Icarus 200 129-146

Elemental composition of 433 Eros. New calibration of the NEAR--ShoemakerXRS data

Lucy F. Lim a, ", Larry R. Nittlerb

,ud, C9i, , ASA= 3uduri Space HigI.i C2n°er, Greenbefr, dais 20771, t;S.kto Cvrnea:e J,7m €!flo g cf !,Vasr€ngron, 52411 Bxaad Pranch Road, N11V, 'ttf^shln^tcn, i3C2001--, 05,A

A B S T R A C T

We present a rnew calibration of the elemental-abundance data for Asteroid 433 Fros taken by the X-rayspectrometer !XRS', aboard the NEAR-Shoemaker spacecraft. WEAR is an acronym for "Near-Earth AsteroidRendezvous,") Quintificatio€1 of the asteroid surface elemental abundance ratios depends critically onaccurate knowledge of the incident solar X-ray spectrum, which was monitored simultaneously withasteroid observations. previously published results suffered from incompletely characterized systematicuncertainties du:e to an imperfect ground calibrations of the NEAR gas solar monitor. The solar monitorresponse function and associated uncertainties have nwN been characterized by cross-calibration of alarge sample of DEAR solar monitor flitrht data against. contemporary broadband solar X-ray data from theEarth-orbiting GOES-8 (Ceostationary Operational Environmental Satellite). The results have been used toanalyze XRS spectra acquired from Eros during eight major solar Flares ,including three that have norpreviously been reported). The end product of this analysis is a revised set of Eras surface elementalabundance ratios with 1IeW error estimates that more accurately reflectreflect the remaining uncertainties inthe solar flare spectra: NlgtSi - 0,753+0.[778, ---0.055, Al si = 0.069±0.055, SiSi =- : 0.005±03 008, Ca,'Si =0,0. 30+0.0231"-0.(324, and fe;'Si — 1.578+(7.338; --0320. These revised abundance ratios are consistentwithin cited uncertainties with the results of Nittler et aL [Nittler, L,R„ and 14 colleagues, 2001. ?Aeteurit.Planet. Sci_ 36, 1673--16951 and thus support the prior conclusions that 433 Eros has a major-elementcomposition similar to ordinary chordrites with the exception of a strong depletion in sulfur, most likelycaused by space weathering.

Published by Elsevier Inc.

A R T I C 1. E I N F 0

Arti e h75to?y:

Received 9 October 2007Revised 12 Septenrl er 20USAccepted 21 Seprembet 2008Availahi,^ online !8 Noaeml^cr 2608

Keswards:

Asteroid Eros

Asteroids, cornpositionAsteroids, surfacesAsteroids

1. introduction

The Near Earth Asteroid Rendezvous INFAR)-Shoemaker space-craft orbited the Asteroid 433 Eros between February 2000 andFebruary 2001. Among its mission objectives (Chong, 1997) wasthe characterization of the surface composition of Eros using X-ray;XRS, Goldsten et al., 1997) and gamma-ray spectrometers (GRS,Goldsten et al„ 1997). XRS results were published during and im-mediately after the mission ky Trombka et al. (2000,1 and Nittler etal. (2001), but were plagued by systematic uncertainties sternmingfront the unlucky failure of one solar monitor and the incompletepre-launch calibration of the other. This paper describes the sub-sequent effort at post-launch calibration of the NEAR gas solarmonitor and the resulting improvement in our understanding ofthe XRS-derived elemental composition of 433 Eros.

The X-ray fluorescence emission measured by NEAR is a prod-uct of the interaction of solar X-rays with the asteroid's surface. As

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0019-I035j$ - see errant matter Published by Elsevier Inc,

the asteroid is exposed to X-rays from the upper solar atmosphere,a fraction of the incident X-rays is photoelectrically absorbed byvarious inner electron shells of atoms in the surface, resulting inthe emission of either an Auger electron or a fluorescent X-ray,with energies characteristic Moseley. 1913 1 of the atoms that pro-duce them.

Each electron shell can only be induced to fluoresce by thatportion of the solar X-ray spectrum that falls alcove its bindingenergy. Moreover, fluorescent X-rays emitted by one atom maybe absorbed by another atom in the asteroid's surface prior toescape into space. The resulting spectrum of fluorescent lines de-pends Both on the abundance of each element in the asteroid'ssurface and on the spectral distribution of the incident X-rays. Ac-curate knowledge of the incident solar spectrum is thus critical toconverting the spectra received by the 'NEAR XRS into elementalabundances oft the asteroid's surface.

NEAR, therefore, carried two X-ray spectrometers dedicated tomonitoring the solar spectrum between 1 and 10 kev, One ofthese, a Si PIN photodiode, failed prior to orbit insertion. The sec-ond consisted of a gas-filled proportional counter similar to the

https://ntrs.nasa.gov/search.jsp?R=20110007227 2019-04-04T04:41:12+00:00Z

130

LE'Lim, U, Ni mi ler j karfis WO (2009] 329-146

Pig. 1. 'Mearencai (CHIANII 5.2; here er al. : 1997; Loath er at., 2006) single-Temperature solar 5, ec,ra at thr°e plasma ternperaiures. vertical dashed Imes represent theK edge energies of major eIenter:ts measured by the NEAR XKS,

asteroid-pointing detectors, but covered by a graded filter ;Clarket al., 1995) designed to attenuate the incoming solar flux andincrease the dynamic range of the detector. Unfortunately, the re-sponse of this filter, particularly at off-normal solar incidence an-gles, was not adequately determined in the laboratory prior tolaunch,

This paper describes the post-launch calibration of the NEARgas solar monitor and its application to the analysis of XRS spectraof 433 Eros acquired during eight major solar flares. The responseof the graded filter and the uncertainties therein were modeledteased on measurements and tolerances as recorded in the engi-neering diagrams. Resulting models of the gas solar monitor's re-sponse function were tested against flight data and checked againstcontemporaneous broadband X-ray data from the Earth-orbitingGOES-8 ;Geostationary Operational Environmental Satellite; to re-duce the range of possible solar monitor response functions tothose that were consistent with the available data. Finally, theimproved solar results were used to analyze data from eight ma-jor solar flares from which asteroid fluorescence was recordedby NEAR, resulting in a recalibrated elemental composition for433 Eros. The remaining uncertainties in the solar spectra wereincorporated into the error analysis for the asteroid's composition.

2. The solar X-ray spectrum

The solar X-ray output has been observed by instrumentsaboard a Number of Earth-orbiting satellites. These have includedvarious GOES (Geostationary Operation Environmental Satellites)broadband detectors: the SMM Bent Crystal Spectrometer (Acton etal., 1950) in the 19805 (1980, then 1954-1939): and the Y€1HKOHBCS and SXT (Bragg Crystal Spectrometer and Soft X-ray Telescope;Yoshimori et al., 1991) in the 1990x_ After the NEAR mission, solarX-ray observations have also been conducted by the CORD 1AS-FX-ray spectrometer RESIX; Sylwester et al., 2005; operated from2001-2003, and RH- SSI {Reuven Ramaty High-Energy Solar Spec-troscopic lmiger; Un. er Al., 2002), launched in 2002,

The solar X-ray spectrum consists of a set of emission lilies Su-perimposed on a continuum. Emission lines in the region observedby NEAR (1-10 keV) come from highly ionized arolns (H and He-

like electron shells). The continuum is produced by bremsstrahlungemission, primarily from hydrogen, and declines steeply with in-creasing energy. Both the slope of the bremsstrahlung continuumand the intensities of the various emission Tines vary greatly withelectron temperature (Pig. 1t. Electron temperatures (Te) in thecorona generally are in the range -2-30 x 106 K (e.g., Phillips,2004), with the highest temperatures being reached only duringmajor solar fares.

The amount of material at a given T Q is described by the "emis-sion measure" ;EM);

EM dV, (i

where n represents the plasma density and V is the volume of thehot plasma. The total spectrum for an isothermal plasma, then. is:

4eanitte^(^•, Te) ( E ff( J, , Te) E fh( i_ T,)"J n2dV (2)

;Garcia, 1994), where Eft; is the emission line spectrum and Eff isthe bremsstrahlung continuum.

Generally, however, the solar spectrum is multithermal (e.g.,Feldman et al., 1995: McTiernan et al., 1999). The thermal portionof the solar X-ray spectrum, then, can be represented by the inte-gral over all temperatures of the amount of plasma at a given tem-perature (known as the "differen

tial emission measure," DEM(T))

multiplied by the spectrum appropriate to that temperature:

4 ta1f A J 00-T) x D M(TjdT, 3)

Typically, DEIM(T) is calculated by observing the relative intensitiesof lilies in the solar spectrum, since different species of ions havedifferent emitting efficiencies as functions of temperature.

Because the NEAR gas solar inonitor could not resolve individ-ual spectral lines, its spectra do not contain enough infor„ nationto permit full inversions of DEM(T). Tice typical structure of theDEM(Tj of a solar flare represents two plasma components, oneemitting at 5-10 MK and a hotter component emitting at 16-

elemental corn.posznon of 433 Errs

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Fig, 2. Single-temperature, ;top, vs two-temperature ft to a DEAR solar monitorspectrum Prom 17-June-26W. The smnoth dashed traces are the mcdeis, tO le thenoisy solid ones are the ?NEAR data. In the lower plat, the dash-dotted traces arethe two isothermal components of the fit. Two-temperaru e modeling was usedthmu&aut the present a;ralysis.

25 MK (e.o., Antonucci and Dodero, 1995: Kepa et al„ 2006`. 3 Wehave therefore .Wade the simplifying assumption that the solar X-ray spectrum can he adequately described by a two-temperaturemodel, so that:

<ra6fr)^ EM I xq_53P,TO+FM2xQ,2z.,Tz). (4)

Fig. 2 illustrates single-temperature and two-temperature fits toa NEAR bas solar monitor flare spectrum.

2.1. Elemental abundances in the solar atmosphere

The line emission in the solar X-ray spectrum depends on theabundances of the emitting elements in the solar atmosphere aswell as on the electron temperature. Generally, the X-ray emit-ting plasmas of solar flares reflect the composition of the solarcorona, which differs substantially from that of the photosphere:in the corona, elements (other than hydrogen') with high first ion-ization potentials are depleted relative to elements with low firstionization potentials (the "I'll'" effect). Although this relative frac-tionation according to FIP is well established, the absolute nor-malization of coronal abundances relative to photospheric ones issomewhat controversial (e.g., Fludra and Schmelz, 199131. in thiswork, we consider the published coronal abundances of Meyer(1985), based on observations in the extreme ultraviolet and X-rayranges, and of Feldman et al. (1992)1

Synthetic solar spectra were generated using the coronal abun-dances of both itleyer (1985) and Feldman et al. {1992; as inputs to

r The saiar tares exam,lTe'd in these papers Fepresenred GOES [lasses C2--X2 am,C8.1, respectively.

Fable tSular corona€ abundances reiarive to hydrogen [op o H = 12.0).

the CHIANTI 5.2 code (Dere et a1., 1997; iandi et al., 2006). In thelatter calculation, a number of minor elements not included in thework of Feldman et at. (1992 1 were assigned abundances based onthe photospheric abundances of Grevesse and Sauval (1998;, withelements with low first-ionization potentials (FIP" increased by aFactor of 3.5 for the "1=11" effect. These are the same values usedin the "sun_coronal_ext" file included with the CHIANTI 5olarsoftpackage (Landi et al., 2006).

Neither abundance set was entirely successful in modeling theNEAR gas solar monitor data: the spectra generated with theFeldman et al, abundances produced greatly superior matches inthe region below 2.5 keV, but performed poorly above 6 keV;whereas the models using the Meyer abundances produced excel-lent fits to the data above 6 keV. Since the hydrogen-dominatedbremsstrahiung continuum is an important contributor to theX--ray spectrum in the high-energy region where emission linesare relatively sparse, the overall metallicity of the Feldman et al.(1992) model was adjusted downward so that the SijH ratio wouldbe the same as that of Meyer SiIH = FejH --= 3.9 x 40-5.The resulting model produced a good fit to the NEAR data at allenergies. Subsequently, additional models were tested with coro-nal metallicities varied to be slightly higher and slightly lower thanthose of the Meyer ;1985) model. The two most successful mod-cis were those with SijH = 3.5 x 10 - ' ("Corona] I" in 'Fable 1) andSi 1H = 3.9 x 10-' ("Coronal 2"). Abundances in all relevant modelsare included in Table 1.

Flare-to-flare variation in solar : elemental abundances has beenobserved by several investigators (Sylvester et al., 1981; Sterlinget al., 1993; Fludra and Schmelz, 1999). For example, Sylwesterer al. (1998) found that the calcium abundance varies from flareto flare over a factor of about 3.5 and is uncorretated with elec-tron temperature or GOES classification. Within a given flare andamong flares associated with the same active region, however, theabundance was found to change only slowly. The NEAR gas so-lar monitor data from the major solar flare of 27 December 2000(Section 6.5) proved impossible to fit with the same abundancesets that had worked for the other NEAR flare data. In particu-lar, the 6.5 keV iron structure was clearly weaker with respect tothe surrounding continuum than was the case in the spectra ofother solar flares. For this reason, additional models were appliedto this flare in which the abundance of iron was reduced by vary-ing amounts.

3. The NEAR gas proportional counters

The energy resolution of the NEAR gas proportional counters,including the gas solar monitor and the three asteroid-pointing de-tectors, varied with energy according to FWHM = 0.340E 1%1 (Starr

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132

L.F. Lira, L.R. Nittler / lcarus 206 "200911. 129-146

Fig, 3. Geometry o€ The NEAR gas solar rnwtsitar graded filter. Left: Erzgrmerirg diagrar;t o€ the graded 151ter assembly as mounted above the ?:EAR gas satac monitcr tube.The Frter pieces A rms 4-7? each !seasoned 2 x .3.5 inches. Right: Schen3atic cross sec ion of the graded filter pinhole wi h nominal dirrensioras. the gas Salar r rotor wasnonmed € n the &umvacd-facing deer of tie NFAR-S} Oemai t!r spacecraft sot fiat the sensor face vxas parallel wah the soy ar panels. Chus, the angle marked (- is the same as" re "panel angle , of the spacecraft.

et al_, 2000), where RVHM is the full width at half lnaximuan ofa Gaussian X-ray line. As discussed earlier, this resolution is notsufficient to resolve individual spectra fines in the solar X-ray spec-trum, precluding inversion of the full DENIJ) (Eq. (3)) and limitingthe information that can be obtained on solar elemental abun-dances. R potential drawback to our method of fitting solar moni-tor spectra to a two--temperature model (Fig. 2) is that the furtherthe actual solar DEM(T) departs from the sum of two delta func-tions at two temperatures ,for example, if there is a major massof plasma contributing at a third temperature, or if the plasmatemperature varies over a wide range such that a roughly equalamount of X-ray flux is contributed from each temperature incre-ment AT), the poorer a representation of the actual solar spectrumour model will be.

Additional complications to modeling spectra fron:r the NEARgas detectors are due to escape peaks and pulse pile-up effects.The NEAR proportional counters were riled with P-10 (Starr eta;,, 2000), a standard mixture of 90% Ar and 10% CH„. Methanedoes not significantly absorb X-rays in the 1--10 keV range; itspurpose is to absorb the low-energy photons emitted by the ar-gon in order to prevent spurious pulses. Argon, however, can causean escape peak: if an incident X-ray induces fluorescence from anAr atom and the fluorescent X-ray escapes the detector, the en-

ergy measured will be 2.97 keV (the K, energy for Ar) below theoriginal energy. Thus, an "escape peak' appears in the output spec-trum for all incident energies higher than the binding energy ofAr (3.2 keV). For the NEAR detectors, the escape fraction was cal-

culated using Monte Carlo methods ,R. Starr, 8 December 2004,personal communication), and was found to be well described bya linear function of energy.

At high count rates, such as those that occurred in the gas so-lar monitor during major solar flares, pulse addition in the detectorelectronics caused a Pile-LIP effect in the entire spectrum, such thateach channel would represent a higher energy than it did at lowcount rates. The size of this "zero shift” in the energy vs chan-nel calibration increased with count rate, and was treated as a freeparameter in the spectral pitting. For context, during the flares de-scribed in the present work, the overall calibration shifts rangedfrom ^2-56 eV.

4. Modeling the NEAR gas scalar monitor

The NEAR gas solar monitor was covered by a graded filter(Clark et al., 1995) intended to attenuate the incoming solar fluxand increase the dynamic range of the detector (Fig. 3 1 . Since theStan's X-ray emission decreases steeply with increasing ener gy, thefilter was designed to admit a greater proportion of "high-energy„(-4--9 keV) X-rays than low-energy ones.

The graded Filter was constructed from thin layers of beryl-lium, aluminum, and the plastics Delrin and Kapton ,Fig, 3). Toprevent the proportional counter from being saturated, most of itsarea was covered by the Al layer. A broad slot (0.295 ± 0.005 by1.181 t 0.005 inches, or 225 crn'; was cut out of the Al layerto admit a portion of the original incident solar radiation. The

VeIrtentat cerepositton e_f433 Eros

1.33

Table 2Nvrn na[ dimensions and engineerin g, tafera€Tees for the graded filter

As nteastired by Goidsten 12003, personal cEigm,.0 ucahonJ. Tn=erance roc sper-&ed in engitleemng rtrawing=

'' Not regarded as a critical dimension acce;ding to the engineering drawings:uncertainties unknown.

According to (Wdsien I20033, this "is the 100 HN process of Kates by Dupont.The single point thickness is 0.35 -1.15 mils for a 1.0 trail nominal thlckr..<.s."

windo;a• of the off-the-shelf gas counter. Not part a € the graded filter.

Delrin and Be layers underneath were pierced by concentric pin-hoies intended to allow a small fraction of the incident low-energyX-rays to reach the proportional counter underneath. ,Wanwhile,higher-energy X-rays would be relatively unimpeded by these ma-terials.

The nominal dimensions of the pinholes and thicknesses of thegraded filter layers are summarized in Table 2. These dimensionsare critical for accurately determining the response of the gas solarmonitor. Unfortunately, variations in these dimensions, even withinthe engineering tolerances of the falter, have substantial effects onthe energy and angular response of the detector. The specifiedmeasurements come from the engineering drawings for the gradedfilter (Goldsten, 2003, personal corn inunIcation). Given pinhole di-ameter uncertainties are the nominal engineering tolerances andmaterial thicknesses are the specified stock thicknesses from themanufacturers.

Because the Deirin pinhole diameter was similar in dimensionto the Delrin stock thickness (Fig. 3), the stock thickness is crit-ically influential in determining the response function of f=ilteredsolar monitor at off-normal solar incidence angles. Unlike the pin-hole diameters, however, the thicknesses of the filter layers werenot marked as critical dimensions in the engineering diagrams.Regrettably, it has proven impossible to recover any pre-launchnaeasurernents that may have been made of these thicknesses.However, a leftover sample of the Be filter foil was later recov-ered by Goldsten et al. ;1997; and measured after the fact to be onaverage 0.0042 inches thick, with individual measurements rang-ing from 0.0039 to 0.0046 inches. The Kapton stock was statedby the manufacturer (Richmond Aircraft Products) to be 1.0 mil(0.001 in.) in thickness, with single-point thicknesses ranging from0,85 to 1,15 mils. No estimates of uncertainty were available on thethicknesses of the Delrin or aluminum stock or on the densities ofthe Delrin and Kapton plastics.

Attenuation coefficients for materials used in the proportionalcounter and graded filter were obtained from KIST ;Hubbell, 1997,available at http:/(www.physics.nisi.gov7[ahysRefData/XrayNiassCoef!cover.html).

4.1. Post-tau rich calibration of the filtered gas solar monitor

In order to reduce the uncertainties associated with the limi-tations of the pre-launch graded filter calibration, flight data fromthe ]SEAR mission were used to determine the range of plausiblegraded filter parameters consistent with the solar spectra collectedduring the mission. The parameter space within the engineeringtolerances of the graded filter was searched systematically. Mach

filter model was tested against actual gas solar monitor outputat a wide range of incident angles and solar activity levels, Onehundred sixty NEAR spectra were selected from solar flares thatoccurred between 4 May 2000 and 1 July 2000. Most of theseflares occurred when the sunlit side of the asteroid was not inthe field of view of the NEAR XRS, so are not represented in theasteroid-pointing data, For each NEAR spectrum, which representsa 50-s integration of the solar monitor, we generated a coi ,respond-ing set of synthetic gas solar monitor spectra. Theoretical (CHIANTI5.2: Here et al., 1937; Landi et al., 2006) models of solar outputat thirty-nine plasma temperatures between 2 and 40 MK wereput through the response function of the candidate graded fil-

ter model, calculated at the correct solar incidence angle for the

time of the observed spectrum, and then convolved with the re-sponse function of the gas counter. The best two-temperature .fitaccording to a X2 test was then recorded, along with the tem-peratures and emission measures of the two isothermal compo-nents.

The free parameters in the fitting process were the tempera-tures of the two single-temperature spectra to be combined; therelative proportions of the low- and high-temperature compo-nents; the overall normalization, which is related to the emissionmeasure of the spectrum; and the zero shift of the detector due topile-up, as described in Section 3. Over a large sample of incidenceangles and solar spectra, the lowest average X2 value should cor-respond to the graded -filter model that best described the flighthardware.

In addition to the goodness of the ht to the solar monitor out-put itself, the second test of our filter models was provided bycontemporary data on solar X-ray emission provided by the GOES-8 satellite, Throughout June and August 2000, the asteroid-Sun-Earth angle was below 30°, so that during this period (but not, forexample, during December 2000) GOES and NEAR were observingsubstantially the same portion of the Sun.

GOES-8 was equipped with two broadband X-ray channels: ashort-wavelength channel with a bandpass of 0.5 to 4 A (24.8to 3.1 keV) and a long-wavelength channel at I to 8 A (12.4 to1,5 kev), Several investigators (Garcia, 1994: Feldman et al., 1995;Thomas et al., 1985) have published formulae for deriving tem-peratures from one or both of the GOES channel outputs. Thesewere used by Trombka et al, (2000) in the earliest NEAR XRSpaper to interpret the asteroid-pointing data, in place of the so-

lar monitor; and similarly by Nittler et al. (2001) to interpret the'.quiet sun" (non-flare) data. However, all of these GOES modelsare based on an isothermal approximation of the flare plasma.In order to test our new rnultithermal fits to the solar moni-tor data, we instead put each synthetic spectrum directly throughthe two GOES transfer functions 'Thomas, 2003; Schwartz, 1998;Garcia, 1994; to model the outputs of the two channels. The ratioof the modeled channel outputs was then compared to the ratioof the actual GOES channel outputs (`GOES ratio") from the sametime period, corrected for light time.

Based on the results of the X2 fitting and comparison to GOESdata, eleven graded-filter models fable 3) were selected for usein the asteroid-fluorescence data analysis. Eight of these represent

the best X3 matches to the solar monitor data on the entire 160-spectrum test sample and the best hatches to the GOES channelratios in the subset (58 of the 160) taken front June 21 throughJuly 1, when the Earth-Sun-asteroid angle was x:16.5 With theseeight models, the median X2 values for the 160 fits in the testsample were under 1.765 and median R141S matches of the calcu-lated vs the measured GOES ratios under 0.032,

Three additional models were included. Model 9 was selectedbecause it produced the lowest median K` Ft to the solar monitordata of any that was tested fX` ^ 1.658), although its performanceon the GOES ratio test was slightly worse than that of a number of

134

? F. Lin-, L.R. N trfer / lcan.is 200 (A091 129- 146

Table 3Selected graded 111ter models.

Table 4Geomerx mforntatior. for eight solar dares.

other models. (Model 1, which produced the lowest median RMSto the GOES channel ratios--0.022—was already included amongthe first eight models.) Models 10 and 11 represented "local min-ima" in both Y2 and GOES ratio RMS comparisons; 10 was theonly model that performed well ire which the Kapton layer wasas thin or thinner than its nominal stock thickness, and 11 wasthe best-performing model among those in which the Delrin wasas thick or thicker than its nominal stock thickness. Although theeight overall best models all had thick Kapton and thin Delrinlayers, the performance of these two models was close enoughthat they could not be ruled out on the basis of the availabledata.

5. Application of the solar monitor resents to the determinationof asteroid elemental abundance ratios

We have applied the new solar monitor models in a new analy-sis of asteroid XR5 spectra for eight solar flares: five from May-jury2000, two from December 2000, and one from 2 January 2001.Note that these include the five flares analyzed by Nittler et al.(2001) and three additional flares for which data have not previ-ously been reported. The time and geometric information for theanalyzed flares are provided in Table 4.

The procedure used to determine surface abundance ratios ofGros from NEAR XRS data acquired during solar flares followedclosely that used by Nittler et al. (2001). The steps to this pro-

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N&4. Assembly of the K AR X-ray asteroid-pointing sensors (Fig, 7 from Goldstenet al. (19 1977 , reprinted by kmd perrnission of Springer Scwace and Business Nedla).To enable analysis of the low-energy X--ray tines, one detector was filtered with athin layer of AI and another was similarly equipped with a dig filter, The centerdetector remained unfiltered. The recrangular faces of the gas counter tube, ("X-raydetectors" were each 2 x 3.5 indies, as with the gas solar monitor tube "'Hg. 3.The same model tubes were used it both cases.

cess were: determination of the appropriate solar X-ray spectrumfrom solar monitor data, extraction of the photon flux in each ofthe major fluorescent lines from the asteroid-pointing spectra, gen-eration of calibration curves relating photon ratios to abundanceratios for a specific incident solar spectrum and viewing geometry,and conversion of photon flux ratios to abundance ratios.

Solar models for each flare were produced using ail elevengraded fitter models, selected as described above, For each fil-ter model, each 5€7-s integration of the gas solar monitor was fitwith a two-temperature model of the solar spectrum, resulting ina model solar spectrum with sufficient energy resolution to dis-tinguish individual solar emission lines. The 50-s two-compolrentmodel spectra were then co-added to produce a time-integratedsolar flare spectrum representing the same time interval as the co-added asteroid spectra (Section 5.2"

The fitting process used to extract asteroid fluorescence countsfrom the asteroid-pointing detector spectra is identical to [hat de-scribed in Nittier et al. (2001 j, with the exception that the on-board energy calibration data has now been analyzed and appliedto constrain the properties of the proportional counters, as de-scribed below.

5.1. Cahbration of the asteroid-painting detectors with the on-board' s Fe sources

Nirder et al. ;2(301) allowed the gains and zeroes of thethree asteroid-pointing detectors to float as free parameters intheir previous analysis of data from five NEAR solar flares. How-ever, the NEAR X125 included three radioactive ' 15 Fe calibrationsources ("Calibration Pod Assembly" in Fig. 4) to monitor the gain(eviMillinel), zero (energy of channel zero;)", and energy resolu-tion of the asteroid-pointing detectors. Several times throughout

Cal€bration RodAssersbty

Ere:r,etital connpsrrion of 433 Eras 135

Tattle 5XR5 asteroid-pointing detector calibration data fitting results. Delo'ctor resolaticm isa function of energy: RI.I Hf41(E) — r1VH vi parameter x F`2

Table GUn :Meted detector characteristics derived from Mare data.

the mission (Table 5) the calibration sources were rotated into thefields of view of their respective detectors for the acquisition ofcalibration data. Making use of the in-flight calibration data re-duces the number of free parameters, increasing confidence in thefitting results. This is especially important for the two filtered de-tectors, in which count rates from the asteroid were always low incomparison with the cosmic-ray-induced background,

The ss Fe sources emitted X-rays in the Mn Ku (88%) and K.(12%) lines at 5.598 and 6.490 keV, respectively. The detectors alsoregistered escape peaks for the two lines at 2.941 and 3.533 keV.For every available set of calibration data, the detectors' responseto the pair of mcdnoenergetic lines received from the 5s Fe sourcewas modeled and Fit to the calibration data. Gaussian shapes wereassumed for all fOUF peaks. The scale of the cosmic-ray back-ground, whose shape was established by calibration-source- andasteroid-free data taken within 24 h of the calibration data, wasalso allowed to float, but usually remained within 1% ,and alwayswithin 2%, for the two filtered detectors) of simple scaling by i1.-

tegration time. Calibration source fitting results are summarized inTable 5.

The Ss Fe source for the unfiltered detector was much wreakerthan the sources for the other two detectors, resulting in poorstatistics on its calibration data and consequently relatively largeerror bars on its gain, zero, and FWHM parameters in Table 5.However, die unfiltered detector had the best statistics of the threein the asteroid fluorescence during the solar flares themselves,and more precise detector characteristics could be derived fromthe flare spectra themselves (Table 6). in contrast, the calibration

136 LE film, L.R. Mrtier/ luirus 200 (2009j 129-146

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Pig. S. XR5 data from the three asteroid-pointing detectors. Left to right: Raw data from the solar flare of 27-Dec-20001 backgraund-subtracted data froth 27-Dec-2000;background-subtracted data from the flare of I7-Jun-2000; background-subtracted data front the bare of 25-Dec-2000, The step at channel 75 in tttc rate data is the ;ise-timediscriininatat limit. solid lines represent the best Gaussian firs to individual XRF peaks; dashed traces represem the Sant of all components. From left to right, the peak, areMg. A., Si, S, Ca, and Fe IN, and Kr,,.

source data gave better statistics than the Flare data for the twofiltered detectors.

The energy resolution was the most variable of the detectorcharacteristics, becoming degraded whenever the instrument wasshut off, for example when the spacecraft was placed in safemode, and taking several weeks to approach its best value (FWHNIparameter --m 0.340). This can be observed in Table 5, as the resolu-tions of the A] and Mg detectors improve slowly front April to lateMay.

52. Extracting photon counts from the asteroid-pointing detector data

As with the solar monitor data, the spectra from the asteroid-pointing detectors were recorded in 50-s integrations, For each so-lar flare, all the spectral integrations from that flare were co-addedto generate a single summed flare spectrum for each asteroid-pointing detector. Cosmic-ray induced background, present in allof the gas proportional counters, was then subtracted from eachco-added spectrum prior to fitting. Since this background was con-stant on time scales of a few hours, background spectra were de-rived for each detector from data taken within 24 It of the flarewhite the asteroid was not in the XRS field of view. These "dark"spectra were added together and scaled to the live time of the rel-evant flare spectra. Examples of co-added asteroid spectra beforeand after background subtraction are plotted for the 27 December2000 flare in Fig. 5.

Following background removal, the spectra from the three de-tectors were fit simultaneously, allowing the Mg- and Al-filters toperform their design function: to compensate For the low resolu-tion of the proportional counters at the Ko. energies of the lightelements Mg, Ai, and Si, The free parameters in the spectral fit-ting were the intensities of the fluorescence lines from each majorelement (Mg, Al, Si, 5, Ca, and Fe) entering the top of the instru-ment, as well as the gains, zeroes and MIHM parameters of thedetectors. For the unfiltered detector, the detector parameters wereallowed to vary freely: while for the Mg- and AI-filtered detec-

tors, they were allowed to float within the limits derived fromthe calibration-source data (Table 5) closest to the date of theflare.

The fitting process for three solar flares is illustrated in Fig. 1In each plot, the grey lines with error bars represent the data Fromeach asteroid-pointing detector. Error bars are Ia, reflecting count-ing statistics, The leftmost plot shov ers the raw asteroid-pointingdata from the flare of 27 December 2000, whereas the three re-maining plots show the data after the cosmic-ray background hasbeen subtracted. The fit to each of the individual fluorescence linesis represented by a solid Gaussian trace. From lowest- to highest-energy. these are the K lines of Mg, Al, Si, S, Ca, and Fe and theK line of Fe. The effect of the balanced-filter system can easilybe observed in these plots: the Si line, which is the most promi-nent feature in the unfiltered data (top plots), has been suppressedin the data from the two filtered detectors. The superimposeddashed trace is the overall fit to the data. Similar plots represent-ing the five previously analyzed flares were printed in Nittier et al.(2001).

53. Conversion of photon ratios to asteroid elemental ratios

The amount of fluorescence in any line that escapes the asteroiddepends not only on the abundance of the fluorescing element, butalso can the abundance of all other elements in the asteroid surfacethat can absorb incident solar radiation on the way in or fluores-cent radiation on the way out, Because of this, it is necessary tomake some assumptions about the entire composition of the aster-oid in order to interpret the XRS data, including, elements whosefluorescence could not be detected. We based our determination ofthe relationships between fluorescence ratios and elemental ratioson data from meteorites.

Once the incident solar spectrum was modeled. theoreticalX-ray spectra (including both fluorescence and coherent scatteringcomponents) that would be induced by the model solar spectrumat the applicable incidence, emission, and phase angles were cal-

E`tnr. eni i ca r pErsi on oj433 Eros

137

Table 7kleienrae 5arples used to convert photon ratios to elemenr ratios,

I References: (1) Nagahara and 02awa (49W0 (71" vdarters and PFInz 1'1f79),Mi arosewich A990 (4) Yanai and kojinna 11995 (book'(, (a) D'dakonova andhhanroncva ;1967; ;Russian;:. {6) Ruseck'1577). Al] anal yses are whole-rock exceprfor the El Taco silicate inclusiGtt in a IA iron.a Used by Nittler et al. (2001) as the basis for an "LL3 without sulfur" conapo-

sttio€i. The sulfur abundance %is set to zero and all other etenents nomiaFS ed to100`5.

eulated for a sample of meteorite compositions of widely differentclasses (Table 7), This is the same method described and usedby Nittler et al. (2001). The Model X-ray spectra for the differ-ent meteorite compositions were then fit using exactly the samemethod as had been applied to the ac€ual XRS spectra to derive

model fluorescence ratios. Calibration curves were calculated byplotting actual meteorite elemental abundance ratios against mod-eled meteorite fluorescence ratios and fitting quadratic curves tothese points. Each quadratic fit provided the formula for convert-ing fluorescent-photon ratios to elemental ratios For a particularincident scalar spectrum and geometry, Fig. 6 illustrates the cali-bration curves for the solar spectrum and geometry of the majorflare from 17 June 2000.

As in Nittler et al. (2001), the coherent scattering backgroundhas been accounted for by inclusion in these calculated meteoritefluorescence ratios rather than by any attempt to subtract it fromthe fluorescent photon signal. The induced Al fluorescence fromthe Al filter in front of the Al-filtered detector has been treatedsimilarly. Because the theoretical spectra are treated exactly thesable way as the real data. this does not introduce significanterrors. However, because the derived fluorescence counts includescattered photons and filter- fluorescence, the photon ratios forAl;'Si and S/Si in the calibration curves (Fig. 6) are nonzero evenat zero concentrations of Al and S.

The angles used in these calculations were averages over thoseprovided in the XRS data products for the individual spectral in-tegrations during a flare. The phase angles were exact, but theincidence and emission angles were averages over all the "plates„of the shape model derived from the NEAR laser rangefinder data(tuber et al., 2000) that were illuminated and within the XRSfleid of view at the time. These derived angles varied much moreduring flares than did the phase angles (Table 4) and thus, in prin-ciple, calibration curves should be determined for each integration.However, the statistics did not permit separate fitting of integra-tions over shall time portions within a single flare. Modeling ofexpected X-ray spectra for an ordinary chondrite composition illu-

urinated by a typical solar flare at a fixed phase angle, but withvarying incidence and emission angles, indicated that the uncer-tainty introduced by using averaged incidence and emission anglesis significantly smaller than that caused by other sources of er-ror in our analysis, for example the solar modeling, (Moreover, theincidence and emission angles that .matter physically for X-ray in-teractions are on a much smaller scale than any possible shapemodel of the asteroid, so this issue is a fundamental limitation inthe analysis of NEAR XRS data.

In their XRS analysis, Mttle; et al. (2001) applied an additionalcorrection to the data to take into account the fact that in mete-orites (and hence probably stony asteroids), the elements are notspread uniformly throughout the asteroidal material, but rathertetad to be segregated into different minerals on spatial scalesthat are important to X-ray absorption and scattering. Nittler et al.!2001 derived "mineral mixing corrections" based on comparisonsof theoretical spectra for mixtures of the dominant individual min-erals found in anhydrous metearites (olivine, pyroxene, feldspar,FL-Ni metal and iron sulfide) with those for homogeneous mix-tures of the same bulk compositions. The average correction factors;from Table 2 in Nittler et al., 2001) are reprinted here in Table 9. Ifapplied, the largest effects are to increase the S/Si and FelSi ratiosby 30-40% and decrease AllSi by 25%. We note that the magnitudeof the Fe/Si correction factor depends strongly on the amount ofmetallic Fe present in the material.

Recently, Foley et al. 1 20100; have questioned the necessity ofthe mineral-mixing correction for NEAR XRS data on the groundsthat impact processing is likely to have reduced Eros` regolith toa well-mixed homogeneous powder. Moreover, calibration data forthe Mars Pathfinder alpha-proton X-ray spectrometer APXS! forpowdered samples !with grain sizes of tens of microns) of Irie-teorites with a large variation in metal abundances gave correctcompositions without requiring such a correction ;Foley, 2002).Additional experiments are needed to clarify whether mineral-mixing corrections are required and we therefore report bothcorrected and uncorrected versions of the asteroid composition(Table 9).

6. Fitting results for specific solar flares

The fitting results for the eight solar flares are summarized inTable 8 and discussed below. Results for five of these !4-May-2000,15 June, 10 July, 27 December, and 2 January-2001; are revisions ofthose previously presented by Nittler et al. ;2001,. For these, thenew photon ratios remain generally consistent with published re-sults (Nittler et al., 2001, Table 3j. Three additional flares for whichdata have not previously been reported (. 20 May, 17 June, 28 De-cember) are also presented here.

Note that for many of the flare data, derived Al photon countsand AltSi photon ratios were very sensitive to any limits placed onthe zero point of the Al-filtered detector. For example, for the 4-Mav-2000 flare, calibration-source data from April 26 and May 10(Table 5) suggest that the Al detector zero should be above —0.04.When so limited, the AljSi photon ratio is 0.092 LL 0.032. How-ever, if the Al-filtered detector zero is allowed to float withouta limit, its value drops to —0.09 and the A115i photon ratio to0.066±0.024. The discrepancy between these solutions has beentreated as a systematic uncertainty and is included in the total un-certainty quoted for this and other flares in Table 8. The effects onElie other element ratios were minor compared to the uncertaintiesfrom counting statistics.

6L 4 May 20f1fl

The May 4, 2000 solar flare induced more asteroid fluorescencefrom the high-Z elements (Fe. Ca, and S) than any other solar flare

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Fig, S, Theoretical calibration cvrees based on a range of buu k nler^ re Composition' s 1 diatnond symbols; lvittler et at.. 20€14) and the solar 5p ectrurn and georneiry app; opriatefor the solar flare observed on 17 June 2000. Curves are quadratic firs to the data and ailow €he derivation ofelemn ,ntal abundance ratios from X-ray €ine flux rahcs observedfrom 433 Eros.

measured by NFAR. The measurements of the Fe/Si, Ca /Si, and S respect to the Start ( J,rea€, 35.53 ). the derivation of the solar spec-Ruorescent photon ratios, therefore, are subject to lever staristi- truan for this flare (and therefore the conversion of the photoncal uncertainties than for any other flare. However, because of the ratios from this flare to elemental abundance ratios; is also thehigh off-normal angle ( „ panel angle" 'T of the gas solar monitor with most sensitive to the graded filter dimensions, i

clernentel coil€pusition ef933 Eros 139

Table 8Rmton counts and ratios for eight solar flares,

Table 9compos€tiara resuln: summary {average of data from eight solar fla.es}.

The solar monitor data for this flare and a representative model:'here based on model 5, fable 3) are plotted as Fig. 7a. Because thelow-energy solar flux is almost entirely cut off from the pinhole inthe thicker-Delrin rnodei, the emission measure of the low-T conh-ponent must be several times higher in order to account for themeasured low-T flux than in the thin-Delrin model, Consequently,the thin-£lelrin filter models imply a much harder solar X-ray spec-trum than the thick-Delrin versions. This bas a profound effect onthe determination of the FeJSi and Ca/Si ratios from the asteroid.If the thin-Deldri filter models are correct, the solar spectrum dur-ing this flare was quite hard, making it possible for a relatively lowabundance of asteroidal iron to produce all the iron signal seen inthe asteroid-pointing detectors, In this case, the Fe'ISi abundanceimplied by the asteroid fluorescence would have been relativelylow (Fe/Si =2.D7:1—.O.11 fur Model 2; 'fable 11). On the other hand,if the thick-Delrin filter model is correct, the solar spectrum of thisflare was much softer, requiring a higher abundance of iron in theasteroid in order for a relatively low number of hard solar X-raysto produce the iron signal detected by the NEAR XRS. Therefore, inthis case the FejSi abundance ratio would have had to have beenmuch higher; Fe/Si = 4.83 = 027 for solar model 11. Ultimately,this means that the Fe/Si (and Ca/Si) results from this flare sufferfrom a large systematic uncertainty stemming entirely from uncer-tainty in the properties of the solar monitor graded filter, in spiteof the good raw photon statistics from Fe and Ca.

62 20 Mcty 2000

The high-temperature component of the flare from May 20,2000 ,Fig. 7b) was relatively cool and weak compared with that ofthe other studied flares. This "softer" X-ray spectrum induced fewiron counts from the asteroid, so the statistical uncertainty in thederived FeJSi value is high. A favorable spacecraft geometry withrespect to the asteroid, however, enabled significant Mg, Al, and Si

fluorescence to be measured by the asteroid-pointing detectors_ Aswith the May 4, 2000 flare, a systematic uncertainty ill the A1jSiphoton ratio due to uncertainty in the At-filtered detector zero isincluded in ",able 8.

6.3. 15Juneand 17June2000

Solar monitor data and corresponding model spectra from flareson June 15 and 17 of 2000 are shown in Figs. 7c and 7d, respec-tively. These two flares were very similar in both inferred solartemperature and geometry. The last calibration-source data be-tween June and August 2000 were taken on 8 June 2000, so thecalibration-based detector characteristics for these flares and thesubsequent one on July 10 are increasingly uncertain. Based onthe unfiltered detector solutions for these flares ('Fable 6) it wouldappear that no resolution-degrading event affected the asteroid-pointing detectors daring this tinhe period. Upper limits of 0,331and 0.396 were assigned to the FWHM 'resolution} parameters ofthe Mg- and AI-filtered detectors based on the 6-8 .tune calibrationdata_

As with the previous flares, the systematic uncertainty in theAI/Si photon ratio due to AI-filtered zero calibration has been in-cluded in Table 8. For the June 15 flare, the high (limited Al-detector zero) and low (floating zero point) values for Altsi are0.095 ± 0.058 and 0.054 ± 0,064, respectively. For the June 17flare, the high- and low-Allsi solutions are 0.046 4. 0.060 and0.1122 10,065, respectively.

6.4. 10 july3 2000

Solar monitor data and a model spectrum from the solar flareOf July 10, 2000 are plotted as Fig. 7e. Although the solar panofangle for this flare was the lowest (closest to normal incidence) ofthose among the eight major solar flares, the X values of the solar

----------

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140

L.F. Lim. L.R. Nirr lep ,[faruS200 (2nCP9) 129- f4C

Eie rner; tai composition rf 433 Eros 141

Table toComposition resin°s: Effect of solar models on eiememai ratios fur 433 fires. Each eon.position is the average of results f om eight solar flares. No mineral-mixing correctionhas been applied.

Table tlCOmPrsi*ion re,ufts^ Individual solar flares. The model numbers) of the graded hirer model 'Table 3) is given n parentheses following the canes ndm.- ratio.

spectral fitting remain relatively high regardless of the graded filtercharacteristics. The X 2 improves with degraded gas solar Monitorresolution, suggesting that this detector's resolution had been de-graded somewhat from its near-optimal values during the previoussolar flares. Fortunately, the effect of degraded solar monitor reso-lution on the geochemical results is much less than the uncertaintydue to the statistical errors in the photon counts. Since no "Fe cal-ibration data had been taken for over a :Month at the time of thisflare, no limits on the zero points of the asteroid-pointing detec-tors were applied. The best-fit flare-derived resolution parametersof the asteroid-pointing detectors were 0.360, 0.373, and 0.439 forthe unfiltered, Mg-.altered, and Al-filtered detectors respectively.Applying an upper limit of 0,390 to the Al-filtered detector resolu-tion ;on the assumption that it usually did not stray too far from

the resolution of the unfiltered detector) did not materially changethe photon ratios.

6.5. 27 0ecemher Z€ 00

This flare was unusual in that its solar monitor data could notbe fit satisfactorily with any of the usual sets of solar elementalabundances (Meyer, 1985; Feldman et al., 1992, or the "Coronal 1"and "Corona] 2" sets that produced good matches to numerousother 'DEAR flares: see Table 1). The 6,5 keV iron emission structurewas less prominent with respect to the bremsstrahlung continuumthan was permitted by these models_ Additional sets of abundanceswere tested: some with overall metallicity decreased further belowthe estimate of Meyer (7985;, so that the relationships between el-

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Fig. S. X125-derived elemental ratiE,s r"or 433 Eros in the context of bulk composi-tions of Various n3etecrfte classes. Elllpses represent 3a uncer€ainnes in averageCompositions as calculated using individual solar rnoMs {7able._ 3 and 30}. Nom€rteral-nifxfng correction ',V. Foley er al., 2005: Nl itt er or al., 2001; has been ap-plied. Gncertainnes in the firm resWts ,large crosshairs; combine uncenamties inhe sc

'at model wirh those due to phomn statistics Irons the asteroid's flu©resc nce.

Thee data are tabulated in Iable 9, -rapt N1gjSi vs F°e(Si. Middle: A,jsi is 0`5i. Bu -tom: %hg"Si us Sisi,

represented by the 3a error ellipses in Fib. 8. No correction formineral-mixing effects has been applied to these values.

Results for each solar flare are individually represented in Ta-ble 11, for each elemental ratia derived from each flare, the maxi-mum and minimum values from among the solar models are tab-ulated. The average value for that flare from all the sciar modelsfollows. The systematic errors due to solar uncertainties are es-timated from the maximum and minimum values derived from

142

LE Lim. LA Nh, tier,, 1corus260(2009) !29-14b

ements other than H and He were unchanged; and some with theiron abundance reduced alone. The Crest fits were produced withonly the Fe abundance reduced, and the (rest-performing abun-

dance model out of the reduced-iron set (Fe 1H == 1.95 x 10- 5 , asopposed to the Meyer (1985) value Fe/H = SijH = 3.9 x 10 -5 ) wasadopted. This model is "Corona) 3" in Table 1. We note that flare-to-flare variability of at least this magnitude in both the Fe/Ca ratioand the FetH ratio has previously been observed (Antonucci and

l larthr, 1995; Fludra and Schmelz, 1999). The actual and modelledsolar monitor data are plotted in Fig. 7f.

The solar monitor gain during this and all subsequent flareswas €1.041.5 keVichannel, an increase from the 0.040 keVlchannelthat had consistently been observed during the summer flares.This may have been caused by space charge effects or other con-

sequences of detector aging. The asteroid-pointing detectors wereunaffected, probably because they had counted far fewer X-raysduring the course of the mission.

6.6. 28 December 2000

The December 28 flare was nor analyzed by Nittler et al. (2001),largely because the solar spectrum could not be modelled sat-isfactorily at that time, 11w CHIANTI 52 code yields reasonablemodels with both the "Corona] 1" and "Corona] 2" corona] abun-clance models.

However, the modelling (Fig. 7g) remains less successful thanwith most of the other flares, largely because of a very large ex-cess of counts at about 3.5 keV. Because of the attenuation ofthe low-energy photons by the graded filter, the gas solar moni-tor is vastly more sensitive at 3.5 keV than it is at 2 keV. Thus,a large number of measured counts at 3.5 keV actually representsfar fewer incident solar photons than a corresponding number at2 keV, and affects the resulting asteroid composition relatively lit-he. For this reason, while fitting this flare, the region between 2.72and 3.44 keV was eliminated from the X2 calculation altogether, sothat the fits in the 2 keV and 6.5 keV regions that are more impor-tant to X-ray production in the asteroid would be undistorted. Theorigin of the excess signal at 3.5 keV remains unknown, though wenote it cannot easily be explained by an increase in the solar K orAr abundances in the flaring plasma, as the required enrichmentfactors (>60x for lf, >5x for Ar) are implausible.

The photon ratios in the asteroid-pointing detectors for thislace, unlike those for the May 4 flare, are insensitive to restric-

tions on the asteroid-pointing detector parameters.

6.7. 2 fanualy 2007

The solar spectra from the 2 January 2001 flare were easilyfitted with the coronal-abundance solar spectral models, lackingeither the 3 keV excess of the December 28 flare or the deficit ofiron emission in the December 27 flare.

The solar monitor gain during this flare was 0.0415 keVlchannel.The FWHivl parameter of the gas solar monitor was increased bySte. (Fitting with the degraded resolution reduced the X2 of thesolar monitor fitting, but the geochemical results were unchangedwhen the solar fats were done with the standard resolution (FWHN4

parameter= 0.340).) 'The integrated data from and models of gassolar monitor output are platted as Fig. 7h.

7. Results and discussion

Table 10 illustrates the effect of the uncertainties in the solarX-ray spectra on the derived composition of 433 Eros. For eachsolar model, Table 10 lists the weighted average of the compositionratios derived from all eight solar flares. "These element ratios are

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Fig. 9. Flare-m- are variatm in XRS-derived elemental ratios for 433 Eros in 'lie context of bulk meteorite composition s_. Error bars represent 1F uncertainties in each ofthe eight single-flare curlpositions, imiuding u uerEa;nries due to uncerrainties in the solar spectra. These data a re aso Tabulated in Table 11.

the various solar models; these have been combined in a root-surnmed-square sense with the independent random errors due tophoton statistics. (The standard deviation would not be an accu-rate reflection of the uncertainties due to the solar uncertaintiesbecause the set of models included is not a random sample of allplausible solar models.;.

Table 9 presents the overall composition results of this work,averaged over all eight solar flares and including errors due touncertainties in the solar flare spectra. The first column ,"un-corrected") lists the compositions without any correction appliedfor mineral-mixing effects. These data are also represented as thelarge crosshairs in Fig. 8. The final column has had the minera.l-mixing corrections applied as in ?littler et al. 12007; and maytherefore be directly compared with the results fro g=, that pa-per, For comparison, the average compositions of the H, L, and LLchondrites from the compilation of Nittler et al. (2004) are alsoshown.

Plotted in Fig. 9 are the Mg/Si, AI!Si, and Fe/4i ratios calculatedfroln the eight individual solar flares, illustrating the flare-to-flarevariability of the data. Eaclh set of crosshairs represents the la un-certainty in composition for a single flare, including both errorsdue to counting statistics and those propagated from the uncer-tainties in the solar spectra. Although the range of element ratiosdetermined from the different flares at first glance might appear toindicate compositional heterogeneity for Eros, in fact no one flare

is more than 3(r away from each other or the ordinary chondritefield in Nlg,si or Al/Si. The flare-to-flare variability of FejSi is largertaut, as discussed below, this ratio is subject to additional system-atic errors not related to solar modeling. Thus, the XRS data alonecan neither establish nor eliminate the possibility of spatial varia-[ion on 433 Eros.

However, the NEAR Msl/Nis investigation (Veverka et al., 2000;Boll et A,, 2002) has provided strong evidence for compositionalholnogeneity over all of Eros, and the chondritic CrfFe ratio thathas been derived from the XRS data r"Foley et al., 2006) also sup-ports the hypothesis that Eros is an undifferentiated object witha chemical affinity to the ordinary chondrites. The averaged com-position in Fig. 8, therefore, probably represents the light-elementcomposition of the whole of Eros.

The composition ratios derived from individual flares havechanged somewhat since the XRS analysis of littler et il. (2001),but the overall averages are mostly similar to the "Best Eros"values quoted by Nittler et al. Of particular importance, the sul-fur(silicon ratio remains substantially below those of chondriticmeteorites. Trombka et al. (2000) and Nittler et al. (2001) sumBested that the sulfur deficiency could be caused by either space

weathering processes (e.g„ sputtering, impact vaporization) or par-tial differentiation with Toss of a S-rich melt. Foley et al_ (2006)determined a chondritic CrfFe ratio for Eros based on XRS datafrom two solar flares and argued on the basis of this that space

144

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v ariotior 0 , °,Si Composi tion Ra -lio wit Anni0

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Fig. 10. Variation of Fe(si and ca,=si .witt y observing geomeEry. sec i is the averagesecant of the incidence (afF normal) angle of the diuninabon of the parrian of433 Eros within the field of view of the E VAR X(L during each saiar flare, sec eis the corresponding ernission a.ngie. Tice data point with the highest FeiSi ratio a^highest (sec I set e; correspnnds to the sotar flare of 28 Uece ber 7f)na: 3towevtcrthe CgSi derived from the same flare is chondritic.

weathering must be responsible for the sulfur deficiency since par-tial melting should also deplete chromium, Optical space weath-ering (Dieters et al., 2000: Hapke, 2001: Sasaki et aL, 2001) iscaused by nanophase reduced iron production and deposition on

grain surfaces. The MSI/NIS measurements zClark et al., 20011 es-tablished that the spectrum of Eros has been altered by spaceweathering. The same processes responsible for nanophase ironproduction, such as sputtering and impact vaporization, likely alsovaporize sulfur and cause sulfur depletion in the surface lay-ers (e.g., Nittler et al., 2001: Killen, 2003; Kracher and Sears,2005).

The new average Fe ratio is slightly higher than that ofNittler et al. 2001), but

!Simost H chondrites fall within its la error

ellipse. As discussed previously (e.g., McCoy et al., 2001 1, how-ever, the NEAR gamma-ray spectrometer (GRS)-derived Fe jsi ratioof 0.8 t 0.3 (Evans et al., 2001) is considerably louver than theXRS derived Fe1Si and more consistent with the low-iron ordinarychondrite groups L and LL. Since the GRS samples to depths oftens of centimeters, whereas the X-rays originate from the top tensto hundreds of microns, this difference suggests that the elevatedFe/Si is a surface phenomenon. However, there are several addi-tional difficulties beyond solar modeling in determining Eras' Fe/Siratio from XRS data, as discussed below.

Okada (2002, 2004) has suggested that the large phase angle ofthe NEAR XRS observations should lead to erroneously high Fe/Siratios due to shadowing effects. For example, in Iaboratory exper-

iments, Okada (2002, 2004) demonstrated that for ground basaltsamples sieved to various particle sizes, the ratios of Ca1Fe andTi/Fe K lines decrease significantly as the phase angle of obser-vation increases. These authors also demonstrated that this effectbecomes much more important as the size of the sieved particlesincreases. Okada 1 2002) concluded that the magnitude of this an-gular effect increases with the energy difference between thelines that are being compared and the effect on Si/Fe Si K, =1.74 keV; should thus be even more pronounced than the observedeffects on Ca/Fe andTi/Fe.

Fig. 10 illustrates an attempt to explore possible geometric ef-fects on the Fe'Si and Ca/Si results, not through phase angle (sinceall the NEAR data had approximately the same phase angle) butby plotting composition results from individual solar flares againsta "path length parameter" which is a function of incidence andemission angle. This parameter, which is the surn of the secant ofthe incidence angle and the secant of the emission angle, repre-sents the path traveled by incoming and outgoing X-rays throughthe overburden of soil above the fluorescing atom. One would ex-pect matrix effects to increase as this parameter increases. Thefigure shows that the two highest single-flare FelSi values do comefrom the pares with the highest values of the path length pa-rameter. However, the Ca/Si result from the highest path-lengthflare (28 December) is apparently not inflated by this geometriceffect.

Another effect that may be important in interpreting the NEARdata is size sorting in the regolith due either to the "Brazil nut" ef-fect (Rosato et al., 19871 or to the reverse Brazil not effect (Hong etal., 2001). If the mineral grains in which Fe is carried have differ-ent physical properties than the low-Fe regolith grains (e,g„ metalversus silicate), size sorting in the regolith could after the Fe/Si atthe surface.

Thus, given the dependence of the measured Fe, f5i ratio on un-certainties i n the solar spectrum, on phase angle effects and on thepossibility of surface or regolith processes, the flare-to-flare vari-ability in FejSi shown in Fig. 9 is much more likely a reflection ofsystematic errors rather than of true elemental heterogeneity onthe asteroid. As discussed earlier, the observed spatial homogene-ity in surface colors and mineralogy ( based on MSI,INIS data , andthe light-element XRS results all point to Eros being an undiffer-entiated asteroid.

Overall, the two-temperature model was successful in model-ing the 1-10 keV NEAR solar X-ray spectra. This approach may beuseful in the analysis of data from the Hayabusa XRS (Okada et al.,2006 11, particularly fit determination of the S/Si ratio of 25143Itokawa ( or an upper limit thereof) since Hayabusa 's onboard stan-dard sample plate lacked sulfur (Okada et al., 2006). This will en-able comparison of ltokawa's SjSi value with Eros' highly depletedSjSi. This approach may also be helpful in analysis of Mercury datafrom the MESSENGER XR5 (X-ray spectrometer; Gold et al., 2001)which is an improved version of the NEAR XRS design. Althoughthe energy resolution of the 5i-PIN solar monitor carried by theMESSENGER XRS is significantly improved from that of the NEARgas counter, it is still insufficient to resolve the closely spaced solaremission lines in the region of the K-edges of the light elementsMg, AL Si, and 5. Thus, it will be necessary to use CHIANTI or asimilar meffind of modeling the solar X-ray spectrum in conjunc-tion with the solar monitor data in order to obtain quantitativecompositional results from the MESSENGER XRS.

Acknowledgments

The authors gratefully acknowledge the efforts of the NEARand NEAR XRS team members, especially Jack '17ornbka, RichardStarr. and Steve Squyres for their support and for many helpfuldiscussions, and John Goldsten for valuable information about the

Elemental ronnpositmi cf 433 Ems

145

construction of the gas solar monitor. kA/e also express our appre-ciation to Ken Phillips for advice on solar physics and the CHIANTIcode. Finally, we wish to thank K. joy and T. € kada for their helpfulreview.

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