Episodically Active Asteroid 6478 Gault

We used the 2.56 m diameter Nordic Optical Telescope (NOT), located on La Palma, the Canary Islands, and the Andalucia Faint Object Spectrograph and Camera (ALFOSC) optical camera. ALFOSC is equipped with a 2048 × 2064 pixel "e2v Technologies" charge-coupled device, giving an image scale of 0214 pixel⁻¹, and a vignette-limited field of view approximately 65 × 65. Broadband Bessel B (central wavelength λ_c = 4400 Å, FWHM Δλ = 1000 Å), V (λ_c = 5300 Å, Δλ = 800 Å), and R (λ_c = 6500 Å, Δλ = 1300 Å) filters were used. The NOT was tracked at non-sidereal rates to follow Gault, while autoguiding using field stars. We obtained a series of images each of 70 s integration during which time field objects trailed by ∼001 on UT 2019 January 10 but by ∼09 on UT 2019 February 21 and ∼06 on UT 2019 April 10. The images were first bias subtracted and then normalized by a flat-field image constructed from images of the illuminated interior of the observatory dome. Photometric calibration of the data was obtained by reference to standard star PG 0918 + 029A (Landolt 1992). Measurements of field stars show that the atmosphere was photometric to ≲0.01 mag. The field stars were also used to measure the extinction, found to be 0.18, 0.12, and 0.06 mag per airmass in the B, V, and R filters, respectively. Seeing was variable in the range 10 FWHM to 13 FWHM. NOT data from UT 2019 February 21 suffered from strong internal scattering due to moonlight, but this was largely removed in the processing of the data.

Additional observations were taken on UT 2019 March 4 at the 3.5 m diameter WIYN telescope, located at Kitt Peak National Observatory in Arizona (see Table 1). We used the One Degree Imager camera mounted at the Nasmyth focus with a rebinned image scale of 0.25 pixel⁻¹ (Harbeck et al. 2014). Observations were taken through the Sloan r' (central wavelength λ_c = 6250 Å, FWHM = 1400 Å) filter with an accumulated integration of 6300 s (180 s individual integration time). Median seeing was 11 FWHM. For data reduction we used the "Quickreduce" pipeline (Kotulla 2014), and photometric calibration of the data was made with reference to the Sloan DR 14 database (Blanton et al. 2017).

We also used publicly accessible observations from the Hubble Space Telescope (HST; GO 15678, PI: Meech) taken on UT 2019 February 5. These consist of five images per visit, with 380 s exposures acquired through the F350 LP broadband filter (central wavelength 6230 Å, FWHM = 4758 Å) using the WFC3 camera. The pixel size was 004 pixel⁻¹. The images were shifted to a common center and median combined to eliminate cosmic rays to produce a composite image that was used for all measurements. Unfortunately, the nucleus of Gault is saturated in the HST data, which therefore cannot be used to study the near-nucleus environment at high resolution. Here, we use the HST composites only to measure the tail position angles (PAs), as recorded in Table 1.

Table 1.  Observing Geometry

UT Date	UT	Tela	Modeb	DOYc	νd	rHe	Δf	αg	θ−⊙h	θ−Vi	δEj	PAAk	PABk	PACk
2019 Jan 10	02:04–05:12	NOT	BVR	10	238.8	2.466	1.833	20.4	304.4	269.8	11.6	291.0 ± 0.5	⋯	⋯
2019 Jan 20	02:11–02:53	NOT	Sp	20	241.3	2.446	1.713	18.4	309.2	270.3	11.6	292.0 ± 1.0	301.0 ± 1.0	⋯
2019 Feb 05	15:08–15:45	HST	F350LP	36	245.2	2.413	1.537	13.4	322.0	271.5	10.6	294.0 ± 0.5	306.0 ± 0.5	⋯
2019 Feb 21	00:27–01:44	NOT	BVR	52	249.3	2.382	1.429	8.2	350.5	272.5	8.2	293.5 ± 0.5	309.6 ± 0.7	⋯
2019 Feb 27	16:17–16:51	HST	F350LP	58	250.9	2.368	1.402	6.9	15.4	272.7	6.7	292.9 ± 0.5	311.2 ± 0.5	⋯
2019 Mar 03	04:43–07:17	WIYN	r'	62	252.2	2.360	1.392	6.7	31.7	272.7	5.9	291.1 ± 0.5	312.5 ± 0.5	⋯
2019 Mar 22	10:53–11:29	HST	F350LP	81	257.1	2.319	1.401	12.4	88.4	271.5	0.70	275.0 ± 0.5	298 ± 2	⋯
2019 Mar 24	00:16–01:21	NOT	R	83	257.6	2.315	1.406	13.0	90.3	271.3	0.26	271.6 ± 0.2	⋯	⋯
2019 Apr 9–10	23:31–00:36	NOT	R	100	262.3	2.278	1.495	19.5	103.0	268.9	−4.0	239 ± 1	151 ± 1	116 ± 1

Notes.

^aNOT = NOT 2.5 m, HST = Hubble Space Telescope 2.6 m, WIYN = 3.5 m. ^bBVR = imaging at 0214 pixel⁻¹, Sp = spectrum, F350LP; see the text. ^cDay of year number, 1 = UT 2019 January 1. ^dTrue anomaly, in degrees. ^eHeliocentric distance, in astronomical unit. ^fGeocentric distance, in astronomical unit. ^gPhase angle, in degrees. ^hPosition angle of projected antisolar direction, in degrees. ⁱPosition angle of negative projected orbit vector, in degrees. ^jAngle of Earth above orbital plane, in degrees. ^kPosition angles of Tails A, B, and C.

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A composite image from UT 2019 January 10, formed by shifting the R-band images of combined exposure time 6790 s to a common center, is shown in Figure 1. The asteroid shows a single, prominent tail ("Tail A") at position angle PA = 2910 ± 05 that is aligned with neither the antisolar direction nor the projected negative heliocentric velocity vector. A single image taken in the process of recording a spectrum on UT 2019 January 20 (see Section 2.4) showed this same tail (PA = 292° ± 1°) plus a second, stubby tail at PA = 301° ± 1°. This second, stubby tail ("Tail B") is better recorded in NOT images from UT 2019 February 21 (Figure 2) and WIYN on UT 2019 March 3 (Figure 3). These later images show that the second tail is shorter and brighter than the first, resulting from more recent ejection of dust. By UT 2019 March 24 (Figure 4), when the Earth passed through the projected orbital plane of Gault, Tails A and B were merged. Observations on UT 2019 April 10 from δ_E = −4° below the plane show Tails A and B widely splayed, and the emergence of new Tail C (Figure 5).

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We searched for evidence of dust between Tails A and B by making plots of the surface brightness perpendicular to the midline between the tails, using the high signal-to-noise ratio image from UT 2019 March 3 (Figure 3). The search is compromised by ultra-faint field galaxies whose trails are aligned roughly parallel to the tail midline, and no Gault-associated dust could be detected.

Time-series measurements of the apparent magnitude of the near-nucleus region, m_V, were obtained from UT 2019 January 10, the data with the longest timebase. We used circular apertures with angular radii 10, 15, and 20 pixels (21, 32 and 43, respectively), with sky subtraction from a contiguous annulus having an outer radius 84. Calibration against field and Landolt stars was made using the same apertures. We used measurements of nearby field stars, obtained with the same photometric apertures, to assess variable atmospheric extinction as the airmass varied in the range 1.3–1.8 over the 3 hr of observation.

In Figure 6 we show a sample photometric time-series measured at ∼2 minute cadence on UT 2019 January 10. In a phase dispersion minimization analysis of the data, we find no evidence for cyclic (rotational) brightness variation at the ∼1% level or larger. The same invariance of the photometry is observed using the 21 and 31 apertures. This is in agreement with the findings of Moreno et al. (2019) and Ye et al. (2019). Kleyna et al. (2019) report evidence for a ∼1 hr periodogram peak in longer time-series from several telescopes. However, they find no convincing light curve, perhaps because of the influence of systematic uncertainties in the data, and/or weak and transient activity. The lack of a measurable light curve is consistent with Gault having a shape that is close to azimuthally symmetric, or a rotation vector parallel to the line of sight, or with the scattering cross section being dominated by dust.

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To address this latter possibility, we computed the absolute magnitude from our data to compare with the absolute magnitude recorded in the JPL Horizons online database. The apparent magnitudes, m_V, and absolute magnitudes, H, are related by the inverse square law

$$\begin{eqnarray}&&H={m}_{V}-2.5{\mathrm{log}}_{10}\left({r}_{H}^{2}{{\rm{\Delta }}}^{2}\right)+2.5{\mathrm{log}}_{10}({\rm{\Phi }}(\alpha ))\end{eqnarray} \tag{ 1 }$$

where r_H and Δ are the heliocentric and geocentric distances expressed in astronomical unit and Φ(α) ≤ 1 is the phase function measured at phase angle α. Equation (1) defines the absolute magnitude, H, as the magnitude the comet would have if it could be observed from r_H = Δ = 1 au and α = 0°. The relevant phase function for Gault is uncertain. For simplicity, we assume $2.5{\mathrm{log}}_{10}({\rm{\Phi }}(\alpha ))=-0.04\alpha$.

We further relate the absolute magnitudes to the effective scattering cross sections, C_e, by

$$\begin{eqnarray}&&{C}_{e}=\displaystyle \frac{1.5\times {10}^{6}}{{p}_{V}}{10}^{-0.4H}\end{eqnarray} \tag{ 2 }$$

where p_V is the geometric albedo. The effective albedo of Gault, consisting of a mixture of light scattered from the nucleus and light scattered from dust, is uncertain. We here assume a nominal albedo p_V = 0.1, while acknowledging that the true value may be larger or smaller by a factor of several.

The catalog value of the absolute magnitude of Gault is H = 14.4 (JPL Horizons software). This is close to the absolute magnitude in NOT data from UT 2019 February 21, but 0.7 mag fainter than H determined on UT 2019 January 10 (Table 2). Through Equation (2), this difference corresponds to ∼20 km² excess in the near-nucleus cross section on January 10. This estimate is uncertain, however, by an amount that depends on the unknown phase function (and also on the unknown accuracy of the catalog absolute magnitude).

Table 2.  Circular Aperture Color Photometry

UT Date	Radiusa	V	Hb	$B-V$	$V-R$	$B-R$
2019 Jan 10	4.3	17.82 ± 0.02	13.73	0.78 ± 0.03	0.40 ± 0.03	1.18 ± 0.03
2019 Feb 21	4.3	17.61 ± 0.02	14.62	0.75 ± 0.03	0.41 ± 0.03	1.16 ± 0.03
Sunc	⋯	⋯	⋯	0.64 ± 0.02	0.35 ± 0.01	1.00 ± 0.02

Notes.

^aAngular radius of circular photometry aperture, in arcseconds. ^bAbsolute magnitude, from Equation (1). The uncertainty is dominated by the unmeasured phase function and is of order several ×0.1 mag. ^cColors of the Sun from Holmberg et al. (2006).

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The apparent magnitudes and effective cross sections of dust tails A and B are best measured in the high signal-to-noise data from UT 2019 March 3 (Table 1). We again rotated the composite image to bring each tail to the horizontal, then measured the signal within projected rectangular boxes aligned with each tail. On Tail A we used a box extending 70'' along the tail and 10'' perpendicular, while for the shorter Tail B, these dimensions were 50'' and 10'', respectively. The sky background was determined from the clipped median signal in a series of adjacent regions. As the visible tails are longer than the measurable tails, it is clear that the results provide lower limits to the true brightness and cross section of the ejected dust. The integrated brightness of Tail A is equivalent to V_A = 15.2 ± 0.2 and of Tail B, V_B = 17.2 ± 0.3, where the errors reflect the difficulty of measuring low surface brightness diffuse structures against structured backgrounds. These correspond, through Equation (1), to H_A = 12.3 ± 0.2 and H_B = 14.3 ± 0.3 (neglecting additional uncertainties due to the unmeasured phase function). The effective cross sections (Equation (2)) are C_A = 175 ± 35 km² and C_B = 28 ± 9 km². Only very crude photometry of Tail C is possible, because it has extremely low surface brightness. We estimate V_C = 19.7 ± 0.7, H_C = 16.8 ± 0.7, and C_C = 3 ± 2 km² from the image on UT 2019 April 10. For comparison, the geometric cross section of a 3 km radius sphere is 28 km².

If contained entirely in spherical particles of density, ρ, and radius, $\overline{a}$, the dust mass is given by ${M}_{d}\sim \rho \overline{a}{C}_{e}$. For example, with ρ = 1000 kg m⁻³, $\overline{a}=0.2$ mm, the implied dust masses are M_A ∼ 4 × 10⁷ kg, M_B ∼ 6 × 10⁶ kg, and M_B ∼ 6 × 10⁵ kg, respectively. Taking the event lifetimes for all three tails as 10–20 days, we infer approximate mass production rates dM_A/dt ∼ 20–40 kg s⁻¹, dM_B/dt ∼ 4–6 kg s⁻¹, and dM_C/dt ∼ 0.4–0.6 kg s⁻¹.

We obtained three pairs of BV measurements on UT 2019 January 10 and two pairs on UT 2019 February 21, in order to determine the optical colors of Gault. Measurements of $B-V$ and $V-R$ using circular apertures centered on the photocenter are summarized in Table 2. Essentially identical central colors are obtained on the two dates, with mean values $B-V$ = 0.77 ± 0.02 and $V-R$ = 0.41 ± 0.02, which are redder than the Sun by 0.12 ± 0.02 and 0.06 ± 0.02 mag, respectively.

As noted above, the cross section in the data from UT 2019 January 10 is dominated by dust, while by UT 2019 February 21 the cross section is within ∼20% of the value obtained from the JPL Horizons database (which presumably represents Gault in an inactive state). The fact that the colors remain unchanged even as the scattering cross section changes from dust-dominated to nucleus-dominated is evidence that the colors of the nucleus and the dust are similar. To directly measure the color of the dust free from contamination by the nucleus, we rotated the composite image from UT 2019 January 10 (Figure 1) to bring the tail to the horizontal, then measured the signal within projected rectangular apertures, with results summarized in Table 3. In the central or nucleus region, we obtained colors that are consistent with those from circular aperture photometry (Table 2). The colors of the dust in Tail boxes A1 and A2 are consistent with those in the central region within the uncertainties of measurement (Table 3), showing that the data provide no evidence for spatial variation of color along the tail of Gault. Tables 2 and 3 show that the color of Gault is stable with respect to time and position.

Table 3.  Rectangular Aperture Color Photometry^a

Regionb	xmin, xmax	ymin, ymax	V	$B-V$	$V-R$	$B-R$
Nucleus	−2.2, 2.2	−2.2, 2.2	17.88 ± 0.01	0.78 ± 0.01	0.40 ± 0.01	1.18 ± 0.01
Tail A	2.2, 44.9	−2.2, 2.2	20.51 ± 0.02	0.77 ± 0.08	0.42 ± 0.05	1.19 ± 0.09
Tail A	44.9, 87.9	−2.2, 2.2	20.94 ± 0.03	0.81 ± 0.10	0.52 ± 0.08	1.33 ± 0.11
Sunc	⋯	⋯	⋯	0.64 ± 0.02	0.35 ± 0.01	1.00 ± 0.02

Notes.

^aAll data from UT 2019 January 10. ^bRectangle defined by ${x}_{\min }\leqslant x^{\prime\prime} \leqslant {x}_{\max }$, ${y}_{\min }\,\leqslant y^{\prime\prime} \leqslant {y}_{\max }$, with the nucleus at x'' = y'' = 0, and x increasing along the tail to the west. ^cColors of the Sun from Holmberg et al. (2006).

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The colors of Gault are compared with those of other asteroid spectral types from Dandy et al. (2003) in Figure 7. Gault is optically too blue to be an S-type, and is closer to the less-metamorphosed members of the C-type complex. While this makes Gault slightly unusual relative to other members of the Phocaea family, 75% of which are S-types, Carvano et al. (2001) reported that 15% of Phocaea family members are C-types. Separately, Novaković et al. (2017) identified a low-albedo family within the Phocaea group that we tentatively associate with the C-types.

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The optical reflection spectrum of Gault was obtained on UT 2019 January 20, again at the NOT. We used a 1'' wide slit with Grism #3, which is ruled at 400 line mm⁻¹ and gives a dispersion 2.3 Å pixel⁻¹. The resulting spectral resolution λ/Δλ ∼ 350. Two integrations of 1200 s each were obtained, together with a 5 s integration on the V = 7.8 mag, G2V solar analog star HIP 53172. The asteroid and the star were observed at comparable airmasses of 1.46–1.54 (Gault) and 1.52 (star), respectively, in order to cancel both telluric and solar spectral features. The atmospheric seeing was 08–09, FWHM.

We extracted the spectrum using a 43 wide region centered on the peak brightness of the continuum. After flattening the data using a near-simultaneous spectrum of a quartz lamp, and wavelength calibration using emission lines from an internal HeNe source, the comet and solar analog spectra were divided to produce a reflectivity spectrum. Finally, we removed the slope of the spectrum using a least-squares fit, and normalized the result to unity at λ = 5500 Å (Figure 8). We calibrated the continuum using the measured V-band (central wavelength λ_c = 5500 Å) magnitude, V = 17.82, and the fact that a V = 0 star has flux density f_λ = 3.75 × 10⁻⁹ erg cm⁻² s⁻¹ Å⁻¹ (Drilling & Landolt 2000). We estimate that the mean V-band continuum flux density of Gault is f_V = 2.8 × 10⁻¹⁶ erg cm⁻² s⁻¹ Å⁻¹.

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Active comets exhibit several emission bands due to resonance fluorescence in cometary gas. The strongest bands in the optical are from OH (3080 Å) and CN (3883 Å), neither of which fall within the sensitive range of the NOT spectrograph. The strongest band in the 4000–7000 Å range is from C₂ ΔV = 0, which is largely confined to the range of wavelengths 5050 Å ≤ λ ≤ 5220 Å (see Farnham et al. 2000). The spectrum of Gault shows no evidence for emission bands at any wavelength. We define adjacent continuum windows of equal width both blueward (4880 Å ≤ λ ≤ 5049 Å, called "B_C") and redward (5221 Å ≤ λ ≤ 5390 Å, "R_C") of the C₂ band in order to assess the noise on the data. These wavelength bands are indicated in Figure 8. Expressed as a fraction of the continuum, the statistical uncertainties are found to be ±0.013, ±0.010, and ±0.013 in the B_C, C₂ ΔV, and R_C bands, respectively. We take the largest of these values, namely 1σ = 0.013, as the best estimate of the fractional uncertainty on the continuum in the C₂ ΔV-band. Then, 3σ corresponds to a flux density f_C2 = 0.039f_V = 6.5 × 10⁻¹⁸ erg cm⁻² s⁻¹ Å⁻¹ (where we have included a correction of 0.6 for slit losses) and this is our empirical upper limit to the gas flux density. Over the Δλ = 170 Å width of the C₂ ΔV-band, the 3σ limit to the flux is F = f_C2Δλ ≤ 1.1 × 10⁻¹⁵ (erg cm⁻² s⁻¹).

Provided that the coma is optically thin, the number of C₂ molecules projected within the slit, N, is directly proportional to F, following

$$\begin{eqnarray}&&N=\displaystyle \frac{4\pi {{\rm{\Delta }}}^{2}F}{g({r}_{H})}.\end{eqnarray} \tag{ 3 }$$

Here, g(r_H) is the fluorescence efficiency factor of the C₂ ΔV = 0 band at heliocentric distance r_H au. We take g(1) = 2.2 × 10⁻¹³ erg s⁻¹ radical⁻¹ (A'Hearn 1982) and scale to the heliocentric distance of Gault by the inverse square law, finding g(2.446) = 3.7 × 10⁻¹⁴ erg s⁻¹ radical⁻¹. Substituting into Equation (3) gives N ≤ 4 × 10²⁶ as the 3σ upper limit to the number of C₂ radicals in the projected 10 × 43 slit.

To scale from N to the production rate of C₂ we need a model to estimate the fraction of the C₂ coma captured within the projected slit. Following cometary tradition, and while recognizing the flaws and uncertainties of the procedure, we use the Haser model formalism, in which the distribution of the radical is assumed to be described by two exponentials with scale lengths characterizing the "parent" and the "daughter" species. We use scale lengths at r_H = 1 au of L_P = 2.5 × 10⁴ km and L_D = 1.2 × 10⁵ km (Cochran 1985), and scale to the heliocentric distance of Gault using ${L}_{P,D}({r}_{H})={L}_{P,D}(1){r}_{H}^{2}$. The speed of outflowing gas molecules, needed to estimate the residence time in the projected slit, was taken to be 0.5 km s⁻¹.

Finally, we find that the non-detection of the C₂ ΔV = 0 band corresponds to a production rate Q_C2 ≤ 1 × 10²³ s⁻¹. In comets, the median ratio of C₂ to hydroxyl production rates is C₂/OH = 10^−2.5, albeit with a tail extending to values as low as 10⁻⁴ (A'Hearn et al. 1995). The median value would give a spectroscopic limit on the OH production rate limit Q_OH ≤ 3 × 10²⁵ s⁻¹ and mass loss rates in water of dM/dt ≤ 1 kg s⁻¹. This limit is comparable to values set spectroscopically on active asteroids (e.g., Jewitt 2012), smaller than the dust production rates inferred in Section 2.2, and 10² to 10³ times smaller than commonly measured in short-period comets. At r_H = 2.446 au, a perfectly absorbing water-ice surface oriented perpendicular to the Sun-Gault line would sublimate in thermodynamic equilibrium at the specific rate f_s = 5.6 × 10⁻⁵ kg m⁻² s⁻¹. The empirical spectroscopic limit then sets a limit to the area of exposed ice f_s⁻¹ dM/dt ≤ 18,000 m² (0.02 km²).

The PAs of the tails (Table 1) are plotted as functions of time in Figure 9. Lines in the figure show the PAs of synchrones computed for a range of dates for each tail. For Tail A, the synchrones span the period UT 2018 October 5 to November 14, with an interval of 10 days. For Tail B, the synchrones span UT 2018 December 19 to 2019 January 3, with an interval of 5 days. Evidently, the PAs of the Gault tails are inconsistent with any single isochrone, but compatible with isochrones for dust emitted over discrete ranges of dates. The middle times for the isochrone models of Tails A and B are UT 2018 October 30 and UT 2018 December 28, respectively, each with an uncertainty of a few days. Results for Tail C (not plotted in Figure 9) are less certain, both because the tail is very faint and difficult to measure and because we so far possess only one measurement from UT 2019 April 10. Our best estimate of the initiation date is UT 2019 February 10 ± 7.

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These results imply that Tail A was ∼72 days old when imaged on UT 2019 January 10 (Figure 1) while Tail B was ∼23 days old when first recorded in the image from UT 2019 January 20 (inset to Figure 1). Tail A extends to the edge of the field of view in Figure 1, an angular distance of 250''. At geocentric distance Δ = 1.83 au (Table 1) this corresponds to a linear distance ℓ = 3.3 × 10⁸ m in the plane of the sky. Particles released from the nucleus with zero initial velocity and accelerated thereafter by radiation pressure would travel a distance ℓ = βg_⊙(1) (Δt)²/(2r_H²), where r_H is the heliocentric distance expressed in astronomical units and g_⊙(1) = 0.006 m s⁻² is the gravitational acceleration to the Sun at r_H = 1 au. Δt is the time since ejection; we set Δt = 72 days (6.2 × 10⁶ s). Dimensionless quantity β is the ratio of the acceleration due to radiation pressure to the acceleration due to solar gravity, and is a function of the particle shape, porosity, density, and composition but, most importantly, of size (Bohren & Huffman 1983). These parameters are unknown for Gault. For convenience, we assume that β = 10⁻⁶/a, with a in meters, which is true for grains of density ρ = 570 kg m⁻³. Substituting, we find β = 0.02, corresponding to a ∼ 50 μm. Because the tail is unlikely to lie in the plane of the sky, ℓ must be considered a lower limit to the true length, and so β ≳ 0.02 and a ≲ 50 μm. (For example, on UT 2019 January 10, the phase angle was α = 20° (Table 1). If the tail were aligned with the antisolar direction, the actual length would be larger than the plane-of-sky length by a factor $1/\sin (\alpha )\sim 3$, giving β three times larger and a three times smaller than our nominal estimate). Larger particles lurk closer to the nucleus. For example, 25'' down the tail the particle size suggested by radiation pressure acceleration is a ∼ 500 μm. The same argument applied to Tail B, which has plane-of-sky length ∼15'' on UT 2019 January 20 (Figure 1), gives ℓ ≳ 2.0 × 10⁷ m and β ≳ 0.1, and a ≲ 10 μm. These order of magnitude considerations indicate that the particles ejected from Gault are all very large compared to the wavelength of light. We estimate a mean particle radius in Tail A $\overline{a}$ ∼ 100 μm.

Figure 4 shows Gault on UT 2019 March 24, from a perspective only δ_E = 026 above the orbital plane. With this viewing geometry, the effects of projection are minimized, although not eliminated, and we obtain a measure of the extent of the dust tail that is perpendicular to the plane of the orbit. Notice that Tails A and B appear merged, indicating that they both lie close to the orbital plane of Gault. To measure the FWHM, θ_1/2, we rotated the image to bring the dust tail to the horizontal and then made a series of vertical cuts across the tail, each 100 pixel (215) wide. The results are shown in Figure 10. The width increases slowly with distance from the nucleus. At its narrowest, ∼25,000 km from the nucleus, we find θ_1/2 = 29 ± 03, corresponding to 3000 ± 300 km. The tail is broad compared to the θ = 10 FWHM seeing in the Figure 4 image composite, indicating that it is fully resolved. To test this, we also measured the higher resolution HST data taken UT 2019 March 22 from a larger angle (δ_E = 07, Table 1) finding a similar width (θ_1/2 = 28 ±03).

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We use θ_1/2 to make a simple estimate of the dust ejection velocity from Gault. Given that this location samples primarily Tail A, which was ejected on UT 2018 October 28, we infer that the dust age is Δt = 1.2 × 10⁷ s. The half-width then gives an estimate of the ejection speed perpendicular to the orbit as V_⊥ = θ_1/2/(2Δt). Substituting, we find V_⊥ = 0.13 ± 0.01 m s⁻¹. This is an upper limit to the speed because the measured width in Figure 10 is potentially still affected by projection, even though the out-of-plane angle is only 026. The escape speed from a non-rotating 3 km radius sphere of density ρ = 10³ kg m⁻³ is V_e ∼ 2 m s⁻¹. Escape with V_⊥ < V_e is consistent with rotation near breakup.

We separately used a Monte Carlo model (developed by Ishiguro et al. 2007) to estimate the dust properties. The advantage of the model is that it allows the influence of specific assumed dust parameters to be systematically explored. The disadvantage is that the number of relevant parameters is very large and the model is under-constrained by the data. We proceeded to adjust the model iteratively in order to test the sensitivity of the tail morphology to different dust and ejection parameters.

The motion of ejected particles is affected by their initial velocity, v₀, by their direction of ejection, and by the magnitude of radiation pressure factor β. The gross morphology of the tail is also influenced by the time profile of the emission. Inspection of the rising portions of the maxima in Figure 2 of Ye et al. (2019) shows that dust emission continued over 10–20 days for both Tails A and B. We parameterized the emission for each tail as an exponential, ${dM}/{dt}\propto \exp (-(t-{t}_{0})/\tau )$, where t₀ is the initiation time and τ is the e-folding time. We assumed that the velocity versus radius relation is of the form $v(a)={v}_{0}{a}^{-\gamma }$, with γ constant, and we tested two values; γ = 1/2 describes particle acceleration against gravity by gas drag, while γ = 0 describes size-independent ejection, as might be expected from rotational breakup. We could not find agreeable solutions using γ = 1/2 and, further motivated by the very slight measured flaring of the dust tail when viewed edgewise (Figure 10), adopted γ = 0 for all models. It is conventional to assume that the particles are distributed in size such that the number of particles with radius in the range a to a + da is n(a) da = Γ a^−q da, where Γ and q are constants. However, we found that acceptable fits to the data could not be obtained using this single power-law relation, regardless of the choice of q. Instead, we introduced a double power law to better fit the data.

For both tails A and B (Table 4), we found acceptable solutions for v₀ = 0.15 ± 0.05 m s⁻¹, which is in excellent agreement with our estimate (0.13 ± 0.01 m s⁻¹) based on analysis of the plane-crossing data. For Tail A, ejection started on t₀ = UT 2018 October 28 and had an e-folding time τ_A = 10 days. For Tail B we found t₀ = UT 2018 December 31 and fading time τ_B ∼ 5 days. For both tails, the size distribution in the range 40 ≤ a ≤ 120 μm has q = 3.0 ± 0.3, while for 120 ≤ a ≤ 5000 μm we find a steeper q = 4.2 ± 0.2. The overall similarity of the solutions suggests that the same physical process is responsible for the loss of material in Tails A and B. The cross-section weighted mean particle radius in this distribution is $\overline{a}=210$ μm, with an uncertainty that is at least a factor of two. We note that these parameters are broadly consistent with the isochrones in Figure 9. Initiation times for Tail A, UT 2018 October 18 ± 5, and Tail B, UT 2018 December 24 ± 1, deduced photometrically (Ye et al. 2019) are both slightly earlier than deduced from the dust tail model. The resulting image-plane models are shown in Figure 11.

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The size distribution found by Ye et al. (2019) is qualitatively similar to that found here, with q = 3.0 for 10 ≤ a ≤ 20 μm and q = 4.0 for larger particles. Moreno et al. (2019) reported three power-law segments with indices q = 2.28 (1 ≤ a ≤ 15 μm), 3.95 (15 ≤ a ≤ 870 μm), and 4.22 (a > 870 μm) and employed a v ∝ a^−γ relation with γ = 1/2, as appropriate for gas drag ejection (although they considered the presence of ice to be unlikely, as do we). A significantly flatter power-law index, q ∼ 1.6, was reported by Kleyna et al. (2019). However, the latter assumed a single power-law distribution from 10 to 10³ μm and did not specify their choice of γ. The models are broadly consistent in their identification of dominantly large particles ejected at speeds comparable to or less than the escape speed from Gault.

The active asteroid closest in semimajor axis to Gault is 354P/(2010 A2; see Figure 12), the photometric and morphological properties of which are all indicative of asteroid-asteroid impact (Jewitt et al. 2010, 2013b, Kim et al.2017a, 2017b). Other examples of likely impact-produced active asteroids are shown in Figure 12 as green-filled circles. However, we reject impact as a likely cause of mass loss in Gault for two reasons. First, both the PA data (Figure 9) and the photometry (Ye et al. 2019) indicate non-impulsive emission occurring over intervals of ∼10–20 days, whereas impact should be impulsive. Second, the existence of three widely spaced tails cannot be reconciled with a single impact in any but the most contrived way, and the probability of three consecutive impacts is negligible.

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Several examples of ice-sublimating active asteroids are known. However, these differ from Gault by ejecting dust smoothly near perihelion (true anomalies ν ∼ 0° ± 90°; see Hsieh et al. 2018) and do not show the discrete emission required to explain Tails A and B. Specifically, it is not obvious why exposed ice would sublimate in fortnight-long windows separated by intervals of months, and Gault is far from perihelion, with true anomaly 240°–260° (Table 1). In addition, the isothermal blackbody temperature in Gault's inner-belt orbit is 180 K, reducing (but, admittedly, not eliminating) the prospects that water ice could survive. Indeed, the best-established ice sublimators are located in the outer belt (filled blue circles in Figure 12), where temperatures are lower. For these reasons we reject ice sublimation as a likely cause of activity in Gault. We also note that the spectra show no evidence for gas (Figure 8), although our data are insensitive to emissions from the likely mass-dominant volatile H₂O.

The active asteroid second closest in semimajor axis to Gault in Figure 12 is 311P/(2013 P5). Figure 13 shows a comparison between these two objects. Object 311P ejected dust impulsively and aperiodically, producing nine separate tails spread over 9 months (Jewitt et al. 2013a, 2015, 2018), with about 10⁵ kg of dust per ejection. In between ejections, the nucleus of 311P appears to have been inactive, which is consistent with the interpretation that each tail formation event signifies the loss of surface fines following local instabilities ("landslides") on a critically rotating body (Jewitt et al. 2013a, Hirabayashi et al. 2015). Although Gault (so far) has only three tails, the morphological similarity to 311P is striking, leading us to suspect that Tails A, B, and C are products of incipient rotational instability on a rapidly rotating nucleus. One potentially important difference is that 311P is very small, with an estimated radius ∼190 ± 30 m (Jewitt et al. 2018), whereas Gault is ∼15 times larger (and ∼3500 times more massive), with equivalent circular radius ∼2.9 km (from Equation (2) with H = 14.4 and p_V = 0.1). Assuming that neither body contains ice, the torque needed to accelerate the spin presumably comes from solar photons and the Yarkovsky–O'Keefe–Radzievskii–Paddack (YORP) effect. The YORP spin-up timescale, all else being equal, is proportional to radius². Gault would take 15² ∼ 225 times longer to reach critical spin than would 311P. The YORP time for 311P is only ∼0.1 Myr (Jewitt et al. 2018), corresponding to 22 Myr when scaled to the size of asteroid Gault. This longer timescale is still short compared to the collisional destruction timescale, which for a 3 km radius main-belt body is ∼10⁹ yr (Bottke et al. 2005). We conclude that YORP spin-up is capable of driving Gault to incipient rotational instability.

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It is interesting to consider the relative amounts of material shed by 311P and Gault. A tail mass M, if spread uniformly over the parent body of radius r_n, would have a thickness, d, given by $d=M/(4\pi \rho {r}_{n}^{2})$. Substituting, for M_A and M_B, we find d_A = 0.4 mm and d_B = 0.06 mm, respectively. For comparison, on 311P (with r_n = 0.29 km; Jewitt et al. 2018) the 10⁵ kg ejected per event corresponds to d ∼ 0.2 mm, which is surprisingly similar to the Gault value. In other words, the ejected mass scales roughly as r_n², as might be expected for a surface instability. The reason behind the long duration of mass loss in Gault (e-folding timescales of 5–10 days) is less clear. Our naive expectation is that mass would fall off the surface on the freefall timescale (Gρ)^−1/2 ∼ hours, rather than days, as observed. Numerical simulations perhaps provide a hint by showing that, contrary to intuition, unstable systems can survive for days and even years before collisional dissipation and secondary spin fission can lead to the final state (e.g., Boldrin et al. 2016).

Sadly, photometry to date provides no convincing evidence concerning rotation, presumably in part because of the diluting effects of near-nucleus dust. However, a test for rotational instability should become possible through the acquisition of a rotational light curve once the near-nucleus dust has cleared. If the hypothesis is correct, we should find that Gault is rotating near the ∼0.1 day critical period for instability (e.g., Pravec et al. 2008). It will probably have a very small light curve amplitude, as a result of the "muffin-top" morphology observed by radar and by direct imaging in several asteroids likely to have been shaped by rotational losses. The identification of additional discrete tails, either in prediscovery data or in observations yet to be made, or both, would further strengthen the resemblance to the nine-tailed 311P.