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

Active asteroids produce comet-like tails and comae that can be driven by many different types of forces different from the comets themselves (Jewitt et al. 2015). While sublimation of water ice is a primary driver for activity in "typical" comets, the ∼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.

The main belt asteroid (6478) Gault (1998 JC₁; "Gault" hereafter) has been the subject of wide interest since the discovery in early 2019 of a comet-tail-like extended emission (Smith et al. 2019). Eventually, three tails were noted in 2019 January (Jewitt et al. 2019b; Ye et al. 2019) 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 et al. 2019; Ye et al. 2019) due to its rotation being spun up by the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect (Bottke 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 Jewitt et al. (2019b) indeed 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 hr, Carbognani & Buzzoni (2020) suggest 3.34 hr, Ferrín et al. (2019) have 3.36 hr, and Kleyna et al. (2019) suggest ∼2 hr. 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 as the signal noise. It should also be noted that others (e.g., Moreno 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 data sets 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 Section 2, we describe the observations from 2019 and 2020. In Section 3, we present the photometry, and in Section 4, we discuss Gault's behavior, spin state, and shape, and summarize the article.

For our analysis, we 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; Bellm et al. 2019; Graham 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 1 to 2020 October 14. All data in this work have been flat- and bias-corrected because only CCDs were used. Tables 1 and 2 list the technical details of each telescope and the particulars about each observing run, respectively, while Tables 3 and 4 are the photometric data plotted for this work and the archival ZTF survey, respectively. We describe below each telescope facility used in our work.

Table 2. Observations of Gault Producing Photometric Lightcurves

Date (UTC) (1)	Telescope (2)	R.A. (3)	Decl. (4)	r (au) (5)	Δ (au) (6)	α (°) (7)	Filter (8)	θs ('') (9)
2019 Jan 8	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

Note. Columns: (1) date of observation, (2) telescope, (3) right ascension at the start of the observation, (4) declination at the start of the observation, (5) heliocentric distance at the start of the observation, (6) geocentric distance at the start of the observation, (7) phase angle at the start of the observation, (8) filter, and (9) in-image seeing at the start of the observation.

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2.1. Mount Laguna Observatory 1.0 m Telescope

2.2. Lulin One-meter Telescope

2.3. Astrophysics Research Consortium 3.5 m Telescope

Between 2019 January 8 UT and 2019 June 6 UT, we observed Gault over six campaigns with the Astrophysics Research Consortium 3.5 m Telescope (ARC) at the Apache Point Observatory before the asteroid headed into solar conjunction (Table 2). Individual observations created lightcurves spanning between 1 hr (2019 March 24 UT) and 4 hr (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 18. Throughout 2019 January and February, Gault remained visibly active, while observations between 2019 March and June displayed just a remnant tail (see Figures 1 and 5).

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2.4. Palomar Observatory 200 inch Telescope

2.5. Zwicky Transient Facility Using the Palomar 48 inch Telescope

2.6. GROWTH-India Telescope

2.7. GROWTH Coordinated Observations

3.1. Active and Inactive States of Gault

Follow-up observations with the ARC 3.5 m telescope at the Apache Point Observatory on 2019 February 25 UT showed evidence for multiple tails. A deep-stack image consisting of 4680 s of exposure is shown on the left side of Figure 1. The surface brightness of Gault in this stack is 24.0 mag arcsec⁻² within a 10,000 km radius aperture. The right side of Figure 1 shows Gault's third tail in a 4320 s deep-stack image from the ARC 3.5 m telescope on 2019 April 26 UT, and the 10,000 km surface brightness was calculated to be 23.8 mag arcsec⁻².

The images were combined in deep, median stacks centered on Gault and then used to compute the calibrated r-band photometry from comparisons to 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 arcsec⁻² found when it was inactive in 2020 June by Purdum et al. (2020). Our deep-stack image taken by P200 in the r band is shown in Figure 2, which lacks cometary features and has a surface brightness of 26.3 mag arcsec⁻², also dimmer than the surface brightnesses from early 2019.

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3.2. Secular Photometry and Updated Absolute Magnitude

Figure 3 shows Gault's reduced-magnitude phase curve from ZTF data taken between 2020 April 2 UT to 2020 October 14 UT. The reduced-magnitude data is described by $r\,-5\,{\mathrm{log}}_{10}(R{\rm{\Delta }}),$ where R and Δ 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

$$\begin{eqnarray}&&r-5\,{\mathrm{log}}_{10}(R{\rm{\Delta }})=H-2.5\,{\mathrm{log}}_{10}\left[(1-G){{\rm{\Phi }}}_{1}(\alpha )+G\,{{\rm{\Phi }}}_{2}(\alpha )\right],\end{eqnarray} \tag{ 1 }$$

where r is the r-band magnitude of Gault taken with a 5'' radius aperture, α is the phase angle of the asteroid at the time of mid-exposure, and Φ₁ and Φ₂ are two basis functions normalized at unity for α = 0° (Bowell et al. 1989; Muinonen et al. 2010; Pravec et al. 2012).

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These best-fit parameters are H_r = 14.631 ± 0.019 and G_r = 0.207 ± 0.020 after the asteroid had exited solar conjunction and was no longer active. This is significantly fainter than the value of 14.31 ± 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. The lack of a large lightcurve amplitude for Gault discussed below implies that the detection of Gault at the limiting magnitude of the survey at the limits of the phase curve was due to the viewing geometry of Gault rather than rotational variations in its brightness (Jedicke et al. 2016). 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'' radius aperture photometry.

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Figure 4 shows the time-series r-band ZTF photometry between 2020 June and October. Gault exited solar conjunction and was observed between 2020 April 2 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 ± 0.019 and phase function slope value G = 0.207 ± 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 1 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. 2020b, 2021).

3.3. Time-series Lightcurves

While Gault was active in 2019, the ARC 3.5 m 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.

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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 2020 August, with the longest single lightcurve of 19 hr on 2020 September 21 UT. The results are displayed in Figures 6 and 7.

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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 mag 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 contains arrows to indicate the small-amplitude, periodic peaks in the asteroid lightcurves based on multiples of 2.5 hr intervals from each other. Solid-colored arrows denote the primary peaks that represent a single rotation of the asteroid, while white arrows point to the half-period peaks at multiples of 1.25 hr from the primary peaks. Due to the minuscule 0.1 mag amplitude of the peaks, many of them are overcome by the noise in the photometry and therefore only a handful appear on each date. Figure 8 shows an example of phase-folded lightcurves from the GROWTH relay of observations on 2020 September 21 UT. Similar to Figures 6 and 7, the telescopes are color-coordinated, and their lightcurves are folded by the double-peaked 2.5 hr period. The MLO and LOT data are stacked in the bottom plot and display modest primary and secondary peaks caused by Gault's periodic rotation. Additional phase-folded lightcurves of each observation date in Figures 6 and 7 can be found in the Appendix.

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A Lomb–Scargle (Lomb 1976) periodogram was constructed from MLO and LOT data of Gault ranging from 2020 August to October and is shown along with a folded lightcurve of Gault in Figure 9. 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 Gault's lightcurve. The comparison stars we selected depended on the maximum frame width that we used through one run and on the similarity of the FWHM estimated between Gault and the chosen stars. By comparing the reference stars' lightcurves, 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 lightcurve data to find the most likely rotation period of Gault. The frequency analysis from the strong peak near ∼20 cycles day⁻¹ in the left panel of Figure 9 gives a rotation period of ∼1.25 hr, 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 ± 0.07 hr. The right panel of Figure 9 displays the lightcurve folded by the rotation period of 2.49 hr, which corresponds to a double-peaked lightcurve. The uncertainty here of ±0.07 hr 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 hr and a 1 − σ uncertainty estimate of 0.07 hr.

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The amplitudes 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 9. Here, the folded phase curves averaged by rebinning them in phase space with a bin size of 0.01 and coadded into an average, and the error bars are the 1σ scatter in data per phase bin.

The surface brightness profiles taken from deep-stacked images of Gault from the MLO 1.0 m 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 2018 October (Ye et al. 2019). The surface brightness measurements of 25.8 mag arcsec⁻² and 26.3 mag arcsec⁻², from MLO and Palomar, respectively, are fainter compared to the surface brightness values of Gault from the ARC 3.5 m Telescope on 2019 February 9 UT, had a measurement of 24 mag arcsec⁻² (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 service. ²⁶ The outbursts for Gault's first two tails were estimated to have occurred on 2018 October 18 ± 5 UT and 2018 December 24 ± 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) estimate it to be 2019 February 10 ± 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 from 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 realigns the photometry in Figure 4. This phenomenon can be attributed to the observing geometry of Gault changing throughout its orbit. The brighter absolute magnitude H_r during the ARC observations in 2019 (see Figure 4) could be due to pole-on observations, while observations during different viewing geometries would result in smaller absolute magnitudes in 2020. The JPL HORIZONS' ephemeris service shows the estimated ecliptic longitude of Gault during observations by Ye et al. (2019) in 2017 November was∼58° while our observations range from ∼3° to ∼5°.

Photometric lightcurve observations with the ARC 3.5 m 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 was 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 the near-Earth asteroids Ryugu and Bennu (Hirabayashi et al. 2020). It is also worth noting that the 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 2017 December (Taylor et al. 2019). At that time, Kim et al. (2018) found Phaethon's peak amplitude was small, ∼0.1 mag, 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 hr and placed arrows in Figures 6 and 7 to indicate the estimations. Some secondary peaks occurred at 1.25 hr intervals from the primary peaks due to the asteroid's geometry displaying a double-peaked lightcurve. Several peaks in the Gault lightcurves show little to no variation in the reference star lightcurve (see August 24, September 21, 23, October 20 in Figures 6 and 7), which is an indication that the peaks are nonanomalous and are a result of the rotation of the asteroid. The periodogram in Figure 9 shows Gault has a rotation period of 2.49 ± 0.07 hr, assuming the frequency of ∼20 cycles day⁻¹ (∼1.25 hr) corresponds to a double-peaked lightcurve. Figures 8 and 11–19 in the Appendix show the lightcurves for our observations spanning 2020 August 14 UT to 2020 October 20 UT (see Figures 6 and 7) folded by a period of 2.5 hr. The stronger primary peak and a fainter secondary peak of Gault's double-peak lightcurve are denoted with arrows, and each figure shows the lightcurves stacked by date. An rms calculation was made for each phase-folded lightcurve as a reference for the noise amplitude when looking at the primary and secondary bumps. Some dates show the peaks clearly, while others do not, due to observation quality. Because the single-peak period of 1.25 hr from our Lomb–Scargle periodogram is physical for an asteroid of Gault's geometry, we only display the double-peak phase-folded lightcurves.

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 and b/c ∼ 1.3 given its maximum possible lightcurve amplitude of ∼0.1–0.3, as seen in our data and the data from Kleyna et al. (2019) ²⁷ and the relation between b/a and lightcurve amplitude of b/a = 10^0.4ΔM from Binzel et al. (1989). It should be noted that the axial ratio inferred from the observed lightcurve amplitude can be affected by the angle between the spin pole and the observer (Vokrouhlický et al. 2017; Hanuš et al. 2018); however, the consistently small lightcurve amplitude from different viewing geometries in the 2019 and 2020 apparitions seems to favor a smaller axial ratio. The critical breakup period of a strengthless ellipsoid as a function of axial ratio is given by Jewitt et al. (2017a) as

$$\begin{eqnarray}&&{P}_{\mathrm{crit}}=\left(\displaystyle \frac{b}{a}\right){\left[\displaystyle \frac{3\pi }{G\rho }\right]}^{1/2},\end{eqnarray} \tag{ 2 }$$

where ρ 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 cm⁻³ (Marsset et al. 2019; Sanchez et al. 2019), consistent with other S-type asteroids (Carry 2012). Figure 10 presents the critical period with which Gault would start shedding surface material as a function of the axial ratio and density. An orange box labeled in Figure 10 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 hr 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 (Ferrín et al. 2019; Jewitt et al. 2019b; Kleyna 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 reorientation of the spin of a ∼4 km asteroid by nondestructive 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 (e.g., Jewitt et al. 2017b; Moreno et al. 2017). Scheeres (2015) theorizes that the surface of an asteroid after YORP spin-up can be "perched" and ready for failure in multiple areas, which can cause multiple epochs of activity similar to active asteroid P/2013 P5 (Jewitt et al. 2013; Hainaut et al. 2014). We believe Gault could have had multiple epochs of activity after an initial YORP spin-up despite losing angular momentum from ejected particles.

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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, 2020a), which are held together by cohesive forces (Sánchez & Scheeres 2014). However, it should be noted that examples of kilometer-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. Because Gault is 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 m 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 m 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 by rapid rotation at its critical period of 2.5 hr.

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 US 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 No. 80NSSC19K0780.

C.F. gratefully acknowledges the support of his research by the Heising-Simons Foundation (# 2018-0907).

M.C. acknowledges support from the National Science Foundation with grant No. 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 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. The 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). The 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.

Facilities: 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. -

Software: Astropy (Astropy Collaboration et al. 2013, 2018), ZChecker (Kelley et al. 2019), Aperture Photometry Tool (Laher et al. 2012).

Figures 11–19 below display additional phase-folded lightcurves of Gault based on the lightcurves in Figures 6 and 7.

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