Version September 12, 2017 Preprint typeset using LATEX style emulateapj v. 08/22/09 ORBITAL EVOLUTION, ACTIVITY, AND MASS LOSS OF COMET C/1995 O1 (HALE-BOPP). I. CLOSE ENCOUNTER WITH JUPITER IN THIRD MILLENNIUM BCE AND EFFECTS OF OUTGASSING ON THE COMET’S MOTION AND PHYSICAL PROPERTIES Zdenek Sekanina1 & Rainer Kracht2 1Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, U.S.A. 2Ostlandring 53, D-25335 Elmshorn, Schleswig-Holstein, Germany Version September 12, 2017 ABSTRACT This comprehensive study of comet C/1995 O1 focuses first on investigating its orbital motion over a period of 17.6 yr (1993–2010). The comet is suggested to have approached Jupiter to 0.005 AU on 2251 November 7, in general conformity with Marsden’s (1999) proposal of a Jovian encounter nearly 4300− yr ago. The variations of sizable nongravitational effects with heliocentric distance correlate with the evolution of outgassing, asymmetric relative to perihelion. The future orbital period will shorten to 1000 yr because of orbital-cascade resonance effects. We find that the sublimation curves of parent molecules∼ are fitted with the type of a law used for the nongravitational acceleration, determine their orbit-integrated mass loss, and conclude that the share of water ice was at most 57%, and possibly less than 50%, of the total outgassed mass. Even though organic parent molecules (many still unidentified) had very low abundances relative to water individually, their high molar mass and sheer number made them, summarily, important potential mass contributors to the total production of gas. The mass loss of dust per orbit exceeded that of water ice by a factor of 12, a dust loading high enough to imply a major role for heavy organic molecules of low volatility in∼ accelerating the minuscule dust particles in the expanding halos to terminal velocities as high as 0.7 km s−1. In Part II, the comet’s nucleus will be modeled as a compact cluster of massive fragments to conform to the integrated nongravitational effect. Subject headings: comets: individual (C/1995 O1) — methods: data analysis 1. INTRODUCTION: MAKING CASE FOR A CLOSE one year before the 1997 perihelion and that the orbit had ENCOUNTER WITH JUPITER originally been more elongated, with a period of slightly The celebrated comet C/1995 O1 (Hale-Bopp) was ex- longer than 4200 yr. Obviously, the object did not arrive ceptional in a number of ways, one of which was its enor- from the Oort Cloud; its previous perihelion passage had mous intrinsic brightness. This trait rendered it possible occurred in the course of the 23rd century BCE. to discover and observe the comet at very large helio- As described by Marsden, this was only a minor part centric distance and to collect astrometric observations of the story. Because the comet’s ascending node places over a long period of time. Discovered visually on 1995 it practically on Jupiter’s orbit, extremely close encoun- July 23, more than 600 days before perihelion, as an ob- ters with the planet are possible, and Marsden (1999) ject of mag 10.5–10.8 (Hale & Bopp 1995), the comet argued that this was precisely what happened 42 cen- was subsequently recognized at mag 18 on a plate taken turies ago on the comet’s approach to perihelion. He even on 1993 April 27 with the 124-cm UK Schmidt telescope ventured to propose that the comet had been captured of the Siding Spring Observatory near Coonabarabran, by Jupiter’s gravity from its original Oort-Cloud-type, N.S.W., Australia (McNaught 1995), 3.9 yr before per- highly elongated orbit. ihelion and 13.0 AU from the Sun. With the latest as- In his investigation, Marsden (1999) was handicapped trometrically measured images from 2010 December 4 by a relatively short interval of time that the comet’s observations then spanned. The last observation he em- arXiv:1703.00928v2 [astro-ph.EP] 11 Sep 2017 (when 30.7 AU from the Sun!), taken with the 220-cm f/8.0 Ritchey-Chr`etien reflector of the European South- ployed was dated 1998 February 8, so that the observed ern Observatory’s Station at La Silla, Chile (Sarneczky orbital arc was only 4.8 yr long, not much more than a et al. 2011), the observed orbital arc covers a period of quarter of the interval of time available nowadays. 17.6 yr, with 13.7 yr of post-perihelion astrometry — an The fascinating problem of the long-term orbital evo- unprecedented feat for a single-apparition comet. lution of C/1995 O1 and the related issues warrant a new No less astonishing is the orbital history of the comet investigation, given in particular that the much greater (Marsden 1999). Soon after its discovery, the orbit could span of astrometric observations currently available al- substantially be improved thanks to the Siding Spring lows us to conduct a considerably more profound exam- pre-discovery observation. Although Marsden eventually ination of the orbital scenario and its potential implica- determined that the near-perihelion osculating orbital tions than it was possible a dozen or more years ago [for period equalled about 2530 yr, he noticed that this was some later efforts similar to Marsden’s (1999), see, e.g., due in part to the perturbations by Jupiter during the Szutowicz et al. (2002) or Kr´olikowska (2004)]. We fur- comet’s approach to within 0.8 AU of the planet about ther propose to confront our approach and results with evidence from the comet’s physical observations made in Electronic address: [email protected] the course of the 1997 apparition and to draw conclusions [email protected] from this data interaction. 2 Sekanina & Kracht 2. DATA, TOOLS, AND METHOD OF APPROACH two consecutive solutions — before and after elimination We began by collecting 3581 astrometric observations of the poor-quality data — could cause that some data of comet C/1995 O1 from the database maintained by points with the residuals slightly exceeding the limit in the Minor Planet Center.1 This is a complete list of the the first solution (and therefore removed from the set of comet’s currently available astrometric data in equinox used observations) just satisfied the limit in the second J2000. Besides the single pre-discovery observation in solution (and were to be incorporated back into the set); 1993 (McNaught 1995), the data set contains 830 obser- while other data points with the residuals just satisfy- vations from the year 1995, 1458 from 1996, 653 from ing the limit in the first solution (and therefore kept in 1997, 295 from 1998, 198 from 1999, 50 from 2000, 51 the set) slightly exceeded the limit in the second solution from 2001, 9 from 2002, 14 from 2003, 14 from 2005 (and were now to be removed from the set). In order to (of which 6 from January–February and 8 from July– comply with the cutoff rule, it was necessaary to iterate August), 5 observations from 2007 October, and 3 from the process until the number of astrometric observations 2010 December 4.2 that passed the test fully stabilized. As described in Section 3 below, the single observa- The primary objective of the first phase of our orbit- ′′ determination effort was to subject the collected set of tion of 1993 is known to be accurate to about 1 , while astrometric observations to tests in order to extract a nearly a half of the observations from 2005 and all from subset of high-accuracy observations. To ensure that this 2007-2010 were made with large telescopes; the more ad- has indeed been achieved requires an introduction of a vanced solutions (Sections 6.2–6.3) showed a posteriori cutoff or threshold of choice for removing from the col- that these data points satisfied the tight limit and were lection all individual observations whose (observed mi- not subjected to the aforementioned test. nus computed) residuals in right ascension, (O C) , With these basic rules in mind, we applied an orbit- − RA determination code EXORB7 , written by A. Vitagliano, or declination, (O C)Decl, exceed the limit. In practice, the task is made difficult− by the fact that a residual ex- both in its gravitational and nongravitational modes. Us- ceeding the limit does so for one of two fundamentally ing the JPL DE421 ephemeris, the code accounts for the different reasons: either because the astrometric position perturbations by the eight planets, by Pluto, and by the is of poor quality or because the comet’s motion is mod- three most massive asteroids, as well as for the relativis- eled inadequately. The aim of the procedure is to reject tic effect. The nongravitational accelerations are incor- the data points with large residuals that are of the first porated directly into the equations of motion (Section 4). category but not of the second category; to discriminate The code employs a least-squares optimization method between the two categories requires an incorporation of to derive the resulting elements and other parameters. an efficient filter. Typically, the category into which an 3. PAST WORK AND PURELY GRAVITATIONAL observation with a large residual belongs is revealed by SOLUTIONS comparing, with one another, observations over a lim- ited orbital arc: if all or most of them exhibit systematic The comet’s pre-discovery image from 1993, measured residuals, the problem is in the comet’s modeled motion; by McNaught (1995), is of major significance, because it if one or a few stand out in reference to the majority, it extends the observed orbital arc by 27 months.