1 MJSB

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_at_noao.edu)

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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
  Sekaninas 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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Spin speak..
k2 0
k2 1
k2 0
From Belton 1991
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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 AHearn (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)

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 Sekaninas
  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/Tempel2 By Boehnhardt et
al (1990). 30 x 30 arc sec FOV with N at the
top. 1 minute exposure. Sekaninas 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 ?exr4/PQH2O
• 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.

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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 abc 843.5 Five active
areas Q 1.7.1028 mol/s Orbit 2P/Encke)
0
-2
-4
SAM
LAM
log10k2
-6
-8
unexcited spin
2
1
log10P?
0
-1
N. Samarasinha
ORBIT NUMBER
-2
0 20
40 60
80
100
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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
The nucleus of P/Tempel 1 is highly elongated
(gt 2.51) something odd here?
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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?

4.48 day periodicity looks real. 18.2 gives
best periodicity for the last three nights.
Excited spin looks like a reality.
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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,dect0) 313.2 -7.52 deg
• T0 JD 2446498.80556

• PT ? 2.84 d
• ? 21.4 deg

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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

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2P/Encke A Comparison of methods
WINDOWCLEAN
STRING LENGTH
Dirty
Window
Relative power
Clean
Residuals
Fernandez thesis (1999) 10.7? data
Frequency (inverse days)
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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
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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
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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
  (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 SAMs P? / P? gt 1 (Samarasinha AHearn,
  1991)
• Must be a LAM..
• If a gt b c then a/b gt 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 bc
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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 Sekaninas 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