Simultaneous visible and near-infrared time resolved
observations of the outer solar system object
(29981) 1999 TD10
Béatrice E. A. Mueller
National Optical Astronomy Observatory1 , 950 N Cherry Ave, Tucson AZ 85719
E-mail: [email protected]
Carl W. Hergenrother
Lunar and Planetary Laboratory, University of Arizona, Tucson AZ 85721
Nalin H. Samarasinha
National Optical Astronomy Observatory1 , 950 N Cherry Ave, Tucson AZ 85719
Humberto Campins
University of Central Florida, Orlando FL 32186 and Lunar and Planetary
Laboratory, University of Arizona, Tucson AZ 85721
Donald W. McCarthy, Jr.
Steward Observatory, University of Arizona, Tucson AZ 85721
Accepted by Icarus, June 17, 2004.
1
The National Optical Astronomy Observatory is operated by the Association of Universities for
Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.
1
ABSTRACT
The outer solar system object (29981) 1999 TD10 was observed simultaneously
in the R, and J and H bands in September 2001, and in B, V, R, and I in October 2002. We derive B-V=0.80±0.05 mag, V-R=0.48±0.05 mag, R-I=0.44±0.05 mag,
R-J=1.24±0.05 mag, and J-H=0.61±0.07 mag. Combining our data with the data from
Rousselot et al. (Astron. Astrophys. 407, 1139, 2003) we derive a synodic period of
15.382±0.001 hr in agreement with the period from Rousselot et al. Our observations
at the same time, with better S/N and seeing, show no evidence of a coma, contrary
to the claim by Choi et al. (Icarus 165, 101, 2003).
Key Words: Asteroids, rotation; Centaurs; Photometry; Infrared Observations;
(29981) 1999 TD10
2
I. INTRODUCTION
The outer solar system object (29981) 1999 TD10 , referred to hereafter as TD10 , was
discovered by the Spacewatch survey (Scotti et al. 1999). It has a perihelion distance of
12 AU, similar to Centaurs and an aphelion distance of 190 AU characteristic of many
scattered disk objects. Consolmagno et al. (2000), assuming an albedo of 0.04, estimate
the object’s major and minor axes as 130 and 70 km respectively (i.e. an effective radius
of 50 km). This indicates a large outer solar system object with an irregular shape.
They find a periodicity in the lightcurve of 5.8 hr (which corresponds to a single peaked
lightcurve) and a gray color. Rousselot et al. (2003) derive a solar phase dependence
in the H-G scattering formalism and a period of 15.382±0.002 hr. Choi et al. (2003)
report a period of 15.448±0.012 hr and derive a solar phase dependence and an effective
radius of 58 km. They also claim to have detected a coma in TD10 .
We compare our results with the literature above and investigate the claim of coma
activity. In section II we describe our visible and near-infrared observations and reductions, in section III, we discuss the photometry, the lightcurve and the colors of TD10 .
In section IV we consider and reject the claim of coma activity, and we summarize our
results in section V.
II. OBSERVATIONS AND REDUCTIONS
TD10 was observed simultaneously in the visible and near-infrared from September
21–22 UT, 2001, with two additional nights in the visible on September 23 and 25, 2001.
It was also observed about one year later in the visible from October 30 – November 1,
2002. The summary of the observational and the geometrical circumstances are given
in Table I.
Table I
Observational and Geometric Circumstances for TD10
Date
Filters ra
∆b
αc
[UT]
[AU] [AU] [deg]
09/21/01
R,J
12.69 11.76 1.7
09/22/01 R,J,H 12.70 11.75 1.6
09/23/01
R
12.70 11.75 1.5
09/25/01
R
12.70 11.74 1.4
10/30/02 B,V,R,I 13.27 12.28 0.6
10/31/02
R
13.27 12.29 0.7
11/01/02
R
13.27 12.29 0.7
a heliocentric distance
b geocentric distance
c solar phase angle
3
sky condition
photometric
photometric
photometric
photometric
photometric
photometric
not photometric
A. Visible data
The visible observations in both runs were taken with the KPNO-2.1m telescope
on Kitt Peak equipped with a 2048×2048 Tektronix CCD chip with 24 µm pixels. At a
focal ratio of f /7.5, the plate scale is 0.00 305 pix−1 and the field of view is 10.0 4. Standard
Harris broad-band filters which are optimized for the Kron-Cousins system were used.
The integration time was limited as not to smear out the rotational signature. The
trailing rates corresponded to less than half the seeing disk. Standard IRAF procedures
were used to reduce the data. The images were bias subtracted and then flat fielded
with combined dome flats to remove the pixel to pixel variations. Dithered object
frames were combined with a rejection criteria to remove the objects and smoothed to
correct for the difference in slope between the dome flats and the dark sky. In addition,
fringe correction frames were constructed from combined object frames in the I-band
to remove the fringing. The resulting reduced images were flat to better than 1%.
Relative photometry was carried out with at least 6 comparison stars in the same
frame to extract the magnitude of TD10 . An aperture diameter of 14 pix (4.00 3) which
was always at least twice as large as the maximum seeing was used for the photometry
of the object and an aperture diameter of 30 pix (9.00 2) was used for the comparison
and standard stars. The aperture correction to tie the object to the comparison stars
was done for every frame separately. There were common stars in frames of subsequent
nights, so that the nights could be tied to a reference night. There were at least two
photometric nights per observing run (Table I) and the absolute calibration was done
using Landolt Standard Star fields (Landolt 1992).
B. Near-infrared data
The near-infrared observations were obtained with the University of Arizona’s Steward Observatory 2.3m Bok telescope on Kitt Peak with the PISCES infrared camera.
PISCES consists of a 1024x1024 Rockwell Hawaii detector with 18.5 µm pixels (McCarthy et al. 2001). The PISCES camera has a final focal ratio of f /3.3 and a plate
scale of 0.00 50 pix−1 at the 2.3m Bok telescope. Standard IRAF procedures were employed to reduce the data. Images were dark subtracted and flat fielded with median
sky flats produced from the individual dithered J and H-band images. A routine was
used to remove the effect of cross-talk between CCD readout quadrants (McCarthy et
al. 2001).
Absolute photometry in J (λc =1.25 µm) and H (λc =1.65 µm) was determined from
observations of standards P309-U, P533-D and S677-D (Persson et al. 1998) at multiple airmasses. Variations in seeing did not allow for the use of a single aperture for
photometry. The standards were measured with an aperture diameter of 6 FWHM
which ranged from 8 to 16 pixels (400 to 800 ). TD10 was measured with an aperture
diameter of 2 FWHM. An aperture correction was determined and used to normalize
the photometry. Both nights were photometric allowing absolute calibrations. The
solar colors in the Arizona infrared photometric system (Campins et al. 1985) were
4
used for conversion from fluxes to reflectances (section III.D).
III. Photometry
A. Lightcurve Analysis
The magnitudes R(1,1,α), i.e. the observed R magnitude corrected to heliocentric
and geocentric distances of 1 AU each, but not corrected for solar phase angle effects
are given in Table II for September 2001 and in Table III for October 2002. The times
in both Tables are light time corrected and refer to the midpoint of the integrations.
Figure 1 shows the R-band data from September 23, 2001 and from October 30, 2002.
In September 2001 we observed a maximum but no minima and in October 2002 we
observed a minimum and a maximum. The peak to peak variation in the lightcurve
is ≈0.50 mag. This variation is consistent with the peak to peak variation of 0.68 mag
given by Consolmagno et al. (2000). As the geometry was different for our observations
compared to that of Consolmagno et al. (2000) and their lightcurve amplitude is
larger than ours, our observations must have been taken when the rotational angular
momentum vector was closer to the line of sight.
The J data for September 21 and 22, 2001 are given in Table IV and the H data
for September 22, 2001 are given in Table V. The times in both Tables are again light
time corrected and refer to the midpoints of the integrations. The lightcurve for the J
data from September 21, 2001 is shown in Figure 2.
B. Solar phase dependence
Before doing a periodicity analysis, our data will have to be corrected first for
changes in heliocentric and geocentric distances and phase angle. The solar phase
dependence of TD10 is not known. We did not adopt the phase dependence of Choi
et al. (2003) because our derived mean absolute magnitudes using their solar phase
coefficient for the September 2001 and October 2002 data do not agree with each
other. Their derivation is also widely different from the range of linear solar phase
coefficients for 7 TNOs by Sheppard and Jewitt (2002). The derived phase coefficient of
β=0.121 mag deg−1 by Rousselot et al. (2003) is in agreement with the mean solar phase
coefficient by Sheppard and Jewitt (2002). However, our mean absolute magnitudes in
September 2001 and October 2002 using this coefficient are still inconsistent with each
other. This could be due to the different nuclear orientations caused by the observing
geometries, but the difference in geocentric (or heliocentric) ecliptic longitude of TD10
between these two dates is only 10◦ and in ecliptic latitude is 1◦ .
We used the maxima in the R-band lightcurve from September 23, 2001 and
from November 1, 2002 to derive the solar phase angle dependence. We get for
the absolute mean magnitude R0 =8.43±0.01 mag, and for the solar phase coefficient
β=0.181±0.015 mag deg−1 . As the two maxima in a double peaked lightcurve do not
have to be equal, we derived the solar phase coefficient by comparing the mean magnitudes for the September 2001 and October 2002 run. We get the same coefficient as that
5
Table II
R-band photometry for TD10 in September 2001
JDa -2450000 R(1,1,α)
2173.8181
8.633
2173.8230
8.635
2173.8292
8.671
2173.8353
8.719
2173.8402
8.710
2173.8443
8.792
2173.8485
8.799
2173.8544
8.802
2173.8590
8.820
2173.8640
8.860
2173.8685
8.876
2174.6474
8.590
2174.6525
8.577
2174.6587
8.539
2174.6657
8.524
2174.6715
8.551
2174.6765
8.520
2174.6905
8.480
2174.6956
8.473
2174.7005
8.500
2174.7049
8.467
2174.7158
8.465
2174.7277
8.431
2174.7840
8.583
2174.7901
8.645
2174.7951
8.628
2174.7992
8.667
2174.8040
8.688
2174.8081
8.685
2174.8210
8.747
2174.8256
8.814
a light time corrected, at
error JDa -2450000 R(1,1,α)
0.014
2174.8306
8.798
2174.8347
8.813
0.015
2174.8392
8.838
0.015
2174.8433
8.843
0.015
2174.8533
8.858
0.016
2175.6512
8.447
0.018
2175.6558
8.456
0.017
0.018
2175.6600
8.469
2175.6645
8.439
0.019
2175.6686
8.438
0.020
2175.6850
8.432
0.019
2175.6895
8.453
0.020
2175.6947
8.476
0.020
2175.7046
8.480
0.018
2175.7091
8.489
0.017
2175.7136
8.495
0.016
2175.7635
8.737
0.016
2175.7683
8.755
0.016
0.015
2175.7726
8.814
2175.7777
8.812
0.016
2175.7888
8.852
0.015
2175.7933
8.850
0.014
2177.7864
8.856
0.014
2177.7912
8.838
0.016
2177.7974
8.781
0.014
2177.8037
8.802
0.014
2177.8079
8.762
0.015
2177.8220
8.644
0.016
2177.8262
8.584
0.015
0.017
2177.8305
8.609
0.017
midpoint of integration
6
error
0.018
0.018
0.018
0.018
0.018
0.017
0.016
0.017
0.016
0.016
0.015
0.015
0.015
0.015
0.014
0.015
0.017
0.017
0.018
0.019
0.020
0.018
0.019
0.019
0.018
0.018
0.017
0.015
0.014
0.015
Table III
R-band photometry for TD10 in October 2002
JDa -2450000 R(1,1,α)
2577.5761
8.410
2577.5839
8.387
2577.5900
8.423
2577.6129
8.527
2577.6240
8.566
2577.6360
8.612
2577.6635
8.703
2577.6693
8.671
2577.6880
8.722
2577.6938
8.749
2577.7044
8.729
2577.7100
8.802
2577.7326
8.657
2577.7383
8.650
2577.7561
8.576
2577.7610
8.560
2577.7725
8.500
2577.7782
8.462
2577.7982
8.433
2577.8158
8.385
2577.8217
8.370
2577.8323
8.348
2577.8762
8.360
2577.8819
8.332
2578.7968
8.315
a light time corrected, at
error JDa -2450000 R(1,1,α)
0.017
2578.8030
8.274
2578.8087
8.291
0.017
2578.8145
8.293
0.017
2578.8193
8.280
0.018
0.017
2578.8242
8.320
2578.8544
8.347
0.018
2578.8606
8.380
0.018
2578.8658
8.398
0.018
2578.8709
8.360
0.019
2579.5627
8.579
0.020
2579.6350
8.636
0.018
2579.6422
8.679
0.020
2579.6495
8.570
0.018
2579.7169
8.317
0.019
2579.7480
8.265
0.017
0.017
2579.7592
8.280
2579.7662
8.251
0.017
2579.7730
8.254
0.018
2579.7798
8.270
0.017
2579.7867
8.279
0.018
2579.8006
8.252
0.018
2579.8086
8.318
0.018
2579.8561
8.510
0.022
2579.8640
8.504
0.022
2579.8713
8.539
0.017
midpoint of integration
7
error
0.014
0.015
0.016
0.016
0.018
0.021
0.021
0.021
0.021
0.037
0.038
0.028
0.039
0.033
0.036
0.013
0.011
0.021
0.031
0.039
0.030
0.022
0.033
0.044
0.044
Figure 1: Visible lightcurve in R from September 23, 2001 (top) and from October 30,
2002 (bottom).
8
Table IV
J-band photometry for TD10 in September 2001
JDa -2450000
2173.68555
2173.68721
2173.68888
2173.69055
2173.69221
2173.69388
2173.69553
2173.69720
2173.69887
2173.70052
2173.70219
2173.70386
2173.70552
2173.70719
2173.70886
2173.71051
2173.71218
2173.72436
2173.72688
2173.72855
2173.73021
2173.73187
2173.73353
2173.73520
2173.73684
2173.73850
2173.74017
2173.74183
2173.74351
2173.74518
2173.74684
2173.74851
2173.75018
2173.75183
2173.75350
J(1,1,α)
7.15
7.10
7.10
7.06
7.22
7.22
7.18
7.11
7.27
7.09
7.26
7.19
7.20
7.03
7.15
7.31
7.13
7.11
7.29
7.29
7.31
7.17
7.26
7.16
7.36
7.02
7.11
7.11
7.26
7.23
7.00
7.23
7.21
7.09
7.27
error JDa -2450000
0.09
2173.75518
2173.79145
0.09
2173.79601
0.09
0.09
2173.79837
2173.80073
0.09
2173.80309
0.09
2173.80546
0.09
2173.80782
0.09
2173.81018
0.10
2173.81254
0.09
2173.81490
0.10
2173.82396
0.09
2173.82632
0.09
2173.82869
0.09
0.09
2173.83105
2173.83341
0.09
2173.83577
0.09
2173.83813
0.09
2173.84049
0.10
2173.84284
0.09
2173.84599
0.09
2173.84834
0.09
2173.85071
0.09
2173.85307
0.09
2173.85542
0.10
0.09
2173.85778
2173.86016
0.09
2173.86252
0.09
2173.86487
0.09
2173.86722
0.09
2173.86958
0.09
2173.87194
0.09
2173.87430
0.09
2173.87666
0.09
0.09
9
J(1,1,α)
7.23
7.20
7.32
7.28
7.35
7.30
7.32
7.41
7.28
7.25
7.46
7.41
7.40
7.43
7.44
7.56
7.49
7.59
7.53
7.54
7.49
7.63
7.50
7.50
7.62
7.47
7.66
7.66
7.67
7.76
7.71
7.66
7.66
7.61
error
0.10
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.09
0.10
0.09
0.09
0.09
0.11
0.10
0.09
0.10
0.09
0.10
0.10
0.10
0.11
0.12
0.10
0.11
0.10
Table IVcontinued
JDa -2450000 J(1,1,α) error JDa -2450000 J(1,1,α)
2174.67352
7.20
0.09
2174.79308
7.56
2174.79474
7.46
2174.67638
7.21
0.09
2174.79641
7.76
2174.67805
7.21
0.09
2174.79808
7.52
2174.67972
7.21
0.10
2174.79973
7.56
2174.68137
7.28
0.10
2174.80140
7.36
2174.68304
7.13
0.09
2174.80306
7.52
2174.68470
7.20
0.09
2174.68637
7.24
0.10
2174.80484
7.38
2174.80650
7.56
2174.68804
7.28
0.10
2174.80818
7.40
2174.68969
7.14
0.09
2174.80985
7.57
2174.69894
7.14
0.08
2174.81151
7.50
2174.70061
7.23
0.09
2174.81317
7.49
2174.70227
7.25
0.09
2174.81484
7.48
2174.70394
7.16
0.09
2174.81650
7.63
2174.70561
7.16
0.09
2174.81816
7.54
2174.70752
7.17
0.09
2174.82007
7.61
2174.70918
7.16
0.08
2174.82172
7.53
2174.71084
7.22
0.08
2174.71251
7.27
0.09
2174.82339
7.52
2174.82504
7.60
2174.71416
7.13
0.08
2174.82671
7.54
2174.71582
7.11
0.08
2174.82838
7.59
2174.71748
7.26
0.09
2174.83004
7.53
2174.71914
7.27
0.09
2174.83170
7.56
2174.72082
7.24
0.09
2174.83337
7.68
2174.78974
7.44
0.09
2174.79141
7.53
0.09
a light time corrected, at midpoint of integration
10
error
0.09
0.10
0.11
0.09
0.09
0.09
0.10
0.09
0.09
0.09
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.09
0.10
0.09
0.10
Table V
H-band photometry for TD10 in September 2001
JDa -2450000 H(1,1,α)
2174.64825
7.22
2174.65054
6.76
2174.65105
6.74
2174.65156
6.95
2174.65207
6.80
2174.65257
6.87
2174.65307
6.50
2174.65358
6.60
2174.65409
6.49
2174.65460
6.74
2174.65539
6.49
2174.65590
7.02
2174.65641
6.84
2174.65692
7.01
2174.65742
6.57
2174.65793
6.32
a light time corrected, at
error JDa -2450000 J(1,1,α)
0.30
2174.65844
6.76
2174.65895
6.50
0.14
2174.65946
6.78
0.18
2174.66018
6.31
0.20
2174.66069
7.18
0.19
2174.66121
6.67
0.18
2174.66539
6.40
0.21
2174.66590
7.02
0.17
0.21
2174.66641
6.67
2174.66692
6.64
0.15
2174.66742
6.76
0.13
2174.66792
6.68
0.19
2174.66843
6.50
0.16
2174.66894
6.51
0.22
2174.66945
6.56
0.16
0.17
midpoint of integration
error
0.20
0.17
0.17
0.15
0.33
0.21
0.17
0.24
0.19
0.23
0.24
0.25
0.15
0.15
0.19
derived from comparing the maxima. This is not surprising since, as the phase plot in
Figure 7 shows, the two maxima in the lightcurve are indeed equal in magnitude. This
solar phase coefficient is inside the range of coefficients quoted by Sheppard and Jewitt
(2002). The derivation of the solar phase coefficient is dependent on the accuracy of
the absolute calibration of the data. We had two photometric nights each in both
observing runs and the difference in absolute magnitude within a run is 0.007 mag in
September 2001 and 0.005 mag in October 2002. If we assume a maximum difference
in absolute magnitudes of 0.012 mag between the two runs, then the corresponding
change in the derived solar phase coefficient β is 0.015 mag deg−1 which is of the same
order as the error of β quoted above. R0 is consistent with Ropp derived by Choi et al.
(2003) and HR by Rousselot et al. (2003).
C. Period Analysis
In order to identify as well as to minimize artifacts, we used two different techniques
for the period search analysis of the R-band lightcurves: fitting harmonics and using
a Fourier Transform (FT) with a subsequent WindowCLEAN algorithm (Belton and
Gandhi 1988, Mueller et al. 2002). The clean spectrum is a deconvolution of the FT
of the observed data (dirty spectrum) with the spectral window. The spectral window
(or dirty beam) is the FT of the sampling function which is 0 when no observation was
11
Figure 2: Near-infrared lightcurve in J from September 21, 2001
12
taken and 1 when an observation was taken.
The χ2 plot of fitting the harmonics and the dirty and clean power spectra for the
WindowCLEAN for the individual data sets from September 2001 and October 2002
are shown in Figure 3.
The minimum for September 2001 in the χ2 plot is at a frequency f of 3.13 dy−1 .
The maximum in the clean power spectrum is at 3.11 dy−1 . Taking the standard
deviations of the power spectrum signatures and the χ2 signatures as the maximum
of the error, we obtain 0.12 dy−1 for the error. The two frequencies are in excellent
agreement with each other. Assuming that the lightcurve is due to an aspherical shape,
the corresponding double peaked periods (P = f2 ) are 15.34±0.3 hr and 15.43±0.3 hr.
For October 2002, the frequencies derived are 3.12 dy−1 from the χ2 plot and
3.14 dy−1 from the clean spectrum, again in good agreement with each other. The
corresponding periods are 15.38±0.3 hr from fitting harmonics and 15.29±0.3 hr from
WindowCLEAN. The minor adjacent peaks to the maximum peak in the dirty spectra
for the 2001 and 2002 data are likely daily aliases. This is confirmed as the phase plots
with their corresponding periods are unacceptable.
The periods derived from our 2001 and 2002 data sets seem to be in conflict with the
single peak period of 5.8 hr quoted by Consolmagno et al. (2000). The corresponding
frequency of the double peaked equivalent is 4.14 dy−1 , which is the same as one of our
minor peaks in the dirty spectrum and is a daily alias. They did not do a detailed
period analysis and their data fit well with any of our periods quoted above (priv.
comm. by S. C. Tegler, 2003). The simultaneous near-infrared data agree well with
the period derived from the R-band data.
We can derive a very accurate period by combining the September 2001 and October
2002 data because of the large time baseline of over one year. We applied the FT and
WindowCLEAN as well as fitting harmonics to the combined data set from September
2001 and October 2002 (Figure 4). Two frequencies at 3.0758±0.0005 dy−1 and at
3.1379±0.0005 dy−1 are left by the WindowCLEAN. Both of these frequencies are also
present in the χ2 plot. The double peaked period corresponding to the first frequency
does not give a satisfactory phase plot and is rejected. The second frequency gives a
double peaked period of 15.297±0.001 hr.
As the gap between the two data sets is about a year, the results of the WindowCLEAN algorithm need to be checked. The maximum peaks in the dirty spectrum
area at frequencies 3.0784 dy−1 and 3.0759 dy−1 . However, phase plots with the corresponding periods are not acceptable. We then checked all the peaks from the dirty
spectrum between frequencies of 3.11 dy−1 and 3.14 dy−1 . This is the frequency range
derived from the September 2001 and October 2002 data separately. Although, some of
the corresponding periods give unacceptable results, some give phase plots that are as
good as the one with the period of 15.297 hr. We also applied WindowCLEAN to the
combined data sets with slightly different solar phase corrections. The dirty spectra
were the same within the errors. The WindowCLEAN picked the adjacent peaks to the
one corresponding to the 15.297 hr period. We do not have enough temporal coverage
13
Figure 3: χ2 plot (top), and dirty (middle) and clean (bottom) power spectra for the
R-band data from September 2001 on the left and for October 2002 on the right.
14
Figure 4: χ2 plot (top), and dirty (middle) and clean (bottom) power spectra for the
R-band data from September 2001 and October 2002 combined. The resolution of the
x-axis increases from left to right.
15
in this case for WindowCLEAN to break all the aliases.
The error in the period due to synodic effects has to be estimated. The time
difference between the maxima in October 2002 and September 2001 corresponds to
634 cycles. The difference in geometry is roughly 10◦ between September 2001 and
P[sec]×10
October 2002 (see above). This gives a change in period of the order of (634×360)
resulting in a synodic effect of less than 0.001 hr.
A phase plot of our data with the period from Rousselot et al. (2003) is acceptable.
A phase plot with the period from Choi et al. (2003) does not fit our data at all. We
checked the dirty spectra from our combined data sets and the data set of Rousselot
et al. (2003) for frequency peaks close to the frequency corresponding to the period
derived by Choi et al. (2003). The frequencies found were different but inside the error
bars from the frequency from Choi et al. (2003). None of the corresponding periods
resulted in phase plots that fit our data or the Rousselot et al. (2003) data.
We applied the same WindowCLEAN algorithm to the data of Rousselot et al.
(2003) and get two peaks, one at 3.120±0.004 dy−1 (P=15.385±0.009 hr) and the other
at 3.138±0.004 dy−1 (P=15.296±0.009 hr) in order of falling power. The first peak
is the same that Rousselot et al. (2003) derive from their data and the second one
is one of the acceptable periods from our combined 2001 and 2002 data. We then
combined our data set with the data set from Rousselot et al. (2003) and obtain a
peak at 3.1205±0.0005 dy−1 (P=15.382±0.001 hr) from the clean spectrum. The same
frequency is present in the χ2 plot as well. The corresponding χ2 -plot and the dirty
and clean spectra are shown in Figure 5.
Because of the large gap in our combined data sets, caution has to be exercised in
accepting the result from the WindowCLEAN algorithm without further checks. We
used the dirty spectra from the Rousselot et al. (2003) data alone, our September
2001 and October 2002 data combined, as well as our data sets combined with the
Rousselot et al. (2003) data, to compare the dirty spectra in the relevant frequency
range. There were three common peaks. The peaks from the data of Rousselot et
al. (2003) are: 3.1025 dy−1 , 3.1205 dy−1 , and 3.1390 dy−1 . The standard deviation for
all three peaks is 0.004 dy−1 . From our combined 2001 and 2002 data sets they are:
3.1030 dy−1 , 3.1205 dy−1 , and 3.1379 dy−1 . The standard deviation for all three peaks
is 0.0005 dy−1 . From our data set combined with the Rousselot et al. (2003) data
they are: 3.1027 dy−1 , 3.1205 dy−1 , and 3.1383 dy−1 . The standard deviation is again
0.0005 dy−1 . The comparison of the dirty spectra is shown in Figure 6. Although the
corresponding peaks are inside the error bars, phase plots of the data from Rousselot
et al. (2003) with periods from our peaks do not fit except for the peak at 3.1205 dy−1 .
The same is true for using the periods from the peaks from the Rousselot et al. (2003)
data for our data set. We conclude that the peak at 3.1205 dy−1 is the only one
consistent with all three dirty spectra. A phase plot with all the data for a period of
15.382 hr is given in Figure 7. The spread and small systematic differences in the phase
plot between our data and the data from Rousselot et al. (2003) can be attributed to
the uncertain solar phase dependence corrections.
16
Figure 5: χ2 plot (top), and dirty (middle) and clean (bottom) power spectra for our
R-band data combined with the Rousselot et al. (2003) data. The resolution of the
x-axis increases from left to right.
17
Figure 6: Comparison of the dirty spectra in the frequency range from 3.09 dy−1 to
3.15 dy−1 . The top panel shows the dirty spectrum from the Rousselot et al. (2003)
data alone, the middle panel from our September 2001 and October 2002 data combined, and the bottom panel shows the dirty spectrum from our combined data sets
combined with the Rousselot et al. (2003) data. The marks on the peaks denote the 3
common peaks discussed in the text.
18
Figure 7: Phase plot of our R-band data from September 2001 (blue), October 2002
(green), and the data from Rousselot et al. (2003) (red) for a period of 15.283 hr.
19
As Choi et al. (2003) did not publish their data in tabulated form, we cannot
phase their data with the period of 15.382 hr. However, in their figure 2, they give the
location of their minimum and we can therfore deduce the locations of their maxima
and compare those with the loaction of our maximum from September 2003 (see our
figure 1). The locations of their maxima is consistent with our period of 15.382 hr
within the errors.
D. Near-infrared and visible colors
In addition to the lightcurve observations in R, we took observations in B, V, and
I on October 30, 2002. Because of the good rotational phase coverage we can derive
accurate colors unaffected by rotational effects. The average of four color observations in each of the above filters gives B-R=1.28±0.02 mag, V-R=0.48±0.05 mag, and
R-I=0.44±0.05 mag. This gives B-V=0.80±0.05 mag. These colors are in excellent
agreement with colors from the literature. A comparison of our colors and those from
the literature are given in Table VI.
The near-infrared data are noisier but have a higher time resolution than the visible
data. We binned the J and H data in order to derive colors. We obtained simultaneous
observations of J and R and of H and R. Comparing the R lightcurve with the J data
and H data and comparing the rotationally phased data gives consistent results. We
derive R-J=1.24±0.05 mag and R-H=1.85±0.05 mag, resulting in J-H=0.61±0.07 mag.
With the above colors this results in V-J=1.72±0.08 mag. Our near-infrared colors and
colors from the literature are again compared in Table VI.
Table VI
Comparison of visible and near-infrared colors for TD10
Object
B-V
V-R
R-I
V-J
J-H
Referencea
TD10
0.80±0.05 0.48±0.05 0.44±0.05 1.72±0.06 0.61±0.07
Mu
0.75±0.06 0.47±0.02
R
TD10
0.77±0.05 0.50±0.04 0.47±0.03
HD
TD10
0.77±0.02 0.47±0.01
TR
TD10
1.81±0.06
Mc
TD10
Sun
0.665
H
Sun
0.36
0.33
HTMC
Sun
1.116
0.310
CRL
a Mu = this work, R = Rousselot et al. (2003), HD = Hainaut and Delsanti (2002),
TR = Tegler and Romanishin (2003), Mc = McBride et al. (2003), H = Hardorp
(1980), HTMC = Hartmann et al. (1990), CRL = Campins et al. (1985)
The solar colors from Table VI were subtracted from the colors of TD10 . We then
derived the relative reflectances of TD10 which are normalized with respect to the
R-band. They are shown in Figure 8.
20
Figure 8: Relative reflectance plot. The plot has been normalized with respect to the
R-band.
21
We also converted our colors to the so called slope parameter or spectral index S
2 )−R(λ1 )
with R the rela[% (0.1 µm)−1 ] (Hainaut and Delsanti 2002) using S = 100 R(λ
(λ2 −λ1 )/0.1
tive reflectivity and λ the central wavelength in µm. Following the approach of Hainaut
and Delsanti (2002), we derived S for V, R, and I through linear regression. The result
is S=7.5±3.1 % (0.1 µm)−1 compared with S=11.9±1.9 % (0.1 µm)−1 from Hainaut and
Delsanti (2002). These values are within each other’s error bars. Jewitt (2002) uses
the V and R filters to derive the normalized reflectivity gradient S 0 [% (0.1 µm)−1 ] from
0 ∆λ
), with (V-R)¯ as the solar color. For TD10 we derive
V-R=(V-R)¯ + 2.5 log( 2+S
2−S 0 ∆λ
S 0 =10.8±0.9 % (0.1 µm)−1 . This value is close to the median S 0 =10 % (0.1 µm)−1 for 9
Centaurs (Jewitt 2002).
IV. ACTIVITY
Choi et al. (2003) claim to have detected cometary activity in TD10 on November 2
and 5, 2000 and on September 22, 2001. Our September 21–23 data are bracketing their
data from September 22. To investigate this claim in our data, we spatially shifted and
combined all the images from September 21–23, 2001 to enhance the signal-to-noise for
TD10 . The same procedure was applied to the stars in the field. The resulting effective
integration time is 3.6 hr, a factor of 1.5 longer than that of Choi et al. (2003). We
used a 2.1m telescope which gives a collection area 4.4 times larger than that from their
1m telescope. Additionally the seeing in our combined image is 1.00 3 compared to their
average seeing of 2.00 3. No evidence of a resolved coma could be detected in our data, in
agreement with the non-detection of a coma in the November 2002 data by Rousselot
et al. (2003). As our September data bracket the data from Choi et al. (2003) on
September 22, an intermittent coma can also be excluded. In Figure 9a the combined
image centered on TD10 is shown. No indication of a coma extension in any direction
is seen. Figure 9b shows a comparison of the spatial profiles of TD10 and a star in the
same field with a similar flux, normalized to the same peak surface brightness. The
error bars have been omitted for the star for clarity.
There seem to be inconsistencies in the paper by Choi et al. (2003). The position
angle of the antisolar direction is 252◦ for the September 2001 data and 66◦ for the
November 2000 data, according to the JPL Horizons ephemeris. This leads to the
conclusion that their coma extension is not in the antisolar direction contrary to their
claim. In addition, the shape of this claimed coma extension is very unusual. The
radial brightness profile for TD10 dips below the profile of the comparison star and
then rises back up to the previous level (see their Figure 6b). Also, the deviation of the
profile of TD10 from that of the comparison star starts after a distance from the center
of the object at 500 . At that distance the noise is dominant in our profile of TD10 (see
our Figure 9b), as well as in the profile from Rousselot et al. (2003) (see their Figure
2), both of which have better S/N than that from Choi et al. (2003).
22
Figure 9: a) Combined image of TD10 from September 21–23, 2001. The figure is 3000
(99 pixels) on the side. North is to the top and East is to the left. The antisolar
direction is to the Southwest (PA=252◦ ).
23
Figure 9: b) Comparison of the spatial profiles of TD10 and a comparison star from
the combined images with a total integration time of 3.6 hr.
24
V. DISCUSSION AND SUMMARY
TD10 is a large outer solar system body with an irregular shape. Its visible colors
are not unusual. Tegler et al. (2003) find a bimodal distribution for Centaurs in
(B-R) for a sample of 22 Centaurs. Peixinho et al. (2003) also find a bimodal color
distribution in (V-R) versus (B-V) for a sample of 20 Centaurs and they group the
Centaurs into either “blue” (like 2060 Chiron) or “red” (like 5145 Pholus). The visible
colors (Table VI) place TD10 in the “blue” group (at the red end). There are only
7 Centaurs in common between the paper of Tegler et al. (2003) and Peixinho et al.
(2003) and only one is outside each others error bars. On the other hand, Bauer et
al. (2003) find a continuous color distribution for 24 Centaurs in their (V-R) versus
(R-I) color-color plot. A direct comparison between the plots of Tegler and Romanishin
(2003) and Peixinho et al. (2003) with those of Bauer et al. (2003) is not possible.
Tegler et al. (2003) have 10 objects in common with Bauer et al. (2003) and only one is
outside each others error bars. Peixinho et al. (2003) and Bauer et al. (2003) have 18
objects in common with 11 objects agreeing well, 2 objects having colors outside their
error bars and 5 objects within each others combined error bars. If we take the V-R
colors from Bauer et al. (2003) and the B-V colors from Peixinho et al. (2003), the
gap in the (V-R) versus (B-V) plot vanishes. However, the error bars from the colors
of Bauer et al. (2003) are generally larger than those from Peixinho et al. (2003). This
emphasizes the need for careful extraction of colors. This includes taking into account
effects of large amplitude variations in the lightcurves due to rotation. On the other
hand, the difference in colors for some objects could be real due to large scale color
variegations on the surface or due to temporal changes of the surface colors.
As other authors noted, there seems to be a prevalence of large aspherical objects
among the TNOs and Centaurs (e.g. Ortiz et al. 2003, Sheppard and Jewitt 2002).
Approximately 8% of main belt asteroids with diameters larger than 90 km have axial
ratios larger than 1.5. With the caveat of small number statistics (total number of
objects is 27), the percentage of large (i.e. HV ≤7.5) TNOs and Centaurs with axial
ratios larger than 1.5 is ≈22%. TD10 was excluded from the statistic as its value of HV is
larger than 7.5. What processes make main belt asteroids of this size more spherical on
average than TNOs and Centaurs. Is this a selection effect or small statistics effect? Is
it an inherent property of TNOs and Centaurs or an evolutionary effect? Sheppard and
Jewitt (2002) note that the distribution of axial ratios of TNOs is not consistent with
the distribution of impact fragment shapes. The knowledge of shapes and rotational
periods of TNOs and Centaurs is clearly a very powerful tool in understanding the
intrinsic and evolutionary properties of these objects.
The summary of our results is listed below.
• The synodic period of TD10 is 15.382±0.001 hr assuming the lightcurve variation
is due to an aspherical nucleus.
• No coma activity is detected. An intermittent coma can be excluded as well.
• We derive visible and near-infrared colors for TD10 including its first J-H color.
25
• The normalized reflectivity gradient is S 0 =10.8±0.9 % (0.1 µm)−1 , and is close to
the median for Centaurs.
ACKNOWLEDGMENTS
It is a pleasure to thank Drs Michael J. S. Belton and Tod R. Lauer for help with
acquiring the data. We are very grateful to Drs Stephen Tegler and Philippe Rousselot
for providing their data in electronic form. This work was supported by Planetary
Astronomy Grants from NASA for BEAM, NHS and HC, and by an NSF Grant for
HC.
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