# Surface Properties of Near-Sun Asteroids

Carrie E. Holt Department of Astronomy, University of Maryland, College Park,
MD 20742, USA  Matthew M. Knight Department of Physics, United States Naval
Academy, 572C Holloway Rd, Annapolis, MD 21402, USA  Department of Astronomy,
University of Maryland, College Park, MD 20742, USA  Michael S. P. Kelley
Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Quanzhi Ye (叶泉志) Department of Astronomy, University of Maryland, College
Park, MD 20742, USA  Henry H. Hsieh Planetary Science Institute, Tucson, AZ
85719, USA  Institute of Astronomy and Astrophysics, Academia Sinica, Taipei
10617, Taiwan  Colin Snodgrass Institute for Astronomy, University of
Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK  Alan Fitzsimmons
Astrophysics Research Centre, School of Mathematics and Physics, Queen’s
University Belfast, Belfast, BT7 1NN, UK  Derek C. Richardson Department of
Astronomy, University of Maryland, College Park, MD 20742, USA  Jessica M.
Sunshine Department of Astronomy, University of Maryland, College Park, MD
20742, USA  Nora L. Eisner Department of Physics, University of Oxford, Keble
Road, Oxford OX1 3RH, UK  Annika Gustaffson Southwest Research Institute,
Boulder, CO 80302, USA

###### Abstract

Near-Earth Asteroids (NEAs) with small perihelion distances reach sub-solar
temperatures of $\geq 1000$ K. They are hypothesized to undergo “super-
catastrophic” disruption, potentially caused by near-Sun processes such as
thermal cracking, spin-up, meteoroid impacts, and subsurface volatile release;
all of which are likely to cause surface alteration, which may change the
spectral slope of the surface. We attempted to observe 35 of the 53 known
near-Sun asteroids with $q\leq 0.15$ au from January 2017 to March 2020 to
search for trends related to near-Sun processes. We report the optical colors
and spectral slopes of 22 objects that we successfully observed and the
measured rotation periods for three objects. We find the distribution of
colors to be overall bluer than the color distribution of NEAs, though there
is large overlap. We attribute large scatter to unknown dynamical histories
and compositions for individual objects, as well as competing surface altering
processes. We also investigated potential correlations between colors and
other properties (e.g., perihelion distance, Tisserand parameter, rotation
period), and searched for evidence of activity. Finally, we have compiled all
known physical and dynamical properties of these objects, including
probabilistic source regions and dwell times with $q\leq 0.15$ au.

Near-Earth objects (1092) — Solar system astronomy (1529) — Asteroids (72) —
Solar system astronomy (1529) — Ground-based astronomy (686) — Optical
astronomy (1776)

††facilities: DCT, SOAR, ING:Newton, LO:0.8m, Hall††software: astropy (Astropy
Collaboration et al., 2018), astroquery (Ginsburg et al., 2019), calviavat
(Kelley & Lister, 2019), ccdproc (Craig et al., 2017), JPL Horizons (Ginsburg
et al., 2019), NEOPOP444https://neo.ssa.esa.int/neo-population-generator
(Granvik et al., 2018), PHOTOMETRYPIPELINE (Mommert, 2017), photutils (Bradley
et al., 2021), seaborn (Waskom, 2021)

##  1 INTRODUCTION

###  1.1 Background

Many comets and asteroids spend part of their dynamical lifetimes with small
perihelion distances (or “low-$q$”) as a result of dynamical interactions with
Jupiter (e.g., Bailey et al., 1992; Farinella et al., 1994; Gladman et al.,
1997; Bottke et al., 2002; Marchi et al., 2009; Greenstreet et al., 2012).
However, even while assuming a loss due to collisions with the Sun or planets,
or an escape from the inner solar system, Granvik et al. (2016) reported a
deficit of asteroids with small perihelion distances ($q\lesssim 0.5$ au),
which they attributed to “super-catastrophic disruption” on timescales of less
than 250 years when an asteroid reaches a perihelion distance less than $q\sim
0.076$ au, with some dependence on asteroid size. Based on the evolution of
debris streams, Ye & Granvik (2019) suggest that disruption is a more gradual
process with timescales of $1-20$ kyr. Granvik et al. (2016) determined that
the disruption of near-Sun asteroids cannot be explained by tidal effects or
thermal vaporization. Potential near-Sun processes that might lead to
disruption over time (e.g., thermal cracking, spin-up, subsurface volatile
release) likely cause surface alteration, which might be observable from the
ground using optical telescopes.

###  1.2 Observed Trends

Low-$q$ comets 322P/SOHO 1, 96P/Machholz 1 and 323P/SOHO have been observed to
have atypical blue colors (Knight et al., 2016; Eisner et al., 2019; Hui et
al., 2022). 322P/SOHO 1 has a cometary orbit and shows evidence of being
active at perihelion (Lamy et al., 2013), but it has an asteroid-like albedo,
density, and fast rotation. 96P/Machholz 1 had the smallest perihelion
distance of any unambiguously active short-period comet until recent
observations of 323P/SOHO, which was observed post-perihelion with a long-
narrow tail, likely caused by immense thermal stress or rotational
instability; 323P has the shortest rotational period of known comets in our
Solar System at 0.522 hrs. 323P/SOHO 1 was recently observed to have bluer
colors than most Solar System small bodies, which changed unprecedentedly over
a few weeks to a color unlike any other small bodies in our Solar System (Hui
et al., 2022). Further characterization of objects with small perihelion
distances is necessary to assess whether these comets are unique or if their
bluer colors are typical of objects that closely approach the Sun. Very few
periodic comets are observed from the ground with a perihelion distance less
than 0.15 au, so additional observations must focus on asteroids.

Spectral trends with perihelion distance have been observed for S- and Q-type
near-Earth asteroids (NEAs) with $q\gtrsim 0.2$ au. Marchi et al. (2006a)
observed that S- and Q-types become spectrally bluer with decreasing
perihelion distance using data from Binzel et al. (2004) and Lazzarin et al.
(2004, 2005), which they attribute to resurfacing caused by close encounters
with planets. Because of their closely related spectra, only different in
features impacted by space weathering (spectral slope and 1-$\mu$m band
depth), Q-types are best explained as resurfaced S-types that have not yet had
enough time for space weathering to alter their surface (e.g., Chapman, 2004;
Brunetto et al., 2015). In agreement with Marchi et al. (2006a), DeMeo et al.
(2014) and Devogèle et al. (2019) found a higher percentage of Q-type
asteroids (which are spectrally bluer than S-types) with smaller perihelion
distances. Graves et al. (2019) argue that resurfacing due to thermal
degradation explains the trend better than planetary encounters after modeling
NEA orbits and tracking spectral slope with planetary encounters or physical
distance from the Sun for each object. More observations of near-Sun asteroids
are needed to determine if this trend holds at smaller perihelion distances.

###  1.3 Overview of Known Properties

This work presents an observational study of known near-Sun asteroids and
searches for any common properties that might be related to near-Sun processes
experienced by these objects. We focus our efforts on objects with perihelion
distance $q\leq 0.15$ au. We chose this limit because 0.15 au is the outer
limit of the Solar and Heliospheric Observatory (SOHO)’s outermost coronagraph
(C3)’s field-of-view, meaning we can potentially view activity or disruption
of these objects using SOHO. There are 53 known asteroids that reach
perihelion at $q\leq 0.15$ au (sub-solar temperatures $\gtrsim 1000$ K) as of
November 1, 2021, including the ones with poorly constrained orbits. All of
the objects reach perihelion within the SOHO field of view each orbit, yet
none have been observed to date, meaning that mass loss near perihelion has
been very low over the last quarter century (to be explored further in Section
4.3).

Campins et al. (2009) and Jewitt et al. (2013) investigated a similar set of
asteroids, but their perihelion distance limits were significantly larger
($q\leq 0.35$ au and $\leq 0.25$ au, respectively). Only seven of their
objects are in our sample. Most low-$q$ asteroids are small and therefore
faint and difficult to study. In-depth studies have not been possible for
low-$q$ objects other than 3200 Phaethon. While there have been a few
serendipitous observations as part of general NEO studies, the available data
are still limited, as detailed below and summarized in Table 1.3.

Table 1: Published Measurements of Near-Sun Asteroids*

Object | $B-V$ | $V-R$ | $B-R$ | Ref. | Rotation Rate [hrs] | Ref. | Albedo | Size [km] | Ref.
---|---|---|---|---|---|---|---|---|---
1995 CR | - | - | - | - | $2.66\pm 0.04$ | 1 | $0.167\pm_{0.079}^{0.101}$ | $0.129\pm_{0.024}^{0.045}$ | 2
2000 BD19 | - | - | - | - | $10.570\pm 0.005$ | 3 | $0.247\pm 0.046$ | $0.97\pm 0.04$ | 4
|  |  |  |  |  |  | $0.123\pm_{0.066}^{0.082}$ | $1.149\pm_{0.241}^{0.513}$ | 5
2000 LK | - | - | - | - | - | - | $0.137\pm_{0.074}^{0.092}$ | $0.610\pm_{0.132}^{0.278}$ | 5
2002 AJ129 | $0.687\pm 0.050$ | $0.405\pm 0.027$ | $1.092\pm 0.057$ | 6 | $3.9222\pm 0.0008$ | 6 | $0.226\pm_{0.116}^{0.141}$ | $0.438\pm_{0.091}^{0.181}$ | 5
| - | - | $1.23\pm 0.10$ | 7 | - | - | - | - | -
2002 PD43 | $0.66\pm 0.05$ | $0.42\pm 0.05$ | $1.08\pm 0.03$ | 7 | - | - | - | - | -
2004 UL | $0.82\pm 0.10$ | $0.54\pm 0.10$ | $1.37\pm 0.10$ | 7 | $38\pm 2$ | 8 | $0.604\pm_{0.264}^{0.258}$ | $0.268\pm_{0.042}^{0.083}$ | 5
2004 XY60 | - | - | - | - | - | - | $0.217\pm_{0.110}^{0.137}$ | $0.389\pm_{0.080}^{0.161}$ | 5
2006 HY51 | - | - | - | - | $3.350\pm 0.008$ | 9 | $0.157\pm 0.071$ | $1.218\pm 0.23$ | 4
2006 TC | $0.60\pm 0.08$ | $0.33\pm 0.03$ | $0.93\pm 0.08$ | 7 | - | - | - | - | -
2007 EP88 | - | - | - | - | - | - | $0.174\pm 0.038$ | $0.636\pm 0.04$ | 4
|  |  |  |  |  |  | $0.531\pm_{0.230}^{0.236}$ | $0.312\pm_{0.051}^{0.098}$ | 5
2008 HE | - | - | - | - | - | - | $0.120\pm_{0.066}^{0.091}$ | $0.779\pm_{0.184}^{0.375}$ | 10
2008 MG1 | - | - | - | - | - | - | $0.431\pm_{0.223}^{0.252}$ | $0.194\pm_{0.038}^{0.084}$ | 10
2008 XM | - | - | - | - | - | - | $0.128\pm 0.032$ | $0.367\pm 0.01$ | 4
2010 JG87 | - | - | - | - | - | - | $0.202\pm 0.040$ | $0.408\pm 0.02$ | 4
2011 KE | - | - | - | - | $8.0\pm 0.1$ | 11 | - | - | -
2011 XA3 | - |  $0.473\pm 0.051$** | - | 12 | $0.730\pm 0.007$ | 12 | $0.347\pm_{0.163}^{0.196}$ | $0.163\pm_{0.029}^{0.056}$ | 10
2017 AF5 | - | - | - | - | $49.68\pm 0.06$ | 13 | - | - | -
3200 Phaethon | $0.67\pm 0.02$ | $0.32\pm 0.02$ | $0.99\pm 0.02$ | 7 | $3.6039\pm 0.0002$ | 14 | $0.16\pm 0.02$ | $4.6\pm 0.3$ | 15

References. — (1) Warner (2014) ; (2) Trilling et al. (2016) (3) Warner
(2015a); (4) Mainzer et al. (2011, 2016); (5) Trilling et al. (2010); (6)
Devyatkin et al. (2022); (7) Jewitt (2013); (8) Warner (2015b); (9) This work;
(10) Trilling et al. (2016); (11) Skiff, B.A. (2011)a(12) Urakawa et al.
(2014); (13) Warner (2017); (14) Warner (2015b);(15) Masiero et al. (2019)

* All uncertainty values are presumed 1-$\sigma$ errors

** Converted from $g^{\prime}-r^{\prime}$ according to Jordi et al. (2006)

a Posting on CALL web site. http://www.minorplanet.info/call.html

####  1.3.1 3200 Phaethon

Phaethon is the most studied low-$q$ asteroid because it is the largest among
the sample (diameter $\sim$5 km) and has a short orbital period (1.43 yr),
allowing for observations nearly every apparition, including a historically
close approach to Earth in 2017. The parent body of the Geminid meteor shower
(Whipple, 1983), Phaethon is the only known unambiguously active low-$q$
asteroid (Jewitt & Li, 2010; Jewitt, 2013; Li & Jewitt, 2013; Hui & Li, 2017)
and the only named asteroid that approaches within 0.15 au of the Sun.
Phaethon is a B-type asteroid (Binzel et al., 2001) with an albedo of
$\sim$0.16 (Masiero et al., 2019) and a rotational period of $\sim$3.6 hours
(Warner, 2015b). Spectroscopy and colors have been measured extensively (most
recently by Lin et al. 2020). The Japanese space agency JAXA’s forthcoming
DESTINY+ mission is expected to fly by Phaethon in 2024 (Ozaki et al., 2022).

####  1.3.2 Albedos

Near-Earth Object Wide-Field Infrared Survey Explorer (NEOWISE), an infrared
characterization survey, has measured diameters and determined albedos for
2000 BD19, 2006 HY51, 2007 EP88, 2008 XM, and 2010 JG87 (Mainzer et al., 2011,
2016). Albedos were derived by combining infrared measurements with previously
reported or follow-up optical magnitudes using the Near-Earth Asteroid Thermal
Model (NEATM; Harris, 1998). Additional albedo measurements were made using
the Spitzer Space Telescope via the ExploreNEOs (Trilling et al., 2010) and
NEOSurvey (Trilling et al., 2016) infrared characterization surveys. We
include both NEOWISE and Spitzer albedos in Table 1.3 for completeness, but we
caution the use of Spitzer measurements with reported albedos that are larger
than the assumed NEO upper limit of $\sim 0.5$ (Gustafsson et al., 2019).

####  1.3.3 Rotation Periods

Rotation rates have been measured for eight low-$q$ asteroids, including
Phaethon. All objects except 2011 XA3 have rotation rates ranging from
$\sim$2.5 hours (1995 CR; Warner, 2014) to $\sim$2 days (2017 AF5; Warner,
2017). 2011 XA3 is the exception with a fast rotation rate of $\sim$45 minutes
(Urakawa et al., 2014). We discuss this object further in Section 4.4.

####  1.3.4 Spectral Properties

Spectral observations are limited for the low-$q$ population. Three objects in
addition to Phaethon have measured IR spectra and classification: 137924 (2000
BD19) is V type, 394130 (2006 HY51) is R-type, and 465402 (2008 HW1) is S-type
(Thomas et al., 2014; Binzel et al., 2019). The variety of taxonomies is
interesting to note considering the majority of NEAs are S-type, while V- and
R- types only make up $\sim 5\%$ of the NEA population (Binzel et al., 2019).

Table 2: Near-Sun Asteroid Propertiesa

|  |  | Orbital Elementsb |  |  |  |  | Source Region Probabilitiesc |  |
---|---|---|---|---|---|---|---|---|---|---
Object |  $H_{V}$d | $q$ | $a$ | $e$ | $i$ | $T_{J}$ | Ue |  $T_{BB}(q)$f |  $T_{SS}(q)$g | $\nu_{6}$ | 5:2 | 2:1 | Hun | 3:1 | Pho | JFC |  $T_{q*}$h | Statusi
| (2005 HC4) | 20.7 | 0.070 | 1.824 | 0.961 | 8.4 | 3.17 | 9 | 1048 | 1482 | 0.76 | 0.04 | 0.00 | 0.01 | 0.18 | 0.00 | 0.00 | -j | A
| (2020 BU13) | 21.2 | 0.073 | 2.471 | 0.970 | 9.2 | 2.44 | 6 | 1028 | 1454 | 0.18 | 0.11 | 0.00 | 0.00 | 0.69 | 0.00 | 0.01 | - | X
| (2017 TC1) | 20.9 | 0.076 | 2.491 | 0.970 | 9.3 | 2.42 | 8 | 1010 | 1428 | 0.19 | 0.13 | 0.00 | 0.00 | 0.66 | 0.00 | 0.01 | - | Ok
| (2008 FF5) | 23.1 | 0.080 | 2.272 | 0.965 | 2.6 | 2.64 | 9 | 986 | 1395 | 0.62 | 0.01 | 0.00 | 0.02 | 0.34 | 0.00 | 0.02 | - | X
| (2017 MM7) | 21.1 | 0.080 | 2.064 | 0.961 | 23.2 | 2.84 | 7 | 983 | 1391 | 0.63 | 0.06 | 0.00 | 0.02 | 0.27 | 0.02 | 0.00 | - | A
| (2015 EV) | 22.5 | 0.081 | 2.036 | 0.960 | 11.4 | 2.90 | 9 | 980 | 1386 | 0.70 | 0.02 | 0.00 | 0.02 | 0.26 | 0.00 | 0.00 | - | X
394130 | (2006 HY51) | 17.1 | 0.081 | 2.588 | 0.969 | 33.6 | 2.30 | 0 | 975 | 1379 | 0.08 | 0.26 | 0.01 | 0.01 | 0.55 | 0.06 | 0.03 | 6.1 | O
| (2021 AF3) | 22.9 | 0.086 | 1.301 | 0.934 | 7.2 | 4.35 | 9 | 946 | 1338 | 0.89 | 0.01 | 0.00 | 0.05 | 0.05 | 0.00 | 0.00 | - | X
| (2016 GU2) | 24.0 | 0.087 | 2.052 | 0.957 | 10.3 | 2.89 | 8 | 941 | 1331 | 0.68 | 0.00 | 0.00 | 0.04 | 0.28 | 0.00 | 0.00 | - | A
| (2019 AM13) | 22.0 | 0.091 | 1.296 | 0.930 | 16.7 | 4.37 | 2 | 922 | 1304 | 0.78 | 0.02 | 0.00 | 0.06 | 0.14 | 0.00 | 0.00 | - | O
| (2019 JZ6) | 21.0 | 0.091 | 2.461 | 0.963 | 24.1 | 2.45 | 9 | 921 | 1303 | 0.12 | 0.15 | 0.01 | 0.00 | 0.70 | 0.01 | 0.01 | - | X
137924 | (2000 BD19) | 17.4 | 0.092 | 0.876 | 0.895 | 25.7 | 6.27 | 0 | 917 | 1297 | 0.52 | 0.00 | 0.00 | 0.33 | 0.13 | 0.01 | 0.00 | 7351.8 | O
374158 | (2004 UL) | 18.7 | 0.093 | 1.266 | 0.927 | 23.8 | 4.45 | 0 | 913 | 1291 | 0.80 | 0.03 | 0.00 | 0.06 | 0.09 | 0.02 | 0.00 | 157.0 | O
394392 | (2007 EP88) | 18.5 | 0.096 | 0.837 | 0.886 | 20.7 | 6.56 | 1 | 900 | 1273 | 0.74 | 0.00 | 0.00 | 0.14 | 0.11 | 0.01 | 0.00 | 13687.6 | O
| (2011 KE) | 19.8 | 0.100 | 2.207 | 0.955 | 5.9 | 2.74 | 1 | 879 | 1243 | 0.75 | 0.05 | 0.00 | 0.01 | 0.19 | 0.00 | 0.00 | 4.0 | O
465402 | (2008 HW1) | 17.4 | 0.103 | 2.587 | 0.960 | 10.5 | 2.40 | 0 | 865 | 1224 | 0.14 | 0.24 | 0.01 | 0.00 | 0.55 | 0.02 | 0.04 | 6.7 | O
| (2015 HG) | 21.0 | 0.105 | 2.102 | 0.950 | 17.7 | 2.85 | 9 | 859 | 1215 | 0.62 | 0.05 | 0.00 | 0.01 | 0.30 | 0.02 | 0.00 | 4.9 | A
| (2012 US68) | 18.3 | 0.106 | 2.503 | 0.958 | 25.8 | 2.44 | 2 | 856 | 1210 | 0.11 | 0.29 | 0.03 | 0.00 | 0.51 | 0.04 | 0.01 | 3.7 | Al
| (2011 XA3) | 20.4 | 0.109 | 1.467 | 0.926 | 28.0 | 3.90 | 0 | 844 | 1193 | 0.76 | 0.03 | 0.00 | 0.05 | 0.15 | 0.02 | 0.00 | 1319.4 | X
399457 | (2002 PD43) | 19.1 | 0.109 | 2.507 | 0.956 | 26.0 | 2.44 | 0 | 841 | 1189 | 0.11 | 0.28 | 0.03 | 0.00 | 0.53 | 0.03 | 0.01 | 2.9 | O
| (2018 GG5) | 19.8 | 0.110 | 1.986 | 0.945 | 16.8 | 3.01 | 7 | 840 | 1187 | 0.71 | 0.03 | 0.00 | 0.01 | 0.23 | 0.02 | 0.00 | 36.4 | O
386454 | (2008 XM) | 20.0 | 0.111 | 1.222 | 0.909 | 5.4 | 4.66 | 0 | 834 | 1180 | 0.84 | 0.03 | 0.00 | 0.02 | 0.11 | 0.00 | 0.00 | 96.9 | O
431760 | (2008 HE) | 18.1 | 0.112 | 2.262 | 0.950 | 9.8 | 2.70 | 0 | 831 | 1175 | 0.68 | 0.08 | 0.00 | 0.01 | 0.21 | 0.00 | 0.01 | 8.4 | O
| (2020 DD) | 23.5 | 0.116 | 2.483 | 0.953 | 2.3 | 2.51 | 8 | 818 | 1156 | 0.22 | 0.01 | 0.00 | 0.01 | 0.68 | 0.00 | 0.08 | - | X
276033 | (2002 AJ129) | 18.7 | 0.116 | 1.371 | 0.915 | 15.5 | 4.20 | 0 | 815 | 1153 | 0.84 | 0.03 | 0.01 | 0.05 | 0.06 | 0.01 | 0.00 | 88.3 | O
| (2020 GB2) | 21.1 | 0.117 | 2.338 | 0.950 | 15.2 | 2.63 | 7 | 814 | 1152 | 0.42 | 0.09 | 0.00 | 0.01 | 0.48 | 0.00 | 0.00 | 1.1 | X
| (2019 VE3) | 23.3 | 0.117 | 1.174 | 0.901 | 2.5 | 4.85 | 9 | 814 | 1151 | 0.70 | 0.00 | 0.00 | 0.04 | 0.26 | 0.00 | 0.00 | - | X
425755 | (2011 CP4) | 21.2 | 0.118 | 0.912 | 0.870 | 9.5 | 6.11 | 0 | 809 | 1144 | 0.95 | 0.00 | 0.00 | 0.02 | 0.02 | 0.01 | 0.00 | 2111.9 | O
| (1995 CR) | 21.8 | 0.119 | 0.907 | 0.868 | 4.1 | 6.15 | 0 | 805 | 1139 | 0.98 | 0.00 | 0.00 | 0.02 | 0.00 | 0.00 | 0.00 | 190.2 | O
| (2000 LK) | 18.3 | 0.121 | 2.184 | 0.945 | 16.6 | 2.79 | 0 | 801 | 1132 | 0.66 | 0.07 | 0.00 | 0.02 | 0.21 | 0.04 | 0.00 | 19.9 | O
| (2007 GT3) | 19.7 | 0.122 | 2.006 | 0.939 | 25.6 | 2.98 | 2 | 796 | 1126 | 0.66 | 0.09 | 0.00 | 0.02 | 0.19 | 0.04 | 0.00 | 5.8 | Am
| (2020 HY2) | 24.9 | 0.124 | 2.314 | 0.946 | 11.4 | 2.67 | 9 | 788 | 1115 | 0.43 | 0.00 | 0.00 | 0.03 | 0.50 | 0.00 | 0.05 | - | X
| (2017 AF5) | 17.8 | 0.124 | 2.480 | 0.950 | 20.9 | 2.50 | 0 | 788 | 1115 | 0.13 | 0.27 | 0.02 | 0.00 | 0.53 | 0.04 | 0.01 | 4.5 | O
| (2004 QX2) | 21.7 | 0.125 | 1.286 | 0.903 | 19.1 | 4.45 | 8 | 786 | 1112 | 0.82 | 0.03 | 0.00 | 0.05 | 0.09 | 0.00 | 0.00 | 16.9 | X
| (2019 YV2) | 21.9 | 0.126 | 1.227 | 0.897 | 6.5 | 4.67 | 9 | 783 | 1107 | 0.76 | 0.02 | 0.00 | 0.03 | 0.19 | 0.00 | 0.00 | 11.0 | X
| (2020 TS2) | 18.9 | 0.126 | 2.509 | 0.950 | 20.1 | 2.48 | 8 | 783 | 1107 | 0.12 | 0.28 | 0.03 | 0.00 | 0.49 | 0.03 | 0.05 | 2.9 | X
| (2021 LM1) | 20.4 | 0.127 | 2.312 | 0.945 | 29.5 | 2.63 | 6 | 780 | 1103 | 0.27 | 0.13 | 0.00 | 0.01 | 0.56 | 0.03 | 0.00 | 2.4 | X
| (2011 BT59) | 20.9 | 0.130 | 2.471 | 0.947 | 3.6 | 2.55 | 9 | 771 | 1091 | 0.33 | 0.07 | 0.00 | 0.00 | 0.54 | 0.00 | 0.04 | 1.5 | A
289227 | (2004 XY60) | 18.9 | 0.130 | 0.640 | 0.797 | 23.8 | 8.52 | 1 | 771 | 1090 | 0.88 | 0.00 | 0.00 | 0.03 | 0.06 | 0.03 | 0.00 | 622.2 | X
| (2015 KO120) | 22.0 | 0.130 | 1.779 | 0.927 | 2.1 | 3.37 | 9 | 770 | 1089 | 0.77 | 0.00 | 0.00 | 0.02 | 0.21 | 0.00 | 0.00 | 5.0 | A
| (2007 PR10) | 20.9 | 0.132 | 1.232 | 0.893 | 20.9 | 4.63 | 1 | 765 | 1082 | 0.84 | 0.04 | 0.00 | 0.04 | 0.07 | 0.01 | 0.00 | 45.2 | Al
| (2021 PH27) | 17.7 | 0.133 | 0.462 | 0.712 | 31.9 | 11.62 | 3 | 762 | 1078 | 0.76 | 0.00 | 0.00 | 0.04 | 0.19 | 0.01 | 0.00 | 2236.6 | X
504181 | (2006 TC) | 18.7 | 0.136 | 1.538 | 0.912 | 19.6 | 3.80 | 1 | 755 | 1068 | 0.77 | 0.00 | 0.00 | 0.06 | 0.14 | 0.03 | 0.00 | 50.6 | O
| (2019 UJ12) | 22.4 | 0.137 | 2.423 | 0.943 | 27.5 | 2.55 | 8 | 751 | 1063 | 0.08 | 0.06 | 0.00 | 0.00 | 0.85 | 0.00 | 0.01 | 0.2 | O
| (2013 JA36) | 21.0 | 0.138 | 2.665 | 0.948 | 42.5 | 2.29 | 8 | 750 | 1061 | 0.04 | 0.36 | 0.05 | 0.00 | 0.50 | 0.02 | 0.02 | 1.7 | A
| (2008 MG1) | 19.9 | 0.139 | 0.783 | 0.823 | 5.7 | 7.08 | 1 | 746 | 1056 | 0.93 | 0.00 | 0.00 | 0.06 | 0.00 | 0.01 | 0.00 | 1685.4 | O
| (2013 HK11) | 20.7 | 0.139 | 2.182 | 0.936 | 17.7 | 2.82 | 9 | 745 | 1053 | 0.64 | 0.05 | 0.00 | 0.01 | 0.28 | 0.02 | 0.00 | 6.0 | A
| (2017 SK10) | 21.4 | 0.140 | 2.051 | 0.932 | 24.5 | 2.95 | 9 | 743 | 1051 | 0.60 | 0.06 | 0.00 | 0.02 | 0.30 | 0.02 | 0.00 | 1.2 | X
3200 Phaethon | (1983 TB) | 14.3 | 0.140 | 1.271 | 0.890 | 22.3 | 4.51 | 0 | 743 | 1051 | 0.67 | 0.06 | 0.00 | 0.18 | 0.06 | 0.03 | 0.00 | 1106.0 | O
| (2020 VL4) | 18.5 | 0.142 | 2.125 | 0.933 | 55.8 | 2.71 | 8 | 737 | 1043 | 0.18 | 0.08 | 0.20 | 0.03 | 0.38 | 0.14 | 0.00 | 363.6 | X
| (2013 YC) | 21.4 | 0.142 | 2.495 | 0.943 | 2.8 | 2.55 | 2 | 737 | 1043 | 0.30 | 0.06 | 0.00 | 0.00 | 0.59 | 0.00 | 0.04 | 1.0 | O
| (2020 HE) | 23.6 | 0.146 | 2.515 | 0.942 | 20.5 | 2.51 | 9 | 727 | 1028 | 0.06 | 0.01 | 0.00 | 0.00 | 0.84 | 0.00 | 0.08 | - | X
| (2010 JG87) | 19.2 | 0.148 | 2.768 | 0.947 | 16.8 | 2.33 | 0 | 723 | 1023 | 0.01 | 0.56 | 0.08 | 0.00 | 0.17 | 0.01 | 0.17 | 2.1 | O

\texta\textafootnotetext: As of November 1, 2021

\textb\textbfootnotetext: According to JPL Horizons

\textc\textcfootnotetext: Probability that the object escaped from each of the
six source regions, totaling one, using the model detailed in Granvik & Brown
(2018). The source regions consist of the $\nu_{6}$ inner main-belt region,
Jupiter resonance complexes: 3:1, 5:2 and 2:1, the Hungarias, the Phocaeas,
and the Jupiter-family comets.

\textd\textdfootnotetext: Absolute $V$ magnitude as reported by JPL Horizons

\texte\textefootnotetext: MPC orbit uncertainty estimate. The range is 0-9,
with 0 being good and 9 being highly uncertain

\textf\textffootnotetext: Equilibrium isothermal, spherical blackbody
temperature at the perihelion distance, K

\textg\textgfootnotetext: Equilibrium sub-solar blackbody temperature at the
perihelion distance, K

\texth\texthfootnotetext: Dwell time with $q\leq 0.15$ au in kyrs according to
Toliou et al. (2021)

\texti\textifootnotetext: O: Observed; A: Attempted but not observed; X: Not
attempted

\textj\textjfootnotetext: Some cells result in a $T_{q*}=0$ in the Toliou et
al. (2021) model after renormalizing each cell of the model according to the
relative fraction of NEOs from each ER, as explained in Toliou et al. (2021)
Sec. 2.4. We use ‘-’ in those instances.

\textk\textkfootnotetext: 2017 TC1 was detected, but was observed in the Milky
Way. Colors could not be determined because too few images were obtained for
effective DIA (see text).

\textl\textlfootnotetext: 2007 PR10 and 2012 US68 were attempted under poor
weather conditions

\textm\textmfootnotetext: 2007 GT3 had an orbit code of 8 at the time of
observations, and was outside the telescope’s field-of-view.

Campins et al. (2009) measured the 7-14 $\mu$m thermal emission spectra of 19
asteroids with $q\leq 0.35$ au, including two objects with $q\leq 0.15$ au:
2000 BD19 and 2004 XY60. They fit the spectra with thermal continuum models to
derive effective diameter, geometric albedo, and beaming parameter of these
objects and suggest that thermal behavior is different for near-Sun asteroids
compared with other NEAs (stronger thermal emission “beaming” at low phase
angles). Jewitt et al. (2013) measured the colors of nine asteroids with
$q\leq 0.25$ au to search for evidence of thermal modification. Five of the
objects have $q\leq 0.15$ au and are therefore a part of our sample. They
found that near-Sun objects have a wide range of colors, but there was no
statistical distinction between such objects and other near-Earth objects.
Both Campins et al. (2009) and Jewitt et al. (2013) consider objects beyond
our perihelion cutoff of 0.15 au and suggest further characterization is
needed.

###  1.4 This Work

Near-Sun asteroids have not been thoroughly examined as a population. Color
observations can provide us with a better understanding of the processes
occurring and the effects they have on near-Sun asteroids. Broadband optical
colors (e.g., $g^{\prime}-r^{\prime}$, $r^{\prime}-i^{\prime}$) can be
obtained quickly and for fainter objects, which makes such observations
optimal for a population study. Over more than three years of observations
from January 2017 to March 2020, we attempted to observe as many near-Sun
asteroids as possible. Of the 53 known asteroids with $q\leq 0.15$ au (summary
of orbital elements in Table 2), we attempted to observe 35, and successfully
observed 22. Nine of the objects we attempted to observe were predicted to be
within our fields of view and above our detection limit but were not
recovered, most likely due to the very large uncertainty in their orbits. We
also observed near-Earth asteroid 2004 LG, which previously spent 2500 years
with a perihelion distance less than 0.076 au, the disruption limit of Granvik
et al. (2016), experiencing extreme temperatures of $\sim 2500$ K at the
surface (Vokrouhlický & Nesvorný, 2012; Wiegert et al., 2020).

##  2 OBSERVATIONS AND DATA ANALYSIS

###  2.1 Data Collection

Data were collected primarily using Lowell Observatory’s 4.3-m Lowell
Discovery Telescope (LDT; formerly known as the Discovery Channel Telescope,
DCT) and the 4.1-m Southern Astrophysical Research (SOAR) telescope,
supplemented by data from the Isaac Newton Telescope (INT) and Lowell
Observatory’s 42-in and 31-in telescopes. Broadband SDSS g′, r′, i′, z′
filters were used at all telescopes except for Lowell Observatory’s 31-inch
and 42-inch, where Johnson-Cousins B,V,R,I filters were used. A summary of the
instruments used can be found in Table 3. All images were acquired at the
asteroid’s ephemeris rate, which frequently resulted in trailed stars.
Whenever possible, we kept the star trails to less than two times the seeing
in order to accurately register the image (see Sec 2.4), but for some objects
long trails were unavoidable. As will be discussed later, this occasionally
hampered absolute calibrations. Exposure times varied with the asteroid’s
brightness and telescope size, but were typically 180–300 seconds. The number
of images acquired for each target varied with time available, though at least
two cycles of filters were achieved for all observations, ordered in a way so
that the mid-time of the observations for each filter is approximately the
same to mitigate rotational variability.

Table 3: Instruments

Telescope | Instrument | Aper Size | FOV | Pix Sca | Binning | Filters
---|---|---|---|---|---|---
Lowell Discovery Telescope (LDT) | Large Monolithic Imager (LMI) | 4.3m | $12.3^{\prime}\times 12.3^{\prime}$ | $0.36^{\prime\prime}$ | $3\times 3$ | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$
Southern Astrophysical Research (SOAR) | Goodman Spectrograph | 4.1m |  $7.2^{\prime}$ diameter | $0.30^{\prime\prime}$ | $2\times 2$ | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$
Southern Astrophysical Research (SOAR) | SOAR Optical Imager (SOI) | 4.1m | $5.26^{\prime}\times 5.26^{\prime}$ | $0.077^{\prime\prime}$ | $2\times 2$ | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$
Isaac Newton Telescope (INT) | Wide Field Campera (WFC) | 2.5m | $11.5^{\prime}\times 23.0^{\prime}$ | $0.33^{\prime\prime}$ | None | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$
Lowell Observatory 31-inch | NASAcam | 0.8m | $15.7^{\prime}\times 15.7^{\prime}$ | $0.46^{\prime\prime}$ | None | $B,V,R,I$
Lowell Observatory 42-inch | NASA42 Camera | 1.1m | $25.3^{\prime}\times 25.3^{\prime}$ | $1.48^{\prime\prime}$ | $3\times 3$ | $B,V,R,I$

\texta\textafootnotetext: Effective pixel scale after binning

###  2.2 Instruments

Northern hemisphere targets were primarily observed with Lowell Observatory’s
4.3-m LDT located near Flagstaff, AZ. All observations were made using the
Large Monolithic Imager (LMI; Massey et al., 2013). LMI has a field-of-view
(FOV) of 12$\farcm$3 $\times$ 12$\farcm$3 and a pixel scale of 0$\farcs$36
after an on-chip 3 $\times$ 3 binning. SDSS broadband $g^{\prime}$,
$r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ filters were used.

Observations of southern hemisphere targets were made using the 4.1-m SOAR
Telescope on Cerro Pachón in Chile. The Goodman Spectrograph Red Camera
(Clemens et al., 2004) and the SOAR Optical Imager (SOI) were used. The
Goodman Spectrograph camera has a circular FOV of 7$\farcm$2 diameter. The
observations were done in 2 $\times$ 2 binning mode with an effective pixel
scale of 0$\farcs$30\. SOI uses two adjacent CCD chips read out through two
amplifiers per chip that cover a 5$\farcm$26 $\times$ 5$\farcm$26 FOV and have
a scale of 0$\farcs$077/pixel after 2 $\times$ 2 binning. Broadband
$g^{\prime}$, $r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ SDSS filters were
used on all images.

We conducted an observing run in January 2017 using the 2.5-m INT at the Rogue
de Los Muchachos Observatory in La Palma, Spain. Observations were made using
the Wide Field Camera (WFC), which has an effective FOV of 11$\farcm$5
$\times$ 23$\farcm$0 and a pixel scale of 0$\farcs$33\. All observations used
broadband $g^{\prime}$, $r^{\prime}$, $i^{\prime}$, and $z^{\prime}$ SDSS
filters.

Supplemental observations were made using Lowell Observatory’s Hall 31-inch
(0.8 m) and 42-inch (1.1 m) telescopes. The 31-inch telescope has a square
field of view of 15$\farcm$7 on a side and an unbinned pixel scale of
0$\farcs$46\. The 42-inch telescope has a square field of view of 25$\farcm$3
on a side and a 3 $\times$ 3 binned pixel scale of 0$\farcs$98\. Observations
using the 31-inch were robotically acquired. All other telescopes used classic
observing mode. Johnson-Cousins $B$, $V$, $R$, and $I$ filters were used.

###  2.3 Data Reduction

Each observation followed the same reduction routine. A master bias frame for
each night was created by averaging 10–20 individual bias frames. The master
bias frame was then subtracted from each frame. At least five sky or dome
flats taken during the same observing period were normalized and median
combined for each filter used. Images were flat-field corrected by dividing
each frame by the median-combined flat-field.

###  2.4 Data Analysis

####  2.4.1 Absolute Calibration

Reduced images were registered using PHOTOMETRYPIPELINE (Mommert, 2017), which
utilizes SCAMP (Bertin, 2006) to match the source catalog of an image created
by Source Extractor (Bertin & Arnouts, 1996) with astrometric catalogs, such
as GAIA. After registration, using PHOTOMETRYPIPELINE, photometry was
completed on the image sources followed by the derivation of the photometric
image zeropoints with the Pan-STARRS DR1 catalog (PS1; Magnier et al., 2013)
using field stars. The aperture size was derived using a curve-of-growth
analysis, where the optimum aperture radius is the smallest aperture radius
where the target and the background fractional fluxes exceed 70% and the
difference between the target and background curves is less than 5% (reducing
systematic offsets in the flux measurements).

We took our calibration one step further by adding a color correction applied
image by image using components of calviacat (Kelley & Lister, 2019). The
difference between instrumental magnitudes and absolute magnitudes of stars is
positively correlated with star color. Using the same in-field stars from the
PS1 catalog, we determined the color-correction coefficient. We used the
previously determined color to calculate the new absolute magnitude. We
repeated this process iteratively until the color converged, usually about
three times.

The zeropoints were then converted to either the SDSS photometry system or
BVRI system depending on the filters used (Tonry et al., 2012). A weighted
average of all object magnitudes of the same filter was measured before
calculating the difference to determine the object colors. Colors determined
in BVRI filters were converted to SDSS colors according to Jordi et al.
(2006).

As previously discussed, observations were not always acquired during ideal
epochs. Therefore, two of the observations (2008 XM and 2018 GG5) include
large star streaks ($\sim 15^{\prime\prime}$) as the telescope tracked the
asteroid during long exposures required to achieve necessary signal-to-noise.
For those observations, we derived the zeropoint from field stars chosen
manually, but still using the PS1 catalog.

Images acquired using the 31-inch telescope did not contain a sufficient
amount of stars for in-field calibration due to a brighter limiting magnitude.
In these cases, we used Landolt standard star fields (Landolt, 1992, 2009) to
determine the zeropoint and airmass extinction coefficient.

Because of our limited observing window, asteroid 2008 HE was observed in
crowded star fields and suffered significant contamination. Difference image
analysis (DIA; Bramich, 2008; Bramich et al., 2013) was used to extract useful
data from such images. The technique models the convolution kernel as a
discrete pixel array, rather than a combination of linear functions. Each
pixel value is solved for using a linear least squares. Using the kernel
model, stars from a reference image can be blurred to match the seeing of each
frame. After subtracting the blurred master from the image, the majority of
the background stars are removed, allowing for more accurate photometry of the
asteroid. This technique was only used for the images of 2008 HE because
images of other asteroids are clean and the improvement form the usage of DIA
is minimal.

###  2.5 Normalization

We estimated the absolute magnitude $(H(1,1,0)$ (or $H$), which is the
apparent $V$-band magnitude at 1 au from the Sun and the Earth, observed at a
phase angle of zero degrees. For observations made using SDSS filters, the
$g^{\prime}$ magnitude value was converted to $V$ magnitude ($m_{V}$)
according to Jordi et al. (2006). To determine the absolute magnitude, we used
the formula:

$H(1,1,0)=m_{V}-5\log_{10}(\Delta r_{\mathrm{h}})+2.5\log_{10}(\phi(\alpha))$
(1)

where $\Delta$ equals the geocentric distance in au, $r_{\mathrm{h}}$ equals
the heliocentric distance in au, $\alpha$ is the phase angle (the Sun-Target-
Observer angle) and $\phi(\alpha)$ is the phase integral, which is the ratio
of the brightness at phase angle $\alpha$ to that at phase angle $0^{\circ}$.
For the majority of the observed low-$q$ asteroids, we used $HG$ formalism
(Bowell et al., 1989) with $G=0.15$ to determine the phase integral. Asteroid
2002 AJ129 was the only object with enough phase coverage to determine the
phase integral using the three-parameter magnitude phase function
($HG_{1}G_{2}$; Muinonen et al., 2010), which we then used to determine a more
accurate $H$ (Section 3.5).

###  2.6 Reflectance Values

SDSS color filters provide sufficient wavelength coverage to study spectral
slope trends (e.g., Thomas et al., 2013; Graves et al., 2018; Thomas et al.,
2021). We followed techniques used by DeMeo & Carry (2013) and Thomas et al.
(2013) to calculate the spectral slope over the $g^{\prime}$ , $r^{\prime}$ ,
and $i^{\prime}$ reflectance values (hereafter $gri$-slope) to represent the
slope of the continuum and $z^{\prime}-i^{\prime}$ color representing the
depth of the possible 1 $\mu$m band. First, known Sloan filter solar
colors111http://classic.sdss.org/dr6/algorithms/sdssUBVRITransform.html
($g^{\prime}-r^{\prime}=0.44$, $g^{\prime}-i^{\prime}=0.55$,
$g^{\prime}-z^{\prime}=0.58$ mag) were removed from the color indices. Then,
the Sun-subtracted color indices were converted into reflectance values,
normalized to the $g^{\prime}$ band:

$\frac{R_{x}}{R_{g}}=10^{0.4[(m_{g}-m_{x})-(m_{g,\odot}-m_{x,\odot})]}$ (2)

The error for each reflectance point is calculated using standard error
propagation. The $R_{g}$ value does not have an error as the other values are
always in relation to $R_{g}=1$.

A linear regression was fit to the three photometric points using the central
wavelength of the filters to calculate the slope. We computed the slope errors
for each object via a Monte Carlo calculation, a technique used by Thomas et
al. (2013, 2021). For each object, the individual reflectance values were
modified by applying an offset of a random number pulled from a Gaussian
distribution where the standard deviation is the 1-$\sigma$ error of the
reflectance value. This calculation was done 20,000 times for each object and
a slope was determined for each altered spectrum. The uncertainty of the slope
was the standard deviation of the altered slopes generated by this process.

Figure 1: Absolute magnitude comparisons between this work and JPL. The solid
line represents equality between the measurements. For all but one point, the
errorbars are all within the marker. We find agreement between the values
suggesting none of the objects were active during observations. All
measurements including the largest difference between magnitudes of 1.02 (2008
MG1) are still within typical estimates for rotational variation.

##  3 Observational Results

###  3.1 Absolute Magnitude H

We find our derived absolute magnitude values to be mostly consistent with
those reported by the Jet Propulsion Laboratory’s (JPL) Small-Body
Database222https://ssd.jpl.nasa.gov/ with a standard deviation of the
difference equal to $\sim$0.3 (Figure 1). An offset in absolute magnitude
larger than the uncertainty due to rotational variability ($A_{max}\lesssim$ 1
mag for small asteroids; Statler et al., 2013) could indicate unresolved
activity during one epoch. However, we do not observe any such offset and will
explore upper limits of activity in Section 4.3.

###  3.2 Color Distribution

Our measured colors are summarized in Table 4 and plotted in Figure 2. For
near-Sun asteroids, we see a wide variety of colors with large overlap between
the near-Sun distribution and the colors reported by Dandy et al. (2003) and
SDSS. Some objects have error bars

Table 4: Summary of Observations and Measured Magnitudes

Object | UT Date | Tel.a |  $r_{\mathrm{h}}$b |  $\Delta$c |  $\alpha$d | Filters |  $H_{V}$e | $g^{\prime}$ | $r^{\prime}$ | $i^{\prime}$ | $z^{\prime}$ | $g^{\prime}-r^{\prime}$ | $r^{\prime}-i^{\prime}$ | $i^{\prime}-z^{\prime}$ |  $gri$-slopef
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
1995 CR | 2017 Jan 25 | INT | 1.415 | 0.520 | 27.700 | $g^{\prime},r^{\prime},i^{\prime}$ | 21.87 | $22.826\pm 0.092$ | $22.169\pm 0.084$ | $21.928\pm 0.181$ | - | $0.657\pm 0.124$ | $0.242\pm 0.199$ | - | $1.36\pm 1.02$
2000 BD19 | 2017 Jan 26 | INT | 1.177 | 0.606 | 56.700 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.53 | $19.260\pm 0.008$ | $18.554\pm 0.003$ | $18.551\pm 0.008$ | $19.120\pm 0.034$ | $0.706\pm 0.008$ | $0.003\pm 0.008$ | $-0.569\pm 0.035$ | $0.59\pm 0.08$
| 2020 Jan 28 | 31in | 1.103 | 0.272 | 57.788 | $B,V,R,I$ | 17.60 | - | $17.071\pm 0.007$ | $16.654\pm 0.007$ | $16.494\pm 0.009$ | $0.547\pm 0.023$ | $-0.074\pm 0.016$ | - | $-0.23\pm 0.11$
| 2020 Jan 30 | 31in | 1.077 | 0.237 | 61.215 | $B,V,R,I$ | 17.40 | $17.624\pm 0.057$ | $16.621\pm 0.037$ | $16.265\pm 0.035$ | $16.317\pm 0.054$ | $0.447\pm 0.092$ | $-0.288\pm 0.070$ | - | $-1.06\pm 0.26$
| 2020 Jan 31 | 31in | 1.064 | 0.220 | 63.355 | $B,V,R,I$ | 17.24 | $17.378\pm 0.043$ | $16.337\pm 0.038$ | $15.888\pm 0.033$ | $16.119\pm 0.034$ | $0.600\pm 0.090$ | $-0.468\pm 0.053$ | - | $-1.10\pm 0.23$
2000 LK | 2019 Jun 25 | SOAR | 2.421 | 1.839 | 22.766 | $g^{\prime},r^{\prime},i^{\prime}$ | 18.50 | $23.223\pm 0.051$ | $22.555\pm 0.037$ | $22.516\pm 0.065$ | - | $0.668\pm 0.063$ | $0.040\pm 0.075$ | - | $0.58\pm 0.36$
| 2020 Mar 1 | LDT | 2.091 | 1.373 | 23.257 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.81 | $22.548\pm 0.048$ | $21.955\pm 0.052$ | $22.073\pm 0.096$ | - | $0.592\pm 0.071$ | $-0.118\pm 0.109$ | - | $-0.22\pm 0.40$
2002 AJ129 | 2018 Feb 9 | LDT | 1.077 | 0.093 | 14.192 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.73 | $14.785\pm 0.013$ | $14.250\pm 0.009$ | $14.203\pm 0.007$ | $14.522\pm 0.009$ | $0.535\pm 0.015$ | $0.048\pm 0.011$ | $-0.319\pm 0.012$ | $0.12\pm 0.09$
| 2018 Feb 10 | LDT | 1.091 | 0.109 | 17.083 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.73 | $15.245\pm 0.008$ | $14.680\pm 0.007$ | $14.658\pm 0.006$ | $14.956\pm 0.008$ | $0.565\pm 0.010$ | $0.022\pm 0.009$ | $-0.298\pm 0.010$ | $0.14\pm 0.08$
2002 PD43 | 2018 Jun 25 | SOAR | 1.239 | 0.836 | 54.575 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 19.38 | $21.795\pm 0.029$ | $21.211\pm 0.028$ | $21.209\pm 0.040$ | - | $0.583\pm 0.040$ | $0.003\pm 0.049$ | - | $0.14\pm 0.22$
2004 UL | 2019 Jun 25 | SOAR | 1.631 | 1.793 | 34.124 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.73 | $22.727\pm 0.115$ | $22.316\pm 0.077$ | $22.277\pm 0.102$ | - | $0.411\pm 0.139$ | $0.039\pm 0.128$ | - | $-0.31\pm 0.56$
2006 HY51 | 2019 Mar 29 | 42in | 2.585 | 2.643 | 22.387 | $B,V,R,I$ | 17.05 | $19.133\pm 0.029$ | $18.309\pm 0.016$ | $17.871\pm 0.004$ | $17.562\pm 0.047$ | $0.581\pm 0.035$ | $0.076\pm 0.052$ | - | $0.38\pm 0.23$
| 2019 Mar 31 | 42in | 1.470 | 0.660 | 34.530 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.22 | $18.960\pm 0.004$ | $18.326\pm 0.004$ | $18.218\pm 0.005$ | $18.578\pm 0.007$ | $0.634\pm 0.006$ | $0.109\pm 0.006$ | $-0.360\pm 0.008$ | $0.71\pm 0.08$
2006 TC | 2019 Oct 21 | SOAR | 1.446 | 0.878 | 42.540 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.73 | $21.636\pm 0.143$ | $20.902\pm 0.029$ | $21.113\pm 0.056$ | - | $0.523\pm 0.153$ | $0.211\pm 0.064$ | - | $0.66\pm 0.64$
2007 EP88 | 2017 Apr 7 | SOAR | 1.571 | 0.664 | 23.890 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.70 | $20.280\pm 0.017$ | $19.654\pm 0.010$ | $19.502\pm 0.009$ | $20.115\pm 0.027$ | $0.626\pm 0.019$ | $0.152\pm 0.013$ | $-0.613\pm 0.028$ | $0.85\pm 0.12$
| 2020 Jan 2 | SOAR | 0.962 | 0.663 | 72.030 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.52 | $20.442\pm 0.019$ | $19.805\pm 0.016$ | $19.643\pm 0.016$ | - | $0.637\pm 0.025$ | $0.162\pm 0.023$ | - | $0.93\pm 0.16$
2008 HE | 2018 Mar 9 | LDT | 1.638 | 1.697 | 34.584 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.49 | $21.465\pm 0.017$ | $20.924\pm 0.017$ | $20.928\pm 0.015$ | $20.853\pm 0.026$ | $0.541\pm 0.024$ | $-0.004\pm 0.023$ | $0.075\pm 0.030$ | $-0.03\pm 0.13$
2008 HW1 | 2017 Apr 7 | SOAR | 2.937 | 1.995 | 8.014 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.97 | $22.705\pm 0.264$ | $22.137\pm 0.105$ | $21.878\pm 0.077$ | - | $0.568\pm 0.284$ | $0.259\pm 0.130$ | - | $1.04\pm 1.31$
| 2017 Jan 24 | INT | 2.194 | 1.802 | 26.249 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.29 | $21.845\pm 0.031$ | $21.208\pm 0.014$ | $21.142\pm 0.040$ | - | $0.637\pm 0.034$ | $0.066\pm 0.043$ | - | $0.56\pm 0.22$
2008 MG1 | 2017 Jul 1 | SOAR | 0.721 | 1.692 | 8.361 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 18.87 | $20.218\pm 0.055$ | $19.646\pm 0.035$ | $19.576\pm 0.041$ | $19.684\pm 0.094$ | $0.572\pm 0.065$ | $0.070\pm 0.054$ | $-0.108\pm 0.103$ | $0.33\pm 0.31$
| 2019 Jun 25 | INT | 1.371 | 0.373 | 15.476 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 20.02 | $19.745\pm 0.009$ | $19.197\pm 0.006$ | $19.177\pm 0.014$ | $19.260\pm 0.017$ | $0.547\pm 0.010$ | $0.020\pm 0.015$ | $-0.083\pm 0.022$ | $0.07\pm 0.09$
2008 XM | 2018 Jan 20 | LDT | 1.506 | 0.596 | 22.826 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 20.29 | $21.476\pm 0.022$ | $20.917\pm 0.002$ | $20.629\pm 0.020$ | $21.021\pm 0.065$ | $0.558\pm 0.030$ | $0.288\pm 0.029$ | $-0.392\pm 0.068$ | $1.11\pm 0.19$
2010 JG87 | 2019 Aug 26 | LDT | 1.785 | 1.683 | 33.732 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 19.35 | $23.520\pm 0.094$ | $22.885\pm 0.062$ | $22.890\pm 0.138$ | - | $0.635\pm 0.113$ | $-0.005\pm 0.152$ | - | $0.30\pm 0.67$
2011 CP4 | 2017 Jan 24 | INT | 1.701 | 0.727 | 7.423 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 20.84 | $22.079\pm 0.042$ | $21.684\pm 0.027$ | $21.797\pm 0.078$ | - | $0.395\pm 0.050$ | $-0.113\pm 0.082$ | - | $-0.77\pm 0.25$
2011 KE | 2018 Apr 14 | LDT | 1.755 | 0.800 | 14.953 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 19.69 | $21.528\pm 0.020$ | $21.085\pm 0.022$ | $20.957\pm 0.028$ | $21.444\pm 0.072$ | $0.443\pm 0.029$ | $0.128\pm 0.035$ | $-0.487\pm 0.077$ | $0.07\pm 0.16$
| 2018 Apr 15 | LDT | 1.768 | 0.820 | 15.624 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 19.69 | $21.645\pm 0.021$ | $21.157\pm 0.022$ | $21.111\pm 0.030$ | $21.512\pm 0.082$ | $0.488\pm 0.031$ | $0.046\pm 0.037$ | $-0.400\pm 0.087$ | $-0.04\pm 0.17$
2013 YC | 2017 Dec 17 | LDT | 1.431 | 0.447 | 0.856 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 21.48 | $20.986\pm 0.051$ | $20.416\pm 0.086$ | $20.284\pm 0.072$ | $20.544\pm 0.054$ | $0.570\pm 0.100$ | $0.131\pm 0.112$ | $-0.260\pm 0.090$ | $0.54\pm 0.56$
2017 AF5 | 2017 Jan 24 | INT | 1.549 | 0.581 | 10.935 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 17.90 | $18.685\pm 0.007$ | $18.137\pm 0.012$ | $18.102\pm 0.010$ | $18.230\pm 0.029$ | $0.547\pm 0.014$ | $0.036\pm 0.016$ | $-0.128\pm 0.030$ | $0.12\pm 0.10$
2018 GG5 | 2018 Apr 23 | LDT | 1.276 | 0.392 | 39.622 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 19.86 | $20.232\pm 0.056$ | $19.710\pm 0.055$ | $19.578\pm 0.074$ | $19.935\pm 0.135$ | $0.523\pm 0.079$ | $0.131\pm 0.092$ | $-0.356\pm 0.154$ | $0.36\pm 0.44$
2019 AM13 | 2020 Mar 1 | LDT | 1.638 | 0.657 | 7.810 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 22.00 | $23.037\pm 0.073$ | $22.496\pm 0.054$ | $22.334\pm 0.152$ | $20.595\pm 0.079$ | $0.540\pm 0.091$ | $0.163\pm 0.161$ | - | $0.54\pm 0.68$
2019 UJ12 | 2019 Nov 4 | LDT | 1.145 | 0.192 | 34.023 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 22.61 | $20.984\pm 0.012$ | $20.572\pm 0.026$ | $20.635\pm 0.123$ | - | $0.412\pm 0.029$ | $-0.063\pm 0.126$ | $0.013\pm 0.166$ | $-0.60\pm 0.35$
Phaethon | 2017 Jan 25 | INT | 2.154 | 2.307 | 25.206 | $g^{\prime},r^{\prime},i^{\prime},z^{\prime}$ | 14.21 | $19.071\pm 0.011$ | $18.703\pm 0.007$ | $18.536\pm 0.010$ | $18.617\pm 0.037$ | $0.368\pm 0.013$ | $0.167\pm 0.012$ | $-0.081\pm 0.039$ | $-0.06\pm 0.09$
2004 LGg | 2019 Mar 31 | LDT | 1.719 | 1.711 | 33.862 | $g^{\prime},r^{\prime},i^{\prime}$ | 17.67 | $21.754\pm 0.041$ | $21.178\pm 0.039$ | $21.355\pm 0.078$ | - | $0.568\pm 0.058$ | $-0.012\pm 0.100$ | - | -

\texta\textafootnotetext: Telescope used: LDT = Lowell Discovery Telescope
(4.3-m), 42in = Hall 42-in Telescope (1.1-m), 31in = 31-in Telescope (0.8-m),
INT = Isaac Newton Telescope (2.5-m), SOAR = Southern Astrophysical Research
Telescope (4.1-m)

\textb\textbfootnotetext: Heliocentric distance, au

\textc\textcfootnotetext: Geocentric distance, au

\textd\textdfootnotetext: Phase angle, degree

\texte\textefootnotetext: Absolute $V$ magnitude measured by this work

\textf\textffootnotetext: The slope of the reflectance values over
$g^{\prime}$, $r^{\prime}$, and $i^{\prime}$ bandpasses [%/$\mu m$]

\textg\textgfootnotetext: 2004 LG was formerly low-$q$ (Vokrouhlický &
Nesvorný, 2012)

Figure 2: Color-color diagram of low-$q$ asteroids. The grey ‘x’s are the
color values of NEAs from the SDSS Moving Object Catalog (Ivezić et al., 2001;
Ivezic et al., 2002). The large capital letters represent the average colors
of taxonomic classes of NEAs from Dandy et al. (2003). The color of comet 322P
from Knight et al. (2016) is shown as a magenta triangle. The first reported
color of 323P from Hui et al. (2022) is shown as the magenta diamond. The red
circles and blue squares are low-$q$ asteroids with $T_{J}$ less than and
greater than 3, respectively.

spanning a broad spectrum, which we attribute to faint objects observed under
less-than-ideal conditions after inspecting each frame individually to rule
out uncertainty due to the occasional background star or poor photometric
solutions. In Fig. 2, we also separate objects by Tisserand parameter $T_{J}$.
Most main-belt asteroids have $T_{J}>3$, most Jupiter-family comets (JFCs)
have $2<T_{J}<3$, and long-period comets (LPCs) have $T_{J}<2$. Therefore,
$T_{J}$, which is related to an object’s encounter velocity with Jupiter can
generally be used to distinguish between types of orbits (Tisserand, 1896;
Kresák, 1972; Carusi et al., 1987; Levison, 1996). The red circles have a
cometary orbit ($T_{J}<3$) and the blue squares have an asteroidal orbit
($T_{J}>3$). We do not see a clear trend with color versus $T_{J}$. The two
objects with the smallest spectral slope in the lower left of the figure are
2011 CP4 and 2019 UJ12. There are several objects with $r^{\prime}-i^{\prime}$
colors most similar to V-types, but some of their $g^{\prime}-r^{\prime}$
colors are more red.

We compared the distribution of colors of low-$q$ objects to the range for
NEAs using the Sloan Digital Sky Survey Moving Object Catalog (SDSS, MOC,
Ivezić et al., 2001; Ivezic et al., 2002), which observed 471,569 moving
objects through March 2007, using five filters, $u^{\prime}$, $g^{\prime}$,
$r^{\prime}$, $i^{\prime}$, and $z^{\prime}$. We restricted the sample from
the SDSS MOC database according to the criteria outlined in DeMeo & Carry
(2013) Section 2.1, which includes filtering faint data, data with large
errors, and data with flags relevant to moving objects and good photometry. We
further reduce the sample by only including objects that are categorized as
NEAs ($q\leq 1.3$ au). Applying the selection criteria, we are left with a
sample of 42. We plot the range of colors as a gray ‘x’s behind our low-$q$
measurements and the average colors of NEA types observed by Dandy et al.
(2003) to give context for our findings. We also included the colors of
322P/SOHO 1 (Knight et al., 2016), 323P/SOHO (Hui et al., 2022), and solar
colors.

In the color-color plot (Figure 2), we observe that low-$q$ asteroids have a
bluer distribution compared to average NEA colors (more in the lower left than
the upper right). To investigate this further, we used a kernel density
estimation (KDE) plot of the colors (Figure 6). Rather than using discrete
bins, a KDE plot smooths the measurements with a Gaussian kernel, producing a
continuous probability density estimate. The data points are weighted by their
1-$\sigma$ uncertainty and the kernel bandwidth is selected according to
Scott’s Rule (Scott, 1992). The result is shown in Fig. 6. The low-$q$
$g^{\prime}-r^{\prime}$ colors appear to have the same distribution as the
colors from SDSS MOC, but shifted bluer. The low-$q$ $r^{\prime}-i^{\prime}$
colors show a wider distribution than the SDSS MOC, but they extend to bluer
colors. The KDE plots confirm our interpretation of the color-color plot.

The reflectance values for each observation can be seen in Figure 3. We use
the reflectance values to determine the $gri$-slope and
$z^{\prime}-i^{\prime}$ color, representing the slope of the continuum and the
1-$\mu$m band depth, respectively. Both of these parameters are affected by
space weathering, which causes a steeper spectral slope and a shallower
1-$\mu$m band depth. We compare our sample to NEAs from SDSS MOC values and
class boundaries reported by DeMeo & Carry (2013) (Figure 4). We find near-Sun
asteroids have a shallower spectral slope compared to the NEA population,
especially those with V-type colors, which agrees with our findings of bluer
colors shown in Figure 2. The $z^{\prime}-i^{\prime}$ reflectance values are
smaller as well, consistent with a steeper 1-$\mu$m band depth.

Figure 3: Spectrophotometry of low-$q$ asteroid observations created by
transforming colors into reflectance values. Our measurements are in blue at
their central wavelength, normalized to the $g^{\prime}$ filter, with
uncertainties shown. The grey bar shows the measured $gri$-slope. The object’s
name and date of observation (YYYYMMDD) are given on each panel. Figure 4:
$gri$-slope and $z^{\prime}-i^{\prime}$ reflectance values of low-$q$
asteroids (blue dots). For comparison we show the distribution of NEAs from
the SDSS MOC4 catalog (gray ‘x’s) and boundaries used to classify SDSS data
from DeMeo & Carry (2013). Low-$q$ asteroids have a flatter spectral slope
than the NEA population.

###  3.3 Spectral Slope Trends with Decreasing Perihelion

We compare the low-$q$ spectral slopes with the trend versus perihelion
distance seen in S- and Q-type NEAs with $q\geq 0.2$ au by Marchi et al.
(2006b) and Graves et al. (2019) to determine if the same trend might extend
to smaller perihelion distances (Figure 5). We can make this comparison
because we anticipate our sample to be predominately S- or Q-type because
together they are the most common NEA types Binzel et al. (2019) and based on
dynamical modeling of source regions, which we discuss in Section 3.6. For our
comparison, we used the trend measured by Graves et al. (2019) who implemented
a windowed moving average, instead of the similar trend determined by Marchi
et al. (2006a), who implemented a point-based moving average. Our data are
consistent with the extended trend at the 1-$\sigma$ level. However, given the
large uncertainty in some of the slopes in our dataset and the short range of
$q$, the trend is virtually indistinguishable from a flat distribution,
indicative of no spectral slope change with perihelion distance. Further
investigation is warranted.

Figure 5: The distribution of $gri$-slope vs. perihelion distance of low-$q$
asteroids. The dashed line and the shaded region show the trend for S- and
Q-type NEAs using data in Binzel et al. (2004); Lazzarin et al. (2004, 2005)
and the uncertainty at a 95% confidence level according to Graves et al.
(2019). Our data are consistent with Graves et al. (2019) at the 1-$\sigma$
level.

###  3.4 Lightcurves

We compiled high-cadence lightcurves of three bright objects (394130 (2006
HY51), 276033 (2002 AJ129) and 137924 (2000 BD19)) in our sample in order to
measure their rotation periods and amplitudes. The methodology for determining
the rotational period follows our approach in earlier papers (e.g., Knight et
al., 2011, 2012; Eisner et al., 2017). Because observing geometry changed
rapidly throughout the night, we corrected our photometric results for the
geometric circumstances image by image. The rotation period was estimated by
superimposing the lightcurves from all nights, with the data phased to a
“trial” period and zero phase at perihelion. We then iterated the trial
period, making direct “better or worse” comparisons between each iteration,
until a rotation period estimation was constrained by eye. We estimate the
uncertainty by determining how much the period can be adjusted before a phased
light curve appears obviously incorrect.

####  3.4.1 2006 HY51

2006 HY51, whose rotation period was previously unconstrained, was observed
over three nights (March 27-29, 2019) using Lowell Observatory’s 42-inch
telescope and the Johnson $R$ filter. We collected $\sim 6$ hours of data each
night with frames every $\sim 300$ seconds. We measured a rotation period of
$3.350\pm 0.008$ hours and a maximum peak-to-trough amplitude of $\sim$0.2 mag
(Fig. 7). The lightcurve has an interesting shape, with one peak larger than
the other, suggesting the shape of the asteroid deviates substantially from a
tri-axial ellipsoid (Magnusson, 1986).

####  3.4.2 2002 AJ129

2002 AJ129 was observed over two nights (February 6-7, 2018) using Lowell
Observatory’s 31-inch telescope in robotic mode and the Johnson $R$ filter,
collecting $\sim 9$ hours of data each night with frames every $\sim 90$
seconds.

Figure 6: Kernel density plot of low-$q$ asteroid colors with underlying
histogram (blue), where data points are weighted by their 1-$\sigma$
uncertainty and the kernel bandwidth is selected according to Scott’s Rule
(Scott, 1992). This allows us to assess the color distribution as a smooth
probability density, instead of only discrete bins in the histogram. The black
filled in curve is the color distribution of NEAs from SDSS MOC. The colors of
the most common asteroid types according to Dandy et al. (2003) are shown as
letters, as well as Solar colors shown as an orange “$\odot$”. We find a
preference towards bluer colors for both $g^{\prime}-r^{\prime}$ (top) and
$r^{\prime}-i^{\prime}$ (bottom).

We found a rotational period of $3.918\pm 0.010$ hours and a peak-to-trough
amplitude of $\sim$0.15 mag (Figure 8). The prepublished period of 2002 AJ129
was reported by the Ondrejov Asteroid Photometry Project (Pravec et al.,
2018)333http://www.asu.cas.cz/p̃pravec/newres.htm as $3.9226\pm 0.0007$, and
Devyatkin et al. (2022) reported a period of $3.9222\pm 0.0008$. Both
measurements are within our uncertainty.

####  3.4.3 2000 BD19

We observed 2000 BD19 over two half-nights (January 30–31, 2021) using Lowell
Observatory’s 31-inch in robotic mode and the Johnson $R$ filter, collecting
$\sim 6$ hours of data each night with frames every $\sim 20$ minutes. Warner
(2015a) observed 2000 BD19 over six nights and report a rotational period of
$10.570\pm 0.005$ hours and a max peak-to-trough amplitude of $0.69\pm 0.04$.
Without full coverage, we are unable to constrain the rotational period
further. However, when phased to the published period, our results are
consistent with the reported period and amplitude (Figure 9).

###  3.5 Phase Coefficient

For most of the objects we observed, the range of phase angles was too small
to determine the asteroid’s phase function. The exception is asteroid 2002
AJ129, which we observed over two nights with Lowell Observatory’s 31-inch
over $\sim 0.8$ – $17.8$ degrees. Using the online implementation of the model
selection stated in Penttilä et al. (2016), we employ the $H,G_{1},G_{2}$
system described in Muinonen et al. (2010). G1 and G2 are determined to be
$0.157\pm 0.035$ and $0.486\pm 0.017$, respectively, which is consistent with
measurements of main-belt asteroids (Muinonen et al., 2010; Vereš et al.,
2015).

###  3.6 Source Region Probabilities

We assessed the origin of low-$q$ asteroids using the Granvik & Brown (2018)
escape region model, which has been progressively developed by Granvik et al.
(2016, 2017, 2018). Given the orbital elements and $H$ magnitude of an object,
this model gives the probabilities that an object “escaped” from each of the
seven source regions, where the sum of the probabilities is equal to one. The
source regions consist of the $\nu_{6}$ inner main-belt region, Jupiter
resonance complexes: 3:1, 5:2 and 2:1, the Hungarias, the Phocaeas, and the
Jupiter-family comets. Source regions and orbital elements are tabulated for
all 53 known low-$q$ objects in Table 2 and the source region with the highest
probability of being the escape region for each object is in bold. All known
objects with $q\leq 0.15$ au most probably escaped from $\nu_{6}$ or 3:1
regions with the exception of 2010 JG87, which most likely escaped from the
5:2 region.

This is unsurprising considering the $\nu_{6}$ region and the 3:1 are the
resonance escape regions for nearly 80 percent of NEAs (Bottke et al., 2002;
Granvik et al., 2018; Binzel et al., 2019). NEAs from these source regions are
mostly S- or Q- type, with $\sim 80-90$ percent having a geometric albedo
greater than 0.1 (Binzel et al., 2019; Morbidelli et al., 2020). These
resonances call for large oscillations of the eccentricity, so even if
asteroids from these regions are not currently low-$q$, they possibly were at
one point in their dynamical history. Around 80 per-

Figure 7: Rotational lightcurve of 2006 HY51 using data from March 2019 using
Lowell Observatory’s 42-inch telescope. The lightcurve is phased to the best-
fit period of $3.350\pm 0.008$ hours. Figure 8: Rotational lightcurve of 2002
AJ129 using data from February 2018 using Lowell Observatory’s 31-inch
telescope. The lightcurve is phased to the best-fit period of 3.918 hours.
Figure 9: Rotational lightcurve of 2000 BD19 using data from January 2020
using Lowell Observatory’s 31-inch telescope. The lightcurve is phased to the
best-fit period of 10.57 hours determined by Warner (2015a). We were unable to
constrain the rotational period further.

cent of all NEAs have experienced a perihelion distance smaller than 0.15 au
at some point since they escaped from the main belt (Toliou et al., 2021). For
our specific sample, we use the lookup table from Toliou et al. (2021), which
utilizes the NEO model from Granvik et al. (2018) to determine the probability
an object with a given set of orbital elements and $H$ magnitude spent time
with a perihelion distance smaller than a certain $q_{s}$ and the estimated
dwell times with $q\leq q_{s}$. Unlike previous models, the Granvik et al.
(2018) model accounts for “supercatastrophic” disruption of NEAs within a
certain $q$, dependent on $H$. We tabulate the estimated dwell times each of
our objects spent with $q\leq 0.15$ au in Table 2. Dwell times range from one
kyr (2013 YC) to 15 Myrs (2007 EP88), consistent with the findings from Marchi
et al. (2009). The time spent with $q\leq 0.15$ au can vary from several
hundred years to a few Myr, averaging $\sim 20$ kyr for NEAs from $\nu_{6}$
(Toliou et al., 2021). Asteroids escaped from the 3:1 resonance and outer
main-belt spend an average of $\sim 5$ kyr and $\sim 300$ yrs with $q\leq
0.15$ au (Marchi et al., 2009).

##  4 DISCUSSION

###  4.1 Near-Sun Processes

Space weathering is the alteration of asteroid surfaces due to the space
environment, which is dominated by ion radiation from the solar wind (Marchi
et al., 2006b; Vernazza et al., 2009; Brunetto et al., 2015), as opposed to
micrometeorite impacts, which have longer timescales (Sasaki et al., 2001).
How space weathering affects an object is dependent on the object’s original
composition (Lantz et al., 2017). Because characterized low-$q$ objects
typically have high albedos, where more than ten percent of incident radiation
is reflected (Mainzer et al., 2012; Granvik et al., 2016), we focus on the
space weathering effects on high-albedo objects. The space weathering effects
on silicates are well understood, where nanophase reduced iron particles
(npFe0) darken and spectrally redden the surface (e.g., Pieters et al., 2000;
Taylor et al., 2001; Hapke, 2001; Clark et al., 2002; Brunetto et al., 2015).
Space weathering of silicates will also suppress the pyroxene-olivine
absorption bands (e.g., Pieters et al., 2000; Hapke, 2001; Gaffey, 2010).
Therefore, when a fresh unweathered surface is exposed by some resurfacing
process, the spectral slope becomes bluer for asteroids with a higher albedo.
This has been observed on NEA Eros by NEAR (Clark et al., 2001) and on
regolith grains brought from NEA Itokawa during the Hayabusa mission (Noguchi
et al., 2011), both of which are S-type asteroids.

There are several potential resurfacing mechanisms that affect asteroids when
they closely approach the Sun. (a) Increasing temperatures can cause material
from lower surface layers to sublimate and allow for progressively less
volatile material to reach sublimation temperatures. Decomposition and
sublimation of refractory organics begins around $\sim$450 K, metal sulfides
at $\sim$700 K, and silicates at 1000–1500 K (see review by Jones et al.,
2017). (b) Many studies have explored resurfacing caused by the tidal forces
experienced during planetary encounters (e.g., Nesvorný et al., 2005; Marchi
et al., 2006b; Binzel et al., 2010; Nesvorný et al., 2010; DeMeo et al., 2014;
Carry et al., 2016; Devogèle et al., 2019). (c) An asteroid with an irregular
surface can experience an increase in spin rate due to asymmetrical radiative
torques, known as the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect
(Bottke et al., 2006), which may result in centrifugal loss of material
(Rubincam, 2000; Vokrouhlický et al., 2015). (d) Thermal fatigue induced by
the diurnal temperature variations can cause boulders and grains to fracture
and break down into smaller regolith, which can then be lost due to outgassing
and/or solar radiation pressure (Jewitt, 2012; Delbo et al., 2014). Such
thermal cracking was observed on asteroid Bennu during the OSIRIS-REx mission
(Molaro et al., 2020). (e) Resurfacing through impacts by high-speed near-Sun
meteoroids that could eventually lead to disruption has also been suggested
(Wiegert et al., 2020). All of these processes can resurface weathered
regolith on low-$q$ asteroids, which would most likely cause an overall bluer
spectrum.

###  4.2 Colors

We found evidence for bluer colors in the low-$q$ population when compared to
NEAs (Dandy et al., 2003), but it is not as obvious as we might expect given
the bluer colors observed in comets 322P, 323P, and 96P (Knight et al., 2016;
Eisner et al., 2019). Additionally, we find agreement with the extended
bluening trend with decreasing perihelion seen in S- and Q-type NEAs at
$q>0.2$ au (Marchi et al., 2006a; Graves et al., 2019). However, uncertainties
are such that over the short range of $q$, the trend is indistinguishable from
no spectral slope change with $q$.

The color distribution of low-$q$ asteroids may be more stochastic because of
competing processes and the potential variety in asteroid properties,
including dynamical properties and regolith properties, such as albedo and
grain size, which play a role in the extent of heating and near-Sun processing
effects. Phase reddening, where the spectral slope increases with increasing
solar phase angle, $\alpha$, is expected to contribute to the scatter in the
distribution; the effect is common among S-group asteroids (Sanchez et al.,
2012; Carvano & Davalos, 2015; Perna et al., 2018), but the extent varies for
each individual asteroid and therefore cannot be modeled out of our
measurements (Carvano & Davalos, 2015; Binzel et al., 2019; Popescu et al.,
2019).

####  4.2.1 Dynamical Considerations

Near-Sun processes are generally influenced by the surface temperature and the
length of time spent at that temperature. Therefore, understanding the
dynamical history of low-$q$ objects is important for interpreting our
results. While dynamical modeling can give a general idea, we cannot know for
certain the dynamical history of any individual object. Some objects could
have recently migrated to a low-$q$ orbit in the last couple hundred years,
while others could have been in a stable low-$q$ orbit for several thousand
years and some objects might have had low-$q$ in the past and have migrated
back for the $n$-th time through resonance oscillations (i.e., Lidov-Kozai
oscillations: Lidov, 1962; Kozai, 1962). There is likely a broad range of
dynamical histories for our sample. However, we can use dynamical modeling to
better understand the temperatures experienced or the duration of heating
throughout an individual asteroid’s lifetime.

Roughly half of the known near-Sun asteroid population have $T_{J}<3$, which
indicates a cometary orbit. If such asteroids are actually dormant comets, we
might expect their colors to be distinct due to compositional differences or
surface changes due to sublimation of volatiles (Jewitt, 2015). The percentage
of NEAs that are dormant comets is estimated to be anywhere from 3 – 20
percent (e.g., Fernández et al., 2005; Bottke et al., 2002; DeMeo & Binzel,
2008; Mommert et al., 2015). We see no evidence for color difference based on
Tisserand parameter with respect to Jupiter. We find the average colors for
objects with asteroidal orbits to be $g^{\prime}-r^{\prime}=0.54\pm 0.11$ and
$r^{\prime}-i^{\prime}=0.10\pm 0.12$ and cometary orbits to be
$g^{\prime}-r^{\prime}=0.56\pm 0.07$ and $r^{\prime}-i^{\prime}=0.05\pm 0.06$.
However, we find that the colors are significantly bluer than cometary nuclei
($g^{\prime}-r^{\prime}=0.68\pm 0.06$ and $r^{\prime}-i^{\prime}=0.23\pm
0.04$; Jewitt 2015). Because dormant comets make up $\sim 10$% of the NEA
population, a larger sample size is needed to investigate such a connection.

Low-$q$ asteroids 2019 UJ12 and 2011 CP4 have the bluest colors in our sample.
The Toliou et al. (2021) model shows an average dwell time of 200 yrs for the
orbital properties of 2019 UJ12, suggesting it is likely experiencing near-Sun
resurfacing processes, such as thermal fatigue, for the first time. However,
2019 UJ12 has a poorly constrained orbit (U = 8), so we consider this result
inconclusive. Other than 2019 UJ12, we observe no clear trend between dwell
times and color. Although, it is important to note that the Toliou et al.
(2021) model uses an integration over the entire dynamical lifetime of an
object. To compliment the Toliou et al. (2021) model, we conducted backward-
integration of the orbits of individual low-$q$ objects over the last 2000 yrs
using the methods described in Hsieh et al. (2021) and found that 2011 CP4 has
had several close encounters with Earth in the past 2000 yrs, which suggests
its very blue color may be due to resurfacing caused by tidal encounters.
However, space weathering occurs on timescales of $\sim 10^{4}-10^{6}$ yrs, so
potential resurfacing events occurring more than 2000 yrs ago must be
considered, but such integrations are beyond the scope of this project.

Formerly low-$q$ asteroid 2004 LG, which spent 2500 years with $q<0.076$ au
(Vokrouhlický & Nesvorný, 2012; Wiegert et al., 2020) does not exhibit any
unusual colors compared to the near-Sun population and other NEAs, though we
would suspect otherwise after being in an extreme environment, within the
catastrophic disruption limit determined by Granvik et al. (2016). 2004 LG may
not be an S- or Q-type and therefore, experiences near-Sun properties
differently. There is also the possibility that surface variability over time
may play a role, which will be discussed below.

####  4.2.2 Varying Surface Properties

Albedo, emissivity, macroscopic surface roughness, and thermal inertia all
affect surface temperature. Surface roughness alone can raise the average
surface temperature by 20–30% (Marchi et al., 2009). Albedo affects the degree
of space weathering and the amount of radiation absorbed vs. reflected. And
thermal inertia governs the temperature distribution on an asteroid’s surface.
These surface properties, as well as rotational properties, influence the
degree of thermal fatigue, which is thought to be the dominant regolith
production process and resurfacing mechanism for near-Sun asteroids (Delbo et
al., 2014; Graves et al., 2019) and involves the formation and expansion of
cracks as a result of diurnal temperature variation. These properties vary
with composition, but can also vary between objects of the same taxonomy.
Because most of our objects have few observations, these properties are
essentially unknown but are expected to vary between objects, contributing to
the observed scatter in the color measurements.

There are more low-$q$ asteroids with colors similar to V-types than expected
given that V-types make up only $\sim$5% of the NEA population (Binzel et al.,
2019). This could simply be small number statistics. However, V-type asteroids
have high albedos ($\sim$0.3; Usui et al. 2013), so the overabundance could be
due to an observation bias. Alternatively, as proposed by Granvik et al.
(2016), higher albedo objects are less likely to experience enough thermal
cracking or sublimation to disrupt at low-$q$ because they absorb less heat
than lower albedo objects. Thus, there may be a survivorship bias that favors
V-type asteroids. Another possibility is that Yarkovsky drift may create a
slower orbital progression timescale for higher albedo objects. If so, a
longer residence lifetime in near-Sun orbits could create a bias toward these
objects being noticed in a survey. However, Granvik et al. (2018) found
Yarkovsky drift on the NEO steady state orbit distribution to be negligible
compared to the gravitational perturbations caused by planetary encounters.
Thus, such an effect may be difficult to detect.

####  4.2.3 Competing Processes

Competing processes are likely contributing to the wide color distribution we
measured compared to the NEA population as shown in the
$r^{\prime}-i^{\prime}$ KDE plot in Fig. 6. The space weathering rate
increases by two orders of magnitude from 1 to 0.1 au because solar
irradiation increases as $r_{\mathrm{h}}$ decreases (Marchi et al., 2006b;
Paolicchi et al., 2007). Similarly, several resurfacing processes are expected
to increase at low-$q$. The effects from Yarkovsky and YORP are expected to
increase with solar irradiation as well. As surface temperature increases, the
diurnal temperature variation increases, allowing for more resurfacing due to
thermal fatigue. Space weathering caused by solar irradiation has a timescale
of $\sim 10$ kyr – 1 Myr (Hapke, 2001; Brunetto & Strazzulla, 2005; Strazzulla
et al., 2005; Brunetto et al., 2006; Loeffler et al., 2009; Vernazza et al.,
2009). The timescale of thermal degradation is thought to decrease with
decreasing heliocentric distance as $r_{\mathrm{h}}^{k}$ where $k>5$ and the
timescale for space weathering should be less than half the timescale of
thermal degradation to explain the decreasing spectral slope with decreasing
perihelion distance trend (Graves et al., 2019). However, those timescales
were estimated based on S- and Q-type NEAs with $q>0.2$ au; those relations
might not be valid at $q\leq 0.15$ au. Additionally, multiple resurfacing
processes can be occurring on the same object at the same time, which can
further counter space weathering.

It is possible that the wide variety of colors we measured in the low-$q$
population is related to the consistent battling of processes. The refreshed
surface continues to be irradiated by the Sun as it is undergoing resurfacing
processes. As time in low-$q$ orbit passes, there is less and less “fresh”
surface to expose. In other words, the resurfaced regolith has already been
irradiated. Binzel et al. (2019) suggest that after enough time, the asteroid
surface may be “saturated” by space weathering and will have maximum redness,
while objects new to low-$q$ might have the most refreshed surface. The result
would be a larger variance in colors with decreasing distance to the Sun.
Comparing the low-$q$ sample with more distant NEAs, we find that the variance
in $r^{\prime}-i^{\prime}$ color (0.010) is higher for our low-$q$ sample
compared to the SDSS MOC NEA population (0.004), but the variance in
$g^{\prime}-r^{\prime}$ color is the same for both (0.008). This theory could
also explain the bluer colors of 2019 UJ12, as well as the redder color of
2007 EP88, which has spent the most time with $q\leq 0.15$ au.

###  4.3 Activity

This study focused on observing surface properties since the goal was to
sample the whole population in $\sim 3$ years. As a result, most were too
faint to meaningfully search for comae. We visually inspected all data and did
not detect any evidence of activity, e.g., tail, coma, or broadened PSF.
Comparing absolute magnitudes at the time of observation to previous data, we
can crudely constrain that the low-$q$ asteroids had no activity in excess of
typical NEA rotational amplitudes.

Since all objects in our sample reach perihelion within SOHO’s FOV, they are
observable every orbit when they are most likely to be active. SOHO’s limiting
magnitude of $\sim$8 is not sensitive enough to detect any objects in our
sample unless they are active. However, because forward-scattering of comet
dust grains is highly efficient (e.g., Marcus, 2007; Hui, 2013), for some
orientations only a small amount of coma is needed in order to be detected. We
constructed a simple model to estimate the observability of the low-$q$
asteroids when in the SOHO FOV ($r_{\mathrm{h}}\leq 0.15$ au). Using the
limiting magnitude of SOHO, we can determine the dust cross-section needed to
be detectable:

$C=\frac{(2.25\times 10^{22})\pi
r_{\mathrm{h}}^{2}\Delta^{2}}{p_{r}\phi(\alpha)}10^{0.4(m_{\odot}-m_{lim})}$
(3)

where $p_{r}$ is the $r^{\prime}$-band geometric albedo, $\alpha$ is the phase
angle (the Sun-target-observer angle), $\phi(\alpha)$ is the phase function
(we use the Schleicher-Marcus comet dust phase function; Schleicher & Bair,
2011), $m_{\odot}$ is the apparent $r^{\prime}$-band magnitude of the Sun, and
$m_{lim}$ is the limiting magnitude of SOHO ($\sim$8). We identified all
instances when each asteroid in our sample was within the SOHO FOV. We then
estimated the depth of global material lost in order for the object to be
detectable by SOHO, assuming an average particle size of 1 $\mu$m, a density
of 3000 kg/m3, an albedo of 0.15, and the diameter estimate for each object.
The minimum depth was $\sim$0.2 ${\mu}m$, though most required more than 1
${\mu}$m, the approximate depth of material needed to be excavated by Phaethon
to produce the amount of dust observed while Phaethon was active near
perihelion (Li & Jewitt, 2013). The apparitions needing the least depth of
material were either Phaethon, the largest low-$q$ object in our sample, or
objects in extreme forward-scattering geometries (${\alpha}>160^{\circ}$).

Phaethon has been repeatedly detected in STEREO images at peak apparent
magnitude of $\sim$11 (Hui & Li, 2017). As this is about $\sim$3 mag fainter
than SOHO’s limiting magnitude, it is no wonder that it has never been
detected in SOHO images. Thus, it seems likely that our simple model is overly
optimistic. There are numerous uncertainties in our estimates, including
assuming spherical grains, uniform grain size, grain albedo, and that asteroid
grains scatter in a manner analogous to comet grains, which might affect the
estimated depth by an order of magnitude. Furthermore, we assumed that such
dust would be present throughout the time the asteroid was in SOHO’s field of
view, but Li & Jewitt (2013) showed that Phaethon’s activity only lasts for a
few days with peak activity $\sim$0.5 days after perihelion, greatly reducing
the window for such dust to be detected on a given apparition. Thus, we can
only exclude activity in the rest of the low-$q$ population at 1–3 orders of
magnitude higher mass-loss rates per unit surface area than Phaethon since
they are significantly smaller. A deeper search of the SOHO data via shifting
and stacking at the ephemeris rate (e.g., Hui & Knight, 2019) could set upper
limits for activity near perihelion for each object in the sample, but is
beyond the scope of the current paper.

###  4.4 Rotation Periods

Only nine low-$q$ objects have reported rotational periods, including 2006
HY51 first reported in this work (Table 1.3; Figure 10). While several low-$q$
objects have rotation periods $\sim$3–4 hours, only one object (2011 XA3) has
a rotation period of $\sim$45 minutes, which is below the critical spin limit
for a rubble pile asteroid (Urakawa et al., 2014). 2011 XA3 has $H=20.4$,
corresponding to a diameter $\sim$200 – 500 meters, depending on albedo.
Because fast-rotating asteroids must resist their own centrifugal force, they
have structurally significant tensile strength.

Both 322P and 96P are among the fastest-rotating known comets being at/near
the spin period limit, with periods of $\sim$3 and $\sim$4 hours respectively
(Knight et al., 2016; Eisner et al., 2019). 323P is the fastest rotating comet
with a period of $\sim$0.5 hrs, which is a suggested driver of the comet’s
activity (Hui et al., 2022). The fast spin-rates could be indicative of
increased YORP effect near the Sun. A larger sample in the future could
support this idea if more low-$q$ objects were found to be fast-rotating.

Figure 10: The distribution of rotational periods vs. diameter of low-$q$
asteroids (red) compared to the general asteroid population from the JPL
Small-Body Database (black). The critical spin limit of 2.2 hours can be seen
for asteroids with diameters greater than 200 meters.

Smaller asteroids are found to have bluer colors (Binzel et al., 2004; Thomas
et al., 2012; Carry et al., 2016), likely due to resurfacing caused by YORP
spin-up and failure (Graves et al., 2018). Therefore, we might assume faster-
spinning objects approaching or above the spin barrier have bluer colors. On
the other hand, a faster-spinning asteroid has a more smoothed-out temperature
distribution in longitude than a slower rotating one, creating less diurnal
variability and lessening the effects of resurfacing due to thermal fatigue.
We search for a trend of colors versus rotational period. However, the sample
is very limited (nine objects) and no definitive conclusion can be made.

###  4.5 Future Surveys

The upcoming Vera Rubin Observatory’s Legacy Survey of Space and Time (LSST)
will increase the number of known NEOs by an order of magnitude. NEOs will be
observed a median of 90 times spread among ugrizy bandpasses (Jones et al.,
2016). A similar analysis to this work with a much larger sample size will
likely be possible. However, if different filters are not obtained
simultaneously, colors might not be easily measured due to geometric and
rotational variation between observations. Because there will be hours to days
between observations of the same object, rotational periods are unlikely to be
determined without dedicated prompt follow-up of LSST discoveries, unless the
period is sufficiently long. LSST will observe NEOs at several epochs with
various phase angles so a phase curve is likely to be obtained. Determining
the phase curve for low-$q$ objects will give us a better understanding of
surface roughness, which can better constrain the effects of regolith
production and resurfacing due to thermal fatigue. LSST will be capable of
monitoring and reporting any activity or disruption events nightly with
potential pipelines and proposed surveys (Schwamb et al., 2018; Seaman et al.,
2018), which will further the study of near-Sun asteroids that are more likely
to be active or catastrophically disrupted (Jewitt, 2012; Granvik et al.,
2016; Ye & Granvik, 2019).

The Near-Earth Object Surveillance Mission (NEOSM, previously NEOCam; Sonnett
et al., 2020) aims to extend the Wide-field Infrared Survey Explorer (WISE)
catalog of diameters and visual albedos by an order of magnitude. NEOSM is
expected to point closer to the Sun than NEOWISE or Spitzer, enabling the
search for near-Sun activity as well as the discovery and albedo measurements
of more low-$q$ objects. More albedo measurements of low-$q$ asteroids will
help us determine the surface temperature these objects reach as well as how
space weathering affects the surface, which varies with composition and can be
distinguished with albedo (Lantz et al., 2017). Additionally, the combination
of NEOSM with increasing cadence of visible observations like LSST (and other
surveys like PANSTARRS, ZTF) should improve the size estimates.

##  5 Conclusions

We obtained magnitude and optical color measurements of 22 near-Sun asteroids
with $q\leq 0.15$ au over three years from January 2017 to March 2020
primarily using various 4-m class telescopes. We obtained lightcurve data for
three low-$q$ asteroids, finding results consistent with previously published
values for two and determining a rotation period for 2006 HY51 equal to
$3.350\pm 0.008$ hr. We provide a summary of all known properties of near-Sun
asteroids including albedos, rotational periods, and spectra. These objects
were studied in order to search for trends relating to surface modification
due to near-Sun processes, particularly those that might lead to disruption.
We find that the observed low-$q$ asteroids exhibit bluer colors overall,
though overlapping with the color distributions of NEAs. However, there are no
clear trends of colors with perihelion distance, Tisserand parameter, or
rotational period. Unknown dynamical histories and compositions for individual
objects combined with competing surface altering processes are likely
responsible for the stochastic color distribution. Finally, future surveys
will enable studies of near-Sun objects with a much larger sample.

## ACKNOWLEDGEMENTS

We thank the anonymous referees for their thoughtful review. CH would like to
thank Mikael Granvik and Robert Jedicke for assistance in generating source
regions for our sample, Richard Binzel for thoughtful ideas, and Anathasia
Toliou for assistance interpreting the dwell times results. CH, MMK, MSK, and
QY are supported by NASA Near Earth Object Observations grant NNX17AH06G. We
thank Lori Feaga, Tony Farnham, and Nick Moskovitz for assisting with some
observations and Brian Skiff and Larry Wasserman for their assistance in
scheduling observations using Lowell Observatory’s 31-inch telescope.

These results made use of the Lowell Discovery Telescope at Lowell
Observatory. Lowell is a private, non-profit institution dedicated to
astrophysical research and public appreciation of astronomy and operates the
LDT in partnership with Boston University, the University of Maryland, the
University of Toledo, Northern Arizona University, and Yale University. The
Large Monolithic Imager was built by Lowell Observatory using funds provided
by the National Science Foundation (AST-1005313).

These results are based in part on observations obtained at the Southern
Astrophysical Research (SOAR) telescope, which is a joint project of the
Ministério da Ciência, Tecnologia e Inovações (MCTI/LNA) do Brasil, the US
National Science Foundation’s NOIRLab, the University of North Carolina at
Chapel Hill (UNC), and Michigan State University (MSU).

The INT is operated on the island of La Palma by the Isaac Newton Group of
Telescopes in the Spanish Observatorio del Roque de los Muchachos of the
Instituto de Astrofísica de Canarias. INT data were obtained under program
I/2016B/02.

The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been
made possible through contributions by the Institute for Astronomy, the
University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society
and its participating institutes, the Max Planck Institute for Astronomy,
Heidelberg, the Max Planck Institute for Extraterrestrial Physics, Garching,
the Johns Hopkins University, Durham University, the University of Edinburgh,
the Queen’s University Belfast, the Harvard-Smithsonian Center for
Astrophysics, the Las Cumbres Observatory Global Telescope Network
Incorporated, the National Central University of Taiwan, the Space Telescope
Science Institute, the National Aeronautics and Space Administration under
Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA
Science Mission Directorate, the National Science Foundation Grant No.
AST-1238877, the University of Maryland, Eotvos Lorand University (ELTE), the
Los Alamos National Laboratory, and the Gordon and Betty Moore Foundation.

Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan
Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space
Administration, the Japanese Monbukagakusho, the Max Planck Society, and the
Higher Education Funding Council for England. The SDSS Web Site is http://
www.sdss.org/.

The SDSS is managed by the Astrophysical Research Consortium (ARC) for the
Participating Institutions. The Participating Institutions are the University
of Chicago, Fermilab, the Institute for Advanced Study, the Japan
Participation Group, The Johns Hopkins University, the Korean Scientist Group,
Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA),
the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University,
University of Pittsburgh, University of Portsmouth, Princeton University, the
United States Naval Observatory, and the University of Washington.

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