Title: 1 MJSB
1Determination 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)
2Determination 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
3Value 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)
4Spin speak..
k2 0
k2 1
k2 0
From Belton 1991
5Comets 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
6Spin 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
7Typical 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.
8Are 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.
9Timescales 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
10Excitation 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
119P/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?
12Periodograms 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.
13The 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
14The case of 1P/Halley Why we know that the spin
state is known to a good approximation, II
151P/Halley spin model fit to H2O production rate
detail
162P/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
172P/Encke A Comparison of methods
WINDOWCLEAN
STRING LENGTH
Dirty
Window
Relative power
Clean
Residuals
Fernandez thesis (1999) 10.7? data
Frequency (inverse days)
182P/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
192P/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
202P/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
21Conclusions
- 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