Jet Propulsion Laboratory
California Institute of Technology
Presented at the First International Conference on Comet Hale Bopp
Peurta de la Cruz, Tenerife, Canary Islands, Spain
2-5 February 1998
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, Calif.  U.S.A.
Abstract: This paper reports on the detection of a satellite around the primary nucleus of comet HaleBopp. Overlapping jet activity from the comet pair will facilitate modeling the exceptionally complex morphology of the dust coma. The detection was made on images taken with the Hubble Space Telescope's Wide Field Planetary Camera 2 in the planetary mode on five days in May-October 1996. An average satellite-to-primary signal ratio is 0.21 +/- 0.03, suggesting that the satellite's diameter is ~30 km, if the main nucleus is ~70 km across. To avoid collision, the separation distance must exceed 50-60 km or more at all times. The satellite's projected distances derived from the images vary from 16O to 210 km, or 0.06 to 0.10 arcsec. The satellite was not detected in October 1995, presumably because of its subpixel separation from the primary. The radius of the gravitational sphere of action of the main nucleus of the assumed size is 370-540 km at perihelion, increasingly linearly with the Sun's distance: the satellite appears to be in a stable orbit. Its orbital period at ~180km is expected to be ~2-3 days, much shorter than,the intervals between the HST observations. If the main nucleus should be no more than 42 km across, Weaver et al.'s upper limit, the satellite's orbit should become unstable and the Object would drift away from the main nucleus after perihelion, contrary to observation. In fact, ground-based detection of multiple nuclei of massive comets is altogether unlikely. Efforts to determine the satellite's orbit and the total mass of the system are expected to get under way shortly.

Key words comet Hall Bopp, orbiting satellite, nuclear size, sphere of action.
1. Introduction

Comet HaleBopp is unquestionably one of the most spectacular comets ever observed. However, one phenomenon conspicuously absent from all reports has been multiplicity of its nucleus, Because of difficulties with detecting nuclear companions, it is prudent to examine this issue on data of the highest available spatial resolution. Luckily, images were taken with the planetary mode (0.0455 airsick/pixel) charge coupled device (CCD) of the Hubble Space Telescope's(HST) Wide-Field Planetary Camera 2 (WPCZ) through an F675W filter; they have kindly been provided to me by H. A. Weaver.

Reported in the following are the results of my computer analysis of the near-nucleus region on the HST images that were taken on six dates between Oct. 23, 1995 and Oct.17, 1996. The circumstances of these observations are presented in Table I of Sekanina (1998). The brightness distribution in the near-nucleus region has been modeled employing an iterative least squares differential-correction technique, which was described in Sekanina (1995) and has bean upgraded since (Sekanina 1998). Its purpose is twofold.

One, it allows its user to deconvolve the contributions from the nucleus and from the coma and thereby to extract the integrated signal of the nucleus. Two, it offers a convenient tool for detecting additional objects as secondary point sources in the immediate proximity of the nucleus. It is in this second capacity that this procedure has been employed in this paper.
2. The Detection and the Results

All runs in which the observed signal distribution assumed to be due entirely to the coma faded to provide converging solutions for images taken  on all six dates, indicating the presence of a sizable nucleus at the peak signal location. Unexpectedly, the optimized solutions that accounted for a coma and a single nucleus failed to offer satisfactory distributions of signal residuals. The problem is exemplified on the image of July 25, 1996 in Table I, with the surface-brightness distribution of the coma approximated by an anisotropic law [of the type A. cf. Eq. (3) of Sekanina 1998). A prominent clump of positive residuals (enclosed in a box), with a maximum access signal of +180 ADU (CCD analog-to digital intensity units per pixel2), is

encircled a ring of distinctly negative residuals, with an extreme signal of -108 ADU. The total amplitude of 288 ADU contrasts with a combined expected noise of only about +/-15 ADU in the critical pixels, suggesting a huge effect. Also present is a strong systematic trend across the field, from negative residuals on the left to positive ones on the right. These perplexities were shown (Sekanina 1995) to be signatures of a point source near the clump's peak that has not been accounted for. Indeed, introducing a second point source into the solution brings the mean residual down significantly, as seen from Table II, where the results for the primary nucleus and its major companion on the image of July 25 are listed as functions of the number of paint sources that were accounted for.

The solution with a total of nine point sources offers a satisfactory fit to the observed signal distribution, improving the match by factor of more than two. One also notices remarkable stability of the derived parameters. This is especially true for the solutions with more than four point sources, even though some of these may in fact be artifacts of instrumental or unknown origin.

In another example, a prominent secondary peak is apparent in Fig. 1, which shows a model brightness distribution for the image of May 20, 1996.

The results are summarized in Table III, after the coma contribution was filtered out using one of two laws, A or B (Sekanina 1998). I submit that the major companions on the five exposures between May 20 and Oct. 17, 1996 are the same object, an orbiting satellite. Its diameter is found to amount to ~33 km by brightness comparison with the main nucleus (Sekanina 1998). This satellite was not detected on the image of Oct. 23, 1995, presumably because of its subpixal separation from the primary nucleus. On the whole, the results are insensitive to the coma law used, even though for May and October 1996 the law B, yielding higher formal errors on the average, Ieads to wider separations. For Sept. 23, the solution based on the law A offers for the satellite two candidates in very different directions from the primary.

Figure 2 shows the satellite's separations from the primary nucleus, with the sizes of both objects drawn to scale. The prevalence of the offsets to the north may be a signature of an elongated orbit's apoapsis, near which the satellite should spend most of the time. I find no strong correlation with the directions of persistent dust jets as listed by Boehnhardt et al. 1998),
Figure 2. The satellite's apparent offsets (on the left) and projected separation distances (on the right) from  
the primary nucleus on five dates in 1996 have been derived from the optimized solutions employing the  
coma law A. In both panels, the demensions of the main nucleus (~70km across) and the satellite  
(~30km across) are drawn to scale. To avoid collision, the separation distance must exceed 50-6-km  
(or more for irregularly shaped objects) at all times. Notice an alternative candidate for the satellite  
on Sept. 23. The pixel size is shown as a shaded square in the upper left corner of the left-hand side panel. 

3. Dynamical Stability of the Comet Pair and the Orbital Period

The existence of an orbiting satellite is attractive conceptually, because it could help understand the comet's extraordinary brightness and the exceptionally complex morphology of its dust coma as products of overlapping activity from two nuclear components.

Of major concern is the dynamical stability of the system, given the separation distances in Table III. in Laplace's classical definition, the boundary of the gravitational sphere of action of a body is the surface on which the force of gravity of this central body expressed in units of the disturbing force of the perturbing body is equal to the force of gravity of the perturbing body expressed in units of the disturbing force of the central body. Identifying the central body with the main nucleus and the perturbing body with the Sun, and considering that the dimensions of the comet's sphere of attraction are orders of magnitude smaller than the distance Sun-comet, one finds for the radius ro (in km) ofthe sphere of action of the primary nucleus and expression

                                         ro=6.24x10(-6)rq Mi 2/5,           (1)

where rq is the comet's heliocentric distance (in AU) and Mi  is the mass of the primary nucleus (in g). The radius of the Earth's sphere of action is 805,006 km, almost exactly twice the Moon's distance at apogee. With a bulk density of 0.2-0.5 g/cm3, one gets for the nucleus of N~70km in diameter (Sekanina 1998) Mi =(3.4-8.6) x IO19g and ro = 370-540 km at perihelion (0.914 AU) and >1000 km at heliocentric distances exceeding ~2-3 AU; the satellite is in a stable orbit even at perihelion. The velocity of escape is 13-19 m/s at the surface of the primary, but only 5-8 m/s at a distance of 180 km. On the other hand, with Weaver et al.'s (1997) estimate of 542 km for the primary's diameter, one finds ro to be <300 km at perihelion and the satellite's orbit should then become unstable.

The orbital period P (in days) of a satellite of mass Mii  which moves at an average distance of S (in km) from the primary of mass Mi (in g) is

                           P  = 8.92 x 106 S 3/2 [Mi  (1+m)]-1/2        (2)

where m = Mii/Mi.  From the signal ratio Tii/Ti (Table III) I estimate that  mabout or equal to 0.1.  At an average distance of S about or equal to 180 km, the orbital period is some 2-3 days if the primary is ~70 km in diameter, but 9-15 days if it is 27 km  across, equal to Weaver et al.'s lower limit for the size of the main nucleus. In either case, the period is much shorter than the 1-2 month intervals between two consecutive HST observations. Although this will complicate the satellite's orbit determination and the finding of the total mass for the  system, there are plans to get these efforts under way shortly.

I thank Harold A. Weaver for providing me with the HST digital charts of the near-nucleus region; for information on the HST image calibration; and for his helpful critique. This work is based on observations made with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Aeronautics and Space Administration. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

Boehnhardt, H., Birkle K., Colas, P., Fiedler, A., Jorda, L., Peschke, S., Rauer, H., Schulz, R.,
       Schwehm, G., Thomas, N., Tozzi, G., and West, R. M.: 1998, this volume.
Sakanina, Z.: 1995, Astron. Astrophys. 304, 296-316.
Sekanina, Z.: 1998, this volume; also: JPL Cometary Science Team Preprint Series, No. 172. Weaver, H. A., Feldman, P. D, A'Hearn, M. F., Arpigny, C., Brandt, J. C., Festou, M. C.,
       Haken, M., McPhate, J. B., Stern, S. A. and Tozzi, G. P.: 1997, Science 275, 1900-1904.