THE ASTROPHYSICAL JOURNAL, 496:L47–L49, 1998 March 20
© 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

Can the Sodium Tail of Comet Hale-Bopp Have a Dust-Impact Origin?

W.-H. IP AND L. JORDA

Max-Planck-Institut für Aeronomie, Postfach 20, D-37191 Katlenburg-Lindau, Germany; ip@linmpi.mpg.de

Received 1997 December 5; accepted 1998 January 22; published 1998 March 6


ABSTRACT

     Consideration is given to the possible mechanisms responsible for the production of the atomic sodium tail of comet Hale-Bopp. It is shown that both photosputtering and ion sputtering of nonvolatile dust grains might not be the main driving force. Instead, the generation of impact vapor by collisional interaction between the cometary dust coma of micron-sized particles and the very small grains (VSGs) of 10–100 Å size could possibly account for the observations if a large amount of VSGs existed in the coma region.

Subject headings: comets: general—radiation mechanisms: nonthermal

§1.  INTRODUCTION

     The close approach to the Sun of comet C/1995 O1 Hale-Bopp has provided many exciting results to cometary science. Besides being extremely bright because of its large size, with a diameter ≈30–40 km, comet Hale-Bopp is also characterized by its large content of dust (Weaver et al. 1997). Comet Hale-Bopp has a higher log (Afρ/Q[OH]) of -24.31 (Farnham, Schleicher, & Lederer 1997) than the dustiest comet observed by A'Hearn et al. (1995) during their long-term photometric survey. This ratio is also 30 times higher than the typical value of -25.82±0.40 given in their Table VI. As a result, it was considered to be the dustiest comet observed in recent time. Another surprising feature has to do with the production of an atomic sodium tail that was discovered by Cremonese et al. (1997) by using a narrowband spectral filter centered on the Na D line emission. Different from the diffusive dust tail, the atomic sodium tail is very straight, with the length traced to a distance as large as 10$\mathstrut{^{10}}$ km in the antisunward direction (see Fig. 1 [Pl. L3]).

Fig. 1

     The radial speed of the sodium atoms reaches a value of 70 km s-1 at 1.4×10$\mathstrut{^{7}}$ km from the comet center. This large velocity of the sodium atoms must be the consequence of solar radiation pressure acceleration. Cremonese et al. (1997) concluded that the sodium atoms were released from a source region in the cometary coma even though the nature of the ejection mechanism is not known.

     It was estimated that the production rate of the sodium atoms is up to 5×10$\mathstrut{^{25}}$ s$\mathstrut{^{-1}}$. This is in principle a relatively small source strength considering that the total gas (H$\mathstrut{_{2}}$O) production rate is about 10$\mathstrut{^{31}}$ molecules s-1 and that the cosmic abundance of Na is given by [Na]/[O] = 2.7×10$\mathstrut{^{-3}}$ (Allen 1976). This only means that the sodium atoms or their parent molecules must have been released from the nonvolatile grains instead of the sublimating cometary ice. Note that the sodium atoms should have a central source if they were emitted together with the water molecules.

     The Na D line emission in cometary comas was generally observed in the optical centers of comets when their solar distances were less than 0.7 AU. The sodium emission would extend tailward as the comets moved to smaller distances from the Sun, and the maximum brightness and tail length of the sodium atoms are found at r≈0.1–0.2 AU (Huebner 1970). As for metallic atoms like Mg and Fe that are locked up in the nonvolatile part of the cometary dust, they will be released only when the dust grains of large latent heat begin to sublimate at a surface temperature ≥1500 K (and r≤0.05 AU).

     It is possible that thermal diffusion will play a role in promoting the emission of Na atoms from the cometary dust grains, even without whole grain evaporation. At the same time, photosputtering and ion impact might be effective in emitting the observed sodium atom (Ip & Axford 1986; Geiss et al. 1986). Finally, collisions among dust grains in the cometary coma could have been instrumental in producing the observed atomic sodium tail. In this Letter, we will attempt to assess the contributions from each of these mechanisms.

§2.  PHOTOSPUTTERING

     At the time of the discovery of the atomic Na tail in 1997 April, comet Hale-Bopp was at a solar distance of about 1 AU, and its gas production rate (Q$\mathstrut{_{{\rm gas}}}$) was about 10$\mathstrut{^{31}}$ H$\mathstrut{_{2}}$O molecules s-1 (Farnham et al. 1997; Biver et al. 1997; Dello Russo et al. 1997). If the mass production rate of the cometary dust particles with radii (a) between 1 and 10 μm is comparable to the gas production rate, $\mathstrut{{\ucpmathaccent{M}{$\mathstrut{_{{\rm gas}}}$≈3×10$\mathstrut{^{8}}$ g s-1, the total number of grains with average radius $\mathstrut{\left\langle a\right\rangle }$=3.3 μm will be given by N$\mathstrut{_{d}}$≈$\mathstrut{\left({\ucpmathaccent{M}{D/v$\mathstrut{_{d}}$, where m$\mathstrut{_{d}}$ is the average mass of the dust grains (≈1.5×10$\mathstrut{^{-10}}$ g), D is the size of the dust coma (≈6×10$\mathstrut{^{4}}$ km), and v$\mathstrut{_{d}}$(≈0.3 km s-1) is the speed of the dust particles relative to the comet center. We therefore have N$\mathstrut{_{d}}$≈5×10$\mathstrut{^{23}}$, and the corresponding value of the total area is A$\mathstrut{_{d}}$≈πa$\mathstrut{^{2}}$N$\mathstrut{_{d}}$≈1.5×10$\mathstrut{^{17}}$ cm$\mathstrut{^{2}}$. In comparison, the total lunar surface is A$\mathstrut{_{{\rm moon}}}$=3.8×10$\mathstrut{^{17}}$ cm$\mathstrut{^{2}}$, while the lunar sodium production rate has been estimated to be 2×10$\mathstrut{^{21}}$–10$\mathstrut{^{22}}$ atoms s-1 (Potter & Morgan 1988; Ip 1991; Hunten & Sprague 1997).

     This scaling argument hence suggests that neither solar photosputtering nor the sputtering effect by the solar wind protons can account for the sodium tail of comet Hale-Bopp—unless the cometary dust is significantly enriched in its sodium abundance relative to the lunar surface material. The appearance of the sodium emission thus must be related to the cometary environment, namely, the ions of cometary origin and the dust coma itself.

§3.  ION SPUTTERING

     With a gas production rate of Q$\mathstrut{_{{\rm gas}}}$≈10$\mathstrut{^{31}}$ H$\mathstrut{_{2}}$O molecules s-1 at a solar distance of 1 AU, a simple consideration of the mass-loading process in a cometary coma (Wallis 1973) suggests that the location (r$\mathstrut{_{s}}$) of the cometary bow shock at the subsolar direction should be at about 8.5×10$\mathstrut{^{5}}$ km. Note that the corresponding position of comet Halley with Q≈10$\mathstrut{^{30}}$ H$\mathstrut{_{2}}$O molecules s-1 during the VEGA and Giotto encounters in 1986 was r$\mathstrut{_{s}}$≈4×10$\mathstrut{^{5}}$ km (Galeev 1987). Also, the plasma measurements by VEGA and Giotto show that at a distance of about r$\mathstrut{_{p}}$≈1.5×10$\mathstrut{^{5}}$ km along the spacecraft trajectories, the solar wind protons began to be reduced substantially (Gringauz et al. 1986). This effect has been interpreted in terms of enhanced charge-exchange interaction between the cometary inflow and the neutral gas coma at this cometopause (Gombosi 1987; Ip 1989). From a scaling of the gas production rate, the subsolar distance of the similar boundary structure at comet Hale-Bopp will be at r$\mathstrut{_{p}}$≈1.6×10$\mathstrut{^{5}}$ km (see Fig. 2).

Fig. 2

     Within the cometopause, the cometary plasma flow speed (u) is expected to change from a value of 100 km s-1 in the outer region to below 10 km s-1 near the center (Neugebauer 1990; Kettmann et al. 1990). At the cometopause, the cometary oxygen ions of keV energy range have a number density of about 10 ions cm-3 (Balsiger 1986; Ip 1989). The corresponding sputtering flux to the cometary dust can be estimated to be f$\mathstrut{_{i}}$≈10$\mathstrut{^{8}}$ ions cm-2 s-1. Now, with a sputtering yield of Y$\mathstrut{_{i}}$≈0.1–1 for a nonvolatile surface (McCracken 1993), the upper limit of the sputtering production rate of sodium atoms from the keV cometary ions would be Q$\mathstrut{_{i}}$≈A$\mathstrut{_{d}}$Y$\mathstrut{_{i}}$f$\mathstrut{_{i}}$X$\mathstrut{_{{\rm Na}}}$≈1.5×10$\mathstrut{^{23}}$X$\mathstrut{_{{\rm Na}}}$ atoms s-1. According to cosmic abundance, the mixing ratio of sodium among the nonvolatile elements is X$\mathstrut{_{{\rm Na}}}$≈1.4×10$\mathstrut{^{-3}}$ (Allen 1976), and we have Q$\mathstrut{_{i}}$≈2.1×10$\mathstrut{^{20}}$–10$\mathstrut{^{21}}$ Na atoms s-1. In fact, the keV cometary ions will be lost via charge exchange within a few times 10$\mathstrut{^{4}}$ km from the cometopause boundary. This means that the ion sputtering mechanism should supply only a very small fraction of the observed atomic sodium population originated from the central coma (Ip & Axford 1986).

     From the above considerations, we find that even though the sodium production rate required to produce the third tail of comet Hale-Bopp is much less than the water production rate, photosputtering and surface sputtering by solar wind protons and cometary ions are not adequate. An additional mechanism must be sought. One remaining possibility concerns the collisional effect of cometary dust grains, which we will explore next.

§4.  HYPERVELOCITY IMPACT BY VERY SMALL GRAINS

     In cometary comas, solid grains are usually charged to a surface potential of a few (plus or minus) volts because of photoemission and electrostatic charging by the ambient plasma (Wallis & Hassan 1983; Horanyi & Mendis 1991; Ip & Chow 1997). If Φ is the equilibrium value of the surface potential, the surface charge of a grain can be given as Q=700eΦa(μm), with the grain radius (a) in units of microns (Mendis 1981). The motion of the dust particles will therefore be subject to Lorentz force and the interplanetary electric field $\mathstrut{{\bmi E}}$=$\mathstrut{{\bmi -u{{\mbox{\boldmath$\times$}}}}}$$\mathstrut{{\bmi B}}$ in the stationary frame of the comet.

     For dust particles of micron size, the charge-to-mass ratio is small enough that their trajectories are only slightly perturbed by the electrodynamical effect. But for very small grains (VSGs) of a≈10–100 Å, the electromagnetic force could become dominant. Upon acceleration by the interplanetary electric field, the VSGs would follow a cycloidal trajectory. The scale length of the cycloidal motion can be expressed as (Ip & Chow 1997)



where ρ is the dust grain density (ρ≈1 g cm-3). Therefore, with the "nominal" values of u, Φ, and B given in equation (1), the gyroradius of a VSG—with a mass ≈10-19 g and a≈30 Å—will be on the order of 1.7×10$\mathstrut{^{4}}$ km. In other words, the tiny grains, once generated, will be picked up by the cometary plasma flow and will be brought to interact collisionally with the dust population surrounding the comet center. Thus, we expect the main dust coma, which is made up of micron dust particles, to be constantly bombarded by VSGs at a relative speed of tens of km s-1. Impact vapor containing sodium atoms will be generated as a result. Was there any evidence for the existence of VSGs in cometary environment?

     The dust particle experiment on VEGA had detected the existence of an extended halo of small dust grains; Sagdeev et al. (1989) and Utterback & Kissel (1990) reported the identification of small grains in the size range of 10-20–10-17 g by the PUMA dust analyzer. These measurements indicated that the VSGs were surprisingly abundant in the coma of comet Halley, with a total mass reaching as much as M$\mathstrut{_{{\rm vsg}}}$≈5×10$\mathstrut{^{15}}$ g, which was nearly 10 times as much as the mass of the gas coma. However, this estimate is most likely too high unless the cometary sublimation and outgassing processes are completely different from our current understanding.

     A different question can be asked here: what is the minimum amount of VSGs required to supply the atomic sodium tail? If, in addition to the fragmentation or formation of a population of solid ejecta, hypervelocity collision between a VSG and a micron-sized dust particle will lead to the production of a vapor cloud, the total vapor production rate can be expressed as



where n$\mathstrut{_{{\rm VSG}}}$, m$\mathstrut{_{{\rm VSG}}}$, and u$\mathstrut{_{{\rm VSG}}}$ are the average number density, mass, and impact speed of the VSGs, respectively; A$\mathstrut{_{d}}$, as defined before, is the total cross-sectional area of the cometary micron-sized dust; and f (assumed to be unity) is the impact vapor mass relative to m$\mathstrut{_{{\rm VSG}}}$. According to the estimate by Cremonese et al. (1997), $\mathstrut{{\ucpmathaccent{M}{$\mathstrut{_{{\rm Na}}}$≈1.9 kg s-1; hence, we have $\mathstrut{{\ucpmathaccent{M}{$\mathstrut{_{{\rm vapor}}}$≈$\mathstrut{{\ucpmathaccent{M}{$\mathstrut{_{{\rm Na}}}$/X$\mathstrut{_{{\rm Na}}}$≈1357 kg s-1. For A$\mathstrut{_{d}}$≈1.5×10$\mathstrut{^{17}}$ cm$\mathstrut{^{2}}$, m$\mathstrut{_{{\rm VSG}}}$≈10$\mathstrut{^{-19}}$ g (with a≈30 Å), and u$\mathstrut{_{{\rm VSG}}}$≈30 km s-1, we have n$\mathstrut{_{{\rm VSG}}}$≈30 cm$\mathstrut{^{-3}}$ in the dust coma region.

     The total mass of the VSGs is M$\mathstrut{_{{\rm VSG}}}$≈n$\mathstrut{_{{\rm VSG}}}$m$\mathstrut{_{{\rm VSG}}}$V$\mathstrut{_{{\rm coma}}}$≈3.3×10$\mathstrut{^{11}}$ g if the effective volume of the dust coma is 1.1×10$\mathstrut{^{29}}$ cm$\mathstrut{^{3}}$ (with a dust coma diameter D≈6×10$\mathstrut{^{4}}$ km). It should be noted that even though this value is much smaller than the value of 5×10$\mathstrut{^{15}}$ g given by Utterback & Kissel (1990) at comet Halley, it still represents a very high production rate: $\mathstrut{{\ucpmathaccent{M}{$\mathstrut{_{{\rm VSG}}}$≈3.2×10$\mathstrut{^{7}}$ g s-1 for a transport time of 10$\mathstrut{^{4}}$ s. In fact, it is possible that grain-grain collision at a lower velocity (say, 5–10 km s-1) could also contribute, hence improving the constraint on the sodium budget.

§5.  DISCUSSION

     As mentioned in § 1, besides erosive and destructive processes, the sodium atoms can be extracted from the cometary dust grains by thermal diffusion. Sodium atoms of such diffusion origin should tend to have a low initial speed (≈0.5 km s-1) corresponding to the surface temperature (≈300–400 K) of the dust particles. On the other hand, the impact effect of the VSGs will likely lead to the generation of atomic sodium population at higher speed (≈1–2 km s-1) (which is in agreement with the observed width of the sodium tail [Cremonese et al. 1997]) since the temperature of the impact vapor cloud can be on the order of 1000–2000 K. In addition, a small component of the sodium atom cloud might be created by the collision of fast-moving grains in the dust coma. Therefore, high spectral resolution measurements of the sodium emission in the vicinity of the central source region could provide important information on the production mechanism of the new sodium tail observed at comet Hale-Bopp. Finally, we should also expect to see a concentration of sodium emission in the vicinity of dust jets plus the continuation of the impact-driven production of sodium atoms in the diffuse dust tail.

ACKNOWLEDGMENTS

     We are grateful to F. Colas and J. Lecacheux for providing us with an image of the sodium tail obtained at the Pic-du-Midi Observatory, prior to publication. We also thank the reviewer, M. A'Hearn, for a useful suggestion.

REFERENCES

FIGURES


Full image (24kb) | Discussion in text
     FIG. 1.—CCD image of comet Hale-Bopp obtained through a sodium interference filter (centered on the Na D doublet at 5889 and 5895 Å, e.g., 5893/28 Å) taken with a photographic camera and a 50 mm lens at Pic-du-Midi (observers: F. Colas and J. Lecacheux) on May 2.86 UT. Note that the field of view is about 7.8×7.0 deg2 and 35×10$\mathstrut{^{6}}$ km by 32×10$\mathstrut{^{6}}$ km.

Full image (35kb) | Discussion in text
     FIG. 2.—A sketch of the VSG dust-impact production of sodium atoms in the coma of comet Hale-Bopp