# Time-series and Phasecurve Photometry of Episodically-Active Asteroid (6478)
Gault in a Quiescent State Using APO, GROWTH, P200 and ZTF

Josiah N. Purdum  Department of Astronomy, San Diego State University, 5500
Campanile Dr, San Diego, CA 92182, U.S.A.  Zhong-Yi Lin∗ Institute of
Astronomy, National Central University, Taoyuan 32001, Taiwan  These authors
contributed equally to this work.  Bryce T. Bolin∗ IPAC, Mail Code 100-22,
Caltech, 1200 E. California Blvd., Pasadena, CA 91125, U.S.A.  These authors
contributed equally to this work.  Kritti Sharma Department of Mechanical
Engineering, Indian Institute of Technology Bombay, Powai, Mumbai-400076,
India  Phillip I. Choi  Physics and Astronomy Department, Pamona College, 333
N. College Way, Claremont, CA 91711, U.S.A.  Varun Bhalerao Department of
Physics, Indian Institute of Technology Bombay, Powai, Mumbai-400076, India
Harsh Kumar Department of Physics, Indian Institute of Technology Bombay,
Powai, Mumbai-400076, India  LSSTC Data Science Fellow  Robert Quimby
Department of Astronomy, San Diego State University, 5500 Campanile Dr, San
Diego, CA 92182, U.S.A.  Kavli Institute for the Physics and Mathematics of
the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The
University of Tokyo, Kashiwa, Chiba 277-8583, Japan  Joannes C. Van Roestel
Division of Physics, Mathematics and Astronomy, California Institute of
Technology, Pasadena, CA 91125, U.S.A.  Chengxing Zhai  Jet Propulsion
Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, U.S.A.  Yanga R. Fernandez Dept. of Physics and Florida
Space Inst., Univ. of Central Florida, 4000 Central Florida Boulevard, Orlando
FL 32816-2385, USA  Josef Hanuš Institute of Astronomy, Faculty of Mathematics
and Physics, Charles University, V Holešovičkách 2, 18000 Prague, Czech
Republic  Carey M. Lisse Johns Hopkins University Applied Physics Laboratory,
Laurel, MD 20723  Dennis Bodewits Physics Department, Leach Science Center,
Auburn University, Auburn, AL 36832, U.S.A.  Christoffer Fremling  Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, U.S.A.  Nathan Ryan Golovich Lawrence Livermore National
Laboratory, 7000 East Avenue, Livermore, CA 94550, U.S.A.  Chen-Yen Hsu
Graduate Institute of Astronomy, National Central University, 32001, Taiwan
Wing-Huen Ip  Institute of Astronomy, National Central University, 32001,
Taiwan  Chow-Choong Ngeow Graduate Institute of Astronomy, National Central
University, 32001, Taiwan  Navtej S. Saini  Jet Propulsion Laboratory,
California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109,
U.S.A.  Michael Shao  Jet Propulsion Laboratory, California Institute of
Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, U.S.A.  Yuhan Yao
Division of Physics, Mathematics and Astronomy, California Institute of
Technology, Pasadena, CA 91125, U.S.A.  Tomás Ahumada  Department of
Astronomy, University of Maryland, College Park, MD 20742, U.S.A.  Shreya
Anand  Division of Physics, Mathematics and Astronomy, California Institute of
Technology, Pasadena, CA 91125, U.S.A.  Igor Andreoni  Division of Physics,
Mathematics and Astronomy, California Institute of Technology, Pasadena, CA
91125, U.S.A.  Kevin B. Burdge  Division of Physics, Mathematics and
Astronomy, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Rick Burruss  Caltech Optical Observatories, California Institute of
Technology, Pasadena, CA 91125, U.S.A.  Chan-Kao Chang Graduate Institute of
Astronomy, National Central University, 32001, Taiwan  Chris M. Copperwheat
Astrophysics Research Institute Liverpool John Moores University, 146 Brownlow
Hill, Liverpool L3 5RF, United Kingdom  Michael Coughlin  School of Physics
and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
Kishalay De  Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  Richard Dekany Caltech
Optical Observatories, California Institute of Technology, Pasadena, CA 91125,
U.S.A.  Alexandre Delacroix  Caltech Optical Observatories, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  Andrew Drake  Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, USA  Dmitry Duev Division of Physics, Mathematics and
Astronomy, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Matthew Graham  Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  David Hale  Caltech
Optical Observatories, California Institute of Technology, Pasadena, CA 91125,
U.S.A.  Erik C. Kool  DivisionThe Oskar Klein Centre, Department of Astronomy,
Stockholm University, AlbaNova, SE-10691, Stockholm, Sweden  Department of
Physics and Astronomy, Macquarie University, NSW 2109, Sydney, Australia
Mansi M. Kasliwal  Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  Iva S. Kostadinova
Division of Physics, Mathematics and Astronomy, California Institute of
Technology, Pasadena, CA 91125, U.S.A.  Shrinivas R. Kulkarni  Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, U.S.A.  Russ R. Laher IPAC, Mail Code 100-22, Caltech,
1200 E. California Blvd., Pasadena, CA 91125, USA  Ashish Mahabal Division of
Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, U.S.A.  Center for Data Driven Discovery, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  Frank J. Masci  IPAC,
Mail Code 100-22, Caltech, 1200 E. California Blvd., Pasadena, CA 91125, USA
Przemyslaw J. Mróz  Division of Physics, Mathematics and Astronomy, California
Institute of Technology, Pasadena, CA 91125, U.S.A.  James D. Neill  Division
of Physics, Mathematics and Astronomy, California Institute of Technology,
Pasadena, CA 91125, U.S.A.  Reed Riddle Caltech Optical Observatories,
California Institute of Technology, Pasadena, CA 91125, U.S.A.  Hector
Rodriguez  Caltech Optical Observatories, California Institute of Technology,
Pasadena, CA 91125, U.S.A.  Roger M. Smith Caltech Optical Observatories,
California Institute of Technology, Pasadena, CA 91125, U.S.A.  Richard
Walters  Division of Physics, Mathematics and Astronomy, California Institute
of Technology, Pasadena, CA 91125, U.S.A.  Lin Yan Caltech Optical
Observatories, California Institute of Technology, Pasadena, CA 91125, U.S.A.
Jeffry Zolkower  Caltech Optical Observatories, California Institute of
Technology, Pasadena, CA 91125, U.S.A.

###### Abstract

We observed Episodically Active Asteroid (6478) Gault in 2020 with multiple
telescopes in Asia and North America and have found that it is no longer
active after its recent outbursts at the end of 2018 and start of 2019. The
inactivity during this apparation allowed us to measure the absolute magnitude
of Gault of $H_{r}$ = 14.63$\pm$0.02, $G_{r}$ = 0.21$\pm$0.02 from our secular
phasecurve observations. In addition, we were able to constrain Gault’s
rotation period using time-series photometric lightcurves taken over 17 h on
multiple days in 2020 August, September and October. The photometric
lightcurves have a repeating $\lesssim$0.05 magnitude feature suggesting that
(6478) Gault has a rotation period of $\sim$2.5 hours and may have a semi-
spherical or top-like shape, much like Near-Earth Asteroids Ryugu and Bennu.
The rotation period of $\sim$2.5 hours is near to the expected critical
rotation period for an asteroid with the physical properties of (6478) Gault
suggesting that its activity observed over multiple epochs is due to surface
mass shedding from its fast rotation spun up by the
Yarkovsky–O’Keefe–Radzievskii–Paddack effect.

††software: Astropy, ZChecker, Aperture Photometry Tool

##  1 Introduction

Active asteroids produce comet-like tails and comae that can be driven by many
different types of forces different from comets themselves (Jewitt et al.,
2015). While sublimation of water ice is a primary driver for activity in
‘typical’ comets, the $\sim$20 known (so far) active asteroids in the Main
Belt seem to lose mass via a wider array of physical effects such as
collisions (e.g., Snodgrass et al., 2010), rotational instabilities (e.g.,
Jewitt et al., 2013), and thermal fracture (e.g., Jewitt et al., 2019a). We
can assess the physics of a particular active asteroid’s activity via
observations over long time baselines that assess the object’s photometric and
morphological development. As more and more active asteroids are discovered,
it is vital to continuously monitor these objects and determine the frequency
of the various phenomena in the Main Belt.

Main Belt asteroid (6478) Gault (1998 JC1; “Gault” hereafter) has been the
subject of wide interest since the discovery in early 2019 of comet tail-like
extended emission (Smith et al., 2019). Eventually three tails were noted in
January 2019 (Ye et al., 2019; Jewitt et al., 2019b) on the S-type Phocaea
family member (Sanchez et al., 2019), suggesting multiple sporadic outbursts
of activity. Ye et al. (2019) assessed the dynamics of the dust seen near
Gault and estimated that two outbursts had actually occurred in late 2018.
Searches through archival data that serendipitously caught Gault revealed that
there had been active episodes in 2013, 2016, and 2017 as well (Chandler et
al., 2019).

Many authors have proposed that the cause of Gault’s activity is the
instability of material on its surface (Hui et al., 2019; Jewitt et al.,
2019b; Kleyna et al., 2019; Moreno, F. et al., 2019; Ye et al., 2019) due its
rotation being spun up by the the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP)
effect (Bottke Jr et al., 2006; Kleyna et al., 2019). A critical observational
test of this hypothesis would be to measure the asteroid’s rotational period.
Unfortunately, due to the dust around the asteroid, the rotational period had
not been well constrained as reflected sunlight from dust grains would swamp
the signal from the asteroid itself and thus suppress short-term lightcurve
variations due to Gault’s shape, as indeed Jewitt et al. (2019b) concluded.
However there have been published reports of some hints of rotational
signatures in lightcurve data. For example, Ivanova et al. (2020) suggest a
rotation period of 1.79 hours, Carbognani & Buzzoni (2020) suggest 3.34 hours,
Ferrín et al. (2019) have 3.36 hours, and Kleyna et al. (2019) suggest $\sim$2
hours. In all cases, the lightcurve amplitude was quite small, on the order of
just a few hundredths of a magnitude, which would be on the same order of the
signal noise. It should also be noted that others (e.g., Moreno, F. et al.,
2019) report no variation in photometry over a time span longer than these
periods. This very small amplitude demonstrates the challenge of
photometrically extracting a rotation period from an active body (see also
Bolin & Lisse, 2020, for an example).

In this paper we report on several sets of imaging and photometry of Gault
obtained in 2019 while it was still active as well as in 2020 when the
asteroid appeared to be quiescent (Purdum et al., 2020). These datasets have
allowed us to constrain the rotation period of Gault. We also use all of the
data to understand the longer-term, secular variations in Gault’s activity. In
§2 we describe the observations from 2019 and 2020. In §3 we present the
photometry, and in §4 we discuss Gault’s behavior, spin state, and shape, and
summarize the article.

##  2 Observations

For our analysis we have made use of both our own, PI-led, pointed
observations using several telescope facilities in the GROWTH (Global Relay of
Observatories Watching Transients Happen) network (Kasliwal et al., 2019) and
other faculties, as well as archival data from the Zwicky Transient Survey
(ZTF, Graham et al., 2019; Bellm et al., 2019). Our pointed observations
occurred on 17 nights between 2019 January 8 and 2020 October 20, and made use
of six telescopes. On 7 of those 17 nights, we were able to have multiple
telescopes follow Gault in a coordinated effort. The observations in 2019
showed Gault to still be active, but all such observations in 2020 showed no
activity, only a point source (Purdum et al., 2020). The ZTF data are from 89
nights from 2018 November 01 to 2020 October 14. All data in this work have
been flat- and bias-corrected since only CCDs were used. Tables LABEL:table1
and LABEL:table2 list the technical details of each telescope and the
particulars about each observing run, respectively, while Tables 3 and
LABEL:table4 are the photometric data plotted for this work and the archival
ZTF survey, respectively. We describe below each telescope facility used in
our work.

###  2.1 Mount Laguna Observatory 1.0-Meter Telescope

Images of Gault were taken with the Mount Laguna Observatory (MLO) 1.0-meter
telescope on 2020 June 24 UT, several months after the asteroid was leaving
Solar conjunction. 120 images were taken with 30-second exposure times each,
culminating 60 minutes of total exposure to measure the morphology of the
asteroid.

Later observations were taken of Gault with MLO with an aim to constrain a
rotation period. This data was taken between 2020 August 23 UT and 2020
October 20 UT over 6 separate campaigns listed in Table LABEL:table2. MLO
lightcurve images were taken in the Johnson-Cousins R filter with between 165
and 190 separate 120-second exposures.

###  2.2 Lulin One-meter Telescope

The time-series observations of Gault using the Lulin one-meter Telescope
(LOT) at the Lulin Observatory, Taiwan, for 2020 August 23 and 24 UT lasted
6.4 hours and 5.2 hours, respectively. The other time span on 2020 September
21 UT and 2020 October 11 UT lasted 6.4 hours and 6.8 hours, respectively.
Except for the use of unfiltered CCD observations early in the campaign, all
observations are acquired with R-filter and obtained through non-sidereal
tracking.

###  2.3 Astrophysics Research Consortium 3.5-meter Telescope

Between 2019 January 8 UT and 2019 June 6 UT we observed Gault over 6
campaigns with the Astrophysics Research Consortium 3.5-meter Telescope (ARC)
at Apache Point Observatory before the asteroid headed into Solar conjunction
(Table LABEL:table2). Individual observations created lightcurves spanning
between 1 hour (2019 March 24 UT) and 4 hours (2019 April 26 UT). Observations
were taken with the ARCTIC optical CCD (Huehnerhoff et al., 2016) in the
$r^{\prime}$ filter with an average seeing of 1.8”. Throughout January and
February of 2019, Gault remained visibly active, while observations between
March and June of 2019 displayed just a remnant tail (see Figures 1 and 5).

###  2.4 Palomar Observatory 200-Inch Telescope

On 2020 Aug 27 UT, the Palomar Observatory 200-inch telescope (P200) observed
Gault in the r band. The 103 exposures each had an equivalent exposure time of
90 seconds, accumulating in a total of 9,270 seconds with an average seeing of
$\sim$1.5”. Observations were made with the Caltech HIgh-speed Multi-color
camERA (CHIMERA, Harding et al., 2016). Although CHIMERA observes in two
simultaneous optical bands, we only use the r band in this work.

###  2.5 Zwicky Transient Facility using the Palomar 48-Inch Telescope

Images of Gault were taken with the Zwicky Transient Facility (ZTF) (Graham et
al., 2019) which is mounted on the Palomar Observatory’s 48-inch telescope
(P48) (Bellm et al., 2019; Dekany et al., 2020). ZTF images are located in the
ZTF archive (Masci et al., 2019) and Gault’s photometry was measured with a 5”
aperture and processed using the ZChecker software (Kelley et al., 2019). The
30-second exposure time observations were made in the r band and color-
corrected using the $g-r$ value of 0.50 $\pm$ 0.04 from Ye et al. (2019). Data
in Figure 4 between 2018 November 1 UT and 2019 February 10 UT are adapted
from Ye et al. (2019). A full list of the ZTF observations starting 2020 April
2 UT and ending 2020 October 14 UT is located in Table LABEL:table4. The
seeing varied between 1.5”–2.5” and the airmasses varied from 1.4 to 2.6
during the span of our observations.

###  2.6 GROWTH-India Telescope

We observed Gault on multiple nights with the 0.7m GROWTH-India telescope
(GIT), using the SDSS $r^{\prime}$ filter and an Apogee KAF3200EB camera
giving a $\sim 11^{\prime}\times 7.5^{\prime}$ field of view. Due to the slow
motion of Gault, we used sidereal tracking and took multiple exposures. Data
were acquired in 120 sec exposures on 2020 September 21, followed by 180 sec
exposures on 2020 October 16 and October 20. Data were downloaded and
processed in real time at our data processing machine at IIT Bombay. We
calibrated images for processing by applying bias correction and flat-
fielding, obtained astrometry solution using offline engine of astrometry.net
(Lang et al., 2010) and finally removing cosmic-rays via Astro-SCRAPPY
(McCully & Tewes, 2019) package. photometry was performed using PyRAF based
processing pipeline. We cross-matched the the sextractor-identified (Bertin,
2011) sources in the GIT image with # II/349/ps1 catalogue (Flewelling, 2018)
using vizier. Magnitudes were calibrated by correcting for zero points.

###  2.7 GROWTH Coordinated Observations

On 2020 September 21 UT, LOT, GIT, MLO, and the Table Mountain Observatory
(TMO) 1.0-meter telescope participated in a 20-hour relay of observing Gault
for photometric lightcurve variation. MLO started the relay at 2020-09-21
04:24:47 UT (airmass 2.0) and ran continuous observations of 120-second
exposure times until 11:35:27 UT (airmass 2.0) the same day, totaling 22800
seconds of exposure time. LOT took over shortly after at 14:26:07 (airmass
1.2) amassing 14130 seconds of 90-second exposures before finishing at
20:29:09 UT (airmass 2.5). GIT observed Gault for roughly 6 hours in 135
images amassing 16,200 seconds of exposure starting from 17:21:31 UT (airmass
1.2), in the middle of the LOT observations, and ending at 23:18:07 UT
(airmass 2.5). TMO observed Gault for roughly 4 hours in 225 images amassing
13,500 seconds of exposure starting at 06:36:37 UT (airmass 1.3), in the
middle of MLO’s observations. Typical seeing for GIT is 2.5” and for TMO is
1.5”. We were able to take data with Table Mountain Observatory despite the
degraded conditions caused by a nearby wildfire. Additional coordination among
the GROWTH network include MLO-LOT observations on 2020 August 23 and 24 UT
and 2020 October 11 UT, TMO-LOT on 2020 September 22 UT, and MLO-GIT on 2020
October 16 and 20 UT.

##  3 Results

###  3.1 Active and Inactive states of Gault

Follow-up observations with the ARC 3.5-meter telescope at Apache Point
Observatory on 2019 February 25 UT showed evidence for multiple tails. A deep-
stack image consisting of 4680 seconds of exposure is shown on the left side
of Figure 1. The surface brightness of Gault in this stack is 24.0
mag/sq.arcsec within a 10,000 km aperture. The right side of Figure 1 shows
Gault’s third tail in a 4320-second deep-stack image from the ARC 3.5-meter
telescope on 2019 April 26 UT and the 10,000 km surface brightness was
calculated to be 23.8 mag/sq.arcsec.

|
---|---
Figure 1: Left: 4680-second Deep-stack image of Gault from the ARC 3.5-meter
telescope at Apache Point Observatory on 2019 February 25 UT. The two tails
indicate two separate epochs of activity. Right: 4320-second Deep-stack image
of Gault from the ARC 3.5-meter on 2019 April 26 UT after it had produced a
third tail.

The images were combined in deep, median-stacks centered on Gault and then
used to compute the calibrated $r$-band photometry from comparisons to a
similar deep-stacked images of reference stars with Solar colors from the same
initial image. We referenced photometry of the reference star from the Pan-
STARRS catalog (Chambers et al., 2016).

Both surface brightnesses were brighter than the surface brightness of 25.8
mag/sq.arcsec found when it was inactive in 2020 June by Purdum et al. (2020).
Our deep-stack image taken by the P200 in the r band is shown in Figure 2,
which lacks cometary features and has a surface brightness of 26.3
mag/sq.arcsec, also dimmer than the surface brightnesses from early 2019.

Figure 2: Deep-stack image of Gault taken with the P200 telescope in 103
90-second images culminating in 9270-seconds on 2020 August 27 UT in the r
band. The image displays a lack of coma or southwest-facing tail implying the
inactivity of Gault.

###  3.2 Secular Photometry and Updated Absolute Magnitude

Figure 3 shows Gault’s reduced magnitude phasecurve from ZTF data taken
between 2017 June 14 UT to 2017 December 2 UT. The reduced magnitude data is
described by $r-5\,\mathrm{log_{10}}(r\Delta)$ where $r$ and $\Delta$ are the
heliocentric and geocentric distances. We can then find the $r$-band absolute
magnitude $H_{r}$ and phase slope parameter $G$ by fitting the reduced
magnitudes to the phase function of the form:

$r-5\,\mathrm{log_{10}}(r\Delta)=H-2.5\,\mathrm{log_{10}}\left[(1-G)\,\Phi_{1}(\alpha)+G\,\Phi_{2}(\alpha)\right]$
(1)

where $r$ is the $r$-band magnitude of Gault taken with a 5″ aperture,
$\alpha$ is the phase angle of the asteroid at the time of mid-exposure, and
$\Phi_{1}$ and $\Phi_{2}$ are two basis functions normalized at unity for
$\alpha=0^{\circ}$ (Bowell et al., 1989; Muinonen et al., 2010; Pravec et al.,
2012).

Figure 3: Reduced magnitude of Gault from Equation 1 as a function of phase
angle. The data points are taken from P48 observations with ZTF starting 2017
June 14 UT and ending 2017 December 2 UT. The line of best fit is based on
$r-5\,\mathrm{log_{10}}(r\Delta)$ in Equation 1 using $H_{r}=14.631\pm 0.019$
and $G=0.207\pm 0.020$.

These best fit parameters are $H_{r}$ = 14.631 $\pm$ 0.019 and $G_{r}$ = 0.207
$\pm$ 0.020 after it had exited Solar conjunction and was no longer active.
This is significantly fainter than the value of 14.31 $\pm$ 0.01 measured by
ZTF when Gault was last seen to be inactive in 2017 (Ye et al., 2019). This
could be caused by the change in observing geometry over time creating a
different line-of-site projection of Gault’s light-scattering cross-section.
Using the updated predicted absolute magnitude of Gault with the blue line in
Figure 4, we can see the instability in the brightness of Gault over time
using 5” aperture photometry.

Figure 4 shows the time-series r band ZTF photometry between June and October
of 2020.

Figure 4: Secular photometry of Gault from 2018 November 01 UT (MJD = 58423)
to 2020 October 14 UT (MJD = 59136). The red points are the apparent
magnitudes of Gault taken by the Palomar Observatory 48-inch telescope and ZTF
in the r band over this time span. Data presented from before 2019 February 10
UTC are adapted from Ye et al. (2019). The black line is the predicted
apparent V-band magnitude from JPL HORIZON’s ephemeris service. The blue line
indicates what the predicted magnitude should be given new values for the
absolute magnitude $H=14.631\pm 0.019$ and slope parameter $G=0.207\pm 0.020$.
While the asteroid is active, the data do not line up with the predicted
magnitude due to dust obscuring the surface of the asteroid. As Gault
continued to be dust dominated as it entered Solar conjunction before MJD
58700, the predicted and observed magnitudes started to align again. After
exiting Solar conjunction, Gault shows that it aligns with the new predicted
values during inactivity. The vertical lines indicate the observation epochs
in this work.

Gault exited Solar conjunction and was observed between 2020 April 02 UT (MJD
= 58941) and 2020 October 14 UT (MJD = 59136). Comparing the measured
equivalent r-band magnitude of Gault from photometry measured in ZTF
observations taken on these dates with the predicted magnitude of Gault based
on our measured r-band absolute magnitude of $H_{r}=14.631\pm 0.019$ and phase
function slope value $G=0.207\pm 0.020$, we do not see any significant
brightening in the actual magnitude of Gault compared to the predicted
magnitudes. This is in contrast to the brightness of Gault in the “active”
portion of its lightcurve between 2018 November 01 UT (MJD = 58423) and 2019
February 10 UT (MJD = 58524). Between 2019 February 24 UT (MJD = 58538) and
2019 July 9 UT (MJD = 58673), the measured brightness and predicted brightness
begin to become similar suggesting that the enhanced cross-section of Gault
caused by dust within its vicinity was beginning to diminish in contrast to
the increase in brightness of comets whose brightness are observed to increase
with steadily increasing activity as they approach the Sun (Bolin et al.,
2020a, b).

###  3.3 Time-Series Lightcurves

While Gault was active in 2019, the ARC 3.5-meter telescope at Apache Point
Observatory took short-period lightcurve images, as shown in Figure 5. Much
like Figure 6 in Jewitt et al. (2019b), this plot shows little variation in
the lightcurve while the asteroid was experiencing activity and producing
comet-like features. The variations that do occur in these lightcurves have
small-amplitude peaks and are caused by noise consistent with the uncertainty
values in their individual differential photometry.

Figure 5: 2019 data from the ARC 3.5-meter telescope. The data are organized
chronologically from top to bottom and are offset by 0.1 magnitude from each
other. The first 3 dates correspond to the epochs in which Gault was active
and where the ZTF photometry is brighter than predicted, and the last 3 dates
were obtained during the dust-dominated epochs that followed, as seen in
Figure 4.

The flatness of the lightcurves is noted even as the brightness of Gault began
to resemble its predicted brightness based on its pre-activity $H_{r}$ seen in
Figure 4. In order to determine the rotational period of Gault after it
returned to an inactive state, we obtained coordinated long-term lightcurves
on nine separate dates starting in August 2020, with the longest single
lightcurve of 19 hours on 2020 September 21 UT. The results are displayed in
Figures 6 and 7.

Figure 6: Coordinated long-term photometric lightcurves of Gault and various
reference stars (offset -0.3mag) starting from 2020 August 14 UT and organized
chronologically to 2020 September 21 UT. The observatories are color-
coordinated and the rotation period of 2.49-hours is denoted with orange
vertical lines near some peaks in the lightcurve which are based on the
arbitrary green $t=0$ line on 2020 September 21 UT. Additional peaks are
marked with light-blue lines are split equally between the orange lines. The
lightcurves continue through 2020 October 20 UT in Figure 7. Figure 7:
Coordinated long-term photometric lightcurves of Gault and various reference
stars (offset -0.3mag) starting from 2020 September 22 UT and organized
chronologically to 2020 October 20 UT. This figure is a continuation of Figure
6 where the observatories are color-coordinated and the rotation period of
2.49-hours is denoted with orange vertical lines near some peaks in the
lightcurve which are based on the arbitrary green $t=0$ line on 2020 September
21 UT. The light-blue vertical lines mark additional peaks that split the
orange lines.

The separate observatories are indicated by color, with MLO as red, LOT as
green, P200 as orange, TMO as purple, and GIT as blue. Each lightcurve for
each observatory has an additional reference star lightcurve normalized to
-0.3 magnitude to show that the reference stars used to calculate the
differential photometry of Gault did not vary over time (or if so, not at the
same period and amplitude as the asteroid’s lightcurves). The reference star
lightcurves have small error bars and have not been corrected for airmass or
weather effects on their photometry and therefore are curved, but display no
strong signs of periodicity.

Each date in Figures 6 and 7 also contain vertical orange lines indicate
small-amplitude, periodic peaks in the asteroid lightcurves based on 2.49-hour
intervals from an arbitrary $t=0$ denoted by the green line in Figure 6. The
peaks roughly halfway between the orange lines are denoted with a vertical
light-blue line. The peaks repeat roughly every 1.25 - 2.5 hours, indicating a
possible rotation period around 2.5 hours.

A Lomb-Scargle (Lomb, 1976) periodogram was constructed from MLO and LOT data
of Gault ranging from August to October of 2020 and is shown along with a
folded lightcurve of Gault in Figure 8. The differential photometry technique
we used to create the periodogram relied on determining the difference between
the brightness of Gault and the comparison stars in the same field of view to
acquire the Gault’s light curve. The comparison stars we selected depended on
the maximum frame width that we used through one run and on the similarity of
FWHM (Full Width at Half Maximum) estimated between Gault and the chosen
stars. By comparing the reference stars’ light curves, some variable stars
were ruled out in the photometric analysis. To combine several photometry runs
through different nights, the mean values of each run were automatically
scaled using an IDL routine that we created. We then searched for significant
periodicities using the Lomb-Scargle periodogram functions on the combined
light curve data to find the most likely rotation period of Gault. The
frequency analysis from the strong peak near $\sim 20$ cycles/day in Figure 8
gives a rotation period of $\sim$1.25 hours, which corresponds to a single-
peaked lightcurve. It is natural to assume a double-peaked lightcurve for
Gault, which computes to a sidereal rotation period of 2.49 $\pm$ 0.07 hours.
The uncertainty here of $\pm 0.07$ hours is estimated using the bootstrap
method (Press et al., 1986) which removed $\sqrt{N}$ data points from the time
series lightcurves and recalculated the period value from the Lomb-Scargle
periodogram. This process was repeated 10,000 separate times with the
resulting central value of 2.49 hours and a $1-\sigma$ uncertainty estimate of
0.07 hours.

|
---|---
Figure 8: Left: Lomb-Scargle Periodogram of Gault’s lightcurve data from MLO
and LOT observations starting 2020 August 23 UT and ending 2020 October 20 UT.
Right: Folded lightcurve of Gault from MLO and LOT with a period of 2.5 hours
averaged over 10 invidual MLO and LOT ligthcurves taken over six nights of
data taken between 2020 August 23 UT and ending 2020 October 20 UT.

The amplitude of the MLO and LOT lightcurves are low, so it is somewhat
difficult to recognize a continuous variation in brightness in the folded
version of the lightcurve, as seen on the right in Figure 8.

##  4 Discussion and Summary

The surface brightness profiles taken from deep-stacked images of Gault from
the MLO 1.0-meter on 2020 July 21 UT (Purdum et al., 2020) and P200 on 2020
August 27 UT indicate that Gault is no longer active after it appeared to have
an outburst of material that caused multiple tails to form starting in October
of 2018 (Ye et al., 2019). The surface brightness measurements of 25.8
mag/sq.arcsec and 26.3 mag/sq.arcsec, from MLO and Palomar, respectively, are
fainter compared to the surface brightness values of Gault from the ARC
3.5-meter Telescope on 2019 February 9 UT, had a measurement of 24
mag/sq.arcsec (Purdum et al., 2020). The fainter measurements in 2020 could
mean that Gault no longer has material surrounding it and can be deemed
inactive.

Gault’s deactivation can also be seen over time in the photometry from ZTF
observations of Gault in Figure 4. The activity of Gault is apparent on the
left side of the plot with the data being much brighter and more variable than
the predicted magnitudes from JPL’s HORIZONS ephemeris
service111https://ssd.jpl.nasa.gov/?horizons. The outbursts for Gault’s first
two tails were estimated to have occurred on 2018 October 18 $\pm$ 5 UT and
2018 December 24 $\pm$ 1 UT (Ye et al., 2019), which is during the “active”
portion of the lightcurve (see Figure 4). The third tail was much dimmer than
the first two and so the exact time of initiation is uncertain, but Jewitt et
al. (2019b) estimates it to be 2019 February 10 $\pm$ 7 UT, right at the time
the “active” portion of Figure 4 ends.

After Gault had produced its third tail, the ZTF photometry started to line
back up with the predicted magnitudes from JPL’s HORIZONS ephemeris service,
indicating that the active stage had come to an end. However, this alignment
did not last as the photometry from ZTF started to dip below the predicted
magnitudes in Figure 4. The misalignment occurred while Gault no longer had
tails but was still surrounded by dust, which can skew photometric
measurements. The right side of Figure 4, however, shows that Gault’s
photometry exiting Solar conjunction was more stable than the active stage of
the plot, therefore providing more evidence for Gault’s inactivity.

Interestingly, Gault no longer aligned with the predicted magnitudes HORIZONS
ephemeris service after it had exited Solar conjunction. We found that
altering the phase parameter $G$ in Equation 1 from 0.25 to 0.21 and the
absolute magnitude $H$ from JPL’s HORIZONS’ 14.3 to 14.6, re-aligns the
photometry in Figure 4. This phenomenon can be attributed to the observing
geometry of Gault changing throughout its orbit. The higher absolute magnitude
$H_{r}$ in 2019 could be due to pole-on observations, while the equator-on
observations would result in a smaller absolute magnitude in 2020.

Photometric lightcurve observations with the ARC 3.5-meter while Gault was
still dust-dominated (see Figure 5) in 2019 started to show some variation as
the activity on Gault diminished, but the low-amplitude of the variations were
not enough to conclude a rotation period. Our observations of Gault in 2020
also produced low-amplitude lightcurves (see Figures 6 and 7), even though it
no longer displayed signs of activity. The viewing geometry is also much
different for our observations in 2020 than from when it was active in 2019.
This means that Gault could have a spherical or top-shaped geometry like Near-
Earth Asteroids Ryugu and Bennu (Hirabayashi et al., 2020). It is also worth
noting that near-Earth Asteroid (3200) Phaethon was imaged by Arecibo radar
observations and was found to have a round, top-like shape when it passed by
Earth in December of 2017 (Taylor et al., 2019). At that time, Kim et al.
(2018) found Phaethon’s peak amplitude was small, $\sim$0.1 magnitudes, which
is somewhat similar to our data in Figures 6 and 7.

Despite the low amplitude in the lightcurves, we did notice periodic small-
amplitude peaks and found they are separated by roughly 2.5 hours and plotted
vertical orange lines to indicate the estimations. Some peaks occurred at 2.5
hour intervals that split the usual periodic peaks and are marked by dashed,
blue lines 1.25 hours in between the orange lines. Several vertical lines in
these figures correspond to peaks in the Gault lightcurve and little to no
variation in the reference star lightcurve (see August 24, September 21,
September 23, October 20 in Figures 6 and 7), which is an indication that the
peaks are non-anomalous and are a result of the rotation of the asteroid. The
periodogram in Figure 8 shows Gault has a rotation period of 2.49 $\pm$ 0.07
hours, assuming the frequency of $\sim 20$ cycles/day ($\sim$1.25 hours)
corresponds to a double-peaked lightcurve.

With the assumption that Gault is nearly spherical or top-shaped (see Harris
et al. (2014) on the determination of an asteroid’s shape from its
lightcurve), we assume the $b$/$a$ axial ratio is close to 1–1.3 given its
maximum possible lightcurve amplitude of $\sim$0.1-0.3 as seen in our data and
the data from Kleyna et al. (2019) and the relation between $b$/$a$ and
lightcurve amplitude of $b$/$a$ = 100.4ΔM from Binzel et al. (1989). The
critical breakup period of a strengthless ellipsoid as a function of axial
ratio is given by Jewitt et al. (2017) as

$P_{crit}=\bigg{(}{b\over
a}\bigg{)}\bigg{[}{{3\pi}\over{G\rho}}\bigg{]}^{1/2}$ (2)

where $\rho$ is the density of the ellipsoid and $G$ is the Newtonian
gravitational constant. Gault should have a density of roughly equal to 2.2
g/cm3 (Sanchez et al., 2019; Marsset et al., 2019), consistent with other
S-Type asteroids (Carry, 2012). Figure 9 presents the critical period with
which Gault would start shedding surface material as a function of the axial
ratio and density.

Figure 9: Adapted from Bolin et al. (2018). The critical rotation period of an
asteroid based on the axial ratio b/a and the density $\rho$. The likely
critical period for Gault is indicated in the orange box, roughly around 2.0 -
3.0 hours.

An orange square labelled in Figure 9 is likely to contain the critical
rotation period for an object with Gault’s geometry. A rotation period like
the one we have found at 2.5 hours seems to be at or near the critical period
of Gault and therefore could be the cause of the activity started in 2018.
Previous authors have also proposed Gault’s activity was caused by rotational
instability induced from the YORP effect (Jewitt et al., 2019b; Kleyna et al.,
2019; Ferrín et al., 2019). Jewitt et al. (2015) determined that the YORP
spin-up timescale for Gault should be roughly 22 Myr, much shorter than the
100 Myr-timescale for the re-orientation of the spin of a $\sim$4 km asteroid
by non-destructive collisions (Farinella et al., 1998). It is therefore
possible that Gault may experience rotational fission if it continues to be
spun up past its rotational breakup limit (eg., Jewitt et al., 2017; Moreno et
al., 2017). Some asteroids are observed to be spinning beyond their rotational
limit, but this is typically for asteroids smaller than the kilometer scale
(Pravec et al., 2008) to smaller than the meter scale (Bolin et al., 2014,
2020) which are held together by cohesive forces (Sánchez & Scheeres, 2014).
However, it should be noted that examples of km-scale asteroids have been
found rotating faster than their critical period (Chang et al., 2017) from
fast rotating asteroid searches in wide-field optical surveys (Chang et al.,
2016, 2019).

Other causes for activity are somewhat less likely than rotational
instability. For instance, unlike Main Asteroid Belt Comets (Jewitt et al.,
2015), there are many clues that point away from ice sublimation as the driver
for Gault’s activity. Since Gault is an S-type and a member of the inner Main
Belt Phocaea family, it likely formed inside the snow line and therefore would
not experience sublimation (Vernazza & Beck, 2016). Additionally, Gault’s
activity was observed with the ARC 3.5-meter telescope when Gault was located
at a heliocentric distance of 2.41 AU on 2019 February 9 UT. When Gault was
observed to be inactive by the MLO 1.0-meter telescope on 2020 June 24 UT, it
had a heliocentric distance of 2.07 AU, suggesting the shorter distance to
perihelion did not drive the activity. Collision events are also unlikely to
be the cause for activity due to the multiple epochs of activity occurring in
the few months Gault was active. Thermal disintegration is also somewhat
unlikely due to Gault’s low-eccentricity orbit. Active asteroids with this
kind of driver typically have highly eccentric orbits which cause large
changes in temperature that lead to fracture (Delbo et al., 2014; Jewitt et
al., 2015). Other processes such as Solar radiation pressure are unlikely due
to Gault’s rotation constantly changing the orientation with respect to the
Sun. Therefore we find that Gault’s activity was likely driven from rapid
rotation at its critical period of 2.5 hours.

Based on observations obtained with the Samuel Oschin Telescope 48-inch and
the 60-inch Telescope at the Palomar Observatory as part of the Zwicky
Transient Facility project. ZTF is supported by the National Science
Foundation under Grant No. AST-2034437 and a collaboration including Caltech,
IPAC, the Weizmann Institute for Science, the Oskar Klein Center at Stockholm
University, the University of Maryland, Deutsches Elektronen-Synchrotron and
Humboldt University, the TANGO Consortium of Taiwan, the University of
Wisconsin at Milwaukee, Trinity College Dublin, Lawrence Livermore National
Laboratories, and IN2P3, France. Operations are conducted by COO, IPAC, and
UW. This work was supported by the GROWTH project funded by the National
Science Foundation under PIRE Grant No 1545949. Part of this work was
performed under the auspices of the U.S. Department of Energy by Lawrence
Livermore National Laboratory under Contract DE-AC52-07NA27344. B.T.B. and
F.J.M. acknowledge support from NASA with grant number 80NSSC19K0780. C.F.
gratefully acknowledges the support of his research by the Heising-Simons
Foundation ($\\#$2018-0907). M. W. Coughlin acknowledges support from the
National Science Foundation with grant number PHY-2010970. This publication
has made use of data collected at Lulin Observatory, partly supported by MoST
grant 108-2112-M-008-001. C.C.N. thanks to the funding from MOST grant
104-2923-M-008-004-MY5. C.Z. acknowledges support from JPL’s internal research
funds of the R$\&$TD, JROC, and ESD HBCU/MSI programs. J. N. P. and R. Q.
acknowledge support from JPL’s ESD HBCU/MSI program under Subcontract 1659249.
The work of J.H. has been supported by the Czech Science Foundation through
grant 20-08218S and by the Charles University Research program No.
UNCE/SCI/023. V.B., K.S., and H.K. thank Kunal Deshmukh for help with data
processing. GROWTH India telescope is a 70-cm telescope with a 0.7 degree
field of view, set up by the Indian Institute of Astrophysics and the Indian
Institute of Technology Bombay with support from the Indo-US Science and
Technology Forum (IUSSTF) and the Science and Engineering Research Board
(SERB) of the Department of Science and Technology (DST), Government of India
(https://sites.google.com/view/growthindia/). It is located at the Indian
Astronomical Observatory (Hanle), operated by the Indian Institute of
Astrophysics (IIA). GROWTH-India project is supported by SERB and administered
by IUSSTF. H.K. thanks the LSSTC Data Science Fellowship Program, which is
funded by LSSTC, NSF Cybertraining Grant #1829740, the Brinson Foundation, and
the Moore Foundation; his participation in the program has benefited this
work. Apache Point Astrophysical Research Consortium 3.5 m telescope, GROWTH
India Telescope, Lulin Optical Telescope, Mount Laguna Observatory 40-inch
Telescope, P48 Oschin Schmidt telescope/Zwicky Transient Facility, Table
Mountain Observatory

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Table 1: Columns: (1) Telescope name; (2) CCD Camera name; (3) Number of Pixels on CCD; (4) Type of binning used; (5) Pixel scale; (6) Exposure Time; (7) Non-sidereal tracking enabled (Y/N). Telescope1 | CCD2 | Pixels3 | Binning4 | Scale (”/pix)5 | Exp (s)6 | NST7
---|---|---|---|---|---|---
MLO 1.0-meter | ULTRAcam | 2Kx2K | 2x2 | 0.358 | 120 | N
Lulin One-meter | SOPHIA | 2Kx2K | 1x1 | 0.385 | 180 | Y
ARC 3.5-meter | ARCTIC | 2Kx2K | 2x2 | 0.228 | 120 | Y
Palomar 200-inch | CHIMERA | 1Kx1K | 1x1 | 0.29 | 90 | Y
Palomar 48-inch | ZTF CCD | 16 6Kx6K | 1x1 | 1.01 | 30 | N
GIT 0.7-meter | Apogee KAF3200EB | 2Kx1K | 1x1 | 0.3 | 120-180 | N
TMO 1.0-meter | sCMOS | 1.6Kx1.6K | 1x1 | 0.225 | 60 | N
Table 2: Columns: (1) Date of observation; (2) Telescope; (3) Right Ascension at the start of observation; (4) Declination at the start of observation; (5) Heliocentric distance at start of observation; (6) Geocentric distance at start of observation; (7) Phase Angle at start of observation; (8) Filter; (9) in-image seeing of at the start of observation. Date (UTC)1 | Telescope2 | RA3 | DEC4 |  $r$ (AU)5 |  $\Delta$ (AU)6 |  $\alpha$ (∘)7 | filter8 |  $\theta_{s}$ (”)9
---|---|---|---|---|---|---|---|---
2019 Jan 08 | ARC | 10 48 15.82 | -12 34 36.1 | 2.470 | 1.865 | 20.8 | $r^{\prime}$ | 1.3
2019 Jan 18 | ARC | 10 48 03.15 | -12 42 42.3 | 2.451 | 1.735 | 18.8 | $r^{\prime}$ | 1.7
2019 Feb 25 | ARC | 10 25 39.71 | -08 20 25.9 | 2.374 | 1.413 | 7.3 | $r^{\prime}$ | 1.4
2019 Mar 24 | ARC | 10 04 25.84 | -01 08 19.5 | 2.316 | 1.406 | 12.9 | $r^{\prime}$ | 1.2
2019 Apr 26 | ARC | 10 02 29.07 | +06 19 04.2 | 2.243 | 1.619 | 23.9 | $r^{\prime}$ | 2.5
2019 Jun 20 | ARC | 10 59 34.47 | +09 20 53.9 | 2.121 | 2.150 | 27.5 | $r^{\prime}$ | 2.7
2020 Jun 24 | MLO | 00 06 26.41 | +13 32 09.8 | 2.071 | 1.873 | 29.3 | $R$ | 2.2
2020 Aug 14 | MLO | 00 41 35.22 | +12 07 57.8 | 2.182 | 1.416 | 21.8 | $R$ | 1.7
2020 Aug 23 | MLO | 00 40 34.98 | +10 35 29.9 | 2.202 | 1.355 | 18.4 | $R$ | 2.2
2020 Aug 23 | LOT | 00 40 31.32 | +10 32 32.2 | 2.202 | 1.354 | 18.3 | $R$ | 2.8
2020 Aug 24 | MLO | 00 40 19.44 | +10 23 30.5 | 2.204 | 1.349 | 18.0 | $R$ | 1.6
2020 Aug 24 | LOT | 00 40 12.37 | +10 18 26.4 | 2.205 | 1.347 | 17.8 | $R$ | 2.5
2020 Aug 27 | P200 | 00 39 30.16 | +09 50 27.8 | 2.210 | 1.334 | 16.9 | $r$ | 1.1
2020 Sep 21 | MLO | 00 24 06.34 | +03 10 17.1 | 2.265 | 1.268 | 4.0 | $R$ | 2.1
2020 Sep 21 | TMO | 00 24 02.45 | +03 08 46.4 | 2.265 | 1.268 | 3.9 | $R$ | 1.2
2020 Sep 21 | LOT | 00 23 22.57 | +02 53 41.4 | 2.267 | 1.268 | 3.4 | $R$ | 1.7
2020 Sep 21 | GIT | 00 23 05.87 | +02 47 37.3 | 2.268 | 1.269 | 3.2 | $r^{\prime}$ | 2.5
2020 Sep 22 | TMO | 00 23 12.10 | +02 49 52.8 | 2.268 | 1.269 | 3.3 | $R$ | 1.6
2020 Sep 22 | LOT | 00 22 39.51 | +02 37 47.3 | 2.269 | 1.269 | 2.9 | $R$ | 1.7
2020 Sep 23 | TMO | 00 22 23.43 | +02 31 43.6 | 2.270 | 1.270 | 2.7 | $R$ | 1.8
2020 Sep 24 | TMO | 00 21 36.54 | +02 14 19.8 | 2.272 | 1.271 | 2.2 | $R$ | 1.2
2020 Oct 11 | MLO | 00 08 16.22 | -02 44 28.5 | 2.310 | 1.339 | 7.5 | $R$ | 3.0
2020 Oct 11 | LOT | 00 08 02.98 | -02 49 37.2 | 2.311 | 1.341 | 7.6 | $R$ | 2.6
2020 Oct 16 | MLO | 00 05 10.29 | -03 58 35.4 | 2.321 | 1.373 | 9.9 | $R$ | 2.0
2020 Oct 16 | GIT | 00 04 45.91 | -04 08 29.4 | 2.323 | 1.379 | 10.3 | $r^{\prime}$ | 3.1
2020 Oct 20 | MLO | 00 03 05.67 | -04 51 51.5 | 2.330 | 1.405 | 11.7 | $R$ | 2.6
2020 Oct 20 | GIT | 00 02 43.96 | -05 01 22.7 | 2.331 | 1.412 | 12.1 | $r^{\prime}$ | 2.7
JD1 | Mag2 |  $\sigma_{Mag}$ 3 | Observatory4
---|---|---|---
2459075.77946 | 0.000828 | 0.025020 | MLO
2459075.78247 | -0.012480 | 0.022338 | MLO
2459075.78466 | 0.005480 | 0.023636 | MLO
2459075.78683 | -0.001881 | 0.021923 | MLO
2459075.78901 | 0.013656 | 0.023636 | MLO
2459075.79117 | 0.002243 | 0.023137 | MLO
2459075.79336 | 0.002003 | 0.022937 | MLO
2459075.79554 | 0.007662 | 0.023037 | MLO
2459075.79771 | -0.002169 | 0.021340 | MLO
2459075.79988 | 0.007134 | 0.021839 | MLO
⋮ | ⋮ | ⋮ | ⋮
Table 3: Photometric Lightcurve data for Figures 6 and 7. Columns: (1) Julian Date; (2) Normalized Magnitude; (3) Normalized Magnitude Uncertainty; (4) Location Observations were taken. Table 4: Observation data for the secular lightcurve taken between 2020 April 02 UT and 2020 October 14 UT by ZTF as shown in Figure 4. Date (UTC)1 | RA2 | DEC3 |  $r$ (AU)4 |  $\Delta$ (AU)5 |  $\alpha$ (∘)6 | mag7 | $\chi_{am}^{8}$ |  $\theta_{s}$ (”)9
---|---|---|---|---|---|---|---|---
2020-04-02 12:14 | 21:43:56.3 | +02:13:35 | 1.924 | 2.480 | 21.9 | 18.72 $\pm$ 0.13 | 2.525 | 4.902
2020-04-02 12:21 | 21:43:56.9 | +02:13:38 | 1.924 | 2.480 | 21.9 | 18.74 $\pm$ 0.13 | 2.399 | 5.154
2020-04-02 12:27 | 21:43:57.4 | +02:13:41 | 1.924 | 2.480 | 21.9 | 18.53 $\pm$ 0.12 | 2.286 | 3.563
2020-04-02 12:34 | 21:43:58.0 | +02:13:43 | 1.924 | 2.480 | 21.9 | 18.93 $\pm$ 0.21 | 2.185 | 4.330
2020-06-24 11:24 | 00:06:30.7 | +13:32:24 | 2.071 | 1.872 | 29.3 | 18.77 $\pm$ 0.07 | 1.273 | 1.706
2020-07-08 09:03 | 00:21:56.5 | +14:10:18 | 2.101 | 1.742 | 28.8 | 18.60 $\pm$ 0.10 | 2.066 | 2.451
2020-07-09 10:56 | 00:22:59.0 | +14:11:41 | 2.103 | 1.732 | 28.7 | 18.60 $\pm$ 0.08 | 1.262 | 2.708
2020-07-10 09:17 | 00:23:52.1 | +14:12:40 | 2.105 | 1.723 | 28.6 | 18.52 $\pm$ 0.09 | 1.81 | 1.847
2020-07-17 10:05 | 00:29:55.6 | +14:13:52 | 2.120 | 1.657 | 27.9 | 18.53 $\pm$ 0.05 | 1.331 | 1.536
2020-07-19 09:20 | 00:31:25.3 | +14:12:06 | 2.124 | 1.639 | 27.7 | 18.56 $\pm$ 0.05 | 1.515 | 1.901
2020-07-20 11:26 | 00:32:12.3 | +14:10:43 | 2.127 | 1.628 | 27.5 | 18.43 $\pm$ 0.04 | 1.11 | 1.861
2020-07-20 11:30 | 00:32:12.4 | +14:10:43 | 2.127 | 1.628 | 27.5 | 18.52 $\pm$ 0.05 | 1.105 | 1.969
2020-07-23 11:03 | 00:34:12.6 | +14:05:21 | 2.133 | 1.601 | 27.1 | 18.36 $\pm$ 0.04 | 1.125 | 1.776
2020-07-25 11:56 | 00:35:26.9 | +14:00:20 | 2.138 | 1.582 | 26.7 | 18.42 $\pm$ 0.07 | 1.076 | 1.506
2020-07-26 11:06 | 00:36:00.0 | +13:57:33 | 2.140 | 1.574 | 26.6 | 18.38 $\pm$ 0.05 | 1.106 | 1.520
2020-07-26 11:35 | 00:36:00.6 | +13:57:29 | 2.140 | 1.573 | 26.6 | 18.31 $\pm$ 0.04 | 1.082 | 1.534
2020-07-29 11:02 | 00:37:33.1 | +13:47:16 | 2.146 | 1.547 | 26.0 | 18.38 $\pm$ 0.05 | 1.098 | 1.763
2020-08-02 08:51 | 00:39:12.9 | +13:29:57 | 2.155 | 1.513 | 25.1 | 18.26 $\pm$ 0.08 | 1.377 | 2.476
2020-08-02 09:58 | 00:39:13.8 | +13:29:43 | 2.155 | 1.512 | 25.1 | 18.19 $\pm$ 0.06 | 1.168 | 1.837
2020-08-03 08:59 | 00:39:34.4 | +13:24:46 | 2.157 | 1.504 | 24.9 | 18.20 $\pm$ 0.08 | 1.33 | 2.256
2020-08-04 09:58 | 00:39:54.8 | +13:19:04 | 2.160 | 1.495 | 24.6 | 18.17 $\pm$ 0.09 | 1.153 | 2.016
2020-08-05 11:04 | 00:40:13.4 | +13:13:01 | 2.162 | 1.486 | 24.4 | 18.21 $\pm$ 0.07 | 1.078 | 1.596
2020-08-11 11:31 | 00:41:24.0 | +12:31:26 | 2.175 | 1.438 | 22.7 | 18.15 $\pm$ 0.04 | 1.082 | 1.670
2020-08-11 11:46 | 00:41:24.0 | +12:31:21 | 2.175 | 1.437 | 22.7 | 18.09 $\pm$ 0.04 | 1.092 | 1.840
2020-08-12 11:34 | 00:41:29.5 | +12:23:22 | 2.178 | 1.430 | 22.4 | 18.10 $\pm$ 0.04 | 1.087 | 1.463
2020-08-13 10:19 | 00:41:33.2 | +12:15:26 | 2.180 | 1.423 | 22.0 | 18.05 $\pm$ 0.24 | 1.085 | 1.361
2020-08-14 11:06 | 00:41:35.1 | +12:06:27 | 2.182 | 1.415 | 21.7 | 18.12 $\pm$ 0.04 | 1.077 | 1.436
2020-08-14 11:39 | 00:41:35.1 | +12:06:15 | 2.182 | 1.415 | 21.7 | 18.07 $\pm$ 0.04 | 1.096 | 1.521
2020-08-15 09:49 | 00:41:35.4 | +11:57:55 | 2.184 | 1.408 | 21.4 | 18.24 $\pm$ 0.16 | 1.104 | 1.612
2020-08-18 09:37 | 00:41:25.2 | +11:28:55 | 2.191 | 1.387 | 20.3 | 18.00 $\pm$ 0.04 | 1.104 | 1.912
2020-08-20 09:38 | 00:41:09.4 | +11:07:50 | 2.195 | 1.373 | 19.6 | 17.95 $\pm$ 0.04 | 1.096 | 2.111
2020-08-20 10:05 | 00:41:09.2 | +11:07:38 | 2.195 | 1.373 | 19.6 | 17.93 $\pm$ 0.04 | 1.078 | 1.776
2020-08-23 11:39 | 00:40:31.0 | +10:32:42 | 2.202 | 1.354 | 18.3 | 17.86 $\pm$ 0.04 | 1.143 | 1.828
2020-08-25 08:49 | 00:39:59.9 | +10:09:44 | 2.206 | 1.342 | 17.5 | 17.92 $\pm$ 0.04 | 1.131 | 1.716
2020-08-26 09:03 | 00:39:40.5 | +09:56:56 | 2.209 | 1.337 | 17.1 | 17.86 $\pm$ 0.05 | 1.107 | 2.218
2020-08-27 09:29 | 00:39:19.3 | +09:43:41 | 2.211 | 1.331 | 16.7 | 17.88 $\pm$ 0.04 | 1.082 | 1.510
2020-09-02 09:11 | 00:36:41.5 | +08:19:24 | 2.224 | 1.303 | 13.9 | 17.76 $\pm$ 0.11 | 1.079 | 1.499
2020-09-02 09:32 | 00:36:41.0 | +08:19:10 | 2.224 | 1.303 | 13.8 | 17.65 $\pm$ 0.11 | 1.142 | 1.998
2020-09-06 08:04 | 00:34:28.6 | +07:18:12 | 2.233 | 1.288 | 11.9 | 17.64 $\pm$ 0.06 | 1.179 | 1.839
2020-09-12 09:28 | 00:30:27.4 | +05:37:19 | 2.247 | 1.273 | 8.6 | 17.49 $\pm$ 0.05 | 1.162 | 1.998
2020-09-12 10:21 | 00:30:25.8 | +05:36:41 | 2.247 | 1.273 | 8.6 | 17.53 $\pm$ 0.05 | 1.248 | 1.954
2020-09-18 08:41 | 00:25:56.9 | +03:51:55 | 2.260 | 1.267 | 5.3 | 17.35 $\pm$ 0.03 | 1.144 | 2.073
2020-09-20 09:39 | 00:24:19.3 | +03:15:05 | 2.264 | 1.268 | 4.1 | 17.30 $\pm$ 0.03 | 1.226 | 1.548
2020-09-21 07:17 | 00:23:36.0 | +02:58:44 | 2.266 | 1.268 | 3.6 | 17.26 $\pm$ 0.03 | 1.164 | 1.785
2020-09-21 07:34 | 00:23:35.4 | +02:58:32 | 2.266 | 1.268 | 3.6 | 17.27 $\pm$ 0.03 | 1.15 | 2.031
2020-09-23 07:54 | 00:21:57.3 | +02:21:58 | 2.271 | 1.270 | 2.4 | 17.17 $\pm$ 0.03 | 1.139 | 1.996
2020-09-26 06:20 | 00:19:33.9 | +01:28:48 | 2.277 | 1.275 | 0.8 | 17.07 $\pm$ 0.03 | 1.22 | 1.520
2020-09-27 09:09 | 00:18:39.1 | +01:08:41 | 2.280 | 1.278 | 0.4 | 16.96 $\pm$ 0.03 | 1.22 | 1.612
2020-10-04 07:07 | 00:13:10.5 | -00:52:54 | 2.295 | 1.302 | 3.8 | 17.39 $\pm$ 0.05 | 1.233 | 1.894
2020-10-06 06:03 | 00:11:42.3 | -01:25:55 | 2.300 | 1.311 | 4.9 | 17.42 $\pm$ 0.05 | 1.265 | 1.621
2020-10-08 06:07 | 00:10:14.9 | -01:58:53 | 2.304 | 1.321 | 6.0 | 17.48 $\pm$ 0.03 | 1.252 | 1.853
2020-10-12 07:07 | 00:07:29.7 | -03:02:29 | 2.313 | 1.346 | 8.0 | 17.62 $\pm$ 0.04 | 1.252 | 2.267
2020-10-14 07:09 | 00:06:14.4 | -03:32:21 | 2.317 | 1.360 | 9.0 | 17.67 $\pm$ 0.03 | 1.262 | 1.848
Table 4: *