /T ratio must be He2+ H+ due to a difference in biases between the alpha particles and the proton population. If substantial anisotropy is present in the He2+ particles with respect to those of H+, i.e., THe2+,k/TH+,k ≫ 1, the ratio of the recovered thermal velocities could be biased. Furthermore, there may also be a larger or more variable suprathermal population for heavier ions than for H+, enhancing the estimates of alpha particle temperatures. Finally, the solar wind populations mosteasilymeasuredbyFIPShavehigherplasmatempera- Figure 10. T /T as a function of solar wind speed for ion H+ tures in general due to the tendency of colder distribution He2+and〈OC〉.Theerrorbarsforeachpointindicatecount- functionstoremainhiddenbehindthespacecraftsunshade. inguncertainty,withthepercenterrorscalingasptheffiffiffiffiinverse square root of the number of measurements, 1/ N. With [49] As indicated by data gaps in the observations of Marsch et al. [1982a] close to the Sun, however, available decreasing solar wind speed, i.e., less Alfvénic turbulence, Helios observations may exhibit an opposite bias. Alpha theplasmatendstowardalowertemperatureratio.Thetem- particles and protons become increasingly more difficult to perature ratio T〈OC〉/THe2+ is approximately equal to m〈OC〉/ separate with increasing T /T ratios using only electro- m , implying similar thermal speeds for heavy ions, as He2+ H+ He2+ static deflection, leading to a possible explanation for the showninFigure9b. increased temperatures measured by MESSENGER when compared with Helios observations. Notwithstanding any study. The proton thermal speed, however, for a measured bias,however,fromFIPSobservations,therearefewrecov- R(cid:3)0.9 scaling for temperature in the fast solar wind in the ered thermal velocities indicating that He2+ and H+ are in inner heliosphere [Totten et al., 1995], increases only by a thermal equilibrium, in striking contrast to data collected at factorofapproximately1.5from1AUto0.4AU,suchthat 1 AU. theoverallratiov /v willincreasebyafactorof1.3,i.e., 3.3.3. Magnetic Turbulent Heating A th,H+ the proton thermal velocity does not scale with the Alfvén [50] To interpret the non-thermal heating and differential speed.AsdiscussedinSection3.2,He2+ionscanbeheated acceleration of heavy ions as a function of heliocentric dis- bypropagatingAlfvénicfluctuationssuchthattheirthermal tance, a comparison of two representative spectra of locally speedapproachesthatoftheAlfvénspeed.Itfollowsthatthe measured magnetic field data in the fast solar wind (v ≈ H+ heliumthermalvelocityduringthesetimesshouldscalewith 500km/s)at0.37and1AUisshowninFigure11.TheACE the Alfvén velocity. At 1 AU, T /T = 4, i.e., equal data were measured by the magnetometer on ACE [Smith He2+ H+ protonandalphathermalspeedscorrespondtotimeperiods etal., 1998] with a maximumtime-resolution of3 vectors/s. of increased magnetic wave activity and differential MESSENGER data were measured with a maximum time- streaming [Kasper et al., 2008]. Inside 1 AU, therefore, if resolutionof 20 vectors/s. Spectraldensities for the traceof He2+ particles have their thermal speeds ordered by the thetotalpoweroffluctuationsinthemagnetic fieldcompo- Alfvén speed, a peak in the ratio T /T ≈ 8 is expected. nents(P )andthetotalpoweroffluctuationsinthemagnetic He2+ H+ Tr From Helios, T /T in the inner heliosphere was 5–6 fieldmagnitude(P )areshown.Foreachspectrum,thereis He2+ H+ |B| [Marsch et al., 1982a]. The average T /T from FIPS apowerlawfitintheinertialfrequencyrange10(cid:3)2Hz<f< He2+ H+ observations, (cid:1)11, is higher than this scaled ratio and 10(cid:3)1 Hz. Figure 11 also marks the gyrofrequencies of H+, nearly twice that of the previous Helios observations. He2+,and〈OC〉. [47] Temperature enhancements measured by FIPS as a [51] In the low-frequency inertial regime, the spectral function of v for He2+ and 〈OC〉 are shown in Figure 10 shape of P is almost independent of heliocentric distance, H+ Tr for an average 〈OC〉 mass of 14.4 amu [von Steiger et al., consistent with Helios observations [Marsch, 1991]. The 2000]. In the fast wind, where Alfvénic turbulence is most power law fits in this region show a slope consistent with prevalent,thetemperatureratiobetweentheheavyions and Kolmogorov scaling, i.e., f(cid:3)5/3 for both spectra. However, protons is largest, with the maximum ratio approaching the the spectral power at 0.37 AU is elevated by a factor of maximum observed heavy ion heating from UVCS mea- 20 in the frequency range 10(cid:3)3 Hz < f < 10 Hz. Following surements[Kohletal.,1998].Theminimumratiosoccurfor the Wentzel-Kramers-Brillouin (WKB) approximation and the lowest measured solar wind speeds, at which Coulomb under steady plasma conditions, P is expected to increase |B| collisionsareexpectedtoplayanincreasinglyimportantrole followingaR(cid:3)3dependenceintheinnerheliosphere[Isenberg inheavyionkinematics.ThetemperatureratioT〈OC〉/THe2+is and Hollweg, 1982], consistent with the observed change approximately equal to m〈OC〉/mHe2+, consistent with results in P|B|. shown in Figure 9b, indicating that heavy ions move with 10of14