JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 94, NO. A1, PAGES 185-196, JANUARY 1, 1989

Pickup Ions in the Unshocked Solar Wind at Comet Halley

K. K•cs••, • T. E. C•V•NS, •' 2. 5 V. V. Aro•'•, a G. Egoos, • E.G. F. xos•o, s Lu GAN, 2 T. I. Gosmosx, •' 2 K. I. GRINGAUZ, a E. KEPPLER, 6 I. N. KLXM•NKO, • R. MARSDEN, ? A. F. NAGY, •' 2 A. P. REM•ZOV, a A. K. RaCHTF•, 6 W. RmDLE•, s

8 I I 1 K. SCHW•OENSCm3H, A.J. SOMOG'n, K. Sz•oO, M. TATRALLYAY,

A. VAROA, • M. I. VE•ao•, '• and K.-P. W•,az•L ?

The Tiinde-M experiment on board the VEGA I spacecraft detected energetic cometary ions as far as 10 million kilometers from comet Halley. The measured ion fluxes increased with decreasing radial distance from the nucleus, in agreement with theoretical expectations. Sharp enhancements spaced at approximately 4-hour intervals were superimposed on the general increase of the ion fluxes on the inbound leg of VEGA 1. Periodic neutral structures originating from gas production by active areas on the nucleus are suggested to explain the recurrent intensity peaks. These neutral density enhancements would then produce the ion density enhancements seen by Tt•nde-M as the spacecraft traversed the structures. This explanation requires a considerably larger neutral expansion velocity (,-6 kin/s) than was actually measured near the nucleus in order to allow the rotation period of the nucleus to generate the observed period of the enhancements. No obvious correlations of the ion fluxes with the limiting energy for pickup were found. However, at a distance of about 10' km from the comet, a weak anticorrelation was found between the ion flux and the angle between the inte•lanetary magnetic field and solar wind direction. Cometary ion distribution functions in the solar wind reference frame were derived from measured counting rates. These distributions are approximately Maxwellfan for energies between about 100 keV and 150 keV. The derived temperatures are between about 5 and 8 keV for most cometocentric distances, although in a region between 10 and 8 million km from the nucleus the ion spectra were harder, with temperatures ranging from 10 to 20 keV.

1. INTRODUCTION

Cometary ions, such as O +, OH +, and H20+, are created from cometary neutrals by photoionization, by charge exchange with solar wind particles, and by electron impact ionization [cf. Mendis et al., 1985; Cravens et al., 1987]. The freshly ionized particles, which are created almost at rest in the cometary frame of reference, are initially accelerated by the motional electric field of the solar wind and are partially "picked up" by the solar wind. The ions initially follow cycloidal trajectories in the E x B direction [cf. Ip and Axford, 1982; Galeev et al., 1985; Cravens, 1986]. The cometary ion distribution function is therefore initially a ring distribution in velocity space with a drift velocity parallel to the magnetic field with respect to the solar wind. This ring/beam distribution is highly unstable and generates Alfv•n waves via an ion cyclotron instability. These waves can pitch angle scatter the ions, and thereby make the distribution nearly isotropic in the solar wind reference frame on a time scale of the order of several gyroperiods [cf. Sagdeer et al., 1986a; Gary et al., 1986]. This isotropization of the ion distribution completes the pickup

•Central Research Institute for Physics, Budapest, Hungary. 2Space Physics Research Laboratory, University of Michigan, Ann Arbor.

3Now at Department of Physics and Astronomy, University of Kansas, Lawrence. 4Space Research Institute, Moscow. SIzmiran, Akademgorodok, USSR. 6Max-Planck-Institute fiir Aeronomie, Katlenburg-Lindau, Federal Republic of Germany. ?Space Science Depamnenk European Space Agency, European Space Research and Technology Center, Noordwijk, The Netherlands. SSpace Research Institute, Crraz, Austria.

Copyright 1989 by the American Geophysical Union.

Paper number 88JA03171. 0148-0227/89/8 8J A-03171 $05.00

process in that the ions are now drifting with the solar wind. Magnetic fluctuations can also result in stochastic acceleration of the ions via the second-order Fermi process lip and Axford, 1986; Gribov et al., 1986; Gornbosi, 1988].

The traversal of the cometary bow shock by ions created upstream is expected to lead to further acceleration and energization of these ions by some combination of gradient B drift, Fermi acceleration, and adiabatic compression [cf. Axford, !981]. Further, acceleration of cometary ions up to several hundreds of keV should also be expected downstream of the bow shock, due to second-order Fermi processes, compression, and perhaps magnetic reconnection of field lines close to the nucleus. Due to the enhanced magnetic field turbulence observed upstream and downstream of the bow shock, second-order Fermi acceleration is probably the most important process among the various mechanisms listed above [Ip and Axford, 1986].

Energetic particle measurements at comet Halley have been made by instruments on board the VEGA 1 spacecraft [$ornogyi et al., 1986a; Kecskern•ty et al., 1986] as well as on the Giotto probe [McKenna-Lawlor et al., 1986a; Daly et al., 1986]. Cometary pick-up ions were observed as far as 10 million km from comet Halley, in the energy range of about 96 to 153 keV (in the spacecraft frame of reference of VEGA 1) and 78 to 270 keV (Giotto, [McKenna-Lawlor et al., 1986b]), extending well above the energies expected on the basis of the original pickup mechanism. The maximum energy of a pickup ion in the cometary frame of reference, and before pitch angle scattering takes place due to magnetic fluctuations, is given by Ema x --2 rnu 2 sin2OvB, where m is the ion mass, u is the solar wind speed, and Ova is the angle between the interplanetary magnetic field and the solar wind. Ema x is about 80 key for u -- 500 km/s, OrB = 90 ø, and for O + ions. This energy is roughly the minimum energy at which heavy ions can be detected by the various energetic ion instruments. The initial pickup energy in the solar wind reference frame is just 1/2 rnu 2, which is typically about 20

185

186 KECSKEI• ET AL: PICKUP IONS AT COIVIET HALLEY

keV for O + ions. Energetic ion observations were made earlier at comet Giacobini-Zinner (G-Z) by instruments on the ICE spacecraft [Hynds et al., 1986; Sanderson et al., 1986a; Ipavich et al., 1986]. The cometary ion distributions measured outside the comet G-Z bow shock by ICE appear to be at least partially isotropized in the solar wind frame and furthermore indicate that significant particle acceleration has taken place [Gloeckler et al., 1986; Sanderson et al., 1986a; Richardson et al., 1986, 1987]. The distributions measured in the vicinity of the shock by ICE appear to be almost completely isotropized.

In this paper we examine energetic cometary ion fluxes measured by the Tlinde-M experiment during the preencounter time period when VEGA 1 was still outside the bow shock of comet Halley. A later paper will investigate data from the region inside the shock. We will show here that, in order for ions to be observed by the Tttnde-M instrument, they must have been both pitch angle scattered and accelerated. Possible acceleration processes are discussed in the light of these observations.

The insu'ument geometry and response of the Tilnde-M instrument are described in section 2. Section 3 gives the ion flux profiles measured by Tiinde-M and presents a correlation study of these fluxes with the magnetic field data measured by the magnetometer on board VEGA 1 [Riedler et al., 1986]. Section 4 presents the cometary ion distribution functions derived from Tilnde-M data for the frame of

reference moving with the solar wind.

2. INSTRUMENTAL AND OBSERVING GEOMETRY

The VEGA mission and the trajectories of the space probes were discussed by Sagdeer et al. [1986b]. In the vicinity of the comet, the VEGA 1 trajectory formed an angle of approximately 111 ø with the Sun-comet axis, and the inclination angle (formed with the plane of ecliptic) was 4.6 ø. The Tiinde-M instrument consisted of a semiconductor

telescope (for detailed information, see Somogyi et al. [1986b]), which pointed normal to the Sun-comet axis in the ecliptic plane and detected particles arriving from a direction approximately opposite to the spacecraft motion. The geometric acceptance was within a cone of about 25 ø half angle (see Figure 1). The geometric factor is 0.25 cm 2 st. The most likely candidates for heavy pickup ions far from the nucleus (r> 105 km)are O + and OH +, whereas H20+ becomes dominant closer to the nucleus. Smaller abundances

of other ion species such as CO2 +, CO +, S +, etc., can also be expected [Gringauz et al., 1986; Balsiger et al., 1986].

Energetic ions which are incident on the detector must first go through an aluminum window and lose some fraction of their energy in traversing this "dead layer." Once an ion enters the silicon semiconductor layer of the detector, it can deposit its energy both in ionizing and nonionizing collisions; only the ionizing collisions contribute to the signal from the detector (i.e., to the "measured" ion energy), and the resulting "defect" in the amplitude of the signal is usually called the "pulse-height defect" (or PHD [see Keppler, 1978]). The nonionizing energy loss, and thus the PHD, depend on both the mass and incident energy of the incident ions. For protons, the PHD is only important for incident energies less than about 10 keV, but for heavier ions (e.g., O +) it is important even for energies as high as 100 keV liparich et al., 1978].

TLJNDE GEOMETRY AND VELOCITY SPACE

0 + IONS

139keV 126 keV

IO6 key V I = 1070 km/s 96keV (101 key )

• { I ;,.,.. : .. , ; ; : .q :. ; ;/• : ; : : •/: :• Vx ;o;,,,:,,;

I

Fig. 1. Diagram of of velocity space in the ecliptic plane and of the Tiinde-M observing geometry. An approximate instrumental observing cone and energy channels am indicated for the T'tinde-M instrument. Possible locations in velocity space of solar wind protons and cometary pickup ions are shown.

The Tttnde-M insuument is capable of measuring fluxes of ions in the energy range from approximately 40 to 490 keV (in 10-keV intervals), and from 490 to 630 keV (in 20-keV intervals, nominal values). These energies refer to energy deposited in the detector via ionizing collisions. The following procedure was used to determine the actual incident energy from a given measured energy for a particular channel. This procedure was required to find the actual energy limits of each channel. First, the energy lost in •raversing the 15-p.g/cm 2 aluminum (AI) window was found by using the stopping-power tables of Northcliffe and Schilling [1970]. Then the PHD for a silicon detector (no window) was taken from Ipavich et al. [1978] assuming that the ions were O +. For a given energy of an O + ion, the deposited (or measured) energy was thus obtained by taking into account both the energy loss in the AI window and the PHD in the silicon detector itself. Table 1 lists the value of

TABLE 1. Tiinde-M Energy Channels

j Channel Channel Limits, No. ke V

Estimated Actual Energies, keV,

for O + Ions

1 43-50 96-106 2 50-64 106-126 3 64-74 126-138 4 74-85 138-153

KECSKElVlL• ET AL.: PICKUP IONS AT COlVIET HALLEY 187

10 2

101

1o o

• 10-1

c 10 o

10-B

10-4

10 -5

10-6

-- RADIAL DISTANCE FROM NUCLEUS (IO 6km) IO 8 6 4 2 I

I I I , I

16 0 8 16 • ' ' z, Hatch 5 Hatch

UT

Fig. 2. Tfinde-M counting rate (counts per second) versus time (UT) for the inbound pre-bow shock phase of the VEGA 1 encounter with comet Halley. Counting rates ½.are shown for the lowest four effective energy channels: j = 1-4. The four channels were labeled as follows: a (j = {), b (j = 2), c (j = 3), d (j = 4), and the counting rates were multiplied by factor• of 10 ©. The background counting rate in channel 1 is about 1.Sx102 counts/s. The smooth solid line shows the relative variation of the total cometary ion mass flux (i.e.,.the total cometary ion number density) along the VEGA 1 trajectory, calculated using a decay scale length of 2 x 10 ø kin.

deposited and incident energies for the four lowest T0nde channels which were operating in the preshock region. The speed of an O + ion (in the spacecraft reference frame) ranges from 1070 km/s fc;r channel 1 up to 1358 km/s for channel 4. The estimated error in the above pulse height defect determination procedure is approximately 5% [Ipavich et al., 1978]. A similar procedure was used by Hynds et al. [1986] to estimate the "actual" energies for comet Oiacobini-Zinner energetic ion data from the European Space Agency/Imperial College/Utrecht energetic ion experiment (EPAS) instrument on ICE.

Figure 1 is a diagram of velocity space in the comet reference frame which illustrates the Tlinde-M observing geometry for VEGA 1. Positive V• (x velocity) is oriented toward the Sun. The plane of the figure lies in the VEGA 1

orbital plane with positive Vy pointing generally away from the comet in the preencounter time period. The apex of the Tiinde-M observing cone is located at the spacecraft velocity vector (in the comet frame). Several of the lowest Tttnde-M energy channels are indicated, as is the velocity vector of the solar wind (protons). Tttnde-M pointed in the positive y direction.

Cometary pickup ions (of any species) will initially form ringfoeam distributions, as discussed earlier. However, in the presence of significant levels of magnetic fluctuations, the cometary ion distribution will rapidly isotropize (due to pitch angle scattering) on a spherical shell centered at the solar wind velocity and with a radius equal to the solar wind speed u. The intersection of such a spherical shell with the V,-Vy plane is indicated in Figure 1 for a solar wind speed of u=480 km/s. It should be emphasized that Tiinde-M is not

able to differentiate whether or not these initially picked-up ions are isotropized, although since the ring will almost never intersect the observing cone, at least partial isotropization is a reasonable assumption. The cometary ions must also be accelerated in order to be observed by TOnde-M. A spherical shell of radius v'= 1070 km/s (in the solar wind reference frame -- SWRF) is also shown in Figure 1. This shell has an energy of 1/2 rnv '2 = 101 keV in the SWRF for O + ions. The ion mass is designated m and 101 keV is roughly the lowest energy of O + ions which can be measured in the lowest (effective) energy channel of Tttnde- M. Actually, Tlinde-M had two-lower energy channels, but they exhibited very high noise levels at all times, and therefore they were not analyzed. One can conclude from the preceding discussion that some acceleration mechanism(s) is required to energize the ions from the initial pickup energy of about 20 keV to the observed energies of 90-100 keV and above (in the SWRF).

3. OBSERVATIONS

Time History of the Tiinde.M Counting Rates

Time histories of the Tttnde-M counting rates in the four lowest effective channels are shown in Figure 2 for the time period preceding the VEGA 1 inbound crossing of the bow shock of comet Halley. Energetic ions were detected as far as =107 km from the nucleus. The ion fluxes (i.e., counting rates) tended to increase with decreasing distance from the shock as discussed by Somogyi et al. [1986a]. This increase is especially steep near a radial distance of r = 3x10 6 kin. The fluxes were especially large near the shock. Large flux

188 KECSKE• ET AL.: PICKUP IONS AT COMET HALLEY

enhancements were superimposed on a background that exhibits a slow increase with decreasing r as will be discussed later. First, the overall trend and its possible explanation will be discussed.

The total density of heavy cometar), ions contaminating the solar wind is expected to be proportional to the ionization rate times the column density of heavy neutral molecules (i.e., H20, OH, O, CO, etc.) along a solar wind streamline upstream of the point where the measurement was made. The mass flux D u is then

pu = IX.U. + n/x) ds (1)

where u is the solar wind speed, p the mass density, m the mass of a picked-up ion, and n the neutral density as a function of radial distance r from the nucleus; p, and u, are, respectively, the density and velocity of the unperturbed solar wind; x is the lifetime of a neutral against photoionization plus charge exchange with solar wind protons (e.g., x • 2x106 s for O+); $ is the path length, and the integral over $ goes from -• (toward the Sun) to $ = 0, which corresponds to the location of the instrument.

Wallis and Ong [1975] showed that, for a simple 1/r 2 variation of the neutral number density, the relative mass flux (which is proportional to the number density of cometary ions) increases as 1/r along the Sun-comet axis. Galeev et al. [1985] calculated the variation of the relative mass flux along the Sun-comet axis taking into account the attenuation of cometary neutrals by photoionization (or any time-independent loss process). That is, for a neutral density n=[i•/(d•vgr2)]exp(-r/)O where {• denotes the gas production rate and v g the neutral gas flow velocity, the relative mass flux varies as

Off - ! = C { (•./r)e 'rg - Et(r•)} (2)

where ([•1-1) is the relative mass flux (t• = uluoo, • = p/P•), C is a constant, E 1 is the exponential integral function, and •. = v s x is the neutral attenuation scale length which is equal to 2x106 km for comet Halley at the time of the VEGA encounters [Gringauz et al., 1986]; v s is about 1 kn•s for water group molecules [Krankowslcy et al., 1986]. The total cometary ion density is proportional to the relative mass flux. A more accurate cometary ion density can be calculated direcfiy by numerically evaluating the integral over s in equation (1) using the appropriate neutral density given above and for a path parallel to the Sun-comet axis but ending at the location of the spacecraft. The relative variation of the calculated total cometary ion density as a function of the radial distance of the VEGA 1 spacecraft is shown in Figure 2.

Of course, the ion flux at higher energies does not necessarily vary in the same manner as the total ion density. The overall trend of the ion flux for the second channel (50- 64 keV "deposited" energy or 106-126 keV actual energy according to Table 1) appears to decrease approximately as the total cometary ion density, although the r variation of the higher-energy channels appears to be more gradual. The overall trend of the ion fluxes measured near comet G-Z by the EPAS instrument on ICE varied with r in a manner

qualitatively similar to that shown by the Tilnde-M fluxes although •. = 1 x 106 km was used in that study and 1 = 2 x 106 km was used here [Sanderson et al., 1986a].

Correlations with Magnetic Field Direction

The overall r dependence of the ion fluxes can be partially explained by the r dependence of the total pickup ion density integrated along an upstream solar wind streamline (which in turn is closely related to the r dependence of the neutral density), but this does not explain the large variability of the fluxes. For example, there are obvious spikes, or enhancements, between 2 and 10 million km radial distances. The energetic ion fluxes measured by the EPAS instrument near comet G-Z also exhibited large fluctuations [Hynds et al., 1986; Sanderson et al., 1986a], which were shown to be positively correlated with the maximum energy for ExB drifting pickup ions:

Emro x -- 2m U 2 Sin20Va (3)

where m is the heavy ion mass, u is the solar wind speed, and Ova is the angle of the interplanetary magnetic field (IMF) with respect to the solar wind velocity vector. This correlation implies that a significant fraction of the detected ions were freshly picked up by the solar wind.

One expects a different pattern of correlation for the Ttlnde-M measurements because the EPAS experiment on ICE was able to observe ions moving in a generally antisolar direction (the direction in which the bulk of the pickup ions move), whereas the Tfinde-M instrument only detected ions at right angles to the Sun-comet axis (Figure 1). One can see that in order for cometar), ions to be detected by TUnde-M, they must have been both pitch angle scattered and accelerated. Moreover, if one wishes to explain the large ion velocities via E xB cycloidal motion, either an improbably high solar wind velocity (>1000 km/s) or a very large ion mass (in excess of 60 amu) would have to be assumed. Furthermore, even with these unlikely conditions, only an extremely narrow band of OVB angles would produce ion "ring" distributions which would have access to the TUnde-M instrument. Practically then, in order for O +, OH +, and H20+ pickup ions to be detected, they must be both pitch angle scattered (isotropized in the extreme case) and accelerated. Consequently, the nature of the correlations with IMF parameters should be different from those correlations characterizing the ICE energetic particle data.

Figure 3 shows sin2OVB and the TUnde-M counting rate for channel 2. The IMF direction was derived from magnetic field vectors measured by the magnetometer experiment on VEGA I [Riedler et al., 1986]. The solar wind speed exhibited only a gradual decrease during the VEGA 1 preshock period (from about 550 to 420 km/s (K.I. Gringauz, private communication, 1986); so that sin2OvB closely corresponds to Ema x.

The outer two energetic ion flux enhancements were located between cometocentric distances 8x106 and107 km

and appear to anticorrelate with sin2OVB; that is, relatively more ions were detected when the solar wind flow was almost

parallel to the field direction. There is also a tendency for the ion fluxes at later times (smaller r) to anticorrelate with sin2OVB , but these anticorrelations are weak. A possible explanation for these anticorrelations with sin2OVB is that the low-frequency electromagnetic waves, which can pitch angle scatter the ions, are more likely to grow for smaller values of OVB [Sagdeer et al., 1986a; Winske et al., 1985]. In this case, one also expects a positive correlation with the

KECSKE• ET AL.: PICKUP IONS AT COML• HAT.T]•' 189

lO 3

lO 2

lO 1

o lO

lO-1

lO -2

10-3

.

ions G-•2GKeV

ß

16 o 8 16 o UT

/+ Morch 5 Morch

Fig. 3. T'•nde-M counting rate for j = 2 (106-126 keV) versus time. Also shown is sin2•)ve where •)VB is the angle of the LMF with the Sun-comet axis. •)vB is calculated from magnetic field vectors measured by the magnetometer on VEGA 1.

amplitude of the magnetic field fluctuations, but this seems to have been the case only for the 1200 UT March 5 peak, and for the region after 2300 UT and up to the shock [Gribov et al., 1986].

Large-Scale Magnetic Field Structure Another possible explanation for the observed flux

enhancements is that the energetic ions originate near the cometary bow shock or are ions which were reflected from the shock. In such a case, a first-order Fermi acceleration mechanism is operating lAxford, 1981]. In order for the Tiinde-M instrument to observe ions accelerated in this

manner, field geometries are required such that the observation point is connected to the shock along a magnetic field line. A variation on this theme is that the magnetosheath region is very turbulent and second-order Fermi acceleration can efficiently energize ions. These ions then leak through the shock and stream along field lines to the VEGA 1 spacecraft. Figure 4 shows magnetic field vectors (projected onto the ecliptic plane) which were calculated from VEGA 1 magnetometer measurements along the spacecraft trajectory. An approximate parabolic fit to the shock position is also shown. The field structure at a selected point along the spacecraft trajectory near 1600 UT, March $ (r--4x106 km), has been estimated using the following procedure.

First, we assumed that a magnetic field vector does not change with time in the SWRF. This is equivalent to assuming that the field is frozen into the solar wind plasma moving with a constant flow speed. A second assumption is that the field in the SWRF is uniform in the direction

perpendicular to the solar wind direction. The SWRF field vectors were obtained from the field vectors measured by the magnetometer along the VEGA 1 trajectory by using the first assumption, and the estimated field line shown in the figure was found from the SWRF vectors by using the second assumption. A solar wind speed of 450 kn•s was employed. The component of the magnetic field perpendicular to the ecliptic was relatively small during the two days before the VEGA 1 encounter; therefore including this component would not change the picture appreciably. Hence, a plausible two- dimensional magnetic field line has been constructed in the

vicinity of a selected observation point, as indicated in the figure. This field line does indeed connect the observation point to the bow shock. The figure suggests that when VEGA 1 was at a radial distance =4 million km from the

10nT

8

x 106km

Fig. 4. The VEGA I trajectory projected into the ecliptic plane. Distances from the nucleus are indicated. A reasonable parabolic bow shock surface is sketched which gives the correct inbound and outbound bow shock crossings, Measured magnetic field vectors (30-rain averages) projected onto the ecliptic plane are drawn along the VEGA 1 trajectory. A reasonable extrapolation of the magnetic field structure upstream and downstream of the trajectory is shown (dashed line; see text).

190 KECSKE• Er AL.: PICKUP IONS AT COMET HAI.I.h'iY

nucleus (March 5, 1600 UT), the shock was quasi-parallel. This does not contradict the fact that VEGA 1 observed a

quasi-perpendicular shock at a radial distance from the comet of approximately 1 million km (12 hours later than 1600 UT, March 5).

Can ions streaming from the shock explain the large flux enhancements seen by Tllnde-M at 1200 UT, March 5? This is possible but unlikely for several reasons.

1. Enhanced fluxes should have existed (if the energetic ions originate at the bow shock) throughout all of the 1200 to 2400 UT, March 5, time period (with r ranging from 2 to 6x106 krn) because it is probable that all of this region was connected to the bow shock. However, enhanced fluxes were present only during part of this time interval.

2. The bow shock must have certainly been extremely weak so far downstream from the nose [Wallis and Dryer, 1986] and incapable of producing such high ion energies via shock-drift acceleration plus reflection. In any case, the shock for this time period (not the same time that VEGA 1 encountered the shock) appears to have been quasi-parallel and hence turbulent.

3. Magnetic field fluctuations are large even far upstream of the shock [Riedler et al., 1986]; hence, the second-order Fermi acceleration mechanism should be more important than the first order Fermi mechanism several million kilometers outside the shock.

It seems even less likely that the ion flux enhancements near 10 ? km were associated with the bow shock. These enhancements were instead probably associated with local magnetic fluctuations in the general vicinity of the spacecraft.

4. COMETARY ION DISTRIB•ON FUNOriONS

• T• SOLA• W• F•ME

Particle detectors like TUnde-M measure the flux of

particles in various channels defined by certain energy limits. However, knowledge of the particle distribution function f(x,v,t) is needed in order to allow comparisons to be made with theoretical predictions. The particle counting rate in channel j (designated Cj) could be easily calculated from a known distribution function f using the instrumental parameters. On the other hand, the inverse of this procedure (that is, the determination of f from the measured values Cj) is nontrivial and requires several prior assumptions. Our method of obtaining the distribution function is to assume a functional form of f and then to calculate a trial counting rate for each channel, C t j, based on this assumption. Both Maxwellian and power law distribution functions were tried. "Observed" values of the distribution function are obtained

by comparing the observed and trial counting rates. A somewhat similar type of transformation, but without using an assumed form of f, was used by Gloeckler et al. [1986] and Ipavich et al. [1986] as well as by Richardson et al. [1986, 1987] to find cometary ion distribution functions in the vicinity of comet G-Z.

The Tilnde-M observing geometry was described in section 2 and in Figure 1. TUnde-M observed particles whose velocity vectors were located in a cone around a fixed direction, perpendicular to the Sun-comet axis. The energy information was •olely derived from the different energy channels; however, there were a large number of channels which allowed very good energy resolution for Tllnde-M. The

disadvantage was that the energy channels overlapped in the SWRF for large solar wind velocities. Therefore the determination of the energy spectrum in the SWRF is sensitive to the energy "boundaries" of the channels, to the angular sensitivity of the detector, and to the assumed functional form of the energy spectrum itself. G loeckler et al. [1986] and Richardson et al. [1986, 1987] were able to obtain further energy information (in the SWRF) because the ICE spacecraft was rotating and they were able to convert measurements in different angular sectors to different energies in the SWRF.

We used the actual solar wind (proton) velocities measured by the Plasmag 1 instrument on VEGA 1 for the transformation to the SWRF which is described below. The

measured solar wind speeds exhibited little variation in the preencounter preshock time period (with values between 550 km/s and 420 krn/s.)

The following assumptions are made in performing the transformation:

1. The ion distribution function in the SWRF. f(E'), is assumed to be uniform in the vicinity of the instrument acceptance angle. The derived distribution will be relevant, in the strictest sense, only to this angular sector. However, if the distributions happened to be completely isotropic (and this cannot be determined from the TUnde-M data), then the derived distribution functions would obviously be more general.

2. The ion distribution function f(E') has the form of a Maxwellian- at least in the relatively narrow energy range in which ions were detected. A power law distribution was also tried to test the sensitivity of the transformation to the choice of distribution function.

Let E'-- 1/2 ,n v '2 be the energy of an 0 + ion with speed v' in the solar wind reference frame (SWRF). The trial counting rate Ctj can be found from the distribution function lIE') using

(,,) (4)

u/•[u(O, •)] A (O) sin O' dO' d•' (5)

Sj(v ø) is the transformation function for channel j. O is the polar angle with respect to the (-Vy)axis, and • is the azimuthal angle. The angles in the spacecraft frame (O, •) can be found from the angles in the SWRF (designated O', •') via a suitable transformation. The function A (O) is the effective detector area for a given angle O, and it varies from 50.3 mm 2 at O = 0 ø to 39 mm 2 at O = 25 ø and then decreases rapidly for O greater than 25% becoming 0 at O = 32 ø. K/(v) is a step function which is 1 for energies within the limits of channel j and is 0 for energies in the spacecraft frame (E = 1/2 my 2) which lie outside the energy limits of channel j. The unprimed variables are in the spacecraft reference frame and the primed ones in the SWRF.

Figure 5a shows Sj (E') (Sj from equation (5) but versus E' rather than v') for j values from 1 through 5, for a solar wind speed of u = 100 km/s. The 100-kn•s results do not apply to this paper but are included to illustrate how the solar wind speed affects the function S j. This solar wind speed is applicable to regions close to the nucleus behind the bow shock. The effective width of each channel is relatively

KECSKE• ET AL.: PICKUP IONS AT CoMEr HAllEY 191

5.0

4.0

3.0

2.0

1.0

0

90 I00 I10 120 130 140 150 160 170 180 190

ENERGY IN SOLAR WIND FRAME (keV)

Fig. 5a. Transformation function •. (E') versus energy in the solar wind reference frame (E• for channels j = 1-4 and for a solar wind speed u = 100 km/s. O •' ions are assumed.

maximum contribution to C tj. Table 3 lists values of •'. for several values of T and for u = 480 km/s. J

The values of the distribution function in the SWRF at •'.

are denoted j• and are found from the measured values of C• using the following procedure:

1. Estimate a reasonable temperature T for energies near œ'. For this paper, which concerns the region upstream of thee bow shock, a single temperature was assumed for all j.

2. Given this T, determine a value of fo from Cj for each j by using equations ($) through (6), with the appropriate value of u and T. This parameter is called foj' Table 2 provides the necessary information in the form of C t) for selected values of T and for a particular value of u. One can write foj as

C.

(8)

narrow. Figure 5b shows Sj (œ') for u = 480 kin/s, and the effective width of each energy channel (in SWRF) is quite large due to the geometrical effect.

Most of the contribution to C tj for a given channel occurs in the lowest-energy part of the channel for distribution functions which fall off very rapidly with energy. We will assume that the distribution function is a Maxwellian--at

least in the relatively narrow energy interval in which ions were detected:

f(œ') =fo exp(-œ'/T) (6)

The trial counting rates in channel j, C tj , produced by such a distribution with fo = 1 are given in Table 2 for several values of the temperature T, and for u = 480 km/s. Our use of a Maxwellian does not imply that the distribution function must be MaxwellJan at all energies. All that is required is that f falls off rapidly in the vicinity of a particular channel. The average energy of the ions detected in channel j for a given T is

_ $ E'. = -- (7)

$

iF'. is the energy at which a Maxwellian would make a

20.0

Vsw = 480krn/s

15.0 -

I0.0

5.0

0

70 90 I10 1:50 150 170 190 210 230 250 270

ENERGY IN SOLAR WIND FRAME (kev)

Fig. 5b. Same as Figure 5a but for u = 480 km/s.

3. Given T, one can determine •'.from equation (7). Table 3 provides values for selected valu/es of T and u.

4. Now the distribution function can be found for each j:

5. A least squares fit of the "measured" points (fjversus •'.t) is used to obtain a new value of T. Note that either 3 or 4'points are used to determine T, which is in turn used in the

procedure to find j• for each of the channels. The whole procedure is repeated until the process

converges, that is, until the derived parameters vary by less than a part in 104 from iteratiort to iteration. Note that this procedure could be generalized for other assumed functional forms of the distribution function, although only Maxwellians were used for the results shown in this paper. Tests made with a power law distribution are described later. Distribution functions in the SWRF calculated using the above procedure are shown in Figure 6 for several points in the preshock period for VEGA 1. Temperatures found from the least squares fitting procedure are also indicated.

Consider now the major (known) sources of error in the above determination of the distribution function:

1. All channels were corrected for background. The background signal results in considerable uncertainty in C• for channel 1. For the other channels, the relative background is quite small at the ion flux enhancements. However, the background is especially a problem at large radial distances for those time periods between enhancements.

2. The channel limits (i.e., the energy discrimination levels set by the electronics of the instrument) were originally determined via a preflight calibration, and these were listed in Table 1 for the four lowest (effective) channels. Unfortunately, the electronic parameters are subject to possible long-term variations, and no in-flight calibration was performed. There are indications in the data shown here (Figure 6) and in data for the region downstream of the bow shock (not shown here) that the energy limit between channels 2 and 3 should be lower. In particular, the counting rate for channel 3 seems to be systematically too high relative to the adjacent channels. For a fairly steep distribution function and for solar wind speeds near 500 km/s, only the lower part of a channel makes a significant

192 KECSKE• ET AL.: PICKUP IONS AT COMET HALLEY

TABLE 2. Trial Counting Rates Ctj forfo -- 1

Channel No.

Temperature, keV

5 10 15 20 25 30

1 3.82(21)* 3.85(25) 1.07(27) 6.24(27) 1.87(28) 3.98(28)

2 9.33(20) 2.51 (25) 1.00(27) 7.04(27) 2.38(28) 5.48(28)

3 3.97(19) 4.51(24) 2.89(26) 2.57(27) 1.00(28) 2.54(28)

4 4.87(18) 1.66(24) 1.55(26) 1.67(27) 7.30(27) 2.01(28)

Solar wind speed is 480 km/s.

*The numbers in parentheses should be read as 1.00(20)=l.00xlO 2ø s 'x.

contribution to the counting rate. In this case, lowering the existing energy limit between channels 2 and 3 will not seriously_affect the derived •, but will lower the derived value ofœ'jforj = 3 (but not forj = 2). In Figure 6 this would correspond to sliding the points for the third channel down to lower energies, but preserving the same values of the ordinate. The placement and slope (i.e., temperature) of the solid lines (the Maxwellian fits to all channels) in Figure 6 would not be significantly affected by this procedure.

3. The largest source of error is certainly the pulse height defect determination; that is, there is considerable uncertainty in assigning an actual energy (for a heavy ion) to the corresponding ionizing energy deposited in the silicon detector. As described in section 2, we used the results of Ipavich et al. [1978] who claim an error of 3%. Due to the difference between our detectors and Ipavich's we estimate that the error is more like 5% (and probably less than 10%). This corresponds to a 5-key error in determining the energy of a 100-keV O + ion, and this uncertainty results

in a factor of 2 or so uncertainty in the derived distribution function for steep energy spectra.

4. There is certainly some error in the transformation procedure itself; in particular, there is uncertainty in the choice of the functional form of the distribution function and

uncertainty in the parameters used. A Maxwellian form was used for convenience only, and it seems to fit the data reasonably well. However, other functional forms, which exhibit similarly rapid falloffs at energies near 100 keV, could have been used. For instance, power law fits were also txied, and they also gave acceptable fits. But then, the average energy œ'. and the magnitude of the derived distribution function were somewhat different. The power law fit gave somewhat larger slopes than Maxwellians would at lower energies and somewhat smaller slopes at higher energies. By fitting a straight line (for a logarithmic-linear scale) to the distribution function points calculated using the power law, one finds an "average temperature" for those points. The "temperatures" (i.e., just the slopes of the curves) from the power law fits are only slightly larger than

TABLE 3. Average Energy in Solar Wind Reference Frame E'.keV J

Channel No.

Temperature, keV

5 10 15 20 25 30

1 88.8 97.0 103.3 108.0 111.5 114.2

2 98.1 107.5 114.5 119.7 123.7 126.7

3 112.8 121.6 128.6 134.0 138.1 141.3

4 123.6 132.8 139.9 145.6 150.0 153.5

Solar wind speed is 480 km/s.

KECSKEMETY ET AL.: PICKUP IONS AT COMET HALLEY 193

I I I I I I

SPECTRA DATE TIME TEMP (UT) (keY)

. +• , MAR.4 21:28 • X 2 MAR. 50l=18 2l.I

10 3 v•. •. 3 MAR. 5 12.28 11.7 X X,• 4 MAR 5 16.08 7.3

• • • 5 MAR. 6 02:38 6.6 O3:48 6.9

•.• 1ø 2

o io I z

z _ o

¸ _ •3 -

• _

• t6 t _

16 2 i 80 90 I00 I10 120 150 140

ENERGY IN SOLAR WIND FRAME (keY)

Fig. 6. Cometary ion distribution function (in solar wind reference frame) versus energy (in solar wind reference frame) for several observation times associated with ion flux enhancements. A

spectrum right at the location of the flux spike associated with the inbound bow shock crossing is also shown. 0 + ions are assumed. A MaxwellJan fit is shown for each spectrum, as well as the resulting temperature. Each spectrum is based on 10 min worth of data. The statistical error associated with the counting rate is only 15% at the very worst and usually is much less than 15%. However, there are other more serious sources of error, as discussed in the text,

those found from the Maxwellian. The difference is only --4% for temperature values of about 5 keV and only 6% for 10 keV. The difference in the derived distribution function

at a fixed energy due to the change in the assumed form of the fitting function is about 20% for T=5 keV and 40% for T=10 keV.

5. The derivation of the distribution function from the

counting rates assumed that the distribution function in the SWRF was uniform over the acceptance cone of the instrument. (This cone is shown in Figure 1.) The solid angle subtended by the acceptance cone is roughly •/8 st. This does not represent a major source of error; E/8 sr is only -- 3% of 4• sr. Even a very anisotropic distribution is probably almost uniform over the required solid angle. A more serious problem is that we cannot in general, use the calculated f(E') (which is determined only for the single direction of the TOnde-M instrument) to infer the distribution function for all other dh'ecfions. However, information from other missions and from theory can be utilized. The ion distribution is likely to be almost isotropic in the vicinity of the bow shock [e.g., Richardson et al., 1986], but the distribution might be quite anisotropic far from the shock [e.g., Sanderson et al., 1986a]. But even at large distances, O + ions which were sufficiently energetic to be detected by TQnde-M must have been accelerated and therefore should be

at least partially isotropized. This is because the pitch

angle diffusion process operates faster than the energy diffusion process [Sagdee• et al., 1986a], and the ion energies TOnde-M can observe are well above the initial ion pickup energy.

6. The shape of the sensitivity function $j significantly affects the transformation and is not known very accurately, since no preflight calibration was performed. This probably results in an uncertainty of a factor of 2 or so in the distribution function, but only a small uncertainty in the derived temperature. Other, smaller errors can be introduced by uncertainties in the solar wind velocity used in the transformation and in the pointing direction of the instrument relative to the solar wind dh'ection.

In summary, the largest error is probably caused by the determination of the pulse height defect. All these uncertainties probably yield an error of less than I key in the derived temperatures T for temperatures less than 10 keV. The errors in the derived distribution function are certainly less than a factor of 10, and probably more like a factor of 2 to 3.

Several features are apparent in the distribution functions shown in Figure 6. Overall, f tends to increase with decreasing radial distance r, as discussed in section 3 for the counting rates. Temperatures were derived for a large range of r and are shown in Figure 7. The temperatures (i.e., the slopes of the distribution functions) in Figure 7 exhibit little variation with cometocentric distance and vary between 5 and 8 keV, apart from a region about 10 and 8 million km from the comet, where the temperatures seem to be significantly higher (T is between 10 and 20 keV). Temperatures derived for this 10 - 8 million km region using the "standard" 10-min integration time fluctuated rapidly from point to point. The temperatures displayed in Figure 7 for this region were found using a larger integration time in order to smooth out these fluctuations. The

temperatures derived in the 10 - 8 million km region are larger and also have a larger error associated with them than those derived outside this region. For r less than--2.4

COMETOCENTRIC DISTANCE (IO skm) 12 I0 8 6 4 2 I

20 I I I I I I I

15

, , I • , , I • • , I , • , I • • , I , , , I •

16 0 8 16 0 8

4 MARCH 5 MARCH UT

Fig. 7. Variation of calculated "temperature" with radial distance from the nucleus. Data from 10-min intervals were used, except for the region near the temperature peak near 8 x 105 km, where 30 to 50-min intervals were used.

194 KECSKE• ET AL.: PICKUP IONS AT COMET HALLEY

million km the ion fluxes increase rapidly with decreasing r, but the temperature increases only slightly. Some possible interpretations of these spectra will be given in the next section.

5. SInViMARY AND DISCUSSION

The Tilnde-M experiment has shown that the energetic ion flux starts to increase (Figure 2) at a distance of 107 km outside of Halley's bow shock, with a number of large flux enhancements superimposed on the general flux level. The overall shape of the spatial distribution of the flux agrees roughly with what would be expected from the total density of pickup ions, as a function of distance from the comet.

A study of possible correlations between the ion flux and sin2OvB did not provide any evidence for the dependence of the flux on the maximum pickup energy, unlike the energetic ions measured by EPAS on ICE [Sanderson et al., 1986a]. The flux enhancements within 2 million km of the bow

shock upstream are not correlated with sin2OvB, while the outermost two peaks even anticorrelate with it. A possible explanation of the anticorrelation is that during times when Ov• is small (i.e., when the magnetic field is quasi-parallel to the solar wind flow direction), the growth rate of magnetic field fluctuations is larger [Sagdeer et al., 1986a] and these fluctuations accelerate particles via the second- order Fermi mechanism [lp and Axford, 1986].

The observation that the maximum pickup energy does not control the flux level is reasonable, since the initial ion

pickup process by itself is not sufficient to produce ions which are detectable by TIlnde-M. Ion acceleration might also be associated with the cometary bow shock. This possibility is supported by the observation [$omogyi et al., 1986a,b] that the flux of energetic ions reaches a maximum in the close vicinity of the bow shock, whereas at comet G- Z the ion intensity did not peak at the inbound wave although it did so outbound [Hynds et al., 1986]. However, the cometary bow shock is very weak, and therefore the first-order Fermi process and the gradient drift acceleration process are probably insufficient to produce the measured energies. Second-order Fermi acceleration in the enhanced magnetic field turbulence associated with the shock is probably a more effective mechanism [Gribov et al., 1986]. But shock acceleration mechanism of any type is not a likely explanation for energetic ions detected more than a couple million kilometers from the shock, as discussed in section 3.

Energy spectra of ions were determined in the solar wind reference frame by fitting Maxwellian distributions to the ion fluxes in the relevant energy range (between about 90 and 150 keV). The derived distribution functions indicate that the temperatures of the Maxwellian at cometocentric distances of 1-2x10 s km are similar to the temperatures measured just outside the bow shock of comet G-Z near a cometocentrie distance of 2 x 20 • km [Gloeclcler et al., 1986]. We are not suggesting that the distributions are complete Maxwellians, only that they fall off rapidly with energy for energies near 100 keV. Since we have four spectral points in a relatively narrow energy band, we cannot extrapolate much below our lowest-energy channel. Therefore, all functions which have similar rapid falloffs near 100 keV are also possible. Other functional forms of f (e.g., f--fo exp (-vlvo) and power law) have been used by

Richardson et al. [1986, 1987]. However, higher energy resolution Tilnde-M data available downstream of the bow

shock indicate that the MaxwellJan form is plausible. The most important role of the assumed functional form is in the determination of the average energy corresponding to each energy channel, and this does not depend strongly on the actual functional form chosen.

The magnitudes of the distribution functions found in this paper can be compared to those found by Gloeckler et al. [1986] if one slightly extrapolates the Gloeckler et al. functions up to energies of 90-100 keV. The comet Halley distribution functions are about a factor of 10 greater than the G-Z distribution functions for the regions just outside the respective bow shocks. The total number density of pickup ions for the two comets should be very similar just outside the shock, regardless of the relative gas production rates, because the shock is located where the total pickup ion number density (i.e., mass addition to the flow) attains a critical value [Galeev et al., 1985]. The fact that f(E') at E' • 100 keV is larger for comet Halley than for comet G-Z, in spite of similar total cometary ion densities, indicates that the ions at comet Halley have undergone more acceleration than the G-Z ions. Perhaps this is just due to the larger length scale of the Halley pickup process.

Now we will discuss the detection of ions at distances of

several million kilometers from the nucleus. Accepting the proposition that second-order Fermi acceleration is likely to energize particles, there is still the question of how cometary neutrals (which eventually get ionized) could travel such a great distance (•107 kin) from the nucleus. Typically, such neutrals have lifetimes against ionization of 1-2x106 s, which gives an attenuation scale length of )•=vgz of 1-2x106 km for neutral outflow velocities v g •1 km/s. The /ravel time from the nucleus to such distances is more than 100

days for this flow velocity. The neutral density is severely attenuated by ionization for these long times (i.e., large distances). Furthermore, the spatial distribution of neutrals might be seriously modified by the time variation of the gas production of comet Halley. If •, • 2 x 106 kin, as assumed in the calculations of the total ion density shown for Figure 2, then only 1% of the neutrals survive out to a cometocentric distance of 107 km. Figure 2 indicates this might be sufficient to account for the detected flux levels. But if •, were only 106 kin, then only • 0.01% of neutrals traveling at 1 krn/s would survive out to 107 km, in which case another source of neutrals is needed.

A surprising feature of the ion fluxes detected by Ttlnde-M (see Figure 2) is that the peaks appear to vary quasi- periodically in time with a period of four hours. There are additional narrow peaks at 0700 UT on March 5 in the j = 3 and 4 channels which also exhibit this periodicity but which were not included in Figure 2 because of the large background level associated with a different operational mode of the instrident. A similar periodicity (7 hours) was seen in the flux of picked-up cometary protons measured by the ion mass spectrometer (IMS) on Giotto several million kilometers from comet Halley [Neugebauer et al., 1986].

The observation of quasi-periodicity in the ion flux enhancements observed between 3 and 10 million km from

the nucleus suggests an explanation based on the spatial distribution of the neutrals. The television observations

made by VEGA and Giotto around their closest approach to the nucleus [Sagdeer et al., 1986c; Keller et al., 1986]

KEC$IL•• El' AL.: PICKUP IONS AT CO• BAILEY 195

indicate that the dust production (and therefore the neutral gas production) is highly variable over the surface of the nucleus with regions which are much more active than others. Suppose that there exists a relatively small active region which is active only when it faces the Sun. This active region would produce short-lived dusty gas jets with a periodicity determined by the rotation period of the nucleus. The resulting neutrals would be distributed in shell-like structures whose radial separation is equal to the gas velocity times the rotation period and whose radial thickness is equal to the gas velocity times the fraction of the rotation period during which the surface is active. Similar, but less sharp, structures would build up from ions which are created from these neutrals and then are picked up by the solar wind. As the spacecraft crossed these shells, flux enhancements would be observed.

The above model of periodic neutral structures places severe restrictions on the velocity distribution of the neutrals. First, the average velocity should strictly correspond to the spatial periodicity. Second, the thickness of the spatial density shells should be small enough such that the shells would not be unduly smeared out as they propagate outward. The observation of peaks separated by about 4 hours along the path of VEGA 1 corresponds to spatial intervals of about 106 km (here we did not take into account the bending of the neutral trajectories in the cometocentric frame which affects the spatial structures of neutrals at large distances from the nucleus as pointed out by Erdi•s and Kecskem•ty [1987] and Daly [1987]). The rotation period of the nucleus of comet Halley has been so far most reliably established by spacecraft optical measurements [Sagdeer et al., 1986] which gave =53 hours (however, a longer, 7.7-day period is favored by some other experiments Millis and $chliecher [1986]). A 53-hour period requires a neutral velocity of •6 km/s in order to permit the neutrals to travel a sufficient distance during one rotation of the nucleus. This is a very high velocity for O molecules and is much larger than the neutral velocities measured by Giotto (0.9 km/s Krankowsky et al. [1986]) in the inner coma. In addition, a rather low dispersion in the velocity distribution is needed so that the shells do not become thicker than was

observed. The observed thickness is roughly Arm 0.3 x 106 km at a cometocentric distance r • 107 km, and the required velocity dispersion is AV/V = Ar/r • 0.03.

One possible source of such high-velocity O atoms is the dissociative recombination of CO + ions in the inner coma of comet Halley (r < 5 x 10 4 km):

Halley's comet [Wenzel et al., 1986; Sanderson et al., 1986b; Daly, 1987]. It is also in agreement, on one hand, with theoretical expectations based on the travel time needed for neutrals to reach the distances required by the VEGA 1 and ICE observations, and on the other hand, with the minimum velocities calculated by Erdi•s and Kecskemdty [1987] based on particle trajectories.

Another possibility is that the ions seen by Ttlnde-M were protons. The initial pickup energy for protons is very low compared to that for heavier species; thus, the required acceleration would have to be quite significant. The protons need to be accelerated above the pickup energy by a factor of =100 in order to be detected by Tllnde-M. This might be possible if one considers that stochastic Fermi acceleration is •15 times more effective for protons than for O + ions [[p and Axford, 1986] at the strong turbulence limit. Still, heavy ions seem preferable.

Acknowledgments. The authors thank the referees for suggestions which significantly improved this paper. The part of the work carried out at The University of Michigan was supported by NASA grants NGR 13-005-015 and NAGW-15, and NSF grants ATM 8417884 and INT 8319732.

The Editor thanks S. M.P. McKenna-Lawlor and I. G. Richardson

for their assistance in evaluating this paper.

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(Received December 30, 1986; revised June 28, 1988;

accepted June 29, 1988.)