A&A 376, 672-685 (2001)
DOI: 10.1051/0004-6361:20011028
C. E. Delahodde1,2 - K. J. Meech3 - O. R. Hainaut1 - E. Dotto4
1 -
European Southern Observatory, Casilla 19001,
Santiago, Chile
2 -
Institut d'Astrophysique de Marseille,
Traverse du Siphon, 13376 Marseille Cedex 12, France
3 -
Institute for Astronomy,
2680 Woodlawn Drive, Honolulu, HI 96822, USA
4 -
Osservatorio Astronomico di Torino,
Strada Osservatorio 20, 100025 Pino Torinese (TO), Italy
Received 11 April 2001 / Accepted 10 July 2001
Abstract
In 2000, comet 28P/Neujmin 1 was an ideal candidate for a phase
function study: during its April opposition it reached a phase angle of
= 0.8
,
and previous observations at similar
heliocentric distances (
AU) indicated that the comet was
likely to be inactive. We observed this comet using ESO's NTT and 2.2m
telescopes at La Silla, on 6 epochs from April to August 2000, covering
= 0.8-8
.
These data were combined with a large set
of data from 1985 to 1997. In order to disentangle the rotation
effects from the phase effects, we obtained complete rotation coverage
at opposition, providing us with a lightcurve template.
We have obtained an improved rotation period of
hrs,
with a full amplitude of
mag, which yields
an axis ratio lower limit of 1.51
0.07.
For each subsequent epochs, we have obtained enough rotation coverage to
re-synchronize the lightcurve fragments with the template, and
determine the magnitude change caused by the phase function.
The average colours of the nucleus,
,
and
,
are similar with those of D-type asteroids
and other comet nuclei. The phase function obtained for the
nucleus has a linear slope of
mag deg-1, less
steep than that of the mean C-type asteroids.
Key words: comets: general: surface properties - comets: individual: P/Neujmin 1 - techniques: photometric
Comet 28P/Neujmin 1 is a short-period (SP) comet with an orbital period
of 18.2 years, an eccentricity of 0.776 and an inclination of
14.2.
The comet is currently moving toward perihelion,
which will be reached in January 2003 (q = 1.56 AU) and has an
aphelion distance of Q = 12.30 AU. Comets may be characterized
dynamically by the Tisserand invariant,
,
which is an approximate
constant of the motion in the restricted three-body problem. Those
comets with
are likely to have originated in the Kuiper
Belt, and are called Jupiter-Family (JF) comets. Comet P/Neujmin 1
has
.
A comet's dynamical history may strongly influence
its chemistry, activity level and nucleus surface properties (Meech 1999).
Comet 28P/Neujmin 1 is a very low activity comet, with typically only a
very faint tail/coma appearing at perihelion. The maximum water
production rate at perihelion has been measured at
mol s-1, which implies an active effective area of 0.52 km2 (A'Hearn et al. 1995). Given the estimated surface area of the
nucleus, this implies that less than 0.1% of the surface is active.
A'Hearn et al. noted that this is a common property of the comets
originating in the Kuiper Belt. Only a handful of comets are known to
have lower perihelion production rates than 28P/Neujmin 1.
Observations in 1984 just past perihelion (r = 1.67 AU) showed only a
small gas production and no apparent dust coma (Campins et al. 1987).
Deep observations at r = 3.88 AU post-perihelion (Jewitt & Meech 1988)
showed no evidence of coma. This makes this comet an
ideal candidate for nucleus studies without the interference of a dust
coma. Chemically, the comet falls in the group of "typical'' SP
comets, i.e., it has not been depleted in carbon-chain molecules.
The depletion, seen primarily in JF-SP comets, has been suggested by
A'Hearn et al. (1995) to reflect a primordial chemical
diversity.
An estimate of the radius has been obtained from thermal infrared
measurements and a standard thermal model (with an assumed phase law
of
mag deg-1), yielding a radius between
8.8 and 10.6 km
5% (with an implied axis ratio of 1:1.45), and an
albedo of p = 0.03 (Campins et al. 1987). A rotation period was
determined by Wisniewski et al. (1990) and Jewitt & Meech (1988)
to be near
hr with a range of
mag. The range implies a projected axis ratio of
.
Using data from three runs, they also determined an estimate of the
linear phase coefficient of
mag deg-1.
Because there are very few in-situ opportunities to study the surfaces
of comet nuclei, we must rely on remote observations. Therefore, we
know very little about the surface properties of cometary nuclei -
with the notable exception of the in-situ measurements for comet
1P/Halley. A still largely unexplored method of investigation for comets
is the study of the solar phase function, which can give us direct
information about the surface roughness as well as some independent
constraints on the albedo. In order to properly describe the phase
function with a photometric model, one has to
obtain measurements not only over a broad phase angle ()
range,
but also at very small phase angle, in order to sample the "opposition
surge'', a brightening of the phase curve occurring at
.
Lumme & Bowell (1981), and
Hapke (1981, 1984, 1986) have developed photometric models of
rough and porous surfaces considering multiple scattering of light
among small particles in atmosphereless bodies. At very small phase
angles, the interparticle shadows tend to disappear causing a
non-linear increase of brightness, while at larger
(but still
90
), the phase behaviour is a linear drop in magnitude. Both
Lumme and Bowell, and Hapke formalisms consider porosity as the main
factor influencing the opposition effect, while the geometric albedo
and large-scale roughness mostly affects the linear part
(see Bowell et al. 1989, for a review). More recently, coherent backscattering has been evoked to explain the opposition
effect and improve theoretical models (Muinonen 1994; Hapke et al. 1998).
Belskaya & Shevchenko (2000) have
shown a linear dependence of the phase coefficient (i.e., the slope of
the linear regime) with the logarithm of the albedo on a sample of 33
asteroids; they find a correlation coefficient of 0.93 in a phase
range of 5-25
,
suggesting that an estimation of the geometric
albedo with an accuracy of about 15-20% can be made with the
evaluation of the phase coefficient alone. The large scale roughness
can be determined using Hapke's equations, but only if disk-resolved
data are available at large phase angles (
).
Meech & Jewitt (1987) performed a detailed investigation of the
scattering properties of the dust in comet 1P/Halley's coma and found
no opposition surge, only a brightening consistent with a small linear
phase coefficient of
= 0.02
0.01 mag deg-1. This was
consistent with observations of the scattering from the dust comae of
four other comets. The dust in the coma originates from the surface of
the nucleus, and as porous aggregates of interstellar grains, it is
expected that coma dust could show enhanced backscattering just as do
Brownlee particles.
Fernández et al. (2000) have conducted a
detailed study of the physical properties of the nucleus of 2P/Encke,
including an analysis of the nucleus phase function using HST, ISO and
ESO data, in addition to a large collection of historical data points.
They used a standard thermal model with their infrared data to
determine a nucleus size and an albedo of
.
Their data
spanned a phase angle range from 2.5
,
and within this range they found a linear phase function of
mag deg-1. From this steep phase function and an attempt to
fit the data to a Lumme-Bowell phase law accounting for multiple
scattering, they infer that the surface of 2P/Encke is very rough.
Like 28P/Neujmin 1, 2P/Encke is a very low activity comet, with less
than 2% of the surface active.
Finally, Lamy et al. (2001) have looked at 55P/Tempel-Tuttle between
3
(from their HST data and
from Hainaut et al. 1998, and Fernández 1999), to obtain a phase
coefficient of
mag deg-1, and compare the phase
curve with the Hapke photometric model of C-type asteroid 253 Mathilde
(Clark et al. 1999). Although no opposition surge can be seen in
Tempel-Tuttle, the Mathilde phase function matches the comet's data
very well, so that the two bodies are likely to be similar in terms of albedo
(
)
and roughness (mostly responsible for the linear
part of the phase curve, cf. Lumme & Bowell 1981). Unlike
the Fernández and Lamy data, which relied on measurements from
space and used a coma-removal technique, most ground-based observations are
usually restricted to phase angles less than
,
which is not enough to obtain a clear interpretation in
terms of roughness, single-particle albedo, texture, as long as in-situ
measurements are non-existent, but a phase function study provides a
useful tool for comparisons with asteroids and extinct comet
candidates, or icy satellites, especially with respect to the
opposition effect determination.
In this paper we will present the results of our investigation of the surface properties of comet 28P/Neujmin 1.
Observations were obtained using a large suite of telescopes and instruments spanning a range of dates from 1985-2000. The observing circumstances are shown in Table 1 and described below. A total of 31 nights was obtained, which correspond to 24 distinct runs for the phase function study.
UT Date | #![]() |
Filter | r![]() |
![]() ![]() |
![]() ![]() |
1985 Sep. 21 | 8 | VRI | 3.876 | 3.962 | 14.666 |
1985 Sep. 22 | 6 | VRI | 3.884 | 3.954 | 14.678 |
1985 Sep. 23 | 6 | VRI | 3.891 | 3.947 | 14.687 |
1986 Mar. 06 | 4 | VRI | 5.035 | 4.721 | 11.073 |
1986 Oct. 30 | 6 | VR | 6.452 | 6.282 | 8.815 |
1986 Oct. 31 | 9 | VR | 6.458 | 6.271 | 8.789 |
1986 Nov. 01 | 4 | R | 6.464 | 6.259 | 8.759 |
1987 Nov. 26 | 4 | V | 8.303 | 7.869 | 6.290 |
1988 Feb. 12 | 3 | R | 8.613 | 7.689 | 2.441 |
1988 Feb. 15 | 3 | R | 8.625 | 7.718 | 2.743 |
1988 Feb. 16 | 3 | VR | 8.628 | 7.727 | 2.837 |
1988 May 17 | 4 | R | 8.969 | 9.340 | 5.890 |
1988 Dec. 09 | 4 | R | 9.665 | 9.127 | 5.032 |
1989 Feb. 09 | 3 | R | 9.855 | 8.889 | 1.230 |
1989 Apr. 06 | 4 | R | 10.018 | 9.603 | 5.317 |
1989 Apr. 11 | 8 | R | 10.033 | 9.699 | 5.487 |
1989 Dec. 27 | 31 | RI | 10.709 | 10.004 | 3.800 |
1990 Dec. 17 | 12 | R | 11.422 | 10.921 | 4.350 |
1991 Feb. 16 | 22 | R | 11.521 | 10.542 | 0.665 |
1992 Jan. 04 | 5 | R | 11.946 | 11.256 | 3.467 |
1992 Mar. 07 | 12 | R | 12.009 | 11.080 | 1.737 |
1993 Jan. 25 | 10 | R | 12.235 | 11.357 | 2.169 |
1994 Jan. 17 | 5 | R | 12.297 | 11.536 | 3.006 |
1995 Jan. 04 | 3 | R | 12.168 | 11.632 | 3.976 |
1996 Feb. 13 | 5 | R | 11.781 | 10.854 | 1.721 |
1997 Dec. 30 | 3 | VR | 10.500 | 10.256 | 5.264 |
2000 Mar. 30 | 12 | VRI | 7.690 | 6.697 | 0.815 |
2000 Apr. 05 | 28 | VRI | 7.662 | 6.667 | 1.403 |
2000 Apr. 06 | 25 | VRI | 7.658 | 6.675 | 1.526 |
2000 Jul. 01 | 11 | R | 7.256 | 7.313 | 7.990 |
2000 Jul. 27 | 5 | R | 7.129 | 7.586 | 7.075 |
On all photometric nights, standard stars from
Landolt (1992) were observed. Some of the nights were not
photometric (see Table 2), having some cirrus present,
and have been recalibrated on photometric nights. This calibration
utilizes the measured relative brightnesses of a large number of field
stars and the comet in each field, and is very accurate for
extinctions as large as
mag.
All of the data obtained using the UH 2.2 m telescope used the
Kron-Cousins photometric system (B:
Å,
Å; V:
Å,
Å; R:
Å,
Å; I:
Å,
Å). Data were obtained
using various detectors: the GEC CCD (
pixel) camera,
the Tek
,
and the Tek
camera. The
specifics of the equipment for each run are shown in
Table 2. The effective plate scale for the GEC detector
varied depending on the focus of the lens in the focal reducer. The
plate scales listed have been fit from astrometric measurements to the
fields.
UT Date | Tel | Inst | Scalea | Gainb | RNc | Seeingd | Conde | Whof |
1985 Sep. 21, 22, 23 | KPNO4m | TI2 | 0.319 | 4.3 | 25 | 1.3 | P | MJ |
1986 Mar. 06 | KPNO2.1m | TI3 | 0.391 | 4.3 | 15 | 1.3 | P | MJ |
1986 Oct. 29, 30, Nov. 01 | KPNO2.1m | TI2 | 0.396 | 4.3 | 5 | 1.5 | P | MJ |
1987 Nov. 26 | UH2.2m | GEC | 0.564 | 1.2 | 6 | 1.8 | P | M |
1988 Feb. 12, 15, 16 | UH2.2m | GEC | 0.58 | 1.2 | 6 | 1.3 | P | M, Be, A |
1988 May 17 | UH2.2m | GEC | 0.576 | 1.2 | 6 | 1.9 | P | M |
1988 Dec. 09 | UH2.2m | GEC | 0.601 | 1.2 | 6 | 1.5 | P | M |
1989 Feb. 09 | UH2.2m | GEC | 0.510 | 1.2 | 6 | 1.3 | P | M |
1989 Apr. 06 | CTIO1.5m | TI2 | 0.55 | 2.9 | 11 | 1.5 | c | M |
1989 Apr. 11 | KPNO4m | TI2 | 0.29 | 4.15 | 8 | 0.8 | P | M, Be |
1989 Dec. 27 | CFHT3.6m | RCA2/FOCAM | 0.207 | 8.9 | 47 | 0.9 | c | M |
1990 Dec. 17 | UH2.2m | GEC | 0.56 | 1.2 | 6 | 1.7 | c | M |
1991 Feb. 16 | UH2.2m | GEC | 0.562 | 1.2 | 6 | 2.1 | P | M |
1992 Jan. 04 | UH2.2m | TEK1024/WFGS | 0.351 | 3.54 | 10 | 1.4 | P | M |
1992 Mar. 07 | CTIO4m | TEK1024 | 0.471 | 7.92 | 9.8 | 1.3 | P | M |
1993 Jan. 25 | UH2.2m | TEK2048 | 0.219 | 1.8 | 10 | 0.6 | P | M, K |
1994 Jan. 17 | UH2.2m | TEK2048 | 0.219 | 3.5 | 20 | 0.8 | P | M |
1995 Jan. 04 | UH2.2m | TEK1024 | 0.219 | 2.0 | 10 | 1.0 | P | M, H |
1996 Feb. 13 | UH2.2m | Tek2048 | 0.219 | 5.4 | 20 | 0.9 | P | M, H |
1997 Dec. 30 | KeckII | LRIS | 0.215 | 2.04 | 6.3 | 0.8 | P | M, H, B |
2000 Mar. 30 | NTT3.6m | SuSI2 | 0.16 | 2.22 | 4.5 | 0.8 | P | D, H |
2000 Apr. 05 | NTT3.6m | SuSI2 | 0.16 | 2.22 | 4.5 | 0.6 | P | D, H |
2000 Apr. 06 | NTT3.6m | SuSI2 | 0.16 | 2.22 | 4.5 | 0.6 | P | D, H |
2000 Jun. 30 | ESO2.2m | WFI | 0.24 | 2.00 | 4.5 | 1.3 | c* | D, H |
2000 Jul. 26 | NTT3.6m | SuSI2 | 0.16 | 2.22 | 4.5 | 0.9 | P | D, H |
- A series of twenty two 300 s exposures of the comet were obtained while guiding at the comet rates. The intent was to get a deep composite image in which neither comet nor the stars would be trailed, to get a photometric point for the heliocentric light curve. The images were not taken with the intent of optimizing S/N in the individual images to look at the rotational light curve.
- Although the night was photometric, the telescope had to close between 06:15-08:45 UT because of high humidity. In addition, there were very high winds (sometimes gusting to 86 km h-1) which affected the image quality.
The observations were made with a TI 800800 CCD camera at the
4 m Prime focus, and with the same detector at the Cassegrain focus of
the 2.1 m telescope. The observations were obtained through the Mould
filter system. Images were tracked at sidereal rates but kept short so
that image trailing was not a problem. The standards of
Christian et al. (1985) were observed for calibration in
1985 and 1986. However, they were not observed at a variety of airmasses and
because absolute calibration is critically important for this project
these fields were recalibrated using Landolt standards on Nov. 26,
2000, using the ESO 2.2 m telescope. A full description of the
observing particulars for these data may be found in
Jewitt & Meech (1988) and references therein.
- The observations on the CTIO 1.5 m telescope were obtained using the
TI#2
CCD binned in 2 by 2 mode to better match the
plate scale to the conditions. The detector had been repaired just
prior to the observing run, and was installed on the telescope just
an hour before evening twilight flats were obtained on our first night.
However, tests showed that the instrument was performing optimally.
- The March 1992 data were obtained using the CTIO 4 m telescope with
the new Tek1024 CCD, and Mould filter R10. Non-sidereal guiding
was not functioning at this telescope, so we kept the individual
exposures short enough that the comet would trail by less than a pixel
(0
47; i.e. half the seeing disk) during the exposure.
Non-sidereal tracking was then achieved by shifting the individual
images later in the composite.
Observations were made using the Faint Object Camera (FOCAM) at the
prime focus. Although there were 31 images taken on this night, the
strategy was to obtain a deep image to search for coma. The exposure
times were therefore limited to 90 s each, so that the comet would
move by no more than 1 pixel (0
21) during the integration. In
this manner, composite images can be constructed which have both
untrailed stars and comet images for comparison.
Images of 28P/Neujmin 1 were obtained on 1997 December 30 on the Keck
II telescope using the LowResolution Imaging Spectrometer (LRIS) in
its imaging mode. Images were taken through the V(
Å,
Å) and R(
Å,
Å) filters, and were
guided at non-sidereal rates.
Most of the 2000 observations were made at the 3.6-m New Technology
Telescope, with the SuSI-2 CCD camera, at the "A'' f/11 Nasmyth
focus. SuSI-2 is a mosaic of two 2k
4k, 15
m (0.08 arcsec)
pixel, thinned, anti-reflection coated EEV CCDs, aimed at direct
imaging with a field of view of
arcmin. In all our
runs, we used the
pixel binning mode, making the pixel
size 0.16 arcsec. We mostly observed through the Bessel R filter
(
Å,
Å), with some
additional V and I images (Bessel V:
Å,
Å, Bessel I:
Å,
Å).
- Observations were obtained with the 3.6-m NTT. The 3 runs took place when the comet was at very small phase angles, where we expect an opposition surge in the phase curve. It was thus very important to obtain the best time coverage in order to establish a rotational lightcurve that can disentangle the shape/albedo amplitude from the phase-induced variations. P/Neujmin 1 was observed during a half-night on March 30, and two consecutive nights during the April runs. Exposure times were chosen to be 900 s, with differential tracking, in order to obtain a high S/N (between 50 and 100 in a 3''aperture, depending on the filters) and to provide good sampling for the lightcurve analysis (see Sect. 3.2). However, we chose to shorten to 300 s some R exposures in April, in order to maintain good lightcurve sampling while at the same time have time for V and I images.
- The first run took place at the ESO/MPG 2.2-m telescope, with the Wide
Field Imager mounted at the f/8 Cassegrain focus. The WFI is a
2k
4k mosaic of 8 CCDs, with a total field of view of
arcmin and a pixel size of 0
24. We used the
filter, a close to the Cousins R filter, with a sharp cut-off at
7400 Å. The comet was placed on the chip with the best quantum
efficiency (FOV
arcmin), and close to the optical axis.
We limited the exposure times to 600 s, in order to avoid trailing.
The comet's apparent motion was 6
/hr, and the seeing 1
3, so
the trailing was undetectable during the exposures. On 2000 July 27
(NTT+SuSI2), five 900 s images through the R filter could be
obtained before the comet set, soon after sunset.
Unless otherwise noted, data were processed in a standard manner using a combination of twilight sky flats and dark sky flats made from dithered object images. This yields extremely flat images, important both for doing precise relative photometry of the comet with respect to field stars and for searching for faint coma. A more detailed description of this method can be found in Hainaut et al. (1998). Images of the comet are shown in Fig. 1. In cases where the comet was observed continuously (and not interspersed between other targets), these are composites of the entire night of data. They were made by using the centers of the field stars to compute frame offsets and then applying an additional offset calculated from the ephemeris rates, image start time and CCD plate scale.
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Figure 1:
Composite images of 28P/Neujmin1 from a) 1985 Sep. 21,
b) 1986 Mar. 06, c) 1988 Feb. 15, d) 1989 Apr. 11,
e) 1989 Dec. 27, f) 1990 Dec. 17, g) 1991 Feb. 16,
h) 1992 Jan. 04, i) 1992 Mar. 07, j) 1993 jan. 25,
k) 1994 Jan. 17, l) 1996 Feb. 13, m) 1997 Feb. 18,
n) 1997 Dec. 30, o) 2000 Mar. 30, p) 2000 Apr. 05,
q) 2000 Apr. 06, and r) 2000 Jul. 01. For Some of the
runs, it has not been possible to produce an image at the same scale
showing clearly the comet, they have therefore not been included in this
figure.
All images are
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The extraction of the comet flux from the CCD frames was done using
both the photometry routines in the MIDAS (Banse et al. 1988; European Southern Observatory 1999)
and IRAF (Tody 1986) software packages.
The flux was accumulated within a circular aperture centered on the
center of light and the sky background flux was determined from an
annulus centered on the comet. The statistical moments of the sky
sample were used to reject any bad pixels or field stars found in the
sky annulus. On some occasions, field stars were placed such that the
sky background had to be determined manually by statistically
accumulating the counts in several different locations in the vicinity
of the comet. The smallest aperture possible (dependent upon seeing)
was selected to minimize the sky error contribution while including
the most light (>99.5%) from the nucleus, and was usually selected
to be 3 times the seeing.
In the 2000 dataset, when the stars appear elongated (i.e., during the
NTT runs), we could not determine an aperture correction factor from
stellar profiles, so we measured the magnitude using a brightness
radial profile routine, integrating the flux over pixel-size annuli,
centered on the object. Using synthetic objects,
Delahodde et al. (1999) found that for data with S/N higher than 25,
the asymptotic region (i.e., no more flux from the object) is detected
and starts at an aperture size of 3 times the seeing. The sky noise
dominates for apertures typically 5-6 times the seeing. In the case
of our data,
90% of the profiles presented an asymptote that
could be interpreted as the real magnitude of the comet; in some cases
however, no clear asymptote could be seen, either because of
stellar/galactic contamination in the sky background, or problems with
differential tracking. In these cases, we then either used the
measurement corresponding to an aperture size equivalent to 3 times the
seeing disk, or rejected the data point (mostly when stellar
contamination was visible). An example of this method is presented in
Fig. 2.
In data sets where there were data obtained over a significant time
interval, attempts were made to ascertain the rotational phase of the
comet (cf. Sect. 3.3). Photometry of the comet relative
to all frame field stars of equal or greater brightness was performed
and the comet brightness was compared to the mean result of the
(constant) field stars. Typically, we used 10-60 stars, except
for the SuSI2 observations in 2000, where only
5 field stars
could be measured, due to the very small FOV of the nightly composite
images.
Photometric calibration was achieved independently on each night with fits to the Landolt (1992) star fields. Fields were observed at several airmasses during the night to fully solve for extinction, system colour terms and zero points. With the large format detectors, the fields often have a large number of standards, so the fits are very robust. However, we have noticed that even on completely photometric nights the extinction can vary with time and position on the sky, so very precise search for brightness variation in the comet requires differential photometry to field reference stars.
The filters used were either from the Bessel or the Kron-Cousins system
(with the exception of the WFI ,
which is close to
K-C). Computing the colour term in the photometric equation ensures
that all the reduced magnitudes are in the Bessel System as described
in Landolt (1992).
Tables 3 and 4 present the photometry
from all of the runs. When there was insufficient time coverage to
present rotational information, the data from each night has been
averaged to increase the S/N. The first nine columns list the
specifics of the observations and the observed magnitudes.
We present in the last three columns the mean magnitude for each run
(from composite images), then our best estimate of the mean Rmagnitude in rotational phase (cf. Sect. 3.3),
assuming a colour
(see
Table 6), and the absolute R magnitude. When there
was not enough time coverage to constrain the rotational phase, we
kept the composite mean magnitude, and assigned it a value of 0.45 mag
as an error bar (i.e., the lightcurve range, see
Sect. 3.2). In this paper, we only present the
composite or average, rotation-free points used for the phase function
study; nevertheless, the details of all the individual measurements
can be found in an electronic form of these tables.
The reduced magnitude m(1,1,)
has been computed using:
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Figure 2:
An example of the magnitude versus aperture radius technique, using a
900 s R exposure taken on April 05, 2000. Thanks to the high S/N,
the brightness tends to an asymptote at about 15 pixels (i.e., 2
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Open with DEXTER |
Date | JDa | UTa | Expb | Airmc | Apd | Fil. | ![]() |
Mag ![]() ![]() |
M![]() ![]() ![]() |
m(1,1,![]() ![]() ![]() |
1985-09-22 | 6330.9375 | 10.4940 | 1225 | 1.525 | 3.5 | R | 14.68 | 18.606 ![]() |
18.64 ![]() |
12.70 ![]() |
1986-03-06 | 6495.7940 | 7.0510 | 600 | 1.790 | 3.0 | R | 11.07 | 19.593 ![]() |
19.59 ![]() |
12.72 ![]() |
1986-10-31 | 6734.9375 | 10.3622 | 9000 | 1.250 | 3.0 | R | 8.79 | 20.493 ![]() |
20.46 ![]() |
12.42 ![]() |
1987-11-26 | 7154.9809 | 12.3952 | 1920 | 1.264 | 3.0 | V | 6.29 | 22.104 ![]() |
21.48 ![]() |
12.42 ![]() |
1988-02-14 | 7205.8375 | 8.0997 | 5100 | 1.060 | 3.0 | R | 2.64 | 21.240 ![]() |
21.19 ![]() |
12.08 ![]() |
1988-05-17 | 7298.8055 | 7.3326 | 3600 | 1.775 | 2.0 | R | 5.90 | 22.035 ![]() |
22.04 ![]() |
12.42 ![]() |
1988-12-09 | 7505.1032 | 14.4778 | 4202 | 1.019 | 2.0 | R | 5.03 | 22.360 ![]() |
22.36 ![]() |
12.63 ![]() |
1989-02-09 | 7566.8189 | 7.6543 | 3300 | 1.262 | 2.5 | R | 1.23 | 22.051 ![]() |
22.05 ![]() |
12.34 ![]() |
1989-04-11 | 7627.7477 | 5.9447 | 2400 | 1.284 | 2.0 | R | 5.49 | 22.264 ![]() |
22.26 ![]() |
12.32 ![]() |
1989-12-27 | 7888.1206 | 14.8949 | 2340 | 1.014 | 2.5 | R | 3.80 | 22.384 ![]() |
22.16 ![]() |
12.01 ![]() |
1990-12-17 | 8243.0345 | 12.8278 | 5400 | 1.121 | 3.0 | R | 4.35 | 22.425 ![]() |
22.43 ![]() |
11.95 ![]() |
1991-02-16 | 8404.0094 | 12.2278 | 6600 | 1.022 | 3.0 | R | 0.67 | 22.687 ![]() |
22.69 ![]() |
12.26 ![]() |
1992-01-04 | 8625.9591 | 11.0183 | 3000 | 1.290 | 3.0 | R | 3.47 | 22.711 ![]() |
22.71 ![]() |
12.07 ![]() |
1992-03-07 | 8688.7046 | 4.9111 | 1800 | 1.550 | 2.0 | R | 1.74 | 22.718 ![]() |
22.72 ![]() |
12.10 ![]() |
1993-01-25 | 9013.0600 | 13.4400 | 9000 | 1.035 | 1.5 | R | 2.17 | 23.007 ![]() |
22.84 ![]() |
12.29 ![]() |
1994-01-17 | 9369.9922 | 11.8128 | 4200 | 1.088 | 2.0 | R | 3.01 | 22.764 ![]() |
22.76 ![]() |
11.92 ![]() |
1995-01-04 | 9722.0163 | 12.3906 | 2700 | 1.177 | 2.0 | R | 3.98 | 22.605 ![]() |
22.61 ![]() |
11.85 ![]() |
1996-02-13 | 10126.9106 | 9.8553 | 3000 | 1.194 | 3.0 | R | 1.72 | 22.647 ![]() |
22.63 ![]() |
12.08 ![]() |
1997-12-30 | 10813.0221 | 12.5302 | 400 | 1.555 | 3.0 | R | 5.26 | 22.230 ![]() |
22.21 ![]() |
12.05 ![]() |
Date | JDa | UTa | Expb | Airmc | Fil. | ![]() |
Mag ![]() ![]() |
M![]() ![]() ![]() |
m(1,1,![]() ![]() ![]() |
2000-03-30 | 11633.6188 | 2.7274 | 9000 | 1.225 | R | 0.82 | 20.614 ![]() |
20.63 ![]() |
12.07 ![]() |
2000-04-05 | 11639.6797 | 4.2717 | 13800 | 1.247 | R | 1.40 | 20.733 ![]() |
20.74 ![]() |
12.21 ![]() |
2000-04-06 | 11640.6862 | 4.3439 | 12900 | 1.257 | R | 1.53 | 20.665 ![]() |
20.76 ![]() |
12.22 ![]() |
2000-07-01 | 11726.5217 | 0.3281 | 7800 | 1.319 | ![]() |
7.99 | 20.863 ![]() |
20.96 ![]() |
12.34 ![]() |
2000-07-26 | 11752.5033 | 23.9539 | 4500 | 1.803 | R | 7.08 | 21.143 ![]() |
21.09 ![]() |
12.43 ![]() |
The period search was performed on the data from March to July 2000,
using an algorithm derived from that of
Harris & Lupishko (1989). The best period matching the observations over 3 months is
h. This result is in good agreement with the
h period found by Jewitt & Meech (1988), and
corresponds to 175 full rotations between March 30 and July 01. The
periods corresponding to 174 and 176 rotations are 12.82 and 12.68 hours, respectively, and do not represent the best fit.
The phased R magnitudes are presented in Fig. 3. An offset is applied for each night of data in the composite lightcurve in order to center the lightcurve on the mean brightness of the comet. This offset corresponds to the phase effect we precisely want to assert for the phase curve (cf. Sect. 3.3). It also includes the uncertainty in the zero point determination, which is why the data points in the figure contain only the error bars from photon noise (the systematic error is removed by the period search program). This effect is taken into account in the phase function study by adding the error on the zero point (as measured each night with Landolt stars) to the uncertainty on the mean magnitude determination.
The rotational lightcurve has an asymmetric, double-peaked shape,
with a range of 0.45 mag, typical of shape-dominated
lightcurves. A lower limit for the elongation ()
can be
estimated as:
![]() |
Figure 3:
Phased rotational lightcurve of P/Neujmin 1, as obtained with a
period
![]() |
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We attempted to find the absolute rotational phase of the observed lightcurve fragments (1985-1997) in order to get the correct rotationally averaged mean magnitude of the comet at these epochs. For that purpose, we first produced an analytical model of the 2000 March to July composite lightcurve. This was done using a Fourier-like sine series limited to the 10 first orders, reproducing the period, amplitude and shape of the observations. The model is a symmetric double peak (i.e., it includes only even terms of the Fourier series) lightcurve.
The mean magnitude of the model was adjusted from -0.5 to +0.5 mag around the mean magnitude of the observed data, with a step
of 0.01 mag. For each value, the phase origin of the model lightcurve
was varied from 0 to P/2 (i.e., covering half a period P=12.75 h,
which is sufficient, since the model is a symmetric double peaked
lightcurve), with a step of 0.005 P. For each of these 104 models, the
of the observations with respect to the model was
computed, weighted by the data errors, as following:
![]() |
(4) |
- The comet was observed during 3 consecutive nights (4-5 points each
night), and the data were recalibrated in Nov. 2000
(cf. Sect. 2.2). The resulting lightcurve is very well
matched by the template (cf. Fig. 5a). As a
consequence, the
is very peaked, resulting in a 0.1 mag error
bar on the mean magnitude.
- There was four images of the comet during one night, and no variation is seen. The data were recalibrated in Nov. 2000 (cf. Sect. 2.2). Therefore, we report only the average magnitude for this run in Table 3, with an error bar for the phase curve equal to the lightcurve range (0.45 mag).
- The comet was observed during three consecutive nights, and the
data were recalibrated in Nov. 2000. Rotational variations are
clearly present and the dataset matches the
template (cf. Fig. 5b); we thus derive an
absolute brightness of
mag.
![]() |
Figure 4:
2-D map of the ![]() |
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- Four data points covering a time span of 1 h show a very steep
magnitude increase that is well matched by the model lightcurve
(Fig. 5c). The
map indicate a 1 h uncertainty
for the rotational phase, and a 0.1 mag uncertainty for the
magnitude. We report the absolute magnitude and error from this model.
![]() |
Figure 5: Observed lightcurve and best fitting lightcurve (solid line) for a) September 1985, b) October 1986, c) November 1987, d) February 1988 e) April 1989, f) December 1989, g) January 1993, h) February 1996, and i) December 1997. |
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- The dataset contains six data points with a total magnitude of 0.5 mag, i.e., slightly more than the amplitude of the template
lightcurve. This is either caused by errors on the individual data
points, or by a missmatch between the actual lightcurve and the
template (see Fig. 5d). A consequence is that the
indicates a larger uncertainty on the average magnitude (0.25 mag).
- With a time baseline of 1 hour for the April 11 KPNO 4 m data, and an average magnitude from the CTIO 1.5 m dataset 5 days earlier, we were able to use the phasing technique described in Sect. 3.3 to determine a fairly good estimate of the average magnitude on this date. The fit is shown in Fig. 5e.
- Although individual images for the 1989
December run lacked sufficient S/N for rotational information, it was
possible to bin the data into 4 groups. The time span for the
observations was 1 hour. With a half period of 6.375 hours, the comet
should go from max to minimum brightness (0.5 mag) in 3.186 hours. In
one hour, we would expect up to a change of
mag. In a
small aperture (2
0, to minimize sky noise), the observed
variation has
mag, which is consistent with
the comet moving from maximum to minimum brightness. Therefore, this
implies that the mean magnitude reported in Table 3 is
likely to be near the middle of the range. The Fourier phase/magnitude
fit is shown in Fig. 5f, and the value is reported in
Table 3.
- There was a total of 12 images obtained on this
night spanning a period of nearly 3 hours. It was not possible to use
the time resolution to determine the rotational phase because of (i) the low S/N of the individual images and (ii) the
complications because the comet passed close to and over a faint field
star. We made a template deep star field by using the relative
positions of all the field stars from frame to frame to compute frame
offsets in x and y and adding the individual shifted images. This
composite star image was scaled, shifted and subtracted from the
individual frames. For some of the frames the subtraction of the
field star worked extremely well, but in others it did not (because of
changes in seeing, which varied from 1
5 to 2
0 during the
night). In the frames where the comet and faint field star were
sufficiently well separated to measure them separately, we computed
the difference in brightness between the comet and faint star. In the
total composite image, with the comet image sitting on top of a faint
star trail, we used the ratio of the areas of the comet and trailed
stars to compute the fractional flux computed by the faint star and
subtracted this from the total flux to arrive at the composite image
comet brightness.
- The lightcurve contains 22 measurements of the comet, but the S/N is too low to exhibit any significant rotational variations. Therefore, we report only the average magnitude for this run in Table 3, with an error bar for the phase curve equal to the lightcurve range.
- As for the December 1988 and February 1989 runs, the comet was too
faint to be measured on individual frames. The images were therefore
co-added, and the comet measured on the composite. With no rotational
information, the error on
has been set to the full amplitude of the
lightcuve.
- The lightcurve fragment contains eight data points over 2 h, perfectly
matched by the template (Fig. 5g). We use directly
the model mean magnitude and -derived uncertainty.
- The lightcurve fragment contains only 4 points over 1 h, with no
variation. The template adjustment fails to constrain the
phase and the mean magnitude. We therefore report the mean magnitude
with an uncertainty equal to the range of the lightcurve.
- The comet was too faint to be measured on individual frames; the
magnitude
reported in Table 3 is the measurement
on the composite image, with an error bar equal to the range of the
lightcurve.
- We examined the photometry results in the
smallest aperture measured (1
0), where the contribution from the
sky noise was the smallest, in order to see if there was any evidence
for rotational variation for which we could try to fit the phase. We
were able to get a fit for phase and mean magnitude. Although the
fit was reasonably good, the locus of the minimum "valley''
was fairly shallow, which resulted in a higher uncertainty on the
phase averaged magnitude (see Fig. 5h). Based on
measurements from the composite image, we then apply an aperture
correction of
mag to recover the full flux reported
in Table 3.
- The colours for the Keck data point were measured independently in 3 apertures (1, 2 and 3'') and while there appeared to be a slight trend (redder in the smaller apertures), the colour was consistent with being constant within the errors, so an average value is reported here for the 2 data points spaced the closest in time (Fig. 5i).
- The comet brightness was measured with the "radial profile'' method
described in Sect. 3.1, and compared with a set of bright
field stars. In the case of NTT data, only 5 stars were common
to all the images in the night composites, since the comet was moving
fast (of the order of 15''/hr), and the field of view was only
arcmin. The frames were rotated to place the trails
vertically and the stars were measured in rectangular apertures. The
variations found in the magnitudes of the faintest stars due to
changes in extinction were of the order of 0.05 mag i.e., well below
the rotational amplitude of the comet. We obtained a total of 62 Rmeasurements, combined altogether to create the template rotational
lightcurve presented in Sect. 3.2. The measurements are
presented in Table 4.
The absolute
obtained from Eq. (1) and
the rotationally averaged magnitudes as described above, are displayed
in Fig. 6a. When there was not enough
time coverage to rephase the lightcurve, we used the rotational range
(i.e., 0.45 mag) as the error bar and weight in the determination of
the phase functions parameters. Those points are represented by
crosses in the figure.
The data points from the 2000 campaign at
ESO, which was aimed at the phase function determination, and which
derive from lightcurves with a good rotational phase coverage, are
represented with open circles.
While this figure seems at first sight to be dominated by strongly
dispersed points with large error bars, it is important to note that
the NTT-2000 data (i.e., with the smallest error bars) show an
opposition surge at
that is statistically
significant. Unfortunately, there is no rotation-free point from the
1985-1997 dataset to further sample this opposition effect. The phase
trend (i.e., the linear drop of brightness at larger
)
is also
clearly visible on the figure.
We therefore decided to model these data using various formalisms for
the phase function. In each case, we took the required precautions to
weight the data using their individual uncertainty in order to exploit
at best the dataset and estimate properly the uncertainties on the
model parameters.
![]() |
Figure 6:
a) Phase curve of 28P/Neujmin 1: data only. The circles correspond to
runs for which we have enough lightcurve coverage to determine the
rotational phase, and therefore the accurate, rotation-free magnitude
(open symbols correspond to the 2000 campaign). Crosses mark points
for which we do not have enough time coverage to determine the
rotational phase; their error bar is arbitrarily set to 0.45 mag,
i.e., the full amplitude of the lightcurve. b) The fitted phase functions,
obtained through a fit of all the data points, presented with the
rotation-free magnitudes (see Sect. 3.3.2). The Lumme
and Bowell curve, very similar to the IAU phase law, was not
represented for clarity. The phase curve of asteroid
Mathilde, of comparable albedo (Clark et al. 1999), is compared to the fits
of P/Neujmin 1 (and has been shifted for clarity). The difference of
shape (both in the opposition effect and in slope) between the two
objects is most likely due to different natures of surface
structures. The slope of each object is represented by the coefficient
![]() |
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We used four models to fit the data:
Each fit was performed by minimizing the
of the observations
weighted by the error bars (from 0.03 to 0.45 mag in the worst
cases), while exploring the whole space of the model's
parameters.
For each model, the absolute magnitude m(1,1,0) was adjusted from 11.5 to
12.5, with a step of 0.01 magnitude. The phase coefficient b in
Eq. (6) varied from 0.01 to 0.05, with a step of 0.001 mag deg-1. The opposition effect parameter a of Eq. (6)
varied from 0. to 1. (step 0.01). Finally, the G and Q parameters
from Eqs. (7) and (8) were chosen to vary from
-0.3 to 0.7 (step 0.01). The best fit results are summarized in
Table 5, and the corresponding phasecurves are
overplotted in Fig. 6b.
Method | Parameters | |||
Linear fit: | m(1,1,0) | = | 12.28 ![]() |
[mag] |
![]() |
= | 0.025 ![]() |
[mag deg-1] | |
Shevchenko: | m(1,1,0) | = | 12.35 ![]() |
[mag] |
b | = | 0.020 ![]() |
[mag deg-1] | |
a | = | 0.42 ![]() |
||
IAU: | H | = | 12.07 ![]() |
[mag] |
G | = | 0.41 ![]() |
||
Lumme & Bowell: | m(1,1,0) | = | 12.06 ![]() |
[mag] |
Q | = | 0.34 ![]() |
The parameter
of the so-called linear model is the slope of
the IAU-adopted phase law, estimated between 15 and 20
.
The value of
is different from the one found for
55P/Tempel-Tuttle (
= 0.041 mag deg-1,
Fernández 1999), and the mean slope of C and P-type asteroids
(Helfenstein & Veverka 1989; Belskaya & Shevchenko 2000), which are primitive, low-albedo
asteroids and are likely to have surface properties similar to comet
nuclei. This discrepancy is illustrated in Fig. 6b
by the phase curve of asteroid 253 Mathilde, a dark C-type asteroid
which has been successfully compared to comet P/Tempel-Tuttle (Lamy et al. 2001).
Not only is the slope of Neujmin 1 more shallow, but
the opposition surge is also steeper than Mathilde's.
However, a mere linear
model neglects the opposition effect, and must be refined. A simple
improvement is done by the Shevchenko equation. In a recent paper,
Belskaya & Shevchenko (2000) used an empirical formalism
to compare the opposition effects of 33 asteroids, among which were 6
C-type and 3 P-type asteroids. They describe the opposition surge by
its amplitude and its width; they find similar behaviours at phase
angles 0-25 for C and P-type asteroids: an amplitude of about 0.15 mag, and a width (the angle of the opposition effect beginning) of
about 3.5
.
The result of our Shevchenko fit (see
Table 5) leads to an amplitude of
mag
and a width of
deg. Surprisingly, this result is in good
agreement only with their sample of medium-albedo M-type asteroids
(
). The comparison is certainly a coincidence, given the
differences in nature between M-type asteroids (metal-rich) and
comet nuclei. Unfortunately, the phase parameters are not available for
any outer Solar System minor bodies, and it is likely that this
situation will not change soon, as TNOs and Centaurs are never
observable at phase angles greater than a few degrees.
The IAU and Lumme & Bowell laws (Eqs. (7) and (8))
give very similar results at low phase angles, but diverge shortly
beyond 15.
For clarity, only the IAU law is plotted in the
figure. They confirm the steepness of the opposition effect compared to
the mean C-type asteroids (Q ranging from 0.07 to 0.12, Lumme &
Bowell 1981). Such steep opposition surges are seen in higher albedo
bodies, such as M-type asteroids or icy satellites and giant planet
rings (Brown & Cruikshank 1983; Karkoschka 1997). The steepness of Neujmin 1's
surge could be the signature of a very porous surface
(cf. Sect. 1), and/or indicate the presence of ices on
the surface. There is no detailed phase curve of D-type asteroids nor
Trojans, to which Neujmin 1 seems to be close in terms of colour and
albedo, because of their relatively large distances (i.e.,
from ground-based observations). However, some D and
P-type asteroids of comparable albedo (0.03-0.05) are reported by
Tedesco (1989) to have G parameters in the 0.27-0.32 range. This is the case for instance of Asteroid 377 Campania (G =
0.31,
pV = 0.05), but more observations are clearly needed for
further comparisons. Finally, data at
larger than 25
are
needed to better constrain the photometric models of Neujmin 1. This
is possible at smaller heliocentric distances (for instance the
unusual gentle slope of the linear fraction of the phase curve could
be infirmed), with possible use of coma-removal technique in case the
comet would show significant activity, as proven successful by Lamy
et al. (Lamy & Toth 1995; Lamy et al. 1998). It would be very interesting to compare the phase parameters of 28P/Neujmin 1 to those of other
comets; we hope that this study will encourage publications on other
comet nuclei.
Figure 7 shows the absolute magnitude m(1,1,0) as a function of the heliocentric distance. For this section, we used the phase correction predicted by the IAU-adopted model using the parameters in Table 5. The plot is compatible with a constant value. We conclude that the comet was totally inactive, i.e., that no unresolved coma escaped our examination of the images and that we observed the bare nucleus during all the runs.
![]() |
Figure 7: m(1,1,0) versus heliocentric distance. The IAU-adopted (H, G) system was chosen here. This figure is compatible with the observation of a bare nucleus. |
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In Table 6, the colour measurements of P/Neujmin 1 are compared to mean values for various classes of minor bodies in the Solar System (Hainaut & Delsanti 2001). We used the R model lightcurve described in Sect. 3.3 to extrapolate the value of R at the moments of the V and Iobservations, and thus derive the colours.
UT Date | r [AU] | V-R | R-I |
1985-09-21 | 3.876 | 0.439 ![]() |
0.624 ![]() |
1985-09-22 | 3.884 | 0.424 ![]() |
0.641 ![]() |
1985-09-23 | 3.891 | 0.518 ![]() |
0.443 ![]() |
1986-03-06 | 5.035 | 0.514 ![]() |
0.571 ![]() |
1986-10-31 | 6.458 | 0.554 ![]() |
|
1988-02-16 | 8.628 | 0.406 ![]() |
|
1997-12-30 | 10.500 | 0.574 ![]() |
|
2000-03-30 | 7.690 | 0.490 ![]() |
0.400 ![]() |
2000-04-05/06 | 7.662 | 0.454 ![]() |
0.413 ![]() |
Plutinos | 0.591 ![]() |
0.55 ![]() |
|
Cubiwanos | 0.625 ![]() |
0.58 ![]() |
|
Centaurs | 0.584 ![]() |
0.57 ![]() |
|
Comets | 0.435 ![]() |
||
In April 2000, the lightcurve sampling in V and I was good enough
to search for rotation-induced variations.
We obtained the rotation-free V-R and R-I colours by adjusting the
template R lightcurve (cf. Sect. 3.2) to the V and Imeasurements. Figure 8 presents all the data points
from those two nights, each filter fitted by this model lightcurve.
The R lightcurve template matches perfectly the V and Iobservations, both in phase and shape, with a simple shift in
magnitude. We therefore conclude that Neujmin 1 does not present
colour variation with its rotation. Mean colours are directly derived
from the offset used to shift the lightcurve template between the
filters; they are listed in Table 6.
The previous observations show that the V-R colour variations and errors
are compatible with the constant value of 0.454 found in April
2000. However, we also report a V-R of 0.574
0.043 (i.e., significantly redder) from December 1997, and the dispersion of R-Icolours is larger than expected from the errorbars; nevertheless,
there is no significant trend. As the comet has been inactive over
the whole period of observation, and as the April 2000 multicolour
lightcurve shows that there is no significant colour change over the
rotation, we do not propose a physical explanation for these changes;
they are most likely caused by the problems intrinsic to the I filter,
such as background fringing, which is difficult to correct.
![]() |
Figure 8: VRI lightcurve for April 5-6, 2000. The data are fitted with the analytical model produced with all the R measurements in 2000 (see Sects. 3.2 and 3.3). No colour variation is detected within half a rotation, which leads to a very good estimate of P/Neujmin 1's V-R and R-I colours (cf. Sect. 3.5). |
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28P/Neujmin 1 is a fairly red nucleus compared to
other nuclei, but slightly bluer than other Outer Solar System minor
bodies. A very low-resolution spectrum can be obtained from
broad-band photometry using
![]() |
Figure 9: Relative reflectance of 28P/Neujmin 1, derived from broad-band photometry (this work: black circles, and Campins et al. 1987: triangle). The spectrum is normalized to 5442 Å (V band). The slope is similar to D-type asteroids (see Sect. 3.5). |
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Acknowledgements
Image processing in this paper has been performed using the IRAF and MIDAS programs. IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation. MIDAS is developed by the European Southern Observatory, and is distributed with a general public license. Support for this work was provided to C. E. D. by the Société de Secours des Amis des Sciences, and to K. J. M. by NASA Grant Nos. NAGW-5015 and NAG5-4495. The authors wish to thank their anonymous referee for his/her useful comments to improve this paper.