Schwassmann–Wachmann 3-C

Icarus 178 (2005) 235–247 www.elsevier.com/locate/icarus

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C ✩ I. Toth a,b,∗ , P. Lamy a , H.A. Weaver c a Laboratoire d’Astronomie Spatiale du C.N.R.S., BP 8, 13376 Marseille Cedex 12, France b Konkoly Observatory, P.O. Box 67, Budapest H-1525, Hungary c The Johns Hopkins University Applied Physics Laboratory, Space Department, 11100 Johns Hopkins Road,

Laurel, MD 20723-6099, USA Received 15 September 2004; revised 14 April 2005 Available online 5 July 2005

Abstract The investigation of fragmented comets provides information on the physical properties and internal structure of cometary nuclei, as well as insights into the mechanisms responsible for cometary breakups. The Jupiter-family Comet 73P/Schwassmann–Wachmann 3 (73P/SW3) fragmented non-tidally into at least four components, and probably more, in the autumn of 1995. Fragment C was detected with the Wide Field Planetary Camera 2 (WFPC2) of the Hubble Space Telescope (HST) on 26 November 2001 when it was 3.26 AU from the Sun and 2.34 AU from the Earth. The high spatial resolution of the HST allowed us to separate the signal of the fragment from that of its coma, and to determine its R magnitude in the Johnson–Kron–Cousins photometric system from four images taken with the F675W filter. Assuming a spherical body with a geometric albedo of 0.04 and a linear phase coefficient of 0.04 mag deg−1 for the R band, we derived an effective radius of 0.68 ± 0.04 km. The pre-breakup radius of the original nucleus was estimated to be 1.1 km, which implies that the volume of fragment C is ∼25% of the total volume of the pre-breakup nucleus. The limited temporal coverage of our observations preclude deriving an accurate shape or rotational period; our measurements are consistent with a rather spherical body but an elongated shape cannot be excluded. Fragment C was very active despite its rather large heliocentric distance, with an estimated dust production rate of ∼1.5 kg s−1 (∼130 metric tons day−1 ). A very large fraction of the surface area of fragment C must have been sublimating to sustain such a high level of activity. Fragment C may be recovered at its next return in 2006, if it does not experience further fragmentation.  2005 Elsevier Inc. All rights reserved. Keywords: Small bodies in the Solar System; Comets, nucleus; Comets, disintegration; Comets, splitting, breakup, comets; Activity, comets; Dead comets; Meteor swarm

1. Introduction Our knowledge of the internal structure of cometary nuclei is extremely limited and is usually derived from indirect evidence. The apparently ubiquitous fragmentation of cometary nuclei, and the study of the subsequent evolution ✩ Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy under NASA contract NAS 5-26555. * Corresponding author. E-mail address: [email protected] (I. Toth).

0019-1035/$ – see front matter  2005 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2005.04.013

of the fragments, remain an essential source of information. Fragmented comets have been extensively discussed by various authors, notably Sekanina (1982), Hughes (1991), Jewitt (1992), Chen and Jewitt (1994), Boehnhardt (2002), and Boehnhardt (2004). An updated review of the internal properties of cometary nuclei is given by Weissman et al. (2002, 2004). Following Boehnhardt (2002), we summarize below some of the global characteristics of cometary fragmentation events in order to lend some perspective to the case of 73P/SW3. 1. The components of fragmented comets are usually separated by a few arcminutes to several degrees (the com-

236

I. Toth et al. / Icarus 178 (2005) 235–247

Table 1 Chronology of events for 73P/SW3 Date (UT)

rh (AU)


(AU)

27, 29 April 1930 2 May 1930

1.20 1.17

0.29 0.26

22–30 May 1930 1 June 1930 28 December 1994 8–12 September 1995 17–30 September 1995 22 September 1995 Autumn 1995 (?) 12–13 December 1995 22 November 1997 1 March 2000 25 April 2000 2 December 2000 27 January 2001 20, 27 July 2001 14 September 2001 26 November 2001 10 December 2001 14 May 2006 8 June 2006

1.05 1.02 3.03 0.96–0.95 1.06–0.93 0.93 0.93–1.34 1.46 5.03 3.44 3.09 1.24 0.93 2.30, 2.36 2.75 3.25 3.15 1.00 0.93

0.08 0.0565 2.35 1.47–1.44 1.61–1.41 1.38 1.31–1.52 1.74 4.12 2.68 3.11 2.04 1.81 2.49, 2.46 2.17 2.33 2.17 0.08 0.22

α (◦ ) 77.0 44.8 63.4 75.2 15.3 42.7–43.8 37.9–47.9 46.5 38.1–48.7 34.5 4.8 12.1 18.7 21.0 20.4 24.1, 24.2 19.4 7.4 2.6 91.8 102.1

Event Pre-discovery plates at Babelsberg, Germany (G. Kronk) Discovery at Hamburg Observatory, Germany (Baldet, 1930; Belyaev et al., 1986) “Stellar nucleus was double” (Schuller, 1930)a Closest approach to Earth. Bare nucleus (rn = 0.2 kmb ) claimed by Baldet (1930) Recovery at Calar Alto (pre-breakup; Birkle et al., 1994) OH outbursts (Crovisier et al., 1995) Visual outbursts reported (Boehnhardt and Käufl, 1995) Perihelion passage Nucleus breakup (Boehnhardt and Käufl, 1995; Sekanina, 1996) First detection of the split comet (Boehnhardt and Käufl, 1995) No detection ⇒ rn < 0.9 km Detection of fragment C (Boehnhardt, 2002) Detection of fragment C (Boehnhardt, 2002) Detection of fragment E (Kadota and Jäger, 2000) Perihelion passage Detections of fragment B (Boehnhardt, 2002) Detection of fragments B and C (Boehnhardt, 2002) Detection of fragment C by the HST (this work) Detection of fragment B Closest approach to Earth Perihelion passage

rh ,
: helio- and geocentric distances (AU). α: solar phase angle (◦ ). a There is no independent confirmation of this double appearance. b Revised to r = 1 km by Sekanina (1989). n

2.

3.

4.

5.

ponents of Sun-grazing comets can have much larger separations) and sometimes have overlapping tails. Cometary fragmentation events seem to be random, although there are several cases of recurrent splitting in the same object. There is no clear trend with heliocentric distance, with fragmentations occurring from Sungrazing distances out to ∼10 AU, nor do the fragmentation events take place preferably pre- or post-perihelion. The majority of the components in a fragmented comet completely “disappear” sooner or later, i.e., within time spans of hours to years, with the components becoming too faint to be detected even by the largest telescopes (e.g., C/1999 S4 (LINEAR), see Weaver et al., 2001). In some cases, only the main component survives for a longer time. The deceleration and lifetime of the components seem to be correlated, suggesting that components with larger deceleration may be smaller and/or lighter, with smaller reservoirs of out-gassing material. The separation velocities, i.e., the relative speed of the fragments shortly after fragmentation, show a correlation with heliocentric distance (Sekanina, 1977, 1982). Several processes may lead to fragmentation: tidal disruption, rotational splitting, breakup due to internal gas pressure, or collisions with other bodies etc., but we are still far from understanding the causes in most cases.

When fragments survive for an extended time, they offer an important opportunity to study pristine material from

the interior of the nucleus that is probably exposed to sunlight for the first time since the comet’s formation, and this is probably the case for 73P/Schwassmann–Wachmann 3. The chronology of events for this comet is listed in Table 1. Comet 73P/Schwassmann–Wachmann 3 (1930 d = 1930 VI) was discovered by Arnold Schwassmann and Arno Arthur Wachmann on 2 May 1930 at the Hamburg-Bergedorf Observatory (Baldet, 1930) thanks to a close approach to Earth at only 0.0565 AU (Belyaev et al., 1986). At that time, Baldet (1930) claimed to have detected its nucleus, setting an upper limit of 0.2 km for its radius (assuming an albedo of 0.10). Subsequently, Sekanina (1989) used a more realistic albedo (0.04) and introduced a correction for the phase effect to revise the radius estimate to 1 km. Orbital calculations over the past 400 years show a rather chaotic evolution, the comet experiencing frequent close encounters with Jupiter, for example, in 1728 at a distance of 0.03 AU, in 1953 at 0.9 AU, and in 1965 at 0.28 AU (Carusi et al., 1985). Consequently, the orbital elements undergo erratic changes, between ∼6.◦ 6 and ∼26.◦ 2 for the inclination angle i, between 0.42 and 0.68 for the eccentricity e, and between ∼0.90 and 2.30 AU for the perihelion distance q. In 1979, its perihelion passage took place 34 days later than predicted (Candy, 1979). The present orbit is characterized by a period of 5.36 years, q = 0.93, e = 0.69, and i = 11.40◦ . There is a meteor stream, the tau-Herculids, associated with 73P/SW3 (Drummond, 1981). A detailed analysis of the evolution of 73P/SW3 and its relation to the meteor stream is given by Gajdoš et al. (1999).

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

At its 1994/1995 return, 73P/SW3 was recovered by Birkle et al. (1994) on CCD images taken with the 3.5-m telescope at Calar Alto when the comet was at rh = 3.03 AU and
= 2.35 AU. It was further reported that the comet was active with a weak dust coma and tail (Boehnhardt et al., 1999). The nuclear magnitude, uncorrected for coma contribution, led to an effective radius of 1.2 km (in fact an upper limit) from both V and R Johnson magnitudes and using standard assumptions for the albedo (0.04) and the phase function (0.04 mag deg−1 ). Extensive radio observations were performed by Crovisier et al. (1995) during the first half of September 1995, a few days before its perihelion passage (22.888 September) and during the second half of October. From 1–5 September, they could only set an upper limit for QOH of a few 1028 molec s−1 , consistent with the empirical law of Jorda et al. (1991) relating QOH and the total visual magnitude of 73P/SW3 at perihelion from past apparitions. Then the OH production rate started to rapidly increase, reaching a maximum of 2.2 ± 0.2 × 1029 molec s−1 on 11–13 September. Again on 15–16 October 1995, they obtained an upper limit of 1029 molec s−1 but between 19 October and 1 November, QOH rose again and varied between 8.7 × 1028 and 1.6 × 1029 molec s−1 . On 12–13 December 1995, Boehnhardt and Käufl (1995) discovered four separate peaks of brightness in the coma of 73P/SW3, signaling that the nucleus underwent a (non-tidal) breakup in the previous weeks or months into at least four components (A, B, C, D). According to the study of Sekanina (1996), the splitting occurred between 24 October and 1 December 1995. If correct, this timing implies that the enhanced activity of the comet was a precursor of the main splitting, possibly resulting from surface or subsurface events such as a crust blow-off and/or ejection of icy fragments. The comet was undetected in 1998 by Lowry and Fitzsimmons (2001) at rh = 5.03 AU, thus putting an upper limit on the radius of the largest fragment of 0.9 km. During its recent apparition in 2000–2001, one orbit after its breakup, the two components B and C were recovered and a new fragment (denoted E) was detected but did not survive perihelion passage. Based on later observations performed in July, September, and December 2001, Boehnhardt et al. (2002) summarized the state of 73P/SW3. Fragment C is the largest surviving component from the 1995 breakup, and it was active at least from 4 AU pre- to 3 AU post-perihelion. Fragment B was active from shortly before perihelion to at least 2.7 AU postperihelion. A later detection of B farther away remains uncertain; a confirmed non-detection would imply a dramatic decline of its activity and an upper limit of 0.2–0.3 km for its radius (Boehnhardt et al., 2002). Altogether, fragment B was about 3 magnitudes fainter than fragment C. Fragment E was detected in December 2000 (Kadota and Jäger, 2000). Fragments A, D, and E were not recovered post-perihelion. If they still exist, their radii cannot be larger than 0.2–0.3 km. The properties of the pre-breakup nucleus of 73P/SW3 were inferred by Sekanina (1989) based on the interpretation of its fan-shaped coma. His model led to the picture of a

237

nucleus in fast precession (∼1.4 deg day−1 ), having a large obliquity and an active region of ∼0.8 km2 located near the pole under almost continuous illumination, using a standard thermal model to relate the water production rate to the area of subliming ice. The above estimate of the pre-breakup radius, rn = 1.2 km, implies an active fraction of
4%. Along with Comets 2P/Encke and 6P/d’Arrest, 73P/SW3 was a potential target of the former CONTOUR mission (Huntress, 1999; Bell et al., 2000) intended to explore the diversity of cometary nuclei. With the explosion of the spacecraft during its injection into interplanetary space, we have unfortunately lost the opportunity of observing a fresh piece of a nucleus, i.e., real pristine material. However, during its next apparition in 2006, Comet 73P will make a close encounter with Earth at
∼ 0.08 AU thus offering a unique opportunity to investigate a split comet at close range. In this article, we report on the detection of fragment C of Comet 73P/SW3 (73P/SW3-C) with the Hubble Space Telescope (HST). We used Hubble’s superior spatial resolution to separate the light from the nucleus and the coma, employing a technique that has already been successfully applied to over two dozen comets (Lamy et al., 1996, 1998a, 1998b, 1999, 2000, 2001; Weaver and Lamy, 1998; see also the review by Lamy et al., 2004). We determine the size of fragment C, assuming an albedo and a phase function, and characterize its dust production by the quantity Afρ (A’Hearn et al., 1984). We then estimate its water production rate and derive its dust production rate and its active fraction. We conclude with some predictions about the fate of this fragment and possible future observations.

2. Observations The observations were performed on 26 November 2001 during two consecutive orbits of the HST, i.e., spanning a time interval of ∼2 h. 73P/SW3-C had already passed its perihelion on 27.689 January 2001 (q = 0.938 AU) and was at heliocentric and geocentric distances of 3.255 and 2.336 AU, respectively, and at a phase angle of 7.◦ 46. We used the Planetary Camera (PC) mode of the Wide Field and Planetary Camera 2 (WFPC2), whose pixel size of 0.045 arcsec translated to a projected distance of 76 km at the comet. Two identical pairs of images with the broadband F675W filter and with an exposure time of 1100 s were obtained during the two orbits. This filter is centered at 670 nm and has an equivalent width of 89 nm (Biretta et al., 1996). Table 2 includes a log of the observations. Fragment C was selected because it is the brightest component and its orbit is the best known. The ephemeris uncertainty was ∼10 , and fragment 73P/SW3-C was found only 2 away from its predicted position, which is also consistent with the estimated absolute pointing uncertainty of HST. All images were processed using the standard “On The Fly” (OTF) pipeline calibration system at the Space Telescope Science Institute, which includes bias subtraction and flat-fielding corrections. A full

238

I. Toth et al. / Icarus 178 (2005) 235–247

Table 2 Journal of HST observations of 73P/SW3-C and results Image

Date (UT) November 2001

Exposure (s)

#1 u65z7w01m #2 u65z7w02m

26.207 26.222

1100 1100

#3 u65z7x01m #4 u65z7x02m

26.274 26.288

1100 1100

Rapp (mag) 1st orbit 22.76 ± 0.05 22.81 ± 0.05 2nd orbit 22.92 ± 0.05 22.81 ± 0.05

rn (km)

Afρ (cm)

log QH2 O (molec s−1 )

Qd (kg s−1 )

0.70 ± 0.02 0.68 ± 0.02

19.6 ± 1.0 19.6 ± 1.0

27.84 27.84

1.5 1.5

0.65 ± 0.02 0.68 ± 0.02

23.2 ± 1.2 20.6 ± 1.0

27.98 27.85

2.1 1.6

Date: mid-point of the exposure. Rapp : apparent R magnitude. rn : effective radius of the nucleus assuming pR = 0.04 and β = 0.040 mag deg−1 . Afρ: dust activity parameter (A’Hearn et al., 1984). QH2 O : water production rate. Qd : dust production rate.

Fig. 1. Image of Comet 73P/SW3-C produced by averaging four individual images (Table 2) taken on 26 November 2001 with the WFPC2 (PC mode) of the Hubble Space Telescope. The displayed isophotes show that the inner coma is nearly circular symmetric. The arrows indicate the anti-solar direction (prolonged radius vector r), the direction of celestial north (N ), and the heliocentric orbital velocity vector (Vorb ) of the comet projected onto the sky plane.

discussion of all the steps in the pipeline reduction process can be found in Holtzman et al. (1995a). Fig. 1 displays the average of the four images, overplotted with isophotal contours to highlight the circular symmetry of the coma of 73P/SW3-C. 3. Data analysis To analyze the data, we applied our standard method of fitting a parametric model of the expected surface brightness

of the comet composed of a nucleus and a coma to the observed images (e.g., Lamy et al., 1998a, 1998b, 1999). The brightness distribution for the comet is modeled as:
 B(ρ) = kc /ρ p + kn δ(ρ) ⊗ PSF, (1) where ρ is the radial distance from the nucleus, power exponent p characterizes the radial distance dependency of the brightness, δ(ρ) is the Dirac delta function, and ⊗ is the convolution operator. The first term represents the coma with the scaling factor kc while the second term is the contribution of the nucleus with the scaling factor kn . The point spread func-

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

239

Fig. 2. Comparison of the linear profiles of the model and the observed image of Comet 73P/SW3-C corresponding to observation #2 (Table 2) made on 26 November 2001. The horizontal (top panel) and vertical (middle panel) profiles are nearly symmetric, indicating that the nucleus was close to the center of the pixel. The bottom panel displays the residuals. In addition, the profiles of the models of the nucleus and of the coma are plotted separately.

tion of the telescope was modeled using version 4.0b of the TinyTIM software written by Krist (1995), which has the ability to include the effect of spacecraft jitter, sometimes conspicuous on long exposures. In order to take into account the subpixel location of the nucleus, which may cause a marked asymmetry of the brightness profiles, the model

images were generated on a finer grid than the original PC pixel, with a resampling factor of 9. The fits to the real images were performed after integrating the model over 9 × 9 subpixels to recover the original pixel of the PC, first using the X- and Y -profiles through the peak pixel (Fig. 2) to get the subpixel location of the nucleus and approximate values

240

I. Toth et al. / Icarus 178 (2005) 235–247

for the model parameters kn and kc . Their final determinations, as well as those of the jitter if any, were performed on azimuthally averaged radial profiles. This is conveniently implemented by performing a polar transformation of the images centered on the nucleus (the pixel having the largest signal), with an angular resolution of 1◦ , and summing the individual profiles. Note that the 1/ρ p function was rigorously calculated in the central 3 × 3 pixels to take into account the finite extent of the pixels; this effect is negligible beyond this central area. The 1σ noise can be expressed as:   2  B + (f B)2 , + s= (2) g g where B is the observed signal in DN, g = 7 electrons DN−1 is the gain,  = 5 electrons is the readout noise, and f = 0.01 expresses the flat field noise as a fraction of the signal. A large improvement in the signal-to-noise ratio results from performing the azimuthal average. Fig. 3 displays the results of the fit on the azimuthally averaged profile for one representative image. Its quality can be checked by inspecting the residuals, which are generally within ±5%. The coma surface brightness distribution always followed the canonical 1/ρ law. Some spacecraft jitter, typically 10 milli-arcsec (rms), was required to obtain the optimum fits. The determination of the absolute magnitudes was performed on the kn PSF images, which measure the brightness

Fig. 3. An azimuthally averaged radial profiles for observation #2 (Table 2) of 73P/SW3-C is shown in log–log representation (top panel). The thick solid line represents data, and the other curves are models for the signal from the nucleus (dash line), the coma (thin solid line), and total cometary signal (dash–dot line). The residuals (data-model) are also shown (bottom panel).

of the nucleus as it would be observed by the HST in the absence of coma. The procedure followed the recommendations of Holtzman et al. (1995b). The so-called instrumental magnitudes were calculated by integrating the scaled PSFs in an aperture of 0. 5 radius, so that no aperture correction is required. The formulae converting the instrumental WFPC2 magnitudes to the standard Johnson–Kron–Cousins R magnitudes require a color correction in first and second orders, of the (V –R) color index. We used (V –R) = 0.52, which is the average value for the fifteen ecliptic cometary nuclei for which we have already obtained two-color photometry from our past HST observations (Toth and Lamy, 2000). The uncertainty in the (V –R) color index has a negligible influence on the derived nuclear magnitude. For example, a variation of 0.1 in (V –R) induces a difference of 0.01 in the magnitude of the nucleus. Thus, the dominant source of uncertainty is the fitting procedure itself. The uncertainty in the kn scaling factor was estimated by examining the residuals between the synthetic and observed images. The contrast between the nucleus and the coma is very high, with the signal from the nucleus exceeding that from the coma by a factor of ∼3 in the central pixel. If kn differs by more than ∼5% from its nominal value, the model fit to the data is clearly degraded with residuals in the core of the image (i.e., within 2 pixels of the brightest one) exceeding 30% of the observed intensity, which is ∼3 times larger than the statistical uncertainty (owing to photon statistics) of the observed signals. The largest uncertainty in our modeling, and the dominant contributor to the error in the size of the nucleus derived below, is the extrapolation of the coma brightness from the region where it is well determined to the region that is unresolved by HST. At the large geocentric distance of our observations, one PC pixel subtends 76 km (i.e., a pixel perfectly centered on the nucleus subtends ±38 km), which means that the coma brightness profile within ∼50 km must be extrapolated from the outer coma, rather than measured. If the true coma spatial brightness profile in the inner coma is different than that assumed, our estimate for the nucleus magnitude, and consequently the derived radius, will be incorrect. It is important to note, moreover, that our extrapolation could be wrong in either direction. In the case of 1P/Halley, the coma spatial profile became flatter relative to the extrapolated outer coma profile within ∼50 km of the nucleus (Thomas et al., 1988; Reitsema et al., 1989). If a similar effect were present in 73P/SW3-C, the brightness of the nucleus derived from our analysis would be underestimated. On the other hand, if the coma spatial brightness profile suddenly became steeper within ∼50 km of the nucleus, we would be overestimating the brightness and size of the nucleus (see the discussion in Section 5 on the possible presence of sublimating, icy grains in the coma). Since there is no independent information on the spatial brightness profile of the coma of 73P/SW3-C within ∼50 km of the nucleus, we must simply recognize this possible source of systematic error and carry on. We note, however, that the use of HST mitigates this problem

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

because its high spatial resolution means that the extrapolation of the coma profile to the surface of the nucleus does not cover as large a distance as required for other telescopes.

4. Size of the C fragment The magnitude of a spherical object viewed in scattered sunlight is related to its optical cross-section by (Russell, 1916; Jewitt et al., 1991): pΦ(α)rn2 = 2.238 × 1022 rh2
2 100.4(m −m) ,

(3)

where m, p, α, and Φ(α) are, respectively, the apparent magnitude, the geometric albedo, the phase angle, and the phase function of the nucleus in a given spectral band (R band in the present case), m is the apparent magnitude of the Sun in the same spectral band (m = −27.09), rh and
are, respectively, the heliocentric and geocentric distances of the nucleus (both in AU), and rn is its radius (in meters). We assumed standard values for the geometric albedo pR = 0.04 and for the phase coefficient β = 0.04 mag deg−1 of the phase law. The four determinations of the effective radius of fragment C (i.e., the radius of the equivalent circular cross-section) from our four HST observations range from 0.65 ± 0.02 to 0.70 ± 0.02 km (Table 2) and average to 0.68 ± 0.04 km. Our determination for the radius of the nucleus is thus smaller than, and therefore consistent with, the pre-breakup upper limit of 1.2 km estimated by Boehnhardt et al. (1999). All of the measured albedos of cometary nuclei for the R band lie in a very narrow range, 0.02 to 0.06 (Lamy et al., 2004). As the size of the nucleus is inversely proportional to the square root of the albedo, the uncertainty on the albedo translates into a factor of ∼1.7 uncertainty in the value of the radius, that is ±0.5 km for 73P/SW3-C. Since the observations were performed at a small phase angle, the uncertainty resulting from the phase coefficient is negligible, at least within the range of phase laws measured for cometary nuclei so far. The question as to whether a “new” fragment, with all or part of its surface being pristine, has the standard albedo of 0.04 is totally open. We note that, in the case of the fragments of Comet C/1999 S4 (LINEAR), the above assumptions for the albedo and the phase coefficient yielded sizes which were consistent with the size estimated for the progenitor nucleus (Weaver et al., 2001). The independent size determinations from the two HST orbits are essentially identical within the errors, so our data are consistent with a spherical-shaped nucleus. However, our data have very limited temporal coverage, and the possibility that the C fragment of 73P/SW3 is elongated cannot be ruled out. The size of the C fragment can be compared to that of the pre-breakup nucleus on the basis of the observation of Boehnhardt et al. (1999). As presented in Section 1, the derived effective radius radius, uncorrected for coma, amounts to 1.2 km. These authors estimated that the contribution of the coma did not exceed 20% of the total light so that we

241

can conservely apply a correction of 0.9 to the radius and finally adopt 1.1 km. This is incidentally in excellent agreement with the value of 1 km that Sekanina (1989) derived from the observation of Baldet (1930). The ratio of the effective radius of the pre-breakup nucleus to that of fragment C is 1.1/0.68 = 1.6, and the volume ratio is ∼4. Therefore, the volume of fragment C is ∼25% of the total volume of the pre-breakup nucleus. Assuming that the bulk density is 0.3 g cm−3 , as is often considered for a dusty-ice aggregate, the mass of fragment C is ∼4 × 1011 kg, and that of the prebreakup nucleus is ∼1.7 × 1012 kg. Assuming a conservative estimate of 0.25 km for the radii of the other four fragments, they represent no more than ∼5% to the volume of the pre-breakup nucleus. So altogether the observed fragments account for only a small fraction (at most ∼30%) of the original nucleus, the bulk (∼70%) being probably in the form of numerous, very small fragments. For example, ∼7500 fragments of radius ∼50 m each are required to account for the “missing matter.” It must be remembered that the above discussion depends entirely upon the estimate of the pre-breakup nucleus radius of 1.1 km presented above. Weidenschilling (2004) reviewed the process of the formation of cometesimals as collisionally processed aggregates, i.e., rubble piles (see also Weissman et al., 2004). Although his 1-dimensional models suggest preferential formation of bodies having a characteristic size of ∼100 m, his more recent 2-dimensional models have a size distribution that is more closely approximated by a power law with only a small depression centered near 1 m in size. The observed fragments of 73P/SW3, and the numerous small, unobserved fragments whose existence is suggested by the results presented here, may be consistent with Weidenschilling’s model, but our observations cannot be used to confirm that model in detail.

5. Activity of the nucleus fragment In order to quantify the activity of fragment C, we calculated the quantity Afρ (A’Hearn et al., 1984): Afρ = 4


2 rh2 Fc (cm), ρ a F

(4)

where ρa is the aperture radius, Fc is the cometary continuum flux in that aperture, and F is the flux from the Sun at 1 AU in the same filter used for the cometary observation. In this formula,
and ρa must be expressed in the same unit (cm), and rh is in AU. The quantity Afρ was introduced because it provides an aperture-independent measure of the dust production rate when the coma spatial brightness profile follows the canonical ρ −1 law, which is the case for 73P/SW3-C. Integration of our best fit coma model for this comet yields Afρ 20 cm, which is an extremely large value for such a small nucleus (rn = 0.68 km) at such a

242

I. Toth et al. / Icarus 178 (2005) 235–247

large heliocentric distance (rh = 3.25 AU). The exact values for each observation, together with their uncertainties, are displayed in Table 2. The uncertainties were estimated by taking into account a typical error of 5% on the determinations of the coma scaling factors kc . An initial estimate for the dust production rate Qd can be obtained by assuming a very simple model of an isotropic, force-free steady state outflow of dust grains, all having the same radius a. Then Qd is related to Afρ by Qd = 66.7

ρd vd a Afρ (g s−1 ), pd Φ(θ )

(5)

where vd (m s−1 ), ρd (g cm−3 ), a (cm), pd , and Φ(θ ), are, respectively, the velocity, the bulk density, the geometric albedo, and the scattering function of the dust grains. For a typical grain size a = 3 × 10−4 cm (3 µm) with ρd = 1 g cm−3 , we found vd = 110 m s−1 (see below). Further, assuming pd = 0.04 and the normalized scattering function of Divine (1981), Φ = 0.84 at the phase angle of our observations and using our determination Afρ = 20 cm, we finally obtained Qd = 1.3 kg s−1 . We next attempted to estimate the dust production rate Qd in the framework of the more rigorous model developed by Newburn and Spinrad (1985), and later re-formulated by Singh et al. (1992), which assumes that the dust grains are ejected from the nucleus by the drag force exerted by the sublimating water ice. We have already used this model to derive Qdust from our past HST observations of comets, e.g., 4P/Faye (Lamy et al., 1996), 19P/Borrelly (Lamy et al., 1998b), 22P/Kopff (Lamy et al., 2002), and 46P/Wirtanen (Lamy et al., 1998a). Assuming that the dust grains are roughly spherical, the mass release rate of dust is given by am Qd =

4π 3 a ρd (a)f (a) da (g s−1 ), 3

(6)

a0

where ρd (a) is the bulk density of grains of radius a and f (a) is the size distribution function: f (a) = k(1 − a0 /a)M (a0 /a)N (cm−1 s−1 ).

(7)

In the above expression, N = 4.2 and M is given by log(M) = 1.13 + 0.62 log(rh ),

(8)

where rh is the heliocentric distance in AU. The minimum radius of the dust grain is set to a0 = 10−5 cm, while the maximum radius am corresponds to the largest grain that can be lifted from the nucleus by the gas drag forces. The rather complex expression for am given by Singn et al. (1992), their Eq. (2) involves the parameters defined in their Table 1. The gas and dust velocities are defined in the model by Newburn and Spinrad (1985), their Eqs. (16)–(18).

The normalization constant k which appears in Eq. (7) is given by 2 Ap(λ) a pd (λ) −1  am     a0 M a0 N a2 1− da (cm−1 s−1 ), × vd (a) a a a0 (9) where the quantity Ap(λ), the product of area and geometric albedo, is derived from the photometry of the coma, and pd (λ) is the geometric albedo of the dust grains irrespective of their size, pd (λ) = 0.04. The velocity vd (a) of the dust grain of radius a was calculated using Eqs. (16)–(18) of Newburn and Spinrad (1985), first using an initial guess of the dust to gas mass ratio χ and then performing a few iterations. The “observed value” of Ap(λ) follows from the equation

k=

π 2ρ

Ap(λ) =

πrh2
2 Fc Φ(θ ) F

(10)

and involves the geometric conditions at the time of observations, the scattering function Φ of the dust grains at scattering angle θ taken from the curve of Divine (1981), and the ratio of the cometary continuum flux Fc to that of the solar flux F for the same filter. The quantities Afρ (Eq. (4)) and Ap(λ) are related by Afρ 4 Φ(θ ). = Ap(λ) πρa

(11)

The various parameters required by this model are unknown, and we have no other choice than adopting “standard” values except for these directly relevant to the nucleus of 73P/SW3-C. We use our determination of its radius, rn = 0.68 km, and an active fraction fa = 1, as justified below. We can assume that the activity is still mostly driven by the sublimation of water ice even at this distance because several comets show water production at similar distances (Table 3), and we must estimate the water production rate QH2 O since no measurements exist. We make use of the empirical correlation between water production rates and visual magnitudes of comets established by Jorda et al. (1991): log QH2 O = 30.74(±0.02) − 0.240(±0.003)mh ,

(12)

where QH2 O is the water production rate (molec s−1 ), and mh is the heliocentric visual magnitude of the comet, i.e., mh = mv − 5 log
with mv , the apparent visual magnitude measured at geocentric distance
(AU). According to the analysis of Crovisier et al. (1996), this relation is accurate to a factor of ∼2–3, which is acceptable for our first-order calculation. To obtain the heliocentric visual magnitude of the coma, we proceeded in several steps. We first computed the R magnitude of the coma based on the continuum flux measured with the F675W filter, after subtraction of the contribution from the nucleus. The coma magnitude generally depends on

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

243

Table 3 Comparison of the water production rates of different comets Comet

Observations date (UT)

rh (AU)

QH2 O (molec s−1 )

Reference

73P/SW3 (pre-breakup) 73P/SW3 (breakup?) 73P/SW3-C C/1999 S4 (LINEAR) 46P/Wirtanena 2P/Encke

28 February 1990 1–5 September 1995 26 November 2001 27.2 January 2000 14 March 1997 7 July 1999

1.44 0.98 3.25 3.29 1.06 1.04

∼4.20 × 1027 9.2 ± 1.5 × 1028 7–10 × 1027 1.2 × 1026 1.4 × 1028 2 × 1027

Fink and Hicks (1996) Crovisier et al. (1996) This work Farnham et al. (2001) Stern et al. (1998) Lisse et al. (1999b)

a At perihelion.

the size of the aperture, but the coma is so weak in this case that we simply integrated over a radius of 15 pixels (0. 675), which is sufficient to get down to the background level. Next we transformed the R magnitude to a V magnitude by considering the spectral reflectivity of the coma of different comets observed by Jewitt and Meech (1986). We averaged the tabulated reflectivities of the Jupiter-family comets and derived a mean (V –R) color index of 0.5. The final step was to transform the V magnitude to the visual magnitude mv . Generally V is close to, but slightly fainter than mv but the correction depends on the strength of the CN, C3 , CO+ , and C2 emissions. Based on the study performed by Kidger (2002), and on results obtained by Mikuz and Dintinjana (2001), the most conservative approach is to adopt mv = V . Then the empirical formula of Jorda et al. (1991) yields a typical water production rate of 7 × 1027 molec s−1 , with an estimated uncertainty of a factor of 2–3. This result is comparable to the water production rate of the original, prebreakup nucleus obtained in 1990 by Fink and Hicks (1996), but at the much smaller heliocentric distance rh = 1.44 AU (Table 3). Our value is about a factor 10 less than the maximum rate determined by Crovisier et al. (1996) from radio observations performed in early September 1995 when the comet was between rh = 0.94 and 1.09 AU and possibly in its pre-breakup process. Table 3 presents some comparisons with other comets, some of which were observed at comparable heliocentric distances to the HST observations of 73P/SW3-C. The split Comet C/1999 S4 (LINEAR) was observed pre-breakup at rh = 3.2 AU, at which time its observed water production rate of ∼1.2 × 1026 molec s−1 implies a lower limit for the radius of the nucleus of ∼0.44 km (Farnham et al., 2001). This latter value is less than a factor of two smaller than the estimated size of the 73P/SW3-C nucleus, so the large difference in water production rates for these two comets probably cannot be explained by a difference in the sizes of their nuclei. We discuss later the comparison with two ecliptic comets, 46P/Wirtanen and 2P/Encke, the latter being a prime example of an evolved, low activity comet. From the above estimate of QH2 O for the nucleus of 73P/SW3-C, we found am = 4.5 cm, and dust velocities of vd = 290 m s−1 for a = 0.1 µm, vd = 150 m s−1 for

a = 1 µm, vd = 70 m s−1 for a = 10 µm, and vd = 20 m s−1 for a = 100 µm. Finally, assuming ρd (a) = 1 g cm−3 , we found a typical dust production rate of Qd = 1.5 kg s−1 (roughly 130 metric tons day−1 ), which can be compared to our initial estimate of 1.3 kg s−1 (Table 2). The calculation of the dust production rate depends critically on the dust velocity, which, in turn, depends on the gas velocity. Neither of these velocities have been observed for 73P-C, so we considered another model of gas dynamics and kinetics of the cometary coma, namely that of Crifo and Rodionov (1997)—see also Rodionov et al. (2002) and the review by Combi et al. (2004)—to assess their influence on our determination of the dust production rate. This model provides a straightforward method for computing these velocities. When applied to the case of 73P-C, it gives an initial gas velocity of 300 m s−1 and a terminal gas velocity of 450 m s−1 . We then found am = 7.3 cm, and dust velocities of vd = 450 m s−1 for a = 0.1 µm, vd = 290 m s−1 for a = 1 µm, vd = 160 m s−1 for a = 10 µm, and vd = 60 m s−1 for a = 100 µm. Using these velocities, we calculated a dust production rate of Qd = 1.1 kg s−1 (roughly 95 metric tons day−1 ), which is ∼30% smaller than the value derived earlier using the Newburn and Spinrad (1985) model. Other systematic uncertainties come from the various assumptions inherent in the model, and from uncertainties in the values of the other parameter. Newburn and Spinrad (1985) have tested their influence and found that Qd is most sensitive to rn and fa , while the sensitivity to other parameters is quite small. Since we accurately determined rn (but assumed a geometric albedo of 0.04), we only tested the influence of fa , and found that Qd increases by 13 and 30% when using fa values of 0.75 and 0.5, respectively. Altogether, the uncertainty in our estimate of Qd is probably a factor of ∼2, as estimated by Newburn and Spinrad (1985). For a comparison, we recall our past results based on similar observations with the HST and derived using the same method. 45P/Honda–Mrkos–Pajdusakova had a dust release rate of ∼1 kg s−1 at rh = 0.96 AU (Lamy et al., 1999). 46P/Wirtanen had Qd = 4 kg s−1 at rh = 2.25 AU. 4P/Faye had Qd = 125 kg s−1 at rh ∼ 1.6 AU.

244

I. Toth et al. / Icarus 178 (2005) 235–247

On the basis of the pre-breakup observations of 73P/SW3 obtained by Fink and Hicks (1996) on 14 February 1990 at rh = 1.44 AU, Sanzovo et al. (2001) derived a dust production rate of 1.67 kg s−1 for a bulk density ρd = 1 g cm−3 . Fragment C had therefore roughly the same dust production rate at rh = 3.25 AU as the pre-breakup nucleus at rh = 1.44 AU. We estimated the fractional active surface of the fragment C of 73P/SW3, which is the active area divided by the total surface area, using the simple formula of Senay and Jewitt (1994): fa =

dM/dt rh2 LH2 O , 4πrn2 F (1 − AB )

(13)

where dM/dt is the water mass release rate (kg s−1 ), LH2 O the latent heat of sublimation of water, AB the Bond albedo of the nucleus, and F the solar flux at 1 AU (1360 W m−2 ). The latent heat is weakly temperature dependent and we adopted LH2 O = 2.78 × 106 J kg−1 at the equilibrium temperature T = 100 K. The Bond albedo AB = pq is the product of the geometric albedo p = 0.04 as assumed above and of the phase integral q. We adopted q = 0.28 as justified by our previous work on cometary nuclei (Lamy et al., 2002; Groussin and Lamy, 2003; Groussin et al., 2004) and which is consistent with the only measured value (0.27 ± 0.01 for 19P/Borrelly; Buratti et al., 2004). We found a typical active fractional area fa ∼ 0.8, indicating that a large fraction of the surface of fragment C was active. We also note that similar large surface active area fractions were obtained for 46P/Wirtanen (Lamy et al., 1998a), for 103P/Hartley 2 (Groussin et al., 2004), and possibly for Hyakutake (100% according to Lisse et al. (1999a) but only 18–40% according to Schleicher and Osip (2002)). Equation (13) implicitly assumes that the whole surface is at the temperature of the subsolar point, so that it overestimates the sublimation rate and, therefore, underestimates the active fraction. In addition, the peak value of QH2 O derived from our third observation (∼1028 molec s−1 ) implies a fractional area fa > 1 (precisely 1.126). On the one hand, there may be more sublimating surface area than the total sunlit area of the nucleus suggesting that at least some of the cometary activity in 73P/SW3-C may be due to icy grains in the coma, as has been inferred for several comets at similarly large heliocentric distances, such as Comet Bowell (1980 E1) (A’Hearn et al., 1984). If sublimating icy grains dominated in the coma of 73P/SW3-C, then the spatial brightness profile could become much steeper than ρ −1 at some distance from the nucleus, and as steep as ρ −2 or more (Jewitt et al., 1991). This effect was not detected in our analysis of the HST images, as the coma was found to follow the canonical law (∝ ρ −1 ) over the entire region where the signal was sufficient to measure the coma. On the other hand, and most likely, the uncertainties are so large that the activity may very well result from the nucleus itself.

6. Predictions The question arises whether the known fragments or new fragments will be seen at the comet’s next return in 2006. If fragment C is not subject to further disruption, its future behavior may be extrapolated from that of the nucleus of 46P/Wirtanen, after scaling for their different activity levels, since they have comparable sizes and orbits. According to the calculations of Groussin and Lamy (2003), the nucleus of 46P may survive for 700–1700 orbital periods. Comparing the water production rates of 73P/SW3-C and 46P (Tables 2 and 3) (1027 and >1028 s−1 , respectively) and adopting a factor 100 as an upper bound to scale the activity level for 73P/SW3-C, we conclude that 73P/SW3-C may survive for a few orbits and that there is a reasonable chance to detect it in 2006, assuming that no fragmentation took place in the mean time. It is also possible that, following a period of intense sublimation resulting from the exposure of fresh icy material, the activity substantially decreases as a result of the depletion in volatiles and the formation of a refractory crust. Such a situation could very much increase the lifetime of 73P/SW3-C. Our size determination of fragment C can be used to predict its apparent brightness for future observations (assuming a geometric albedo of 0.04 and a phase coefficient of 0.04 mag deg−1 ). It will reach aphelion on 3 October 2005 at rh = 5.18 AU,
= 5.0 AU and at a phase angle of 11◦ ; its apparent magnitudes will be V = 26.2 and R = 25.7. Its closest approach to Earth will take place on 13–14 May 2006 at rh = 1.0 AU,
= 0.08 AU, and at a phase angle of 92◦ ; at which time the nucleus will have V = 16.6 and R = 16.1. The next perihelion passage will take place on 8 June 2006 at rh = 0.93 AU,
= 0.22 AU and at a phase angle of 103◦ . At this time, the apparent magnitudes of the nucleus will be V = 19.4 and R = 18.9. The case of the other fragments is more problematic: there may be some hope to recover B but very little hope to recover A, D, and E on the basis of the past observations of Boehnhardt et al. (2002). According to Boehnhardt (2002), fragment E has already disappeared. There are different observations and predictions about the meteor swarm associated with Comet 73P/SW3 which is an Earth-grazing comet (Sekanina, 1989). The list of Earth’s close encounters with comets (Sekanina and Yeomans, 1984) indicates that 73P/SW3 approached Earth at 9.2 × 106 km on 30 May 1930. A meteor shower was predicted and reported by Japanese observers on 9 and 10 June 1930 (see the ZHR values and other detail reported by Nakamura (1930) and Ridley (1990)). A meteor stream associated with Comet 73P/SW3 was identified as tau-Herculids with a miss-distance to the Earth’s orbit of ∼0.02 AU (Cook, 1970; Drummond, 1981). 73P/SW3 is the only known comet producing a shower of class A meteors (using Ceplecha’s classification, Ceplecha, 1966), which are type I carbonaceous chondrites of probable cometary origin (McCrosky and Ceplecha, 1970). In addition, there is a possible as-

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

sociation of the dust from 73P/SW3 with an isotopically anomalous cluster of interplanetary dust particles collected in June–July of 1991, as suggested by Messenger and Walker (1998). Owing to the 1995 breakup of 73P/SW3, increased activity or another meteor outburst could occur in 2006 (Gajdoš et al., 1999). If the comet no longer exists in 2006, this meteor stream may survive as in the case of Comet 3D/Biela (Sanzovo et al., 2001).

7. Conclusions Observations of the nucleus of the C component of the fragmented Jupiter-family Comet 73P/Schwassmann– Wachmann 3 with the Wide Field Planetary Camera 2 of the HST on 26 November 2001 lead to the following conclusions and predictions. 1. The light from the fragment nucleus was clearly separated from the coma light, and we used our previouslyproven technique to determine an average effective radius of 0.68 ± 0.04 km, assuming a geometric albedo pR = 0.04 and a phase coefficient β = 0.04 mag deg−1 . The short time span of the observations did not allow determination of either the shape or rotational period of the fragment. 2. On the basis of a pre-breakup radius of 1.1 km derived from the observations of Boehnhardt et al. (1999), the volume of fragment C represents only ∼25% of the volume of the original nucleus. Altogether, the detected fragments comprise at most ∼30% of the volume of the original nucleus, which implies that ∼70% of the original mass is probably in the form of small debris with radii smaller than ∼200 m. 3. Fragment C was very active, despite its large heliocentric distance of 3.25 AU, and we determined an Afρ of ∼20 cm. After estimating the water production rate and using an empirical law, albeit with a large uncertainty, we calculated a dust production rate of 1.5 kg s−1 (∼130 metric tons day−1 ). This requires that a large fraction of the surface of the fragment must be active. 4. By analogy with the nucleus of 46P/Wirtanen, we speculate that fragment C may survive for at least a few orbits and should be recovered during its next return in 2006. The survival of the other fragments is more problematic. 5. An increase of the activity (possibly a storm) of the tauHerculids meteor stream associated with 73P/SW3 may be expected, as the 1995 breakup has likely enriched the swarm in new meteoritic particles.

Acknowledgments We thank N. Biver, Y.R. Fernández, M. Kidger for their advice on the V to visual magnitude conversion, as well

245

as S.C. Lowry and an anonymous referee for their valuable comments and suggestions. This work was supported by the “Programme National de Planétologie” funded by CNRS and CNES, and by the Hungarian State Research Foundation for Sciences (OTKA) through Grant No. T025049. I. Toth acknowledges support from the Université de Provence and from the Hungarian Academy of Sciences through Grant No. 9871. H. Weaver acknowledges financial support by NASA through Grant HST-GO-8699.01-A from the Space Telescope Science Institute (STScI), which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

References A’Hearn, M.F., Schleicher, D.G., Feldman, P.D., Millis, R.L., Thompson, D.T., 1984. Comet Bowell 1989 b. Astron. J. 89, 579–591. Baldet, F., 1930. C. R. Acad. Sci. Paris 190, 1382. Bell III, J.F., Veverka, J., Belton, M., Benkhoff, J., Cheng, A., Clark, B., Cochran, A., Farquhar, R., Feldman, P., Kissel, J., Mahaffy, P., Malin, M., Murchie, S., Niemann, H., Owen, T., Schwehm, G., Squyres, S., Thomas, P., Yeomans, D., 2000. CONTOUR: A Discovery mission to explore the diversity of cometary nuclei (63rd Annual Meteoritical Society Meeting). Meteorit. Planet. Sci. 35 (Suppl.), A23. Belyaev, N.A., Kresák, L., Pittich, E.M., 1986. Catalogue of ShortPeriod Comets. Slovak Academy of Sciences, Astronomical Institute, Bratislava. Biretta, J.A., 18 colleagues, 1996. In: Biretta, J.A. (Ed.), Wide Field and Planetary Camera 2 Instrument Handbook. Version 4.0. Space Telescope Science Institute, Baltimore. Birkle, K., Boehnhardt, H., Schwehm, G., 1994. Periodic Comet Schwassmann–Wachmann 3 (1994 w). IAU Circ. 6122. Boehnhardt, H., 2002. Comet splitting—Observations and model scenarios. Earth Moon Planets 89, 91–115. Boehnhardt, H., 2004. Split comets and comet outbursts. In: Festou, M., Weaver, H.A., Keller, H.U. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ. In press. Boehnhardt, H., Käufl, H.U., 1995. Comet 73P/Schwassmann–Wachmann 3. IAU Circ. 6274. Boehnhardt, H., Rainer, N., Birkle, K., Schwehm, G., 1999. The nuclei of Comets 26P/Grigg–Skjellerup and 73P/Schwassmann–Wachmann 3. Astron. Astrophys. 341, 912–917. Boehnhardt, H., Holdtstock, S., Hainaut, O., Tozzi, G.P., Benetti, S., Licandro, J., 2002. 73P/Schwassmann–Wachmann 3—One orbit after breakup: Search for fragments. Earth Moon Planets 90, 131–139. Buratti, B.J., Hicks, M.D., Soderblom, L.A., Britt, D., Oberst, J., Hillier, J.K., 2004. Deep Space 1 photometry of the nucleus of Comet 19P/Borrelly. Icarus 167, 16–29. Candy, M.P., 1979. Comet 1979 g. IAU Circ. 3393. Carusi, A., Perozzi, E., Valsecchi, G.B., Kresák, L., 1985. Long-Term Evolution of Short-Period Comets. Adam Hilger, Bristol, p. 350. Ceplecha, Z., 1966. Classification of meteor orbits. Bull. Astron. Inst. Czech. 17, 96–97. Chen, J., Jewitt, D., 1994. On the rate at which comets split. Icarus 108, 265–271. Combi, M.R., Harris, W.M., Smyth, W.H., 2004. Gas dynamics and kinetics in the cometary comae: Theory and observations. In: Festou, M., Weaver, H.A., Keller, H.U. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ. In press. Cook A.F. 1970. Discrete levels of beginning height of meteors in streams. SAO Special Report No. 324. Crifo, J.F., Rodionov, A.V., 1997. The dependence of the circumnuclear coma structure on the properties of the nucleus. I. Comparison between

246

I. Toth et al. / Icarus 178 (2005) 235–247

a homogeneous and an inhomogeneous spherical nucleus with application to P/Wirtanen. Icarus 127, 319–353. Crovisier, J., Biver, N., Bockelée-Morvan, D., Colom, P., Gerard, E., Jorda, L., Rauer, H., 1995. Comet 73P/Schwassmann–Wachmann 3. IAU Circ. 6227. Crovisier, J., Bockelée-Morvan, D., Gérard, E., Rauer, H., Biver, N., Colom, P., Jorda, L., 1996. What happened to Comet 73P/Schwassmann–Wachmann 3? Astron. Astrophys. 310, L17–L20. Divine, N., 1981. A simple radiation model of cometary dust for P/Halley. ESA SP 174, 47–54. Drummond, J.D., 1981. A test of comet and meteor shower association. Icarus 45, 545–553. Farnham, T.L., Schleicher, D.G., Woodney, L.M., Birch, P.V., Eberhardy, C.A., Levy, L., 2001. Imaging and photometry of Comet C/1999 S4 (LINEAR) before perihelion and after breakup. Science 292, 1348– 1353. Fink, U., Hicks, M.D., 1996. A survey of 39 comets using CCD spectroscopy. Astrophys. J. 459, 729–743. Gajdoš, Š., Galád, A., Klaˇcka, J., Pittich, E.M., 1999. Orbital evolution of Comet 73P/Schwassmann–Wachmann 3 and its meteor streams. In: Evolution and Source Regions of Asteroids and Comets, Proc. IAU Coll. 173, pp. 103–108. Groussin, O., Lamy, P., 2003. Activity on the surface of the nucleus of Comet 46P/Wirtanen. Astron. Astrophys. 412, 879–891. Groussin, O., Lamy, P., Jorda, L., Toth, I., 2004. The nuclei of Comets 126P/IRAS and 103P/Hartley 2. Astron. Astrophys. 419, 375–383. Holtzman, J.A., 17 colleagues, 1995a. The performance and calibration of WFPC2 on the Hubble Space Telescope. Publ. Astron. Soc. Pacific 107, 156–178. Holtzman, J.A., Burrows, Ch.J., Casertano, S., Hester, J.J., Trauger, J.T., Watson, A.M., Worthy, G., 1995b. The photometry performance and calibration of WFPC2. Publ. Astron. Soc. Pacific 107, 1065–1093. Hughes, D.W., 1991. Possible mechanisms for cometary outbursts. In: Newburn, R.L., Neugebauer, M., Rahe, J. (Eds.), Comets in the Post-Halley Era. Kluwer Academic, Dordrecht, pp. 825–854. Huntress Jr., W.T., 1999. Missions to comets and asteroids. Space Sci. Rev. 90, 329–340. Jewitt, D., 1991. Cometary photometry. In: Newburn, R.L., Neugebauer, M., Rahe, J. (Eds.), Comets in Post-Halley Era, vol. 1. Kluwer Academic, Dordrecht/Norwell, MA, pp. 19–66. Jewitt, D., 1992. Physical properties of cometary nuclei. In: Brahic, A., Gerard, J.-C., Surdej, J. (Eds.), The 30th Liège International Astrophysical Colloquium: Observations and Physical Properties of Small Solar System Bodies. Inst. d’Astrophysique, Univ. Liège Press, Liège, pp. 85– 112. Jewitt, D., Meech, K.J., 1986. Cometary grain scattering versus wavelength, or, “What color is comet dust?” Astrophys. J. 310, 937–952. Jorda, L., Crovisier, J., Green, D.W.E., 1991. The correlation between water production rates and visual magnitudes in comets. In: Asteroids, Comets, Meteors 1991, Flagstaff, AZ. Lunar and Planetary Science Institute, Houston, pp. 285–288. Kadota, K., Jäger, M., 2000. Comet 73P/Schwassmann–Wachmann 3. IAU Circ. 7534. Kidger, M.R., 2002. Spanish monitoring of comets: Making sense of amateur photometric data. Earth Moon Planets 90, 259–268. Krist, J., 1995. Simulation of HST PSF using Tiny TIM. In: Shaw, R.A., Payne, H.E., Hayes, J.J.E. (Eds.), Astronomical Data Analysis Software and System IV. In: ASP Conference Series, vol. 77, pp. 349–352. Lamy, P.L., Toth, I., Grün, E., Keller, H.U., Sekanina, Z., West, R.M., 1996. Observations of Comet P/Faye 1991 XXI with the Planetary Camera of the Hubble Space Telescope. Icarus 119, 370–384. Lamy, P.L., Toth, I., Jorda, L., Weaver, H.A., 1998a. The nucleus and the inner coma of Comet 46P/Wirtanen. Astron. Astrophys. 335, L25–L29. Lamy, P.L., Toth, I., Weaver, H.A., 1998b. Hubble Space Telescope observations of the nucleus and inner coma of Comet 19P/Borrelly 1994 l. Astron. Astrophys. 337, 945–954.

Lamy, P.L., Toth, I., A’Hearn, M.F., Weaver, H.A., 1999. Hubble Space Telescope observations of the nucleus of Comet 45P/Honda–Mrkos– Pajdusakova and its inner coma. Icarus 140, 424–438. Lamy, P.L., Toth, I., Weaver, H.A., Delahodde, C., Jorda, L., A’Hearn, M.F., 2000. The nucleus of 13 short-period comets. Bull. Am. Astron. Soc. 32, 1061. Abstract [36.04]. Lamy, P.L., Toth, I., Weaver, H.A., Delahodde, C., Jorda, L., A’Hearn, M.F., 2001. The nucleus of 10 short-period comets. Bull. Am. Astron. Soc. 33, 1093. Abstract [31.01]. Lamy, P.L., Toth, I., Jorda, L., Groussin, O., A’Hearn, M.F., Weaver, H.A., 2002. The nucleus of Comet 22P/Kopff and its inner coma. Icarus 156, 442–455. Lamy, P., Toth, I., Fernández, Y.R., Weaver, H.A., 2004. The sizes, shapes, albedos, and colors of cometary nuclei. In: Festou, M., Weaver, H.A., Keller, H.U. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ. In press. Lisse, C.M., Fernández, Y.R., Kundu, A., A’Hearn, M.F., Dayal, A., Deutsch, L.K., Fazio, G.G., Hora, J.L., Hoffmann, W.F., 1999a. The nucleus of Comet Hyakutake (C/1996 B2). Icarus 140, 189–204. Lisse, C.M., Christian, D., Dennerl, K., Englhauser, K., Trümper, J., Desch, M., Marshall, F.E., Petre, R., Snowden, S., 1999b. X-ray and extreme ultraviolet emission from Comet P/Encke 1997. Icarus 141, 316–330. Lowry, S., Fitzsimmons, A., 2001. CCD photometry of distant comets II. Astron. Astrophys. 365, 204–213. McCrosky, R.E., Ceplecha, Z., 1970. Fireballs and the physical theory of meteors. Bull. Astron. Inst. Czech. 21, 271. Erratum: Bull. Astron. Inst. Czech. 21, 381. Messenger, S., Walker, R.M., 1998. Possible association of isotopically anomalous cluster IDPs with Comet Schwassmann–Wachmann 3. Lunar. Planet. Sci. 29. Abstract 1906. Mikuz, H., Dintinjana, B., 2001. CCD photometry of Comet C/1995 O1. Int. Comet Quart. 23 (1/117), 6–16. Nakamura, K., 1930. On the observations of faint meteors, an experienced in the case of those from the orbit of Comet Schwassmann–Wachmann 1930 d. Mon. Not. R. Astron. Soc. 91, 204–209. Newburn Jr., R.L., Spinrad, H., 1985. Spectrophotometry of seventeen comets. II. The continuum. Astron. J. 90, 2591–2608. Reitsema, H.J., Delamere, W.A., Williams, A.R., Boice, D.C., Huebner, W.F., Whipple, F.L., 1989. Dust distribution in the inner coma of Comet Halley—Comparison with models. Icarus 81, 31–40. Ridley, H.B., 1990. Meteors associated with Comet P/Schwassmann– Wachmann 3. J. Brit. Astron. Assoc. 100, 92–93. Rodionov, A.V., Crifo, J.-F., Szeg˝o, K., Lagerros, J., Fulle, M., 2002. An advanced physical model of cometary activity. Planet. Space Sci. 50, 983–1024. Russell, H.N., 1916. On the albedo of the planets and their satellites. Astrophys. J. 43, 173–195. Sanzovo, G.C., de Almeida, A.A., Misra, A., Miguel Torres, R., Boice, D.C., Huebner, W.F., 2001. Mass-loss rates, dust particle sizes, nuclear active areas, and minimum nuclear radii of target comets for missions Stardust and Contour. Mon. Not. R. Astron. Soc. 326, 852–868. Schleicher, D.G., Osip, D.J., 2002. Long- and short-term photometric behavior of Comet C/Hyakutake (1996 B2). Icarus 159, 210–233. Schuller, F., 1930. Comet Schwassmann–Wachmann (1930 d). IAU Circ. 288. In: Stromgren, E. (Ed.), BCTA, IAU, 1930 June 16, Copenhagen. Sekanina, Z., 1977. Relative motions of fragments of the split comets. I. A new approach. Icarus 30, 574–594. Sekanina, Z., 1982. The problem of split comets in review. In: Wilkening, L.L. (Ed.), Comets. Univ. of Arizona Press, Tucson, pp. 251–287. Sekanina, Z., 1989. Nuclei of two Earth-grazing comets of fan-shaped appearance. Astron. J. 98, 2322–2345. Sekanina, Z., 1996. Comet 73P/Schwassmann–Wachmann 3. IAU Circ. 6301. Sekanina, Z., Yeomans, D.K., 1984. Close encounters and collisions of comets with Earth. Astron. J. 89, 154–161.

Hubble Space Telescope observations of the nucleus fragment 73P/Schwassmann–Wachmann 3-C

Senay, M.C., Jewitt, D., 1994. Coma formation driven by carbon-monoxide release from Comet Schwassmann–Wachmann 1. Nature 371, 229–231. Singh, P.D., de Almeida, A.A., Huebner, W.F., 1992. Dust release rates and dust-to-gas mass ratios of eight comets. Astron. J. 104, 848–858. Stern, S.A., Parker, J.Wm., Festou, M.C., A’Hearn, M.F., Feldman, P.D., Schwehm, G., Schultz, R., Bertaux, J.–L., Slater, D.C., 1998. HST midultraviolet spectroscopy of Comet 46P/Wirtanen during its approach to perihelion 1996–1997. Astron. Astrophys. 335, L30–L36. Thomas, N., Boice, D.C., Huebner, W.F., Keller, H.U., 1988. Intensity profiles of dust near extended sources on Comet Halley. Nature 332, 51–52. Toth, I., Lamy, P., 2000. Spectral properties of the nucleus of short-period comets. Bull. Am. Astron. Soc. 32, 1063. Abstract [37.05]. Weaver, H.A., Lamy, P.L., 1998. Estimating the size of Comet Hale–Bopp’s nucleus. Earth Moon Planets 79, 17–33.

247

Weaver, H.A., Sekanina, Z., Toth, I., Delahodde, C.E., Hainaut, O.R., Lamy, P.L., Bauer, J.M., A’Hearn, M.F., Arpigny, C., Combi, M.R., Davies, J.K., Feldman, P.D., Festou, M.C., Hook, R., Jorda, L., Keesey, M.S.W., Lisse, C.M., Marsden, B.G., Meech, K.J., Tozzi, G.P., West, R., 2001. HST and VLT investigations of the fragments of Comet C/1999 S4 (LINEAR). Science 292, 1329–1333. Weidenschilling, S.J., 2004. Formation of planetesimals/cometesimals in the solar nebula. In: Festou, M., Weaver, H.A., Keller, H.U. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ. In press. Weissman, P.R., Bottke Jr., W.F., Levison, H.F., 2002. Evolution of comets into asteroids. In: Bottke, W.F., Cellino, A., Paolicchi, P., Binzel, R.P. (Eds.), Asteroids III. Univ. of Arizona Press, Tucson, AZ, pp. 669–686. Weissman, P.R., Asphaug, E., Lowry, S., 2004. Structure and density of cometary nuclei. In: Festou, M., Weaver, H.A., Keller, H.U. (Eds.), Comets II. Univ. of Arizona Press, Tucson, AZ. In press.