Most likely solutions for the rotational period of SW3

Time Variability of Component C of Fragmented Comet
73P/Schwassmann-Wachmann 3
Shaye P.
1
Storm ,
N.
2
Samarasinha ,
3
Mueller ,
4
Farnham ,
5
Fernandez ,
6
Kidder ,
6
Snowden ,
B.
T.
Y.
A.
D.
6
4
6
7
8
Harris , M. Knight , J. Morgenthaler , C. Lisse , F. Roesler
1NOAO & MIT, 2NOAO & PSI, 3PSI, 4UMD, 5UCF, 6U of Wash, 7APL/JHU, 8U of Wisc
M.
4
A'Hearn ,
W.
Most likely solutions for the rotational period of SW3-C are 8.8 ± 0.3, 13.2 ± 0.3, or 27.2 ± 0.3 hours
Observations
Overview
SW3 is a Jupiter-family comet with an orbital period of 5.3 years. During the 1995
apparition, SW3 broke up into several components, including B and C. The observations
for this study were taken during the 2006 apparition, where component B broke apart a few
more times, while C seemed to remain intact. These breakups exposed more unaltered
material from the nucleus, in addition to providing clues to the structural parameters of the
comet.
Component C (hereafter SW3-C) was chosen for this study because in order to constrain a
rotational period for the comet, details of the coma morphology needed to be closely
analyzed. Without consequent breakups, there was less confusion from breakup debris in
the coma of SW3-C.
In the analysis, we assumed a least-energy rotation state
corresponding to a principal axis rotation for SW3-C. The breakup in 1995 likely put the
component into an excited rotational state, which could have damped out by 2006. If that
was the case, then it provided an opportunity to study the damping of rotation.
• 4-meter Mayall telescope on Kitt Peak May 3 –10, 2006 UT
• Geocentric Distance: .11AU – .08AU ; Heliocentric Distance: 1.06AU – 1.02AU
• Imaging with MOSIAC camera using H-B narrowband filters
Component C
•Guiding Problems:
Star trails in every image revealed a wavy pattern, and had 1–3 arcsec offsets when compared with input
(ephemeris) values. Therefore, the near-nucleus features were significantly affected by this offset and had to
be disregarded for this study. The further out features were sufficiently far away from the nucleus and diffuse
enough not to be affected by a 1–3 arcsec offset. The telescope and the rapid motion of the comet both
contributed to the guiding difficulty.
N
Credit: William Reach, et al., JPL, Caltech, NASA
Image Enhancements
Coma Morphology
• Fine details of the coma features did not deviate much from the “background” coma the reduced images
needed to be enhanced.
• Continuum images
Azimuthal
average
enhancement
Unenhanced
PA j
• Strong dust tail in the anti-sunward direction (SW), and a dust feature in the NE. The dust feature in the NE
appeared to oscillate between a position angle of 35°and 80°.
Dust
Black lines are gaps
between MOSAIC chips
Two enhancement techniques used:
• Division by an azimuthal average (primary technique)
• Compensates for radial fall-off in flux
• Division by an ``average mask'' for the entire observing run (sanity check – are features real?)
• Shows variations in features by dividing out “steady-state” background
E
CN
• CN images
• Two strong gas features, in the NW and SE direction. The position angle of the NW feature seemed to
oscillate between 310°and 0°.
• Measurement of position angles had an error of ±10°. (SE feature not yet analyzed)
Results
Least-squares approaches used to narrow down search for correct rotational period
M
A = ∑ ( fm )
m =1
2
N
B = ∑ (0.5 − f n )
n =1
2
Statistic A, where fm is the
rotational
phase
difference
between a pair of morphologically
similar images, and M is the total
number of similar pairs.
Least-squares
D = A+ B
M
A = ∑ ( f m )2 / M
m =1
Statistic B,
where fn is the
rotational
phase
difference
The first approach
used pairs
of similar
and
between a pair of morphologically
dissimilar dust images.
dissimilar images and N is the total
Statistic A, where
fm is
the rotational
number
of dissimilar
pairs. phase
difference between a pair of similar images, and M
N
is the total number of similar
pairs.
B= ∑
(0.5 − f n )2 / N
=1 rotational phase
Statistic B, where fn is nthe
difference between
a pair
of dissimilar
A&
B combined
into images
statisticand
D to
N is the total number
dissimilar
take ofinto
accountpairs.
the fits for both
morphologically
and
A & B combined
into statistic D similar
to take into
The dissimilar
periods at
account the fits dissimilar
for both images.
similar and
the relative
D are ofthose
images. The periods
at the minima
relative of
minima
D
are those with thewith
bestthe
fit.best fit.
D = A+ B
Second approach Coma
used the Analysis
Since the PA of a feature is The best overall periods are those with a small G, and
periodic, images with similar those with a smooth plot of PA as a function of
position
angle
(PA)
of
the
dust
and
approaches used to narrow down
search
for correct
rotational
period
phase.
rotational
phases should
have rotational
CN features:
similar PA’s (assuming very little
10
2
G = [ ∑ ( ∑ ( PAi − PA j ) )] / Z
j =1 i
Black lines are gaps
between MOSAIC chips
Brightness
Coma Analysis
First approach used pairs of
morphologically similar and dissimilar
dust images:
Both images
~9000 km X ~9000 km
N
All images
~34000km X ~34000km
Run
“mask”
enhancement
E
~50 arcsec
• With any enhancement technique, artifacts can be introduced use more than one technique to provide a
check to confirm that features are real.
Filters: Narrowband H-B
CN: λ= 3870 Å , ∆λ= 62 Å
BC: λ= 4450 Å , ∆λ= 67 Å
GC: λ= 5260 Å , ∆λ= 56 Å
RC: λ= 7128 Å , ∆λ= 58 Å
The second
approach
used the
position angle of the
change
in observing
geometry).
dust andTherefore,
CN features.
Since rotational
the position angle of a
the correct
feature isperiod
periodic,
with
rotational phases
willimages
produce
a similar
“smooth”
should have
(assuming
very little
plot similar
of PAposition
as a angles
function
of
change inrotational
observing
geometry).
the correct
phase
(see plotTherefore,
to the
rotational right).
period will produce a “smooth” plot of position
10
angle as a function
G = [ ∑of
( ∑ (rotational
PAi − PA j )2 )] / Zphase (see plot to the
j =1 i
right).
The statistic,
G, was evaluated,
The statistic,
G, was evaluated,
where Z is the total
Z used,
is the PA
totalisnumber
of angle of the
the position
number ofwhere
images
i
PAand
the isPA
i is PA
theofaverage of such
feature forimages
a givenused,
image,
j
the feature
a given
position angles
for allforthe
imagesimage,
in a bin where the
PAspace
of such
j is the
rotational and
phase
is average
divided into
10 equal bins.
PA’s for all the images in a bin
The periods
at thethe
relative
minima ofphase
G are those with the
where
rotational
best fits. space
The best
overall periods
those with a small
is divided
into 10are
equal
G, and those
bins. with a smooth plot of position angle as a
function of rotational phase.
Combining the D statistic, G statistic, and
position angle plots, we were able to narrow
down the possible rotational periods to a
testable number. The images were phase
ordered for each remaining period. Periods
of 8.8 ± 0.3, 13.2 ± 0.3, and 27.2 ± 0.3 hours
produced the best phase orderings. It is
possible that the 27.2 hour rotational period
is an alias of the 8.8 hour period.
In order to confirm a single rotational period,
modeling needs to be done. The velocity of
outflow for dust and gas needs to be
estimated, along with the spin axis direction.
Having two active jets in CN should make it
possible to constrain a spin axis direction.
Having those parameters will make it
possible to run simulations and model the
data.
Work of Others: Other investigators using
different techniques have derived periods
ranging from a few hours to more than ten hours
(e.g., HST data by Toth et al. and Radar data by
Nolan et al. at this meeting).
Acknowledgements: We gratefully acknowledge funding from the National Science Foundation (NSF) through Scientific Program Order No. 3 (AST-0243875) of the Cooperative Agreement No. AST-0132798 between
the Association of Universities for Research in Astronomy and the NSF, and the NASA Planetary Atmospheres Program.