spin axis direction of comet 19p/borrelly based ongram. the ds1 encounter with 19p/borrelly occurred...

Spin Axis Direction of Comet 19P/Borrelly Based on

Observations from 2000 and 2001

Nalin H. Samarasinha and Béatrice E.A. MuellerNational Optical Astronomy Observatory∗, 950 N. Cherry Ave., Tucson AZ 85719,USA. ([email protected],[email protected])

Abstract. We calculate the direction of the rotational angular momentum vector,M, of comet 19P/Borrelly based on rotational lightcurve data from 2000, ground-based imaging of the coma during the Deep Space 1 encounter, and the basicnear-nucleus coma morphology as revealed by the Deep Space 1 spacecraft. Forthe most likely direction, we derive a family of solutions (with center at RA=221◦,Dec=−7◦) if the direction of M is towards the sunward hemisphere during theDeep Space 1 encounter, whereas if the rotation is of opposite sense, the diametricallyopposite family of solutions (with center at RA=41◦, Dec=7◦) would result. Weargue that the coma morphology in September 2001 is consistent with the nucleusbeing a principal axis rotator or one observationally indistinguishable from it. There-fore, for all practical purposes, the direction of the rotational angular momentumvector coincides with the spin axis. We also discuss why the determination of thespin axis direction based on observations from the last apparition is in disagreementwith the current result.

Keywords: Comet 19P/Borrelly, Rotation

1. Introduction

Jupiter family comet 19P/Borrelly attracted considerable interest asit was the final flyby target of the Deep Space 1 (DS1) spacecraft, atechnology validation mission under the NASA New Millennium pro-gram. The DS1 encounter with 19P/Borrelly occurred a few days afterperihelion on September 22, 2001 (Soderblom et al., 2002). It is thesecond cometary nucleus to be imaged by a spacecraft after comet1P/Halley.

We use groundbased observations together with the basic near-nuc-leus coma morphology of 19P/Borrelly as revealed by the DS1 space-craft to determine the direction of the spin axis of the nucleus. Thenext section of this paper describes the groundbased observations weused, while section 3 is focussed on deriving the direction of the spinaxis. Section 4 addresses the likely spin state and a possible reason for

∗ The National Optical Astronomy Observatory is operated by the Associationof Universities for Research in Astronomy, Inc., under cooperative agreement withthe National Science Foundation.

c© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

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2 Samarasinha and Mueller

the incompatible derivations of the rotation axis based on observationsfrom prior apparitions. The last section summarizes the conclusions.

2. Observations and Analysis

2.1. NUCLEAR LIGHTCURVE OBSERVATIONS FROM 2000

Nuclear lightcurve observations of 19P/Borrelly were taken at the CTIO1.5 m telescope in broadband R from July 28-Aug 1, 2000. The readeris referred to Mueller and Samarasinha (2002) for a detailed descriptionof those data and the corresponding analysis. Based on those data, aperiod of 26.0±1 hr was derived assuming a double-peaked lightcurve.As described in section 3, we use the brightness variation in thatlightcurve (approximately 0.84–1.0 mag) to determine the spin axis of19P/Borrelly. The lightcurve is consistent with a principal axis rotationaround the short axis.

2.2. GROUNDBASED R-BAND COMA IMAGES FROMSEPTEMBER 2001

We imaged the coma of comet 19P/Borrelly on September 21, 22, and23 in 2001 bracketing the DS1 encounter of the comet. Observationswere carried out at the KPNO 2.1m telescope in broadband R. Table Ilists the geometrical circumstances for these observations. Unfortu-nately as the comet was a morning object, each night’s observationswere limited to less than 2 hrs. Figure 1a represents an azimuthallyrenormalized image from September 22 (this enhancement techniquedestroys radial information while it enhances azimuthal variations).Figure 1b shows the same in (ρ, θ) representation, where ρ is theprojected radial distance from the nucleus (optocenter) while θ is theazimuth. Remarkably, the strong sunward linear jet at position angle(PA) of 93◦±1◦ shows no detectable change over the three nights. Thisjet is the brightest coma feature up to about 7 × 104 km from thenucleus after which the tail starts to dominate. The full-width at half-maximum for this jet (after background subtraction) is 35◦. We identifythis jet with the strong straight jet seen in the DS1 images, which isthe same as the eastward jet at a PA of 93◦ in the near-simultaneousHST images (Stern et al., 2002). Lack of curvature in this jet over7 × 104 km, corresponding to dust released over a day or more forsub km s−1 grain outflow velocities (i.e., a time interval at least of theorder of the 19P/Borrelly rotation period), points to a source regionat or near the rotation pole of the nucleus for an assumed principalaxis rotator. However, if a broad range of grain velocities are present,


Rotation Axis of Comet 19P/Borrelly 3

even for a jet source region clearly offset from the pole, the curvatureof the jet can get smeared and appear straight except when close tothe nucleus (cf. effect shown in figure 3 of Samarasinha et al. (1999)).As the high-resolution HST images too show no detectable curvature(A. Stern, personal communication), we conclude that the jet is indeedemanating from the pole or from somewhere nearby. This is consistentwith the conclusion of the DS1 observations (Soderblom et al., 2002).

Table I. Geometrical circumstances for 19P/Borrelly in September 2001.

Date UT range rah [AU] ∆b [AU] αc [deg]

September 21, 2001 10:48-12:15 1.360 1.479 41.1

September 22, 2001 10:54-12:06 1.361 1.475 41.2

September 23, 2001 10:48-11:09 1.363 1.471 41.3

a heliocentric distanceb geocentric distancec solar phase angle

3. Constraining the Spin Axis

First, we use nuclear lightcurve observations from 2000 to place initialconstraints on the spin axis. We assume (a) scattered light from thecomet received at Earth is proportional to the cross sectional area ofthe nucleus exposed to sunlight (strictly speaking this holds true forLambertian scattering occurring at zero solar phase angle), (b) theratio between the long and intermediate axes of the nucleus, a/b, isapproximately 2.5 (cf. results from the MICAS instrument aboard DS1spacecraft, lightcurve from HST (Lamy et al., 1998)), and, (c) thenucleus is in principal axis spin state around the short axis (whichwe justify later). Then the approximate lightcurve variation of 0.84–1.0 mag corresponds to a spin axis inclined to the line of sight byapproximately 60◦–85◦ during the July 2000 lightcurve observations(two lightly shaded strips in Figure 2 correspond to directions in thesky compatible with this condition). We assumed that the phase angleeffects on the lightcurve amplitude are negligible as the solar phaseangle was near zero degrees (eight degrees).

The directions of the spin axis compatible with the PA of the polarjet (93◦±1◦) seen in groundbased images of September 2001 are shownby the darkly shaded region in Figure 2. Therefore, the intersection oflightly shaded and darkly shaded regions provides the solutions for the



Figure 1a. Azimuthally renormalized 19P/Borrelly image from September 22 withnucleus at the center. Each side is 2.6×105 km. North is to the top and east is to theleft. The projected solar direction is at PA of 101◦. White denotes bright features.After about 7× 104 km from the nucleus, the dust tail starts to dominate.

Figure 1b. (ρ, θ) representation of the image of Figure 1a. Leftmost azimuth is northand the PA increases to the right. Radial distance increases towards the top and theradial extent is 1.3× 105 km. The jet (on the left) has a nearly constant width.



Figure 2. Spin axis direction of the nucleus of comet 19P/Borrelly. Earth symboldenotes the sub-Earth directions with respect to the comet for the dates listed.Intersection of lightly and darkly shaded regions (and the diametrically oppositedirections) provides the solutions for the spin axis direction. The solutions are highlyconstrained in a direction which approximately aligns with Declinations but poorlyconstrained in the direction normal to it. ZS denotes the direction proposed bySekanina (1979).

directions of the spin axis (as well as that of the strong sunward jet)compatible with the before mentioned observations. It is worthwhilenoting that there are two narrow bands of solutions with their centersat (RA=221◦, Dec=−7◦) and (RA=184◦, Dec=7◦). Furthermore, as wedo not have any evidence as to the sense of rotation, the diametricallyopposite solutions with corresponding centers at (RA=41◦, Dec=7◦)and (RA=4◦, Dec=−7◦) are also possible for the spin axis direction.We stress that the entire family of solutions are equally acceptable andmid points are provided only for convenience. Independent determi-nations by Soderblom et al. (2002), Schleicher et al. (2002), Farnhamand Cochran (2002), Thomas et al. (2001), and Ho et al. (2002) basedon different sets of observations point to directions of the spin axisconsistent with the first value (i.e., RA=221◦, Dec=−7◦) or that dia-metrically opposite of it. Interestingly, these spin axis directions are inthe neighbourhood of asymptotic directions predicted for the long-termevolution of the rotational angular momentum vector due to torquesinduced by sublimation (e.g., Samarasinha, 1997). We urge observers tocarefully perform enhancements of comet 19P/Borrelly images taken atdifferent epochs to detect any coma feature with curvature which maybe useful in eliminating the ambiguity due to the sense of rotation.



4. Discussion

4.1. SPIN STATE OF COMET 19P/BORRELLY

For calculating the spin axis direction, we assumed that the nucleus of19P/Borrelly is in principal axis rotation around the short axis. Usingthe characteristics of the strong sunward jet of 19P/Borrelly, we showthat indeed the nucleus is at this rotation state or at a slightly excitedstate. We argue that the latter is observationally indistinguishable fromthe former. Figure 3 depicts different spin states of a nucleus andtheir primary observationally identifiable characteristics. Depending onwhether the short axis or the long axis moves about the rotationalangular momentum vector, M, rotation can be categorized into twomodes. They are called Short Axis Mode (SAM) or Long Axis Mode(LAM), respectively (Julian, 1987; Samarasinha and A’Hearn, 1991).In Figure 3, M stands for the rotational angular momentum, and E forthe rotational kinetic energy, while Il, Ii, and Is represent the momentsof inertia around long, intermediate, and short axes, respectively. Pψdenotes the rotation or oscillatory period (depending on LAM or SAM)around the long axis, whereas Pφ stands for the mean precession periodof the long axis around M. θ is the angle between the long axis andM, while Aψ is the amplitude of the oscillatory motion of the long axisfor SAM. The angle θ is 0◦ for the principal axis rotation around thelong axis while it is 90◦ for the principal axis rotation around the shortaxis. The following is an analysis of the spin states compatible withobservations for 19P/Borrelly.

Principal axis rotation around the long axis (M2

2E = Il): As the DS1images show that the sunward linear jet is emanating from a directionnearly normal to the long axis, the nucleus could certainly not be inthis highest energy state. Otherwise, the sweeping motion of the jetwould result in a curvature representative of the rotation rate.

Non-principal axis rotation near M2

2E = Il: Since θ is near 0◦, the

character of the coma morphology will be similar to the previous case.Therefore, we rule out these states.

Non-principal axis rotations near M2

2E = Ii: For these states, Pψ ÀPφ and for coma morphology, effects due to precession of the long axisdominate. As the groundbased images do not indicate any signatureof curvature nor changes in PA of the jet over a few days (i.e., thereis no indication of the rotation/oscillatory motion of the long axis) weconclude that these states are unlikely.

Non-principal axis rotations near M2

2E = Is: Since Aψ is near 0◦, coma

morphology due to a jet will be indistinguishable from that due to a



M2

2E= Il

P same order as P� ; � near 0�

LAM

EM"

P � P� ; � near 90�

M2

2E= Ii

P � P� ; A near 90�

SAM

P > P� ; A near 0�

M2

2E= Is

Figure 3. Basic characteristics of various spin states.

nucleus undergoing principal axis rotation around the short axis1. Inother words, a slightly excited non-principal axis rotation state cannotbe excluded based on coma morphology. Furthermore, such a statecannot be identified from a groundbased lightcurve either.

Therefore, a nucleus undergoing principal axis rotation around theshort axis or one slightly excited from this state together with a sourceregion at or nearby to the pole can reproduce the strong sunward jetof comet 19P/Borrelly. Coma simulations indicate that the proposedspin axis direction together with a polar jet is consistent with thegroundbased observations during the DS1 encounter.

4.2. PRIOR DETERMINATIONS OF THE SPIN AXISDIRECTION

There are derivations of the spin axis direction of 19P/Borrelly based onobservations from prior apparitions. Fulle et al. (1997) follow the comastructure of comet 19P/Borrelly during its 1994 perihelion passage and

1 There is a another rotation component to the spin state represented by anodding motion of the long axis; however as the amplitude of that component iseven smaller than Aψ, it is not considered in the discussion.



in early 1995 to derive the direction of the spin axis. When the cometwas near perihelion in late 1994, there is a clear sunward structuresimilar to the sunward jet of September 2001. Fulle et al. (1997) usedthe PA of this structure and its evolution over time in their derivationof the spin axis direction. They find that a single spin axis directioncannot explain the evolution of the PA, and therefore they adopt aprecession model and derive a precession period of 2.5 yrs for the spinaxis.

As the orbital period of 19P/Borrelly is 6.87 yr (i.e., close to aninteger number) between the 1994 and 2001 perihelion passages, theobserving geometries from the Earth during the 1994 and 2001 appari-tions are qualitatively similar. Also, the same source region causing thestrong sunward jet of September 2001 should be exposed to constantsunlight around the 1994 perihelion passage (assuming there was nosignificant change in the direction of the angular momentum vectorduring the two apparitions — a reasonable assumption for a nucleus aslarge as 19P/Borrelly under the corresponding outgassing torques dueto the polar jet). Table II lists the observing circumstances for the Fulleet al. (1997) data for our spin axis direction of (RA=221◦, Dec=-7◦).The penultimate column of the Table lists the PAs of the projectedM whereas the PAs of the sunward structure as measured by Fulle etal. (1997) are given in the last column. The least agreement betweenthese two columns can be found for the last few entries in Table II.Note that the sun-comet-angular momentum angle is increasing withtime. Especially during February and March 1995, the angular mo-mentum vector, and therefore the source region for the strong sunwardjet, is near or below the terminator. If the spin axis direction is near(RA=184◦, Dec=7◦), the strong sunward jet would turn-off even earlierthan February 1995. Therefore, we argue that the evolving structureof Fulle et al. (1997) does not represent the same jet during the entireduration of their observations. We think that the evolution of thatstructure was caused by contributions from other source regions on thenucleus in addition to the projection effects. Indeed, evidence for otherpossible jet activity on the nucleus is present in DS1 images (Soderblomet al., 2002).

For the 1994 HST images of Lamy et al. (1998), the PA of the spinaxis is 96◦ for a spin axis direction of (RA=221◦, Dec=-7◦). We measurea PA of 98◦±2◦ for the sunward structure in 1994 HST image shown infigure 1 of Lamy et al. (1998). Therefore, this PA is in good agreementwith the PA in the previous sentence. A similar agreement was alsofound independently by L. Jorda (personal communication). The 1994HST images were taken only less than 2 days prior to the third entryin Table II. However, the PA measured by Fulle et al. (1997) for the


Rota

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Axis

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/B

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9

Table II. Geometrical circumstances for Fulle et al. (1997) data

Date RAa Decb rh ∆ PAcS ECS

d ECMe SCMf PAgM PAhF

[yy] [mm] [dd] [deg] [deg] [AU] [AU] [deg] [deg] [deg] [deg] [deg] [deg]

94 10 21 288 -9 1.37 0.80 99 46 66 21 94 90

94 11 06 298 -18 1.37 0.70 102 44 76 32 93 95

94 11 30 313 -36 1.40 0.62 96 37 88 50 97 102

94 12 01 314 -37 1.41 0.62 95 37 88 51 97 102

94 12 03 315 -38 1.41 0.62 94 36 89 53 98 102

94 12 04 316 -39 1.42 0.62 94 36 89 53 98 105

94 12 07 317 -42 1.43 0.62 91 35 90 55 99 104

94 12 15 321 -48 1.45 0.63 84 33 92 61 102 108

94 12 24 325 -54 1.49 0.65 74 30 92 67 105 109

94 12 27 326 -56 1.51 0.67 70 30 92 69 106 110

95 1 03 328 -60 1.54 0.70 60 29 92 73 108 110

95 1 08 328 -63 1.57 0.73 52 28 91 76 108 110

95 1 09 328 -63 1.57 0.74 50 28 91 77 108 109

95 1 29 324 -68 1.69 0.89 16 27 88 88 105 111

95 2 01 323 -69 1.71 0.91 11 27 88 89 104 110

95 2 03 323 -69 1.72 0.93 8 27 88 90 103 110

95 2 06 322 -69 1.74 0.96 3 27 87 92 102 110

95 3 11 317 -64 1.96 1.33 322 27 86 106 98 120

a RA of the sub-Earth direction; b Dec of the sub-Earth directionc PA of the projected solar direction; d Earth-comet-Sun anglee Earth-comet-angular momentum angle; f Sun-comet-angular momentum angleg PA of projected M; h PA of the evolving sunward structure from Fulle et al.

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sunward structure in the corresponding image for the third entry is102◦, leading us to suspect that the errors in the measured PAs quotedin Fulle et al. (1997) are more than 1◦ or 2◦.

Sekanina (1979) derived a spin axis direction from the PAs of thesunward structures quoted in the literature. These data correspond toearly twentieth century apparitions of the comet. The Sekanina solutionis marked as ZS in Figure 2 for reference. However, this solution is notcompatible with the PA of the strong sunward jet seen in September2001. If the polar source region seen in DS1 images is directly facing theSekanina spin axis direction, we find that the source region should bein the night side during the DS1 encounter. If we use the diametricallyopposite direction, the PA of the polar jet as seen from the Earth duringthe DS1 encounter should be 46◦ — in direct conflict with the measuredvalue of 93◦.

5. Conclusions

The main conclusions of this study are:(a) The rotation state of comet 19P/Borrelly is either in the principalaxis rotation around the short axis or in a state slightly excited whichis observationally indistinguishable from the former. For the principalaxis spin around the short axis, the nucleus rotates around the shortaxis with a period of 26.0 hr.(b) The strong sunward jet seen in groundbased images taken aroundthe DS1 encounter is emanating from a source region at or near thepole.(c) The most likely spin axis direction for comet 19P/Borrelly is eithernear (RA=221◦, Dec=−7◦) or near the diametrically opposite direction(RA=41◦, Dec=7◦). One of these solutions can be ruled out if the senseof rotation is known.(d) Prior determination of the spin axis direction based on the previousapparition, illustrates the difficulties and traps that one should be awareof when the observations used consist only of coma morphology.

6. Acknowledgements

We thank Dr. Tod R. Lauer for assistance during the September 2001observing run and the KPNO support personnel for their prompt re-sponses. This work was supported by a grant from the NASA PlanetaryAstronomy program.



References

Farnham, T.L. and Cochran, A.L.: 2002, ‘McDonald Observatory observations ofcomet 19P/Borrelly: Placing the Deep Space 1 observations into a broadercontext’, Icarus, submitted

Fulle, M., Milani, A., and Pansecchi, L.: 1997, ‘Tomography of a sunward structurein the dust tail of comet 19P/Borrelly’, Astron. Astrophys. 321, 338-342

Ho, T.M., A’Hearn, M.F., Boice, D.C., Bonev, T., Jockers, K., Meech, K.J.,Soderblom, L.A., and Thomas, N.: 2002, ‘Comparison of Earth-based and DeepSpace 1 observations of comet 19P/Borrelly’, In Abstracts for IAU Coll. 186:Cometary Science After Hale-Bopp, pg 22

Julian, W.H.:1987, ‘Free precession of the comet Halley nucleus’, Nature 326, 57-58.Lamy, P.L., Toth, I., and Weaver, H.A.: 1998, ‘Hubble Space Telescope observations

of the nucleus and inner coma of comet 19P/1904 Y2 (Borrelly)’, Astrophys. J.337, 945-954

Mueller, B.E.A. and Samarasinha, N.H..: 2002, ‘Visible lightcurve observations ofcomet 19P/Borrelly’, these proceedings

Samarasinha, N.H.:1997, ‘Preferred orientations for the rotational angular momen-tum vectors of periodic comets’, Bull. Am. Astron. Soc. 29, 743

Samarasinha, N.H. and A’Hearn, M.F.: 1991, ‘Observational and dynamical con-straints on the rotation of comet P/Halley’, Icarus 93, 194-225

Samarasinha, N.H., Mueller, B.E.A., and Belton M.J.S.: 1999, ‘Coma morphologyand constraints on the rotation of comet Hale-Bopp’, Earth, Moon, and Planets77, 189-198

Schleicher, D.G., Woodney, L.M., and Millis, R.L.: 2002, ‘Comet 19P/Borrelly atmultiple apparitions: Seasonal effects in gas and dust’, Icarus, submitted

Sekanina, Z.: 1979, ‘Fan-shaped coma, orientation of rotation axis, and surfacestructure of a cometary nucleus. I. Test of a model on four comets’, Icarus 37,420-442

Soderblom, L.A., Becker, T.L., Bennett, G., Boice, D.C., Britt, D.T., Brown, R.H.,Buratti, B.J., Isbell, C., Giese, B., Hare, T., Hicks, M.D., Howington-Fraus,E., Kirk, R.L., Lee, M., Nelson, R.M., Oberst, J., Owen, T.C., Rayman, M.D.,Sandel, B.R., Stern, S.A., Thomas, N. and Yelle, R.V.: 2002, ‘Observations ofcomet 19P/Borrelly by the miniature integrated camera and spectrometer aboardDeep Space 1’, Science, in press

Stern, S.A., Weaver, H.A., and Parker, J.Wm.: 2002, ‘HST/STIS observations ofcomet 19P/Borrelly during the Deep Space 1 encounter’, Astron. J., submitted.

Thomas, N., A’Hearn, M.F., Boice, D.C., Britt, D.T., Meech, K.J., Sandel, B.R.,Soderblom, L.A., and Yelle, R.V.: 2001, ‘Jet morphology in the inner coma ofcomet 19P/Borrelly observed by the Deep Space 1 MICAS imaging system’, Bull.Am. Astron. Soc. 33, 1074


spin axis direction of comet 19p/borrelly based ongram. the ds1 encounter with 19p/borrelly occurred...

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