Michael J.S. Belton National Optical Astronomy Observatories, Tucson, AZ 85716. USA

1. Determination of the Spin State of a Cometary Nucleus From Remote Observations: Application to 9P/Tempel 1, 1P/Halley, & 2P/Encke Michael J.S. Belton National Optical Astronomy Observatories, Tucson, AZ 85716. USA (mbelton@noao.edu) 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

2. Determination of Cometary Spin States: Overview – • To learn about cometary nuclei from Earth-based remote observations the spin state must be determined. • Several cometary nuclei may be in excited spin states. • How may such a spin state be determined from remote observations? • Application to comets of space exploration interest – 9P/Tempel 1, 1P/Halley, and 2P/Encke. Conclusions – • The spin state of 1P/Halley is excited and known • The spin state of 10P/Tempel 2 may be known; Sekanina’s hypothesis on the origin of sunward fans needs testing. • The spin states of other comets are not known • 9P/Tempel 1 and 2P/Encke are challenging cases…… 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

3. Value of Knowledge of Spin States • Interpretation of coma phenomena in terms of the properties of active sources on the nucleus. • Understanding observed orbital evolution under the influence of non-gravitational forces and what it tells us about processes on the nucleus. • Knowledge of excited spin states can put constraints on mass distribution in the nucleus and its shape. • Preparation for spacecraft encounters Reviews – Sekanina, Z. (1981), Whipple, F.L. (1982), Wallis, M.K. (1984), Belton, M.J.S (1991), Jewitt (1997) 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

4. Spin speak….. k2 = 0 k2 = 1 k2 = 0 From Belton 1991 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

5. Comets for which the Spin State is known: With known spin state: • 1P/Halley 3.69 d 7.1 d Belton et al (1991); Samarasinha & A’Hearn (1991) Possibly with known pole position and periodicities (hrs) • 10P/Tempel 2 8.94 Sekanina 1991; Mueller & Ferrin (1996) • 2P/Encke 15.08 8.7 Sekanina (1988); Luu & Jewitt (1990); this work. With known periodicity: • 31P/Schwassmann-Wachmann 2 5.8 hrs Luu & Jewitt (1992) • 95P/Chiron 5.9 Bus et al (1989) • 107P/Wilson-Harrington 6.1 Osip et al (1995) • C/Hyakutake 6.23 Schleicher et al (1998) • C/Hale-Bopp 11.30 Farnham & Schleicher (1997) • 28P/Neujmin 1 12.68 Campins et al (1987) • 49P/Arend-Rigaux 13.46 Millis et al (1988) • 29P/Schwassmann-Wachmann 1 14.0 32.3 Meech et al (1993) • 21P/Giacobini-Zinner 19.0 Leibowitz & Brosch (1986) • C/IRAS-Araki-Alcock 51.36 Sekanina (1988) • 109P/Swift-Tuttle 67.5 McDavid & Boice (1995) Spin-states we need to know: • 9P/Tempel 1 107.5 or 18.2 or 10.7 Meech & Belton (unpub) • 46P/Wirtanen 7.6,6 (?)Bauer et al (1996); Lamy et al Bold: complex ? Italics: time variable 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

6. Spin Determinations are not straightforward…… • Can the nucleus spin state be fully derived from Earth-based remotely sensed observations alone? • Photometric periodicities Millis & Schleicher (1986) • Periodic coma structures e.g. jets, arcs Hoban et al (1988) • Thermal-IR light curves Campins et al (1987) • Coma fans Sekanina (1979, 1988, 1991) • Evolution of non-gravitational forces Whipple & Sekanina (1979); Królikowska et al (1998) • Dependence of lightcurve amplitude on phase. Lightcurve epochs. Magnusson et al (1989) • 2P/Encke and 10P/Tempel 2 appear to indicate that the answer is yes. A test of Sekanina’s hypothesis is needed. Excited spin: 8 parameters Pure spin: 6 parameters needed 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

7. Typical coma fan structure used by Sekanina to determine pole positions. R- filter image of 10P/Tempel2 By Boehnhardt et al (1990). 30 x 30 arc sec FOV with N at the top. 1 minute exposure. Sekanina’s hypothesis: Emission fans are the products of ejection events that proceed either continually or quasi-continually from a vent (or vents) located in the general vicinity of the sunlit pole of a comet nucleus whose spin axis is oriented near the orbital plane. 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

8. Are comet nuclei in excited spin states common? • Discussed by Samarasinha et al (1986, 1995) and Jewitt (1991, 1997) • Jewitt (1997) finds ex ~ 0.1r2 yrs or about 2.5 yrs for a 5 km radius nucleus at 1AU. • Samarasinha (1999) has compared a number of comets with 1P/Halley which is known to be in a excited state: ex~r4/P*QH2O • ROSETTA target, 49P/Wirtanen, is most likely to be in an excited spin state. CONTOUR (2P/Encke) and DEEP IMPACT (9P/Tempel 1) targets are a possibility…. 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

9. Timescales for cometary processes (after Jewitt (1997) damp – Damping timescale ex – Spin excitation time dyn – Median dynamical lifetime of SPCs SPC – SPC mean orbital period dv - Devolatilization timescale  c – Max. period with no strength 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

10. Excitation in an 2P/Encke orbit. (Initial period= 2 days; a:b:c = 8:4:3.5; Five active areas; Q = 1.7.1028 mol/s; Orbit =2P/Encke) 0 -2 -4 LAM SAM log10k2 -6 -8 unexcited spin 2 1 log10P 0 -1 N. Samarasinha ORBIT NUMBER -2 0 20 40 60 80 100 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

11. 9P/Tempel 1 – an illustration of difficulties Spin periodicities determined from light curves (March 1999) by K. Meech P = 18.2 or 10.7 hrs P = 4.48 d 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000 ** The nucleus of P/Tempel 1 is highly elongated (> 2.5:1) …………something odd here?

12. Periodograms for 9P/Tempel 1 • An outburst present on the first night? • 18.2 and 10.7 are aliased frequencies? • Is excited rotation present? 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000 ** 4.48 day periodicity looks real. 18.2 gives best periodicity for the last three nights. Excited spin looks like a reality…….

13. The case of 1P/Halley: Why we know that the spin state is known to a good approximation, I: • Method: • Assume symmetric top based on shape. • Use VEGA and GIOTTO images to calculate P , , M(RA,dec), P (RA,dec) at T0 (time of VEGA 2 encounter). • Use Millis & Schleicher lightcurve to determine P. • Use Hoban et al Jet structures to map active areas on the nucleus. • Test: • Track complexities of Water production variability……. Spin State (Belton et al 1991): • P = 3.69 d; P = 7.1 d •  = 66 deg. • M(RA,dec) = 6.2, -60.7 deg • P (RA,dec;t0) = 313.2; -7.52 deg • T0 = JD 2446498.80556 • PT 2.84 d •  = 21.4 deg 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

14. The case of 1P/Halley: Why we know that the spin state is known to a good approximation, II: 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

15. 1P/Halley spin model fit to H2O production rate – detail: 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

16. 2P/Encke: Determination of periodicities • String-length (Dworetsky 1983) and phase-dispersion (Stellingwerf 1978) methods are usually used. • WindowCLEAN algorithm makes use of the “sampling window” function to remove aliases. Spurious frequencies are still possible…….. • Roberts et al (1987) • Foster (1995) • Belton & Gandhi (1988): Meech et al (1993) • Four independent data sets available: 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

17. 2P/Encke – A Comparison of methods WINDOWCLEAN STRING LENGTH Dirty Window Relative power Clean Residuals Fernandez thesis (1999) 10.7 data Frequency (inverse days) 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

18. 2P/Encke –results: Frequency (inverse days) 3.175 inv.days; P = 15.12 hr. Jewitt & Meech R Oct/Nov 1986 3.2au Jewitt & Meech R Sept 1985 4.1au Fernandez 10.7 July 1997 1.2 au Luu & Jewitt R Sept 1988 3.8au 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

19. 2P/Encke –WindowClean of 3.1 inv.day whitened data Luu & Jewitt R Sept 1988 3.8au Fernandez 10.7 July 1997 1.2 au Jewitt & Meech R Sept 1985 4.1au Jewitt & Meech R Oct/Nov 1986 3.2au Frequency (inverse days) 8.68 inv. days 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

20. 2P/Encke – Second frequency is an unexpected result. Implications if the nucleus is in an excited spin state: • Two frequencies: 1 = 3.175 inv. Days; 2 = 8.68 inv days • Using model simulations to identify periodicities (Kryszczyska et al 1999; Meech et al 1993): • 1 = 2/P & 2 = 2/P + 2/P • P= 15.2 hrs • P = 8.7 hrs • SAM or a LAM? • For SAM’s P / P> 1 (Samarasinha & A’Hearn, 1991) • Must be a LAM….. • If a > b ~ c then a/b > 2.1 consistent with lightcurve amplitudes • If a/b ~ 2.6 (Fernandez thesis using Sekanina pole) then:  ~ 52 deg • Total spin period ~6.1hr; spin vector (S) is inclined to angular momentum vector (M) by ~ 33.5 deg and circulates once every 15.2 hrs. M S P= 15.2 hrs PT = 6.1 hrs 33.5 deg P = 8.7 hrs  = 52 deg If a/b = 2.6 and b~c 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

21. Conclusions: • Spin states need to be determined if coma phenomena and molecular production rates are to be understood in terms of active areas on the nucleus. • Time-series photometry AND imaging are required. • The typical observational baselines (two or three 3-day runs of unevenly sampled data) are inadequate. • A test of Sekanina’s hypothesis on the origin of emission fans needs to be devised. • Use of the sampling window to remove alias periodicities in the transforms of unevenly sampled time-series is important; spectral “whitening” is recommended to get the most out of a data set. • The spin state of 1 P/Halley is approximately known – and could be improved; 10P/Tempel 2 is approximately known. • 49P/Wirtanen, 2P/Encke and 9/Tempel 1 could be in excited spin states 33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000