Spitzer Albedos of Near-Earth Objects

Spitzer Albedos of Near-Earth Objects

Annika Gustafsson    David E. Trilling    Michael Mommert    Andrew McNeill    Joseph L. Hora    Howard A. Smith    Stephan Hellmich    Stefano Mottola    Alan W. Harris
Abstract

Thermal infrared observations are the most effective way to measure asteroid diameter and albedo for a large number of near-Earth objects. Major surveys like NEOWISE, NEOSurvey, ExploreNEOs, and NEOLegacy find a small fraction of high albedo objects that do not have clear analogs in the current meteorite population. About 8% of Spitzer-observed near-Earth objects have nominal albedo solutions greater than 0.5. This may be a result of lightcurve variability leading to an incorrect estimate of diameter or inaccurate absolute visual magnitudes. For a sample of 23 high albedo NEOs we do not find that their shapes are significantly different from the 2019McNeill near-Earth object shape distribution. We performed a Monte Carlo analysis on 1505 near-Earth objects observed by Spitzer, sampling the visible and thermal fluxes of all targets to determine the likelihood of obtaining a high albedo erroneously. Implementing the McNeill shape distribution for near-Earth objects, we provide an upper-limit on the geometric albedo of for the near-Earth population.

visible: asteroids — infrared: asteroids — surveys — techniques: photometry, thermal modeling — characteristics: albedo
Corresponding author: Annika Gustafssonag765@nau.edu, agustafsson@lowell.edu\move@AU\move@AF\@affiliation

Department of Physics and Astronomy, P.O. Box 6010, Northern Arizona University, Flagstaff, AZ 86011

\move@AU\move@AF\@affiliation

Department of Physics and Astronomy, P.O. Box 6010, Northern Arizona University, Flagstaff, AZ 86011

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Lowell Observatory, 1400 W Mars Hill Rd., Flagstaff, AZ 86011

\move@AU\move@AF\@affiliation

Department of Physics and Astronomy, P.O. Box 6010, Northern Arizona University, Flagstaff, AZ 86011

\move@AU\move@AF\@affiliation

Center for Astrophysics |Harvard & Smithsonian, 60 Garden Street, MS-65, Cambridge, MA 02138

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Center for Astrophysics |Harvard & Smithsonian, 60 Garden Street, MS-65, Cambridge, MA 02138

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Institute of Planetary Research, Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

\move@AU\move@AF\@affiliation

Institute of Planetary Research, Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

\move@AU\move@AF\@affiliation

Institute of Planetary Research, Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

1 Introduction

Asteroids are some of the most primitive bodies in our Solar System and hold important clues regarding Solar System formation and evolution. Near-Earth objects (NEOs) are the subset of small bodies whose orbits bring them close to the Earth, with perihelion distances less than 1.3 au. They are a diverse population that represent the composition and dynamics throughout the Solar System. Due to their close approach to Earth, they pose a threat as potential impactors, present a unique opportunity as mission accessible targets, and are a potential source of mining resources. As a result, it is important we understand the physical properties of these objects.

Only absolute visual magnitudes (H-magnitudes) and orbital parameters are known for most NEOs. On discovery, the only physical information available for an NEO is its visible brightness, and the current rate of discovery of NEOs is far exceeding progress in physical characterization (e.g., albedo, diameter, composition). As a result, physical characterization surveys are essential to help inform hazard assessment, mitigation efforts, and mission planning for nearby NEOs. These surveys also provide an improved understanding of the distribution of physical properties which can inform NEO population models (2018Granvik).

Thermal infrared observations are critical for determining diameter and albedo for a large number of targets. ExploreNEOs (2010Trilling), IRAS (2010Ryan), AKARI (2014bOkamura; 2014Okamura), NEOSurvey (2016Trilling), NEOLegacy, and NEOWISE (2016Nugent; 2017Masiero; 2018Masiero) are infrared characterization surveys that determine diameter and albedo of small bodies across the Solar System. Albedos are particularly important in helping to infer composition when ambiguities exist in the classification of visible and near-infrared reflectance spectra (2003Delbo). Albedo and diameter are derived using thermal models (1998Harris; 2003Delbo; 2006Mueller; 2007Harris; 2015Delbo), which assume equilibrium between absorbed solar energy and thermal emission (2003Delbo).

ExploreNEOs, NEOSurvey, and NEOLegacy observed over 1500 near-Earth objects as of June 2017 using the Spitzer/IRAC instrument (2004Fazio). 121 targets in the 2017 sample () have nominal derived albedos () greater than 0.5 (Figure 1). Using the 2011Thomas average albedo for taxonomic complexes in combination with the 2019Binzel NEO taxonomy distribution, we expect only of a sample ( targets in this case) to have albedo values greater than or equal to 0.5. We find Spitzer high albedo targets in excess by a factor of about 8. As a result, 2010Trilling; 2016Trilling suggest that the most likely explanations for such high albedos are H-magnitudes that are photometrically inaccurate and/or sampling bias of objects from high amplitude light curves that give a high albedo solution.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefDiameter-albedo distribution of targets. The left panel is the diameter-albedo relationship for the Spitzer sample. The right panel is the number density as a function of albedo. 8% of the targets in this sample have albedo values greater than 0.5, a factor of about 8 more than expected for the NEO population from work by 2011Thomas and 2004Stuart.

2 Lightcurve Effects on Albedo

NEOs with large lightcurve amplitudes can lead to high albedo values. The albedo-amplitude relationship is derived from the diameter-albedo equation (1989Bowell):

(1)

For a poorly sampled lightcurve, the lightcurve amplitude can have a strong effect on the derived albedo. We expect the lightcurve induced albedo discrepancies are strong in our Spitzer observations as we only observe targets for a relatively short period of time. Using Equation 1 to solve for , we find that the derived albedo falls in the range shown in Equation 2 below where is the peak to trough lightcurve amplitude.

(2)

Figure 2 shows the albedo-amplitude relationship for a generic NEO () with different visible lightcurve amplitudes from 0 to 2 magnitudes and different characteristic albedo values. The shaded regions in Figure 2 represent the distribution of albedo misestimates for each lightcurve amplitude. The solid line is the mean albedo derived for each amplitude and is always the true albedo of the target. For a target whose true albedo value is 0.3, a 1 magnitude lightcurve amplitude can easily bring the derived albedo above 0.5. For a target whose true albedo is larger, a derived albedo greater than 0.5 can be achieved at much smaller lightcurve amplitudes.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefAmplitude-albedo distribution for a generic NEO (). By poorly sampling the lightcurve for an elongated object, and thus, miscalculating H, the albedo of the target can easily be determined to be greater than or equal to 0.5. Each panel indicates an NEO whose true albedo is shown for a lightcurve amplitude of 0, but can have an identified albedo anywhere in the shaded region for varying lightcurve amplitudes if the H-magnitude is incorrectly identified. For larger intrinsic true albedo values, a smaller lightcurve amplitude is required to allow for albedo values greater than 0.5.

To test whether the observed high albedos in the data represent truly high albedos or modeling outliers, we employ a Monte Carlo analysis of Spitzer NEOs to investigate the contributions of poorly sampled lightcurves and large thermal model input uncertainties. Table 2 outlines terminology, data samples, and populations that will be used in this work. In Section 3 we investigate high amplitude lightcurves with photometry. We outline the methods and results of our Monte Carlo technique in Sections 5 and 6 and discuss possible true high albedo targets in Section 7.

\H@refstepcounter table \hyper@makecurrenttable\hb@xt@ Table 1. \Hy@raisedlink\hyper@@anchor\@currentHrefGlossary of Import Terms and Data Samples

Name Definition Terminology: High Albedo Albedo greater than or equal to 0.5 Intrinsic Albedo Inherent albedo of the target Nominal Albedo Derived albedo of the target Spitzer Data Samples: # Spitzer 2017 1505 NEOs observed with ExploreNEOs, NEOSurvey, and NEOLegacy as of JD 2457921 Spitzer 2017 High Albedo 121 NEOs in the Spitzer 2017 sample with albedo greater than or equal to 0.5 DCT Photometry 22 Spitzer 2017 High Albedo NEOs observed with DCT Calar Alto Photometry 7 6 of the 22 DCT High Albedo NEOs & 1 other High Albedo NEO observed at Calar Alto Astronomical Observatory LCDB 25 Spitzer 2017 High Albedo NEOs with previously measured lightcurves reported to the Asteroid Lightcurve Database Spitzer 2018 1999 NEOs observed with ExploreNEOs, NEOSurvey, and NEOLegacy as of JD 2458278 Spitzer 2018 High Albedo 181 NEOs in the Spitzer 2018 sample with albedo greater than or equal to 0.5 Measured Taxonomy 54 NEOs in the Spitzer 2018 High Albedo sample with a measured Bus-DeMeo taxonomy classification Populations: Observed Fraction Spitzer 2017 albedo distribution MC Fraction Monte Carlo albedo distribution using the Spitzer 2017 data sample Residual Fractional difference between the Observed fraction and MC fraction Observed NEO Population Albedo distribution using the mean taxonomic albedos with the NEO taxonomy distribution MC Fraction of Real Also known as MC Fraction Same as Residual but normalized to 100% for albedo greater than 0 [Treated as an independent population] High Albedo Sample Same as Measured Taxonomy sample described above

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3 Observations

3.1 Spitzer Space Telescope

The target sample considered for this work consists of 1505 NEOs observed with the Spitzer/IRAC instrument (2004Fazio) as part of ExploreNEOs (2010Trilling), NEOSurvey (2016Trilling), and NEOLegacy. This dataset contains all targets observed by these Spitzer surveys as of JD 2457921 (2017-06-16). We will refer to this dataset as the Spitzer 2017 sample. ExploreNEOs collected observations in the 3.6 and 4.5 m bands, while NEOSurvey and NEOLegacy observed targets in only the 4.5 m band. For this work, we consider thermal fluxes from the longer wavelength band where the NEO is typically brightest. A table of the observations and results is maintained in an online database333http://nearearthobjects.nau.edu. A detailed description of the observing methods and lightcurve results are provided in 2018Hora.

Diameters listed in the online database are obtained with a modified version of NEATM described in 2016Trilling. This modified NEATM is the 1998Harris Near-Earth Asteroid Thermal Model (NEATM) to fit diameter and geometric albedo in combination with a Monte Carlo simulation to estimate the uncertainties associated with the output diameter and albedo. The model uses input Spitzer fluxes from the 4.5 m band and absolute H-magnitudes from the Asteroids Dynamic Site444http://hamilton.dm.unipi.it/astdys/ (AstDyS) (2012Knezevic). The 2012Pravec correction is applied to the AstDyS H-magnitudes to create the input for the NEATM model. The corrected AstDyS H-magnitudes have a mean 1–sigma uncertainty of 0.24 mag. NEATM also uses a variable beaming parameter () to account for surface roughness, thermal inertia, and other effects in a zeroth order approximation (1998Harris). A linear relation is used to derive an appropriate based on the phase angle () where larger is used for higher phase angle observations. This relationship between and is not well constrained and is thus primarily responsible for the overall uncertainties in the model results (2016Trilling). The uncertainty in derived in this way contributes up to 90% of the overall uncertainty in albedo for all objects (2016Trilling).

There are 121 NEOs from the Spitzer 2017 sample with nominal derived albedo values greater than 0.5. We collected lightcurve photometry for 23 of these objects to place limits on the visible lightcurve amplitudes and determine if lightcurve effects could be a significant contributor to the high albedo values found in the Spitzer dataset. 22 objects were observed using the Lowell Observatory 4.3–m Discovery Channel Telescope (DCT) in Happy Jack, AZ. We observed 6 of those 22 DCT targets along with one other high albedo target using the 1.23–m Calar Alto Astronomical Observatory in Almería, Spain.

3.2 Discovery Channel Telescope

Data for 22 high albedo NEOs were collected using the Large Monolithic Imager (LMI) on the DCT. LMI has a 12 field of view with a /pixel unbinned pixel scale. Images were taken in 22 binning mode for a /pixel on seven separate nights from 2015 to 2017. All targets were observed in the Johnson V filter and at sidereal rates with exposure times ranging from 15 to 60 seconds. The net integration time of a given target ranged from 10 minutes to 2 hours with a majority of the targets observed in the 10–20 minute range, resulting generally in partial lightcurves. A total of 36 separate observations were made of the 22 unique targets. A full description of the DCT observations is provided in Table 2.

All data were bias-corrected and flat-fielded using biases and twilight flats taken at the beginning of each observing night. On the night of 2016–05–30, no twilight flats were taken, so the flat field was created using sky flats where the first images at each pointing were median combined and normalized to create a master flat.

3.3 Calar Alto Astronomical Observatory

Calar Alto data were collected using the DLR-MKIII camera on the 1.23-m telescope. The camera is a 40004000 pixel array with a pixel scale of /pixel and a field of view of .

We observed 7 high albedo targets over multiple nights. A total of 61 separate observations were made of the 7 unique targets. The filters of the targets varied between V, R, and clear within and across different nights of observations to measure colors and assign composition. The targets were observed over varying phase angle (). All images were bias-corrected and flat-fielded. A full description of the Calar Alto observations is provided in Table 3.

3.4 Photometry

Automated photometric analysis was performed on all of the reduced DCT and Calar Alto images using the Photometry Pipeline (2017Mommert). Photometry Pipeline uses Source Extractor (1996Bertin) and SCAMP (2006Bertin) to perform aperture photometry and astrometry on all objects in the field of view. The tool utilizes a curve-of-growth analysis to optimize the aperture size. All targets were located using the Pan-STARRS reference catalog (2017Chambers). We performed visual rejection for exposures within the proximity of a nearby star or where the target was not correctly identified. Visual inspection was favored as it usually leads to a more conservative rejection of potentially compromised photometric measurements as compared to an automated rejection scheme based on Source Extractor flags.

4 NEO Shape Distribution

We determined lower limit amplitudes () for all 23 targets using Equation 3 from the photometry where is the magnitude of the target.

(3)

The lower limit amplitudes are listed in Table 2 and Table 3. We compare these amplitudes to the 2019McNeill NEO shape distribution.

We combined the lower limit amplitudes for our 23 DCT and Calar Alto targets with 25 high albedo targets from the Asteroid Lightcurve Database (LCDB) (2009Warner). These 25 targets have albedo values greater than 0.5 in the Spitzer 2017 dataset and have previously observed lightcurve information (Table 4). The lower limit amplitudes of these 48 high albedo targets are phase corrected using the 1990Zappala phase-amplitudue relationship (Equation 4) which describes a linear relationship for phase angles from . In Equation 4, is the peak to trough lightcurve amplitude, is the phase angle of the observation, and is the slope parameter defined for each taxonomy.

(4)

The observations of these 48 high albedo targets cover a phase angle range from . Using a slope parameter of for all targets and Equation 4, we derive a cumulative distribution of corrected lower limit amplitudes. For phase angles larger than , the derived fit defined in 1990Zappala is non-linear. The cumulative distribution of corrected lower limit amplitudes using both the linear (Equation 4) and non-linear fits (1990Zappala) are consistent across the observed phase angle range of . The cumulative distribution of lower limit amplitudes using the linear fit is shown in Figure 4 in orange.

2019McNeill finds a Gaussian shape distribution for the NEO population with a mean axis ratio of , describing the elongation with respect to spherical (). From this distribution, we use a Monte Carlo model to generate peak to trough lightcurve amplitudes () following Equation 5 below. We assign object obliquity values following the distribution constrained by 2017Tardioli which leverages the Yarkovsky effect and its dependence on an asteroid’s obliquity.

(5)

The derived cumulative fraction of amplitudes using this method is shown in Figure 4 in blue. For the 48 high albedo targets (23 DCT/Calar Alto, 25 LCDB), we find a preference for less elongated objects when compared to the NEO shape distribution 2019McNeill. We also find three potential candidates for extreme elongated objects: 1865 (1971 UA), 416186 (2002 TD60), and 2010 NR1. These are objects which have a phase corrected lightcurve amplitude greater than 1 magnitude (2018McNeill). Because these are lower limit amplitudes, there may be other candidates in our sample, and so we cannot rule out highly elongated objects as a contributor to the factor of 8 increase in high albedos () derived in the Spitzer 2017 dataset.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefCumulative NEO amplitude distribution derived from the 2019McNeill shape distribution (Modeled; blue). Overplotted in orange is the observed cumulative lower limit amplitude distribution of 23 targets from DCT and Calar Alto and 25 targets with previous observations submitted to the LCDB (2009Warner). All amplitudes have been corrected for phase angle following the relationship derived in 1990Zappala. We find three candidates for extreme elongated objects in our sample (i.e. objects with a phase-corrected lightcurve amplitude  magnitude (2018McNeill)) and a maximum lower limit amplitude in our sample of 1.58 magnitudes.

5 Modeling

There are many possible contributors to the unexpectedly high albedo values including rotational lightcurve variability (leading to a misestimate of asteroid diameter), inaccurate absolute visual magnitudes (either from poor photometry or lightcurve effects), or effects from non-simultaneous observations due to changes in observing geometry, phase angle, and rotational phase. We use Monte Carlo (MC) simulations to explore albedo offsets as a result of these factors.

We perform a MC simulation on all Spitzer targets to assess the effects of amplitude on the resulting albedo distribution of our dataset. We select a peak to trough lightcurve amplitude in the range of 0.1 magnitudes to 1.6 magnitudes. We assume that all targets in our sample have a sinusoidal lightcurve of the same amplitude. We also assume that the lightcurve variability is consistent between the visible and thermal wavelengths.

The following steps are applied in the MC simulation:

  1. Given a lightcurve amplitude, we randomly sample a rotational phase for each target from a uniform distribution of where is the corrected AstDyS H-magnitude and is the peak to trough lightcurve amplitude we have assigned for all targets. By sampling the rotational phase, we simulate the uncertainties associated with observing partial lightcurves.

  2. Using for each target found in Step 1, we apply a photometric uncertainty by randomly sampling from a normal distribution of where is the photometric error provided for the corrected AstDyS H-magnitude of the target. The randomly selected value is .

  3. Steps 1 and 2 are similarly applied to the thermal lightcurve where flux () and are from the Spitzer measurements. Using the equivalent lightcurve variability for the thermal as visible wavelengths, we select a rotational phase and corresponding flux () from a uniform distribution, then apply a photometric uncertainty to from a normal distribution to select .

  4. We create a distribution of slope parameters () using the 2019Binzel taxonomy distribution for NEOs and the 2015Veres mean values for each taxonomy. For each target, we randomly sample a value from a distribution of 10,000 NEOs shown in Figure 4.

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    Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefDistribution of G values from 2015Veres with the 2019Binzel NEO taxonomy distribution. The distribution is randomly sampled as input for the MC simulation.

  5. The heliocentric distance (), geocentric distance (), and phase angle () for the asteroid are obtained from the NASA JPL Horizons Database555https://ssd.jpl.nasa.gov/horizons.cgi at the midpoint time of the Spitzer observation. The resulting H-magnitude (), thermal flux (), slope parameter (), and observing geometry of the target () are used as inputs in the modified NEATM (2010Trilling; 2016Trilling) to generate an albedo for each target.

  6. 2010Trilling and 2016Trilling account for uncertainties in a MC approach in the NEATM that varies . The resulting uncertainties due to are reflected in the upper and lower 1– published albedo uncertainties. Our observations show no preference for high albedo objects observed at high phase angle (Figure 6). As a result, we can treat uncertainties due to equally for all targets. We create a distribution of the 1– upper and lower albedo uncertainties for the targets provided by 2010Trilling; 2016Trilling. We randomly select an upper and lower uncertainty, and use the mean of those values as sigma to create a normal distribution about the NEATM-derived albedo from Step 5. Our final albedo value is sampled from this normal distribution of .

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    Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefAlbedo vs. Phase Angle for 1505 Spitzer 2017 targets. There is no preference for high albedo objects observed at high phase angle.

We consider this technique for three different definitions of high albedo thresholds (0.4, 0.5, 0.6).

6 Results

Figure 6 shows the overall fraction of targets with high albedo (0.4, 0.5, 0.6) as a function of input amplitude, as derived from our MC model. From the observations, 17% of Spitzer targets have albedo values greater than 0.4, 8% have albedos greater than 0.5, and 5% have albedos greater than 0.6. These three observational thresholds are indicated as horizontal dashed lines with Poisson uncertainties () shown as the shaded regions around the dashed line. We use MC simulations to find the probability that a Spitzer target with a given lightcurve amplitude (horizontal axis) has a MC derived albedo value greater than a given high albedo threshold (0.4, 0.5, 0.6). The MC probability distribution is plotted as individual data points with 1– uncertainties for each lightcurve amplitude. The color of the data points matches the threshold value in consideration.

We find a large fraction of Spitzer targets at the albedo threshold 0.4. As a result, we require large lightcurve amplitudes consistent with extreme elongated objects ( magnitude) to describe the observations with shape alone. Thresholds of 0.5 and 0.6 are consistent with the observations at the mean lightcurve amplitude (vertical black line) derived for the NEO shape distribution in 2019McNeill. These results lead us to conclude the following:

  1. We require NEOs in our sample to have intrinsic albedos up to 0.5. For , we find a larger Observed fraction than the MC fraction, implying a compositional influence on albedo rather than lightcurve effects.

  2. We match the Observed fraction of targets with high albedo () in the Spitzer 2017 dataset at lightcurve amplitudes consistent with the mean amplitude of the NEO shape distribution (Figure 6). When we adopt the 2019McNeill shape distribution for lightcurve amplitude, we place an upper limit on intrinsic albedo in the NEO population of . Thus, high albedo targets are not required in our dataset.

  3. We can explain the factor of 8 increase in targets with as a result of lightcurve sampling and thermal model uncertainties.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefProbability for targets to have derived high albedo (0.4, 0.5, 0.6) as a function of lightcurve amplitude, as derived from our MC model. The three observational thresholds are indicated as horizontal dashed lines with 1– shaded uncertainties. The MC probability distribution is plotted as individual data points with 1– uncertainties for each high albedo threshold at different lightcurve amplitudes. The 2019McNeill mean lightcurve amplitude is shown as the vertical black line with 1– uncertainties. We see that for the 0.5 and 0.6 albedo threshold, we can match the observations at the mean NEO lightcurve amplitude. However, for the 0.4 albedo threshold, there is an excess of targets in the observations with respect to the MC derived fraction.

7 Investigation into Intrinsically
High Albedo NEOs

While our result does not require intrinsically high albedo NEOs (), it also does not exclude them. We investigate the need for high albedo NEOs by adopting the 2019McNeill shape distribution described in Section 3.4, and employ a MC technique. For each target, we select from the NEO shape distribution of amplitudes for both the visible and thermal lightcurve. We repeat Steps 1–6 described in the previous MC (Section 5).

We compare this derived MC albedo to the published Spitzer 2017 albedo for the target and find the fraction of targets with MC albedo greater than the published Spitzer 2017 albedo. The top panel of Figure 7 shows the cumulative distribution function of albedo for the Spitzer published values in blue – what we call the Observed fraction. Poisson uncertainties () are represented as a shaded region around the data. In orange, we plot the mean fraction of targets from our MC trials with MC albedo values larger than that of their published Spitzer albedo. We only consider the cases where the MC albedo falls in a higher 0.1–width albedo bin. An example is a Spitzer 2017 target with albedo of 0.57 (0.5–0.6 albedo bin) and a MC derived albedo for that target of 0.62 (0.6–0.7 albedo bin). The MC derived albedo is in a larger albedo bin, so we consider this target in our analysis. We expect there to be equally as many cases where the MC albedo is less than the published Spitzer 2017 albedo, however, we are only interested in situations which produce a high nominal albedo. The situations which produce a low nominal albedo fall out of the scope of this work and are therefore not considered. In Figure 7, the 1– uncertainties from all MC trials are displayed as a shaded region around the MC fraction. The first bin shows that of the targets in the sample that have published albedo values in the range 0–0.1 have “upper” MC albedo values greater than 0.1. The MC fraction thus represents the fluctuation and uncertainty in the derived albedo value due to both lightcurve and thermal model input uncertainties used in the MC simulation.

The bottom panel of Figure 7 shows the cumulative fraction of derived intrinsic albedo targets. We find the residual of the two datasets from the top panel for each albedo bin using Equation 6. We define the residual to be the fractional difference between the Observed fraction and the MC fraction where is the Observed fraction (blue) and is the MC fraction (orange):

(6)

The uncertainties provided on the residual are 1– fractional uncertainties from the Observed fraction and MC fraction added in quadrature. The residual represents the fraction of targets in the Spitzer 2017 dataset which we believe to have the displayed intrinsic albedo values. That is, we do not require any targets to have intrinsic albedos where the cumulative fraction goes to zero. The result found in the residual is consistent with previous work by 2019Binzel and 2011Thomas. We can place an upper limit on albedo in the NEO population of 0.50.1 beyond which high albedo targets are not necessary to describe our observations. The precision in our upper limit is limited by our sampling size of 0.1–width albedo bins. However, the residual is formally nonzero to arbitrarily large values.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefTop: The Observed fraction is a cumulative distribution function of the 1505 Spitzer 2017 targets for albedo values from 0.1–1.0 (horizontal axis). The MC fraction represents the fraction of targets with albedo in a 0.1 bin width (i.e., 0.1–0.2, 0.2–0.3, etc.) that move out of their published albedo bin to a larger bin due to fluctuations from the lightcurve and diameter uncertainties sampled in the MC model. The 1– uncertainties are shown for both trend lines as shaded regions. Bottom: The residual is the cumulative fraction of observed targets with the MC fraction of targets removed. That is, the lightcurve and diameter fluctuations which produce a large nominal albedo are removed from the sample. The result is the fraction of targets in the Spitzer dataset with real albedo values, finding a maximum nominal albedo of 0.50.1. The 1– uncertainties shown as a shaded region. We find an upper limit on albedo of where the Residual is consistent with zero for albedo bins greater than 0.5. For the high albedo bins, the fluctuations are high and we find all targets leave their starting bins. This, however, does not exclude targets from having intrinsically high albedos.

We explore the possibility that high albedo targets exist in the range , and may as a result, be interesting due to their unique shape or composition. We compare our MC fraction of real albedo targets (Residual; Figure 7) to the albedo distribution of the known NEO population (2011Thomas; 2019Binzel). We normalize the cumulative MC fraction of real albedo targets to 100% for , treating this as a standalone population. The two distributions are shown in Figure 7.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefTop: The cumulative albedo distribution for the NEO population from 2011Thomas and 2019Binzel shown in blue. For comparison, we plot the normalized cumulative MC fraction of real albedo targets (orange). The albedo distributions are consistent for albedo greater than 0.3, but we see fewer low albedo targets in the Spitzer dataset compared to the NEO population. Bottom: The difference between the Observed fraction (blue) and the MC fraction (orange). The Spitzer observations are biased toward higher albedos and lack a range of low albedo asteroids. The Differential in the bottom panel may be reflective of this bias.

The observed distribution is determined from 2019Binzel ground-based observations of the NEO taxonomy distribution and mean albedo values for each taxonomy defined by 2011Thomas. We find that the cumulative fraction of MC targets is consistent within 1– for . However, there is a excess of low albedo MC targets () compared to the NEO population which may be a result of objects appearing brighter in the infrared than the visible. This bias may contribute to the trend seen in the Differential (Figure 7; bottom).

In Figure 7, we include the cumulative fraction of NEOWISE albedos for NEOs published in 2019Mainzer. Because NEOWISE operates in survey mode, they are only biased toward detectability and not in target selection. As a result, we expect a higher fraction of low albedo objects in the NEOWISE sample than is present for the optically-selected Spitzer sample and the observed NEO population. This is consistent with the trend we observe in Figure 7 where of the NEOWISE sample has an albedo less than 0.3.

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Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefThe cumulative albedo distribution for the observed NEO population (2011Thomas; 2019Binzel) shown in blue, the MC fraction shown in orange, and the NEOWISE dataset (2019Mainzer) shown in red. The albedo distributions for the MC fraction and the NEOWISE dataset are similar with relatively high fractions of both low and high albedo targets. These trends are unlike the Observed NEO Population which has most of its targets in the albedo range of 0.2-0.4.

We have shown Figure 7 that we have targets in our Spitzer 2017 dataset with true albedos up to 0.5. For the purpose of this investigation, we will explore those with potentially rare high albedos () where both shape and composition play a role in influencing their unexpected high albedo values.

In the Spitzer 2018 sample from ExploreNEOs, NEOSurvey, and NEOLegacy of 1999 targets as of JD 2458278 (2018-06-08), 181 (9%) possibly have intrinsic high albedo values. We compare the taxonomy distribution of the 181 high albedo Spitzer 2018 targets with that of the known NEO population (2019Binzel; 2011Thomas) in an effort to disentangle shape influences from compositional influences on albedo. We adopt the taxonomic complexes defined in 2011Thomas as shown in Table 7. We hypothesize that a taxonomic distribution of these high albedo targets will favor complexes with higher intrinsic mean albedos (X-, R-, and V-types) if we have intrinsic high albedo outliers in our sample. Of these three taxonomy complexes, observations of the NEO population find R-types are the least common (), V-types represent , and X-types (2019Binzel). Of the X-type complex, Xe- and E-types are known to have the highest mean albedo at (2013DeMeo).

\H@refstepcounter table \hyper@makecurrenttable\hb@xt@ Table 5. \Hy@raisedlink\hyper@@anchor\@currentHrefTaxonomy Complex

Complex Types D D, T 0.02 0.02 0.01 C B, C, Cb, Cg, Ch, Cgh 0.23 0.15 0.13 S S, Sa, Sk, Sl, Sr, K, L, Ld 0.26 0.04 0.03 Q Q, Sq 0.29 0.05 0.04 X X, Xc, Xk, Xe, E, M, P 0.31 0.08 0.07 R R *0.340 *0.034 *0.034 V V 0.42 0.13 0.11

Note—Types included in each taxonomy complex with average albedo values from 2011Thomas and *2004Stuart.

Of the 181 Spitzer 2018 targets with nominal albedo values greater than 0.5, 54 (30%) have measured taxonomies (2002Binzel; 2011Thomas; 2014Thomas; 2016Carry; 2017Erasmus; 2018Perna). Table 5 shows a complete list of these targets. A comparison of the taxonomy distributions of these high albedo targets with the NEO population is shown in Figure 7 in order of increasing mean albedo. We find an excess of X-, R-, and V-type complexes in the high albedo sample with respect to the NEO population, with only the X-type fraction significantly greater than the NEO population (Figure 7). 30% of the classified high albedo X-types have been identified as E-types (2011Thomas), supporting a compositional-driven influence for a fraction of the targets in this high albedo sample. While the R- and V-type fractions are within 1– of the NEO population, there is a large excess of X-types in the high albedo sample, most likely a result of Xe- and E-types. While the Xe- (2009DeMeo) and E-types (1984Tholen) are defined using different classifications, they are nearly identical (2019Binzel). From here on, we will refer to Xe- and E-types together as Xe.

\H@refstepcounter

figure \hyper@makecurrentfigure

Figure 0. \Hy@raisedlink\hyper@@anchor\@currentHrefThe NEO taxonomy distribution is shown in order of increasing mean taxonomic albedo (2011Thomas) from left to right using NEO taxonomy data from 2019Binzel. The 48 high albedo targets with classified taxonomies are distributed over all represented taxonomic complexes in the NEO population. We find evidence for higher nominal mean albedo taxonomies (X-, R-, V-types) and less of a preference for D-, C-, and S-, and Q-types. The strongest excess is in the X-types which we believe is due to the presence of high albedo Xe-types in our sample.

2019Binzel, 2018Granvik, and 1992Gaffey all find a strong signature for the inner Main Belt Hungaria region as a source for the Xe-type NEOs. Xe-types show strong mineralogic similarity to the enstatite-rich aubrite meteorites (2018Lucas) with mean albedos greater than 0.5 (2013DeMeo). In this high albedo sample, we also find representation from D-, C-, S-, and Q-type taxonomic complexes. There is only 1 object each of D-type (2016Carry) and C-type (2001Whiteley) taxonomies of the lowest mean albedos classified with spectrophotometry. We believe these objects may belong to the X-type complex based on their extreme nominal high albedos, but this has yet to be confirmed spectroscopically. D-, C-, and X-types have similar featureless red sloped spectra in the visible to near-infrared, but with varying degrees of spectral reddening, so it is not unreasonable for them to be misclassified due to the similarity in color between the three types. It is, however, unreasonable for an object with high albedo to be classified as D- or C-type.

We find a similar fraction of S-type objects in our high albedo sample in comparison to the NEO population where we would have expected a deficit. For an S-type object with albedo 3– above the mean, we require a lightcurve amplitude of at least 0.5 and a poor measurement to derive an albedo greater than 0.5. As a result, it is possible that a fraction of the S-type objects in our sample produce nominal high albedo values due to influence from both shape and composition.

8 Summary

Major infrared surveys find that the fraction of NEOs with high albedos is a factor of 8 more than expected based on average albedos from the literature and the known NEO taxonomy distribution. This excess in high albedo values is easily explained by offsets in photometry introduced due to incomplete lightcurve sampling and uncertainties on remaining thermal model input parameters including the beaming parameter. With full visible lightcurves, the H-magnitudes can be improved and uncertainties reduced, but without a full thermal lightcurve, we cannot derive accurate intrinsic albedos. For a sample of 48 high albedo NEOs with lower limit amplitudes, we do not find that their shapes are significantly different from the 2019McNeill NEO shape distribution. We adopt the McNeill NEO amplitude distribution in a MC model sampling uncertainties on thermal model input parameters and find that the upper limit on albedo in the NEO population is .

There is a significant fraction of Xe-type objects, which have high albedos, present in our catalog of high albedo objects, and perhaps, an excess of X-, R-, and V-type complexes above the NEO population taxonomy distribution. However, the mean albedo for each of these taxonomies all lie near or under the 0.5 high albedo threshold. As a result, these findings are consistent with previously published works which also find an upper limit albedo in the NEO population of 0.5.


\onecolumngrid
# Designation Taxonomy Reference
C-Complex:
152637 1997 NC1 0.541 0.228 0.231 [25]
D-Complex:
225312 1996 XB27 0.544 0.289 0.261 [7]
Q-Complex:
23183 2000 OY21 0.904 (0.640) 0.404 (0.076) 0.426 (0.076) [8]
136849 1998 CS1 0.504 0.356 0.298 [22]
341816 2007 YK 0.75 0.432 0.393 [19]
R-Complex:
257838 2000 JQ66 0.673 0.452 0.399 [3]
482566 2012 WK4 0.612 0.276 0.269 [20]
S-Complex:
1620 1951 RA 0.560 (0.290) 0.354 (0.038) 0.316 (0.038) [6]
1865 1971 UA 0.578 (0.4797) 0.311 (0.4074) 0.289 (0.4074) [3,6,24]
1915 1953 EA 0.535 0.303 0.274 [1,6]
3199 1982 RA 0.531 0.379 0.324 [6]
5131 1990 BG 0.834 0.497 0.470 [4]
10165 1995 BL2 0.567 (0.372) 0.353 (0.198) 0.309 (0.198) [3,6]
25143 1998 SF36 0.496 0.222 0.210 [2,7]
42286 2001 TN41 0.548 0.422 0.338 [11]
87024 2000 JS66 0.669 0.280 0.289 [5]
153953 2002 AD9 0.556 0.350 0.309 [3,14]
159609 2002 AQ3 0.736 0.336 0.342 [9,21]
200754 2001 WA25 0.501 (0.21) 0.208 (0.204) 0.209 (0.204) [3,8,18]
200840 2001 XN254 0.646 0.262 0.281 [5]
252399 2001 TX44 0.647 (0.478) 0.338 (0.157) 0.316 (0.157) [3]
274855 2009 RB4 0.539 0.304 0.277 [5]
416186 2002 TD60 0.496 0.294 0.262 [17]
2005 ML13 0.516 0.235 0.216 [20]
2015 JD1 0.507 0.307 0.247 [20]
V-Complex:
54509 2000 PH5 0.556 0.272 0.254 [3,12]
137052 1998 VO33 0.621 0.374 0.338 [3,9]
470975 2009 SC15 0.620 0.281 0.275 [15]
1999 SH10 0.523 0.239 0.223 [10]
2014 HR178 0.801 0.347 0.330 [5]
X-Complex:
3671 1984 KD 0.625 0.262 0.277 [4,6]
*3691 1982 FT 0.537 (0.593) 0.368 (0.120) 0.311 (0.120) [4,6]
*5751 1992 AC 0.497 0.306 0.265 [4,16]
7474 1992 TC 1.225 0.490 0.543 [3,9]
*10302 1989 ML 0.559 0.274 0.251 [2,3]
*17511 1992 QN 0.766 0.249 0.279 [4,14]
*33342 1998 WT24 0.816 (0.654) 0.261 (0.13) 0.292 (0.13) [18]
*54789 2001 MZ7 0.556 (0.856) 0.277 (0.145) 0.275 (0.145) [8,24]
*136564 1977 VA 0.584 0.287 0.280 [3]
136818 1997 MW1 0.781 0.277 0.315 [2,25]
138893 2000 YH66 0.693 0.343 0.343 [3]
162004 1991 VE 0.699 0.271 0.298 [19]
162581 2000 SA10 0.564 0.250 0.245 [14]
163132 2002 CU11 0.809 (0.408) 0.301 (0.061) 0.321 (0.061) [24]
170086 2002 XR14 0.512 0.221 0.219 [9]
275792 2001 QH142 0.814 0.347 0.368 [24]
376848 2001 RY47 0.818 0.295 0.315 [17]
407656 2011 SL102 0.577 0.281 0.276 [23]
412976 1987 WC 0.498 0.278 0.242 [5]
416151 2002 RQ25 0.792 0.277 0.286 [24]
462559 2009 DD1 0.783 0.383 0.355 [20]
2005 TS15 0.728 0.405 0.357 [5]
2012 PG6 0.496 0.297 0.247 [20]
2014 YD 1.102 0.428 0.418 [10]
Table 5: High Albedo Taxonomy
\LTpost

Note—High albedo NEOs with measured taxonomy. Those objects noted with * are previously identified E-types in the X-type complex. The Spitzer albedos are listed in the second column with 1–sigma uncertainties. NEOWISE albedos from the 2019 NASA PDS release are listed in parentheses where available (2019Mainzer). References— [1] 1983Binzel, [2] 2001Binzel, [3] 2004Binzel, [4] 2004cBinzel, [5] 2019Binzel, [6] 2002Bus, [7] 2016Carry, [8] 2010DeLeon, [9] 2013DeMeo, [10] 2019Devogele, [11] 2017Erasmus, [12] 2007Gietzen, [13] 2007Harris, [14] 2012Hasselmann, [15] 2014Kuroda, [16] 2004Lazzarin, [17] 2005Lazzarin, [18] 2010Lazzarin, [19] 2018Lin, [20] 2018Perna, [21] 2013Sanchez, [22] 2010Somers, [23] SMASS Website, [24] 2014Thomas, [25] 2001Whiteley

\twocolumngrid
\twocolumngrid


This work is based in part on the observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech.

Some of the data utilized in this work were obtained at the Discovery Channel Telescope, operated by Lowell Observatory in Happy Jack, AZ, and at the Calar Alto Astronomical Observatory in Almería, Spain.

We acknowledge the NASA JPL Solar System Dynamics group for their online Horizons ephemeris service as well as the Asteroids Dynamic Site (AstDyS) Database.

This work was made possible in part by the funding support of the NASA NEOO grant NNX17AH06G.

Facilities: Spitzer (IRAC), Discovery Channel Telescope (LMI), Calar Alto Astronomical Observatory (LDR-MKIII) Software: Source Extractor (1996Bertin), SCAMP (2006Bertin), Photometry Pipeline (2017Mommert)

\bibliography@latex

SpitzerAlbedo_Final


\onecolumngrid
# Designation UTC V Airmass Exptime Duration m
(yymmdd) (mag) () (s) (hour) (mag)
3199 1982 RA 161129 18.6 32.7 1.4 60 0.33 0.13
3691 1982 FT 161129 17.8 15.2 1.2 60 0.30 0.31
5131 1990 BG 161129 18.0 18.5 1.3 60 0.33 0.82
5604 1992 FE 170403 16.4 41.6 1.2 60 0.22 0.11
170403 16.4 41.6 1.5 60 0.21 0.08
5751 1992 AC 170629 18.7 10.0 1.6 60 0.45 0.11
10165 1995 BL2 170403 19.5 41.0 1.3 60 0.21 0.23
23183 2000 OY21 170325 21.1 22.8 1.5 60 0.24 0.97
170517 20.2 22.7 1.1 60 0.54 1.03
170629 19.1 11.7 1.3 60 0.19 0.76
24443 2000 OG 170517 21.9 9.3 1.2 60 0.52 0.08
54789 2001 MZ7 170403 17.3 17.3 1.2 30 0.13 0.06
170403 17.3 17.3 1.5 30 0.63 0.14
170517 17.7 47.6 1.2 30 0.14 0.64
87024 2000 JS66 170403 19.0 35.6 2.2 45 0.63 0.84
170517 20.1 55.5 1.8 30 0.37 0.86
90373 2003 SZ219 170325 21.7 26.0 1.5 60 0.54 0.42
170403 21.5 23.1 1.6 60 0.21 0.47
170517 20.5 20.5 1.5 60 0.33 0.18
136818 1997 MW1 170629 17.9 27.6 1.2 15 0.58 0.80
162882 2001 FD58 170403 19.3 7.1 1.4 30 0.21 0.07
162980 2001 RR17 150920 19.7 32.0 1.3 60 0.09 0.48
185716 1998 SF35 170325 21.1 32.8 1.6 60 0.60 0.42
170403 21.0 31.1 1.6 60 0.34 0.46
170517 20.4 19.2 1.2 45 0.21 0.34
170629 21.0 23.7 1.0 60 0.21 0.45
222073 1999 HY1 170517 17.8 31.6 1.2 15 0.87 0.44
170629 19.5 54.7 1.0 15 1.52 0.62
226198 2002 UN3 170403 19.6 40.0 1.0 45 0.27 0.24
232368 2003 AZ2 170325 20.5 44.2 1.3 45 0.28 0.36
170403 20.3 45.3 1.3 30 0.32 0.60
170629 18.0 58.7 1.0 30 1.52 0.36
285638 2000 SO10 150920 20.2 19.3 1.0 30 1.90 0.25
311066 2004 DC 150920 22.4 25.5 1.1 60 0.09 0.49
354876 2006 BG55 170403 18.6 71.0 1.6 30 0.13 0.54
416151 2002 RQ25 150920 22.3 44.8 1.0 60 0.09 0.81
Table 2: DCT Observations Log
\LTpost

Note—UTC date of observations and V-magnitude from Horizons. Airmass from midpoint of observations. Exposure time of individual frames. Duration is net integration time on object and is the lower limit amplitude from the observations.

\twocolumngrid
\twocolumngrid


\onecolumngrid
# Designation UTC V Airmass Exptime Duration m
yymmdd (mag) () (s) (hour) (mag)
3691 1982 FT 160728 19.6 23.6 1.4 300 0.70 0.07
160729 19.6 23.7 1.5 180 1.17 0.46
160730 19.6 23.8 2.0 180 1.30 0.20
160801 19.6 24.0 1.7 180 1.71 0.17
160804 19.6 24.4 1.5 180 1.64 0.45
160805 19.6 24.5 1.6 180 2.19 0.37
160806 19.6 24.6 1.7 180 1.72 0.13
160807 19.6 24.7 1.5 180 2.72 0.50
160808 19.6 24.8 1.7 180 2.78 0.34
161226 17.9 19.1 1.0 150 9.0 0.11
161227 17.9 19.4 1.0 150 7.63 0.12
161229 18.0 20.0 1.1 150 7.17 0.30
161230 18.0 20.2 1.1 150 6.64 0.16
5751 1992 AC 151203 18.7 25.1 1.8 300 3.90 0.14
151206 18.8 25.6 1.8 300 3.79 0.21
151208 18.8 25.9 1.8 300 2.62 0.08
151215 18.9 26.9 1.7 300 2.53 0.11
151216 18.9 27.0 1.7 300 2.33 0.19
**137052 1998 VO33 151107 20.1 26.0 1.1 300 5.19 0.25
151108 20.1 25.6 1.1 300 5.91 0.46
151118 20.5 20.5 1.0 300 4.78 0.49
151206 19.5 9.2 1.0 300 9.20 0.37
151210 19.4 6.8 1.0 300 1.97 0.64
151213 19.3 5.3 1.0 300 5.07 1.15
151214 19.3 4.9 1.0 300 9.10 0.35
151217 19.3 4.4 1.2 300 8.75 0.42
162980 2001 RR17 160408 18.2 75.5 1.5 300 1.81 0.16
160409 18.2 74.5 1.5 300 1.83 0.22
160410 18.2 73.8 1.6 300 1.07 0.45
160411 18.2 73.0 1.5 300 1.72 0.29
160413 18.3 71.5 1.3 300 2.15 0.40
160414 18.3 70.8 1.5 300 1.64 0.19
160415 18.3 70.0 1.7 300 0.47 0.31
160430 18.5 61.1 1.5 300 2.71 0.28
160502 18.6 60.1 1.4 300 0.70 0.19
160728 19.0 27.5 1.8 130 0.91 0.30
160731 19.0 26.9 1.6 130 0.91 0.33
160801 19.0 26.7 1.6 130 1.35 0.65
160804 19.1 26.2 1.6 130 1.29 0.51
160806 19.1 25.9 1.6 130 1.29 0.51
160807 19.1 25.8 1.6 130 1.33 0.50
275792 1998 SF35 160728 21.0 23.7 1.3 100 0.70 0.15
160729 21.0 23.8 1.3 300 0.89 0.17
160730 21.0 24.0 1.3 100 0.07 0.14
160804 21.0 24.7 1.2 300 2.35 0.26
160805 21.0 24.8 1.2 300 2.26 0.38
**285638 2000 SO10 151015 20.0 15.2 1.0 300 3.82 0.63
151109 20.5 23.4 1.0 300 6.17 1.08
151110 20.5 23.8 1.3 300 1.36 0.84
151111 20.5 24.1 1.0 300 4.80 0.81
151113 20.5 24.8 1.0 300 5.67 0.95
151114 20.6 25.1 1.0 300 5.20 1.06
151115 20.6 25.4 1.0 300 4.61 1.16
354876 2006 BG55 151208 19.3 18.9 1.4 300 5.12 0.67
151210 19.4 17.7 1.3 300 1.39 0.13
151211 19.4 17.2 1.4 300 2.09 0.15
151212 19.4 16.7 1.3 300 0.71 0.11
151213 19.4 16.2 1.3 300 3.84 0.23
151214 19.4 15.9 1.3 300 4.81 0.62
151215 19.4 15.6 1.4 300 4.03 0.22
151217 19.5 15.2 1.3 300 4.15 0.53
Table 3: Calar Alto Observations Log
\LTpost

Note—UTC date of observations and V-magnitude from Horizons. Airmass from midpoint of observations. Exposure time of individual frames. Duration is net integration time on object and is the lower limit amplitude from the observations. ** Indicate the two objects which have full lightcurve coverage. 137052 has a derived period of hours (2018Warner). We derive in this work a preliminary period of hours for 285638.

\twocolumngrid
\twocolumngrid


\onecolumngrid
# Designation Amplitude Photometry Reference
() (mag)
1620 1951 RA 19.0 1.0 [19]
1865 1971 UA 21.8 2.1 [20]
1915 1953 EA 33.3 0.2 [2]
3671 1984 KD 37.1 0.23 [7]
5879 1992 CH1 23.2 0.45 [14]
17511 1992 QN 11 0.84 [18]
25143 1998 SF36 5.0 0.70 [9]
33342 1998 WT24 69.8 0.29 [13]
42286 2001 TN41 14.8 0.44 [16]
53110 1999 AR7 32.7 0.37 [10]
54509 2000 PH5 31.9 0.83 [4]
136849 1998 CS1 22.8 0.16 [21]
138893 2000 YH66 32.1 0.7 [5]
162004 1991 VE 41.8 1.11 [11]
172034 2001 WR1 25.3 0.95 [17]
257838 2000 JQ66 37.6 0.63 [15]
374158 2004 UL 21.2 1.2 [11]
399167 2015 FG36 58.1 0.59 [8]
416186 2002 TD60 3 1.4 [6]
441825 2009 SK1 8.7 0.6 [12]
443880 2001 UZ16 84.5 0.97 [12]
2001 SQ3 35.7 0.39 [3]
2010 NR1 20.8 1.8 [1]
2014 YD 72.3 0.2 [8]
2015 FS332 64.5 0.84 [12]
Table 4: LCDB Lower Limit Amplitudes
\LTpost

Note—Lightcurve amplitudes and phase angle are from the Asteroid Lightcurve Database (2009Warner). References— [1] 2010Farmer, [2] 1989Harris, [3] 2011Hergenrother, [4] 2007Lowry, [5] 2012Polishook, [6] 2005Pravec, [7] 2006Pravec, [8] 2016Thirouin, [9] 2004Warner, [10] 2015cWarner, [11] 2015hWarner, [12] 2016cWarner, [13] 2016hWarner, [14] 2017bWarner, [15] 2017cWarner, [16] 2017iWarner, [17] 2018hWarner, [18] 2015Waszczak, [19] 1990Weidenschilling, [20] 1997Wisniewski, [21] 2009Ye

\twocolumngrid
\twocolumngrid

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