The Astrophysical Journal Letters, 737:L9 (6pp), 2011 August 10 doi:10.1088/2041-8205/737/1/L9
C
2011. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
THERMAL MODEL CALIBRATION FOR MINOR PLANETS OBSERVED WITH WISE/NEOWISE:
COMPARISON WITH INFRARED ASTRONOMICAL SATELLITE
A. Mainzer
1
, T. Grav
2
, J. Masiero
1
, J. Bauer
1,3
, E. Wright
4
,R.M.Cutri
3
, R. Walker
5
, and R. S. McMillan
6
1
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA; amainzer@jpl.nasa.gov
2
Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218, USA
3
Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
4
UCLA Astronomy, P.O. Box 91547, Los Angeles, CA 90095-1547, USA
5
Monterey Institute for Research in Astronomy, Monterey, CA, USA
6
Lunar and Planetary Laboratory, University of Arizona, 1629 East University Blvd., Kuiper Space Science Bldg. #92, Tucson, AZ 85721-0092, USA
Received 2011 April 29; accepted 2011 June 23; published 2011 July 19
ABSTRACT
With thermal infrared observations detected by the NEOWISE project, we have measured diameters for 1742 minor
planets that were also observed by the Infrared Astronomical Satellite (IRAS). We have compared the diameters
and albedo derived by applying a spherical thermal model to the objects detected by NEOWISE and find that they
are generally in good agreement with the IRAS values. We have shown that diameters computed from NEOWISE
data are often less systematically biased than those found with IRAS. This demonstrates that the NEOWISE data
set can provide accurate physical parameters for the >157,000 minor planets that were detected by NEOWISE.
Key words: atlases – catalogs – infrared: general – minor planets, asteroids: general
Online-only material: color figures
1. INTRODUCTION
Understanding the formation and evolution of the minor
planets in our solar system requires good knowledge of the
physical parameters that describe each population of asteroids
and comets. Models of asteroid migration, for example, are
critically dependent on measurements of number counts, sizes,
and albedos. Visible light surveys have supplied most of the
discoveries of asteroids and comets to date; however, these
surveys tend to be biased against low albedo objects and
so they are underrepresented in number counts. Furthermore,
diameters derived from visible light observations are highly
uncertain due to their linear dependence on albedo, which can
vary by an order of magnitude for many types of asteroids.
Radar observations, stellar occultations, and in situ spacecraft
imaging provide powerful means of obtaining precise diameter
measurements, but these observations are limited to a small
subset of the ∼500,000 minor planets known to exist today.
While diameter and albedo can be measured more precisely than
with visible light by applying radiometric models to objects for
which thermal infrared data have been obtained, the size and
albedo distributions obtained in this way will still be biased if
the underlying source population was discovered by visible light
surveys. In order to mitigate against these biases, it is necessary
to undertake a survey that is capable of independent detection
and discovery of asteroids at thermal infrared wavelengths. Yet
the physical parameters such as size and albedo that are derived
from such a new survey must be checked against other well-
characterized data sets to ensure their reliability.
The Wide-field Infrared Survey Explorer (WISE)isaNASA
Medium-class Explorer mission designed to survey the entire
sky in four infrared wavelengths: 3.4, 4.6, 12, and 22 μm
(denoted W 1, W 2, W 3, and W 4, respectively; Wright et al.
2010; Liu et al. 2008; Mainzer et al. 2005). The final mission
data products are a multi-epoch image atlas and source catalogs
that will serve as an important legacy for future research. The
portion of the pipeline dedicated to finding minor planets (called
NEOWISE) has yielded observations of over 157,000 minor
planets, including near-Earth objects, Main Belt Asteroids,
comets, Hildas, Trojans, Centaurs, and scattered disk objects
(Mainzer et al. 2011a). This represents an improvement of nearly
two orders of magnitude more objects observed than WISE’s
predecessor mission, the Infrared Astronomical Satellite (IRAS;
Tedesco et al. 1988; Tedesco 1992;Matson1986). The WISE
survey began on 2010 January 14 and the mission exhausted
its primary tank cryogen on 2010 August 5. Exhaustion of the
secondary tank and the start of the NEOWISE Post-Cryogenic
Mission occurred on 2010 October 1, and the survey ended on
2011 January 31.
In Mainzer et al. (2011b), we demonstrated that thermal mod-
els created for minor planets using the WISE/NEOWISE data
set produce results that are in good agreement with diameters
independently measured by radar, stellar occultations, and in
situ spacecraft imaging. By taking the previously measured di-
ameters from methods derived independently of infrared ther-
mal model assumptions, we were able to verify the accuracy
of the color corrections given in Wright et al. (2010)forlow-
temperature objects such as asteroids. We used the previously
measured diameters combined with the Wright et al. (2010)
color corrections in conjunction with a faceted spherical ther-
mal model based on the Near-Earth Asteroid Thermal Model
(NEATM; Harris 1998) to predict the WISE magnitudes for
∼50 asteroids; these were compared with the observed WISE
magnitudes. We found that there were no systematic offsets
between predicted and observed magnitudes for these objects,
indicating that the color corrections given in Wright et al. (2010)
adequately describe the system response. For objects with WISE
measurements in two or more bands with good signal to noise
(for which the beaming parameter η can be fit), we found that di-
ameters can be determined to within ±10%, and visible albedo
p
V
to within ±20%.
In this Letter, we compare diameters and p
V
obtained with
WISE/NEOWISE observations for 1742 asteroids to those
determined by IRAS and find that they are generally in good
1
The Astrophysical Journal Letters, 737:L9 (6pp), 2011 August 10 Mainzer et al.
Figure 1. Comparison of the difference in diameters given by Tedesco et al. (2004a) and the diameters found by applying a spherical NEATM model to NEOWISE
measurements for 1742 asteroids. It can be seen that the values from Tedesco et al. (2004a) tend to be slightly smaller than NEOWISE-derived diameters. The
NEOWISE diameters diverge widely from IRAS for the smallest objects; however, these objects are observed by NEOWISE with high signal-to-noise ratio.
(A color version of this figure is available in the online journal.)
agreement with some slight systematic differences. This work,
combined with Mainzer et al. (2011b), demonstrates that the
NEOWISE observations of minor planets will produce good
physical parameters that will enable a wide range of scientific
investigations.
2. OBSERVATIONS
We have assembled a list of objects that were observed
by IRAS that NEOWISE detected during the fully cryogenic
portion of its mission. Of the ∼2200 asteroids observed by IRAS
(Tedesco et al. 1988; Tedesco 1992;Matson1986), we identified
NEOWISE detections for 1742 objects. The observations of
these objects were retrieved by querying the Minor Planet
Center’s (MPC) observation files to look for all instances of
individual WISE detections of the desired objects that were
reported using the WISE Moving Object Processing System
(WMOPS; Mainzer et al. 2011a). The resulting set of position/
time pairs were used as the basis of a query of WISE source
detections in individual exposures (also known as “Level 1b”
images) using the Infrared Science Archive. In order to ensure
that only observations of the desired moving object were
returned from the query, the search radius was restricted to
0.3 arcsec from the position listed in the MPC observation file.
Additionally, since WISE collected a single exposure every 11 s
and observes each part of the sky an average of 10 times, the
modified Julian date was required to be within 2 s of the time
specified by the MPC. The following flag values were allowed:
cc_flags = 0, P, or p and ph_qual = A, B, or C. Objects brighter
than W3 = 4 and W 4 = 0 magnitudes were assumed to have
flux errors equivalent to 0.2 mag due to changes to the shape
of the point-spread function as the objects became saturated,
and a linear correction was applied to the W 3 magnitudes
in this brightness regime (the WISE Explanatory Supplement
contains a more detailed explanation). As per the Explanatory
Supplement (Cutri et al. 2011), objects brighter than W 3 =−2
and W 4 =−6 were not used. Each object had to be observed a
minimum of three times in at least one WISE band, and it had
to be detected at least 40% of the time when compared to the
band with the maximum number of detections (usually, though
not always, W 3). The WMOPS system is designed to reject
inertially fixed objects such as stars and galaxies in bands W 3
and W 4. Nonetheless, the individual images at all wavelengths
were compared with WISE atlas coadd and daily coadd source
lists to ensure that inertially fixed sources such as stars and
galaxies were not coincident with the moving object detections.
2
The Astrophysical Journal Letters, 737:L9 (6pp), 2011 August 10 Mainzer et al.
Figure 2. Comparison of the difference in diameters given by Ryan & Woodward (2010) and the diameters found by applying a spherical NEATM model to NEOWISE
measurements for 1155 asteroids. The diameters found by Ryan & Woodward (2010) tend to be larger than those found by NEOWISE.
(A color version of this figure is available in the online journal.)
This check is particularly important in bands W 1 and W 2 where
the density of background objects (and hence the probability
of a blended source) is higher than at longer wavelengths.
Any remaining blended sources in bands W 1 and W 2were
removed. Some objects were observed at multiple epochs, and
observations separated by more than three days were modeled
separately.
3. THERMAL MODEL AND REFLECTED
SUNLIGHT FITS
In the Standard Thermal Model (STM) of Lebofsky &
Spencer (1989), the temperature of an asteroid is assumed
to be maximum at the subsolar point and zero on the point
opposite of this; this is the case of an object with zero
thermal inertia. In contrast, in the Fast Rotating Model (FRM;
Lebofsky et al. 1978; Veeder et al. 1989; Lebofsky & Spencer
1989), the asteroid is assumed to be rotating much faster than
its cooling time, resulting in a constant surface temperature
across all longitudes. The so-called beaming parameter (η)
was introduced by Lebofsky (1986) in the STM to account
for the enhancement of thermal radiation observed at small
phase angles. The NEATM of Harris (1998)alsousesthe
beaming parameter η to account for cases intermediate between
the STM and FRM models. In the STM, η is set t o 0.756 to
match the occultation diameters of (1) Ceres and (2) Pallas,
while in the FRM, η is equal to π. With NEATM, η is a free
parameter that can be fit when two or more infrared bands are
available.
We modeled each object as a set of triangular facets covering
a spherical surface with diameter equal to the ground-truth
measurement (cf. Kaasalainen et al. 2004). The temperature
for each facet was computed, and the Wright et al. (2010) color
corrections were applied to each facet. The emitted thermal flux
for each facet was calculated using NEATM along with the band
centers and zero points given in Wright et al. (2010); nightside
facets were assumed to contribute no flux. The emissivity, ,was
assumed to be 0.9 for all wavelengths (cf. Harris et al. 2009). The
objects’ absolute magnitudes (H) were taken from Warner et al.
(2009) when available; otherwise, the values were taken from
the MPC’s orbital element files. Unless a direct measurement
of G was available from Warner et al. (2009), we assumed a G
value of 0.15. In general, minor planets detected by NEOWISE
in bands W 1 and W 2 contain a mix of reflected sunlight and
thermal emission. Thus, it was necessary to incorporate an
estimate of reflected sunlight into the thermal model in order
to use data from bands W 1 and W 2. In order to compute the
fraction of reflected sunlight in bands W
1 and W 2, it was also
3
The Astrophysical Journal Letters, 737:L9 (6pp), 2011 August 10 Mainzer et al.
Figure 3. Comparison of the difference in albedos given by Tedesco et al. (2004a) and the diameters found by applying a spherical NEATM model to NEOWISE
measurements for 1742 asteroids. It can be seen that the values from Tedesco et al. (2004a) tend to be slightly higher than NEOWISE-derived albedos.
(A color version of this figure is available in the online journal.)
necessary to compute the ratio of the albedo at these wavelengths
compared to the visible albedo (p
IR
/p
V
); the solar spectrum was
approximated as a 5778 K blackbody. As described in Mainzer
et al. (2011b), we assumed that p
IR
= p
3.4 μm
= p
4.6 μm
.The
flux from reflected sunlight was computed for each WISE band
using the IAU phase curve correction of Bowell et al. (1989).
Thermal models were computed for each object by grouping
together observations having no more than a three-day gap
between them.
Error bars on the model magnitudes and subsolar temper-
atures were determined for each object by running 25 Monte
Carlo (MC) trials that varied the objects’ H values by 0.3 mag
and the WISE magnitudes by their error bars using Gaussian
probability distributions. The minimum magnitude error for all
WISE measurements fainter than W 3 = 4 and W 4 = 3 magni-
tudes was 0.03 mag, as per the in-band repeatability measured
in Wright et al. (2010). For objects brighter than W 3 = 4 and
W 4 = 3, the error bars were increased to 0.2 mag, as these mag-
nitudes represent the onset of saturation (see the WISE Explana-
tory Supplement). For those objects for which η and p
IR
/p
V
could not be fitted, η was set to 1.0 and allowed to vary in the
MC trials by 0.25, and p
IR
/p
V
was set to 1.4 and allowed to
vary by 0.5. These default values were used because they are
the mean and standard deviation of η and p
IR
/p
V
for the objects
for which these parameters could be fit. The error bar for each
object’s model magnitude was equal to the standard deviation
of all the MC trial values.
Although many asteroids are known to be non-spherical, the
WISE observations generally consisted of ∼10–12 observations
per object uniformly distributed over ∼36 hr (Wright et al.
2010; Mainzer et al. 2011a), so on average, a wide range of ro-
tational phases was sampled. Although the variation in effective
spherical diameter resulting from r otational effects tends to be
averaged out, caution must be exercised when interpreting ef-
fective diameter results using spherical models for objects that
are known to have large-amplitude light curve variations. In our
sample, 179 objects have NEOWISE observations at multiple
epochs (meaning that the groups of observations were separated
by more than 10 days). Of these, all but 24 had diameters that
agreed to within 10%, and most of the remaining objects had
W 3 peak-to-peak amplitudes >0.3 mag, indicating that they
are likely to be non-spherical. Non-spherical objects observed
at different viewing geometries can lead to different diameters
when using a spherical model. However, since 87% of the ob-
jects with multi-epoch observations have diameters that agree to
within 10%, we conclude that multiple observational epochs do
not contribute significantly to the differences observed between
IRAS and NEOWISE diameters.
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The Astrophysical Journal Letters, 737:L9 (6pp), 2011 August 10 Mainzer et al.
Figure 4. Comparison of the difference in albedos given by Ryan & Woodward (2010) and the albedos found by applying a spherical NEATM model to NEOWISE
measurements for 1155 asteroids. The albedos found by Ryan & Woodward (2010) tend to be lower than those found by NEOWISE.
(A color version of this figure is available in the online journal.)
4. RESULTS
Tedesco et al. (2002) reported observations of ∼2200
asteroids within the Supplemental IRAS Minor Planet Survey
(SIMPS). The diameters and albedos in that work were
computed using the STM. Similar to the work of Walker (2003),
who computed NEATM diameters and albedos for 654 asteroids
using IRAS fluxes, Ryan & Woodward (2010) applied a spher-
ical NEATM model to ∼1500 asteroids found in the SIMPS
and Mid-Course Space Experiment (Tedesco et al. 2004b) data.
Figures 1 and 2 show the comparison between diameters found
using NEOWISE observations and those given by Tedesco et al.
(2004a) and Ryan & Woodward (2010), respectively. Figures 3
and 4 show the comparison between NEOWISE and Tedesco/
Ryan albedos. The diameters given by Tedesco et al. (2004a)are
systematically lower than the NEOWISE diameters, while the
diameters computed by Ryan & Woodward (2010) are systemat-
ically higher. Also, p
V
given by Tedesco et al. (2004a)issystem-
atically higher than the NEOWISE p
V
values, but the Ryan &
Woodward (2010) values tend to be slightly lower. In Figure 5,
we show the diameters of Tedesco et al. (2004a) and Ryan &
Woodward (2010) compared to the diameters of 78 objects, with
diameters measured by radar, occultation, or spacecraft imag-
ing (see Mainzer et al. 2011b for a complete list of references).
These objects have been selected to have W 3 peak-to-peak
amplitudes <0.5 mag to avoid the worst complications caused
by applying spherical models to highly elongated objects. As
can be seen in the figure, the Tedesco et al. (2004a) diameters are
skewed toward slightly smaller sizes than the radar, etc., mea-
surements, whereas the Ryan & Woodward (2010) diameters
are biased toward larger sizes. We propose that these biases are
caused by the band-to-band color corrections derived for IRAS.
As described in Tedesco et al. (2002), band-to-band corrections
were derived by requiring that the 10 and 20 μm IRAS observa-
tions simultaneously matched a diameter derived from a stellar
occultation of (1) Ceres. Because the STM parameters were set
to match Ceres, Tedesco et al. (2002) found a 7% difference
between diameters derived for 13 objects, with diameters mea-
sured from stellar occultations. The NEATM model applied by
Ryan & Woodward (2010) does not appear to address this issue.
Furthermore, Ryan & Woodward (2010) applied cutoffs to η
of 0.75 and 2.75. As described above, in our NEATM models
applied to the NEOWISE data, we cut off η at the limit predicted
by the FRM, π . In the STM, η was set to 0.756 by matching the
diameters of Ceres and Pallas; however, there is no reason in
principle why it cannot range to lower values. In our application
of NEATM, we allow η to range arbitrarily low and find no fitted
η values less than ∼0.53.
5
