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

33rd COSPAR Scientific Assemby, Warsaw, Poland 20 July, 2000

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Determination of the Spin State of a Cometary Nucleus From Remote Observations:

Application to 9P/Tempel 1, 1P/Halley, & 2P/Encke

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

([email protected])


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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……


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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)


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Sp

in sp

eak…

..

From

Belton 1991

k2 =

0

k2 =

1

k2 =

0


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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


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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


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Typical coma fan structure used by Sekanina to determine pole positions.

R- filter image of 10P/Tempel2By 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.


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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….

Comet Effective Radius (km)

Period (d)

Q H2O (Perihelion)

ex/Halley Observed

spin state 46P/Wirtanen ~0.6 ~0.3 1.3-2.5.1028 0.08 - 0.15 ? 1P/Halley 5.2 2.8 1.3.1030 1 Excited 2P/Encke 3-5 0.63 4.5.1028 14 - 110 ? 9P/Tempel 1 2.7-3.8 0.5-4.5 2.1028 3 – 104 ? C/Hale-Bopp ~30 0.46 1.5.1031 584 Pure 29P/S-W 1 8.6 –15.4 0.58 5.1028 (CO) 939-9,655 Excited (?)


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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


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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 20 40 60 80 100

ORBIT NUMBER

0

-1

-2

1

2

-8

-6

-4

-2

0

SAM LAM

unexcited spin

log 10

k2

log 10

P

N. Samarasinha


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9P/Tempel 1 – an illustration of difficultiesSpin periodicities determined from light curves (March 1999) by K. Meech

P = 4.48 d P = 18.2or 10.7 hrs


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Periodograms for 9P/Tempel 1

- An outburst present on the first night?- 18.2 and 10.7 are aliased frequencies?- Is excited rotation present?


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The case of 1P/Halley: Why we know that the spin state is known to a good approximation, I: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

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…….


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The case of 1P/Halley: Why we know that the spin state is known to a good approximation, II:


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1P/Halley spin model fit to H2O production rate – detail:


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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:

Observers Telescope Year Dates Data points

R(au)

Jewitt & Meech KPNO 4m R 1985 Sept. 22-23 25 4.06 Jewitt & Meech KPNO 2.1m R 1986 Oct. 30-31;

Nov. 01-03 15 47

3.15

Luu & Jewitt McGraw-Hill 2.4 m

R 1988 Sept. 3,6,7 101 3.83

Fernandez thesis ESO 3.6m 10.7 1997 July 17-19 ~50 1.2


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2P/Encke – A Comparison of methods

Frequency (inverse days)

Rel

ativ

e p

owe r

Dirty

Clean

Window

Residuals

STRING LENGTH

WINDOWCLEAN

Fernandez thesis (1999) 10.7 data


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2P/E

nck

e –results:F

requ

ency (in

verse days)

Fern

and

ez 10.7 Ju

ly 1997 1.2 au

Lu

u &

Jewitt R

Sep

t 1988 3.8au

J ewi tt &

Me ec h

R S

ept 1 98 5 4 .1 a u

J ewi tt &

Me ec h

R O

c t/Nov 1 9 8 6 3. 2 au

3.175 inv.d

ays;P

= 15.12 h

r.


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2P/E

nck

e –Win

dow

Clean

of 3.1 inv.d

ay w

hiten

ed d

ata

Freq

uen

cy (inverse d

ays)

Fern

and

ez 10.7 Ju

ly 1997 1.2 au

Lu

u &

Jewitt R

Sep

t 1988 3.8au

J ewi tt &

Me ec h

R S

ept 1 98 5 4 .1 a u

J ewi tt &

Me ec h

R O

c t/Nov 1 9 8 6 3. 2 au

8.68 inv. d

ays


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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 (Kryszczyska 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.

P = 15.2 hrs

P = 8.7 hrs

PT = 6.1 hrs

= 52 deg

33.5 deg

M

If a/b = 2.6 and b~c

S


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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

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

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