Active Asteroid 311P/PanSTARRS: Rotational Instability as the Origin of its Multitails?

It was conventionally considered that comets and asteroids are different types of small solar system bodies (Jewitt & Hsieh 2022). In recent years, however, the discoveries of active asteroids have blurred the boundary line between asteroids and comets. Active asteroids usually exhibit detectable mass loss in confined segments of their orbits. More than 40 known active asteroids have been discovered at the time of this writing. There are several different physical mechanisms to explain such mass-loss activity, including water sublimation (e.g., 1 Ceres; Küppers et al. 2014; and 288P; Agarwal et al. 2017), impact ejecta (e.g., 354P/LINEAR; Kleyna et al. 2013; Kim et al. 2017), P/2016 G1 (Moreno et al. 2016), rotational instability (e.g., 331P/Gibbs; Drahus et al. 2015; and P/2013 R3 Jewitt et al. 2014), and thermal effects (e.g., 3200 Phaethon' Jewitt et al. 2013c). Activated asteroids display comet-like tails which consist of a large number of dust grains emitted from the nucleus. The information about mass-loss mechanisms and the physical properties of dust particles could be inferred by analyzing the dust tails of active asteroids.

In this paper, we focus on the active asteroid 311P (also known as P/2013 P5), which is an interesting target for space exploration. The orbital parameters of 311P (collected from the JPL Small-Body Database) are as follows: semimajor axis a = 2.189 au, eccentricity e = 0.116, and inclination i = 4968, yielding a Jupiter Tisserand parameter T_J = 3.66. 311P was discovered on 2013 August 18 by the Pan-STARRS1 telescope (Bolin et al. 2013). In follow-up observations using the Hubble Space Telescope (HST), it was found that 311P generated multiple comet-like tails, suggesting multiple outbursts occurred in early 2013 (Jewitt et al. 2013a, 2015). Rotational disruption (Jewitt et al. 2015) or rubbing of binary components (Hainaut et al. 2014) is the most likely driving mechanism for 311P's activities. The observations by Jewitt et al. (2018) strongly suggest that 311P is a binary system, which implies that the activities of 311P may be caused by rubbing of the binary components.

The absolute magnitude of the active asteroid 311P measured by Jewitt et al. (2018) with the HST is H _V = 19.14 ± 0.02, and the photometry of its nucleus implies that the radius of 311P is r_e = (0.19 ± 0.03) km. The lower limit of the rotation period of 311P is about 5.4 hr, which is derived from the light curve of 311P observed by the HST (Jewitt et al. 2018). Hainaut et al. (2014) estimated the peak times of the activities and total mass production around the activity peaks by analyzing images from the Canada–France–Hawaii Telescope (CFHT), the Perkins Telescope, the New Technology Telescope (NTT), and the TRAnsiting Planets and PlanetesImals Small Telescope (TRAPPIST)-South. Moreno et al. (2014) analyzed the observation images obtained by the HST as well as the Gran Telescopio CANARIAS (GTC), modeled a three month activity resulting from spin instability, and estimated the total dust mass, which is of the order of 10⁷ kg. Furthermore, Moreno et al. (2014) indicated that an isotropic ejection model does not fit 311P's activities based on the HST data. After estimating the initial time of each ejection, Jewitt et al. (2015) measured the total dust quantity around the nucleus, and obtained the upper and lower limits of grain sizes and the surface brightness profiles of the tails by analyzing data from the HST. Moreover, the activity mechanism of 311P was also discussed in Jewitt et al. (2015).

In this paper, we perform data reduction and reanalysis of the observational data from the HST program 13609 (PI: David Jewitt), which was previously analyzed by Jewitt et al. (2015). Our work provides new aspects on the activities and tails of 311P, which are shown as follows. The length of each tail at each observation epoch is obtained (Table 2). The upper limit of the duration of each emission activity (Table 3) is estimated by analyzing the widths of the tails. The number of dust particles of different grain radii (Figure 5) and the dust mass integrated along the radial distance of the tail from the nucleus (Figure 7) in each tail are determined by applying the Finson–Probstein theory to the surface photometry result. For most of the tails of 311P, we observed that (Figure 6) the dust size distributions are steeper for the tails with a larger average grain size, and their indices are close to that of the power-law distribution of self-organized critical sandpiles. We also discuss the effect of the tidal forces of planets (Figure 8(b)), which is ruled out as the origin of activity.

We also revisit some aspects that were previously addressed by Jewitt et al. (2015). We use the same method of fitting synchrones to the tails' position angles to derive the start times of ejections (Table 3), the results of which differ a bit from Jewitt et al. (2015) because we use the boundaries of the tails for fitting instead of the brightest lines. We estimate the minimum grain size in each tail by fitting the tails' boundaries with syndynes, the method of which is different from Jewitt et al. (2015) where the minimum grain size was determined from the tail's length, but leads to consistent results. We adopt the same method to obtain the tail's surface brightness profile (Figure 4) for each tail in all observed epochs, and our results are generally consistent with Jewitt et al. (2015) where the surface brightness profiles of certain selected tails were shown. Besides, we discuss and rule out the possibilities of sublimation (Figure 8(a)) and continuous impacts as activity mechanisms, and show that rotational instability remains a possible activation cause of 311P, which is consistent with Jewitt et al. (2015).

The forthcoming Chinese deep space mission Tianwen-2 (previously known as the ZhengHe mission) will explore 311P (Zhang et al. 2021), which is planned to be launched around 2025. On board the Tianwen-2 spacecraft there will be a dust analyzer, which is capable physically analyzing dust particles (Zhao et al. 2022). Research on the dust environment of 311P is helpful and important for science and mission planning of Tianwen-2.

The paper is organized as follows. Archival images and data reduction are described in Section 2. An analysis of the dust tail morphology using a syndyne–synchrone diagram is presented in Section 3. We analyze the surface brightness of the dust tails in Section 4. In Section 5, we estimate the total amount and the size distribution of dust contained in each tail. The possible activity mechanisms of 311P are discussed in Section 6. Finally, the conclusions of this paper are summarized in Section 7.

The observational data of 311P shown in this section cover a two year period, starting from 2013 August to 2015 July. We review the previous observational data of 311P from seven ground and space telescopes, including CFHT, TRAPPIST-South, NTT, the 1.23 m Calar Alto (CA1.23m) Telescope, GTC, HST, and Perkins. Table 1 summarizes the observing geometries of these observational data. It should be noted that only the data from the HST (Section 2.7) are used for the analysis in this manuscript.

2.1. CFHT

2.2. The Perkins Telescope

2.3. TRAPPIST-South

2.4. NTT

2.5. Calar Alto Telescope

2.6. GTC

2.7. HST

HST was used to observe 311P with Target-of-Opportunity time on 2013 September 10 and 23 (program number 13475, PI: David Jewitt; Jewitt et al. 2013a), 2013 October 18, 2013 November 13, 2013 December 8, 2013 December 31, and 2014 February 11 (program number 13609, PI: David Jewitt; Jewitt et al. 2015). During all observing epochs, a total exposure time of 1973 s was obtained with the 2K subarray of the WFC3 camera, which has a pixel scale of 004 pixel⁻¹ (Bouwens et al. 2010). Figure 1 shows the position of the Earth–Sun–311P in the ecliptic coordinate system ECLIPJ2000. 311P passed perihelion at a distance of 1.93 au on 2014 April 16, and all of the HST observations were made before perihelion.

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The publicly accessible observations of 311P are acquired from the Mikulski Archive for Space Telescopes (MAST; see details of MAST in Padovani 1998). Data reduction and frame adding are completed with the Astroart software (Nicolini et al. 2003).

It is known that 311P manifests unique cometary characteristics, i.e., a compact coma and several extended tails. In order to make a morphological analysis of 311P and estimate the quantity of the dust in the tails, the set of raw HST data (available on the MAST website https://archive.stsci.edu) is used in this paper. For each image, cosmic ray removal is done within the full raw image (Joye & Mandel 2003). Cleaned images are obtained by interpolating regions of each image affected by cosmic rays using the average pixel count from regions surrounding each cosmic ray (Bertin & Arnouts 1996). We stack the images from the seven epochs separately to increase the signal-to-noise ratio (S/N) of the dust tails, and also apply a median subtraction algorithm to highlight the features of the structures of the outer tail (Piccardi 2004). Meanwhile, we apply brightness contour fitting to improve the clarity of the tails, with the aim of determining the accurate position angles of the tails (Bertin & Arnouts 1996).

We identify the morphology of 311P's tails from the observational data. First, the boundary of each tail in the image whose features have been enhanced is roughly determined manually. After that, we evaluate the local S/N to get the details of general tail structure, with the local resolution set to 4 × 4 pixels. Combining the tails' contours in each image, we obtain three streamers representing the boundaries and the brightest line of each tail, as shown in Figure 2. Note that the dust tail looks very faint from the image observed on 2014 February 11, but we still identify a line whose S/N reaches a value of 5 over a length of 214 at a position angle of 66°. Finally, the position angles and the lengths of the tails are obtained by fitting the morphologies of the tails using contours. The measurements of the tails' features are listed in Table 2.

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The physical properties of the dust can be derived by analyzing the morphology of 311P. The epochs of ejections can be derived from the position angles of the tails, the size range of dust particles can be deduced from the length of a tail, and an upper limit of the duration of the activity can be estimated from the measurement of the widths of the tails. After leaving the nucleus, the particles are mainly subjected to solar radiation pressure and solar gravity. The forces acting on particles are parameterized with the dimensionless constant β

$$\begin{eqnarray}&&\beta =\frac{\mathrm{Radiation}\ \mathrm{Force}}{\mathrm{Solar}\ \mathrm{Gravity}},\end{eqnarray} \tag{ 1 }$$

which is further expressed as a parameter related to dust properties (Burns et al. 1979)

$$\begin{eqnarray}&&\beta =\displaystyle \frac{{C}_{\mathrm{pr}}{Q}_{\mathrm{pr}}}{{\rho }_{{\rm{d}}}a}.\end{eqnarray} \tag{ 2 }$$

Here, Q_pr is the scattering efficiency for solar radiation, and is assumed as 1. The variable ρ_d is the bulk density of dust in units of g cm⁻³, a is the particle radius in centimeters, and the constant C_pr = 5.76 × 10³ g cm⁻². The variable β is inversely proportional to a, so for smaller grains the effect of solar radiation pressure on the motion of particles is stronger.

No dust trail was detected within 40'' of the nucleus on 2015 March 19, which is different from the active asteroid 354P (P/2010 A2), whose trail dominated by centimeter-sized particles was still visible more than four years after a mass-loss event. The absence of a dust trail (Jewitt et al. 2013b, 2018) may imply that the activity mechanism of 311P is different from that of 354P.

The upper limit of the grain size can be roughly estimated by analyzing the equilibrium between solar radiation pressure and 311P's gravitational force. Particles larger than the upper limit of the grain size will drop back to 311P's surface (Hui & Li 2017). Assuming that 311P is a prolate spheroid, with a long-axis radius of b, and two equal short-axis radii of a, where the ratio of these axes is b/a = 1.3 (Jewitt et al. 2018), according to Equation (6) of Hui & Li (2017), the minimum value of β that corresponds to the largest dust particle is estimated as

$$\begin{eqnarray}&&{\beta }_{\min }=\displaystyle \frac{16\pi {cG}{\rho }_{{\rm{d}}}^{2}{R}^{2}{r}_{e}}{9\left(1+A\right){S}_{\odot }{f}^{3/2}}.\end{eqnarray} \tag{ 3 }$$

Here, c is the speed of light, G is the gravitational constant, r_e is the radius of the nucleus, ρ_d is the bulk density of the dust that is assumed to be 3.3 g cm⁻³, R is the heliocentric distance when 311P is active, A is the geometric albedo that is assumed to be 0.29 (Jewitt et al. 2015), f is the ratio of the axes, and S_☉ is the solar constant (1361 W m⁻²). We derive that the minimum value of β of ejected particles is about 0.0002, which corresponds to an upper limit of the grain size of 5 mm approximately.

We adopt the Finson–Probstein theory to analyze the dust tails (Finson & Probstein 1968). The Finson–Probstein theory proposes the concept of the syndyne–synchrone diagram. A syndyne represents the loci of particles with the same value of β, while a synchrone represents the loci of particles released at the same time. In this paper, the ejection speed is assumed to be zero. We first verify the validity of the assumption of the zero ejection speed by using Equation (6) of Agarwal et al. (2016)

$$\begin{eqnarray}&&\displaystyle \frac{E}{m}=\displaystyle \frac{{E}_{{\rm{n}}}}{{m}_{{\rm{n}}}}+{v}_{{\rm{n}}}{v}_{{\rm{ej}}}+\displaystyle \frac{1}{2}{v}_{{\rm{ej}}}^{2}+\displaystyle \frac{{{GM}}_{\odot }\beta }{R},\end{eqnarray} \tag{ 4 }$$

where the left side of the equation is the energy term of the particle, E is the particle's energy, and m is the particle's mass. The first item of the right side of the equation represents the energy per unit mass of 311P, E_n is 311P's energy, and m_n is the mass of 311P. The variable v_n is the speed of the nucleus, v_ej is the particle's relative velocity to 311P, G is the gravitational constant, M_⊙ is the mass of the Sun, and R is the heliocentric distance of 311P. The assumption of a zero ejection velocity is valid if the term v_n v_ej is negligible compared to the solar radiation pressure term $\tfrac{{{GM}}_{\odot }\beta }{R}$ by using Equation (7) of Agarwal et al. (2016), i.e.,

$$\begin{eqnarray}&&{v}_{\mathrm{ej}}\ll \beta \displaystyle \frac{{{GM}}_{\odot }}{{{Rv}}_{{\rm{n}}}}=\beta \,\times \,2.4\,\times \,{10}^{4}\,{\rm{m}}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 5 }$$

For 311P, v_n ∼ 1.9 × 10⁴ m s⁻¹ and R ∼ 2 au. For a minimum β of 0.0002 estimated by Equation (3), we obtain the minimum value of the right side of Equation (5) as 4.8 m s⁻¹. Thus, for dust particles with a radius less than 5 mm, if v_ej ≪ 4.8 m s⁻¹, the effect of the initial velocity on the evolution of particles is much smaller than that of solar radiation pressure, i.e., the zero ejection velocity assumption is valid. Later in this section, we will demonstrate that the majority of dust particles satisfy v_ej ≪ 4.8 m s⁻¹.

We estimate the point-spread function (PSF) of each image by measuring the FWHM of the field star trails, and find that PSF of each image is narrower than one-third of the FWHM of each tail of 311P. Thus, the straight-band morphology of 311P's tails from the observational data can be analyzed by using a syndyne–synchrone diagram (Finson & Probstein 1968; Vincent 2014). We also estimate the projected width caused by the initial speed, and find that this value is much smaller than the width of each tail at the observation epoch, which indicates that the effect of the initial speed on the projected width of the tail is negligible. Here we take Tail F for instance, which contains the smallest particles with the largest initial speeds among all tails (as shown later in Table 3 and Equation (6)). Assuming that the component of the initial velocity perpendicular to the orbital plane is equal to the one in the orbital plane, the distance traveled by the smallest particle of Tail F in the direction perpendicular to the orbital plane due to the initial speed estimated by Equation (6) during the time interval between emission and observation (2013 September 10) is about 58 km, which is much smaller than the FWHM (∼480 km) at its maximum length. Therefore, the upper limit of the duration of each activity can be estimated from the width of the tail by using the synchrone analysis.

The position of a dust grain relative to the nucleus depends on both the value of β and the difference between the observation epoch and release time (denoted as τ). To analyze the appearance of the dust tails, we plot a diagram of syndynes (loci of particles with constant β) and synchrones (loci of particles with constant τ) at various epochs in various dates of observations based on the Finson–Probstein model. In this diagram, the syndynes are calculated for β = 0.05, 0.02, 0.01, 0.005, 0.002, 0.001, 0.0005, 0.0002, 0.0001, 0.00005, 0.00002, and 0.00001, and each synchrone corresponds the trajectories of particles that were emitted simultaneously before each observation date with a step of 1 day. For better visualization, the more sparsely distributed syndynes and synchrones than what we use are shown in Figure 3.

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To determine the start epochs and end epochs of dust release and the value of β that can describe the dust tails, we fit syndyne–synchrone diagrams to the composite images, and select the syncurves which can best simulate the morphology of the tail. The epochs of dust emission and the size range of dust can be inferred by fitting the synchrones and the syndynes to the boundaries of the tails, respectively. For each tail, we fit all the observations at the different epochs with the syndyne–synchrone model. It is found that for the same tail the fitting results by using observations at different epochs are basically consistent with each other.

Inserting values of ρ_d = 3.3 × 10³ kg m⁻³ (Jewitt et al. 2015) to Equation (2), the particle radius a in microns is calculated by the formula by a = 1/β. The start and end times of the mass-loss events, and the size range of dust particles in each tail derived by the syncurve fitting process are summarized in Table 3. In the oldest Tail A, the size range of dust particles is roughly 2–40 mm, while the radius of the dust particles in the youngest Tail H is significantly smaller, ranging from about 0.025 to 0.6 mm. Note that the values of starting dates of emission are a bit different from the previous results of Jewitt et al. (2015). Possible reasons could be that the value of the S/N threshold used by us to define the boundaries of the dust tails is lower and the boundaries of the tails instead of the brightest line are used to fit the synchrones.

The ejection speed is estimated by the size-dependent velocity fitting formula from Moreno et al. (2014)

$$\begin{eqnarray}&&{v}_{\mathrm{ej}}=0.12{\beta }^{1/8}.\end{eqnarray} \tag{ 6 }$$

According to Table 3, the smallest grains are 0.006 mm (in Tail F), which gives a value of ${\beta }_{\max }$ as 0.016. Substituting ${\beta }_{\max }$ into Equation (6) yields an upper limit of the ejection speed of 0.09 m s⁻¹, the value of which satisfies Equation (5), which suggests that zero-velocity assumption is valid. Our estimation of the upper limit of the ejection speed (0.09 m s⁻¹) is generally consistent with that of Jewitt et al. (2015) (0.03 m s⁻¹).

We adopt the photometric method by Hsieh et al. (2004) to analyze the surface brightness profiles of all tails that appear in the images. For this purpose, composite images of different dates are rotated to align the tails with the horizontal direction, and then the radial profile of each tail is extracted. We use two different sizes of rectangular apertures to measure the brightness of the tails and the sky background. For the tails, the size of each aperture used to determine the brightness is set to 12 pixels along the tail axis and 24 pixels in the direction perpendicular to the tail axis. The sky background is measured with two apertures of size of 12 × 12 pixels located above and below the measured aperture of the tails, and then is subtracted from the tail images. An illustration of this scheme can be found in Figure 7 in Hsieh et al. (2004).

For each tail, we measure the tail surface brightness along the tail axis within 18'' (15,000–30,000 km) away from the nucleus. The tails' surface brightness profiles are measured in counts per aperture width along the length of the tails, integrated across the perpendicular direction, normalized to the geocentric distance of 1 au, and then further normalized to the ratio of the average count rate from the tail to that from 311P's nucleus, which is measured with a 5 × 5 pixel box. This procedure facilitates the comparison of the brightness profile of the same tail between different observation dates. The value of displayed uncertainty is originated from the rms variation measured in the sky background. The readers are referred to Section 4.1 of Hsieh et al. (2004) for details of this photometric method.

The radial brightness profiles of different tails for seven dates of observations are shown in Figure 4. It is seen that the change in intensity is not exactly proportional to the distance from the nucleus. We describe the characteristics of eight tails' brightness profiles shown in Figure 4 as follows.

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Tail A: the brightness distribution ∑(l) of the tail is described by a power-law function as ∑(l) ∝ l^s , where l is the angular distance along the tail from the nucleus in arcseconds as seen by the observer. On 2013 September 10 and 23, the brightness distribution of Tail A can be characterized by a shallow power-law function with index s = −0.25 ± 0.05. The exponent gradually reduced to 0 in the follow-up observations although the integrated brightness increased significantly on 2013 December 31. The peak of the curve at the radial distance of 9'' (12,000 km) on December 8 is produced by the incomplete removal of cosmic rays.

Tail B: detected on 2013 September 10 and 23. On 2013 September 10, the index s = −0.35 ± 0.07. The brightness profile of the dust tail became flatter and the integrated brightness decreased slightly on 2013 September 23.

Tail C: on 2013 September 10, the brightness profile of Tail C is similar to that of Tail B. On 2013 September 23, Tail C is difficult to distinguish from Tail B.

Tail D: at the first epoch of observation on 2013 September 10, the brightness followed a power-law distribution with a slope of about −0.5 within the measurable distance. On 2013 September 23, the brightness of the dust tail remained at a high level without obvious fluctuations.

Tail E: on September 10, the surface brightness followed a broken power-law distribution, i.e., the slope of the brightness profile was close to −1.58 ± 0.09 for the inner tail (1''–10''), while the slope was flatter (∼−0.4) for the outer tail. The bulge at 16'' (13,000 km) is attributed to a field star hidden under the tail. In the latter observation on September 23, it was found that the exponent s decreased to −1.81 ± 0.11 within a distance of 7'' (6000 km) from the nucleus.

Tail F: appeared only in the image observed on 2013 September 10.

Tail G: for Tail G, the slope of the brightness profile decreased with increasing distance from the nucleus, and the integrated brightness increased unusually from 2013 September 10 to 23. On 2013 November 13, Tail G was almost merged with Tail H.

Tail H: streamers with above-average S/Ns were detected in the direction of Tail G on 2013 November 13 and December 8 and 31. On November 13, the brightness profile satisfied a power-law distribution with index s = −0.81 ± 0.06 within a distance of 18'' (21,000 km) from the nucleus, and the slope reduced to −0.62 ± 0.04 on December 8 and −0.21 ± 0.02 on December 31. The integrated brightness of the dust tail showed a trend of gradual decrease with an increase of the observation epoch.

Usually, the brightness profile of a dust tail at a greater distances from the nucleus is flatter than that of the coma at a nearer distance to the nucleus (Rosenbush et al. 2017). Similarly, for all observing epochs of 311P, the brightness distribution of the outer tail was flatter than that of the inner tail. It is also found that our results are generally consistent with Figure 10 of Jewitt et al. (2015) where the surface brightness profiles of Tails D, E, G, and H at certain selected epochs were shown.

In this paper, the total dust mass of each tail is approximated as the dust mass within the region of 18'' (15,000–30,000 km) from the nucleus, where most dust particles of each tail are located. The dust quantity in the first observation of each tail could give the best approximation of the total dust mass compared to the later observations, because over time some dust particles are pushed away from the region (18'' relative to the nucleus) within which we calculate the dust mass. Besides, the S/N of the first observation is the highest (the error introduced by the sky background is the lowest). Thus, we choose the earliest observation for each tail to analyze. We have found that the value of the size distribution indices calculated by using the later observations are consistent with the one found by using the first observation.

In order to estimate the total mass of dust in each tail, we use a sequence of linear apertures perpendicular to the tail with a size of 1 × 24 pixels to evaluate the flux along the tail axis. By employing Equation (2) of Jewitt & Luu (2019), the effective scattering cross-section per pixel, C_e [km²], is related to the absolute magnitude of each pixel, by

$$\begin{eqnarray}&&{C}_{e}=\frac{1.5\times {10}^{6}}{A}{10}^{-0.4{H}_{\mathrm{pix}}},\end{eqnarray} \tag{ 7 }$$

where H_pix is the absolute magnitude of each pixel, which is derived from the heliocentric and geocentric distances, the phase angle, the photometric zero-point, and the flux in CCD ADUs per pixel.

We adopt the photometric method by Hainaut et al. (2012), which is summarized as follows. The total cross-sectional area of a single aperture is obtained by adding the contribution of each pixel in this aperture. The tails' brightness distribution as a function of the distance to the nucleus constitutes a "grain radius spectrum" of the dust, and the total cross-sectional area in each single aperture is converted to the number of dust grains at the given distance from the nucleus. Two assumptions (Hainaut et al. 2012) are made regarding the physical properties of the dust particles:

• 1.  
  Based on the Finson–Probstein model used in Section 3, the tails of 311P are considered as several collections of synchrones.
• 2.  
  All particles contained within a single aperture in the dust tails are assumed to be of the same grain size.

Following the above method, the number of particles for different grain radii in the eight tails are determined and shown in Figure 5. A power-law relation n(a)da ∝ a^q da is fitted to the distribution of the grain sizes of tails in Figure 5, leading to exponents of q = −2.29, −1.97, −1.88, −1.78, −1.57, −2.11, −1.45, and −1.67 for Tails A to H, respectively. We find that for all tails except Tail H, the dust size distributions are steeper for tails with a larger average grain size (Figure 6). Besides, the dust distribution profiles of 311P's tails are similar to those of the two tails of (6478) Gault, of which the dust size distribution indices are ∼−1.64 and ∼−1.70 in 2018, respectively (Kleyna et al. 2019).

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The mass of particles in the tails, which are obtained by integrating dust grains of each single aperture starting from the nucleus, are shown in Figure 7. It is seen that compared to the oldest Tail A, the total mass of the youngest Tail H is an order of magnitude smaller. From Figure 7 we estimate that 311P ejected at least 3 × 10⁷ kg of dust between 2013 March and October, and the total mass of ejecta is equivalent to a sphere with a radius of 13 m. Our estimation of the total mass is an order of magnitude larger than that of Jewitt et al. (2015). The main reason for this difference is that Jewitt et al. (2015) estimated the quantities of dust particles within a radius of 59 around the nucleus, while we estimate the total mass of dust grains populating all tails within 18'' around the nucleus. In other words, our estimation includes small- and medium-sized particles at further distances from the nucleus. It was estimated by Hainaut et al. (2014) that the total mass of dust for particles smaller than 1.5 mm is about 2.9 × 10⁷ kg, which agrees well with our results.

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Mass-loss rates are estimated by combining with the upper limit of the duration of each eruption in Section 3, which are 11.7 kg s⁻¹ for Tail A, 13.6 kg s⁻¹ for Tail B, 30.3 kg s⁻¹ for Tail C, 5.8 kg s⁻¹ for Tail D, 1.56 kg s⁻¹ for Tail E, 4.6 kg s⁻¹ for Tail F, 1.08 kg s⁻¹ for Tail G, and 6.6 kg s⁻¹ for Tail H, respectively.

In this section the possible activity mechanisms of 311P are discussed. We first examine the possibility of ice sublimation as the driving mechanism of 311P's activities. The surface temperature of a main-belt comet is associated with its orbital location (Snodgrass et al. 2017). Assuming the Sun as a blackbody, the equilibrium surface temperature of an asteroid is derived as

$$\begin{eqnarray}&&T={\left[(1-A)\frac{{r}_{\mathrm{Sun}}^{2}}{4{R}^{2}}\right]}^{\tfrac{1}{4}}{T}_{\mathrm{Sun}},\end{eqnarray} \tag{ 8 }$$

where r_Sun = 6.957 × 10⁸ m is the solar radius and T_Sun = 5777 K is the effective temperature of the Sun. From Equation (8) it is estimated that 311P experiences temperatures ranging from ∼162 K at aphelion to ∼186 K at perihelion. Consequently, the active asteroid 311P, located within 5 au from the Sun, is subjected to temperatures that are not low enough for water ice to form (Snodgrass et al. 2017; Chandler et al. 2019). Besides, Figure 8(a) shows the variations of the heliocentric distance and the surface temperature as functions of the true anomaly of 311P at the start time of emission, and it is found that the sequence of activity began near aphelion and ceased before perihelion, which is different from what is expected for sublimation-driven activity.

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We also examine the effects of the tidal force caused by Mars and Jupiter. A rough estimate of the tidal effect is obtained by the dimensionless parameter ε

$$\begin{eqnarray}&&\varepsilon =\frac{{F}_{{\rm{T}}}}{{F}_{{\rm{G}}}},\end{eqnarray} \tag{ 9 }$$

where F_T and F_G are the tidal force of the planet and the internal gravity of 311P at the surface of 311P, respectively. Figure 8(b) shows that at the start time of emission the strength of the tidal effect caused by Mars is only of the order of 10⁻² of that caused by Jupiter, and the effect of Jupiter's tidal force on 311P is only of the order of about 10⁻¹³ of the internal gravity of 311P. Thus, it is unlikely that 311P's activities are correlated with tidal forces caused by Jupiter and Mars.

Another possible driving mechanism is impacts. 311P had experienced multiple eruptions, and the likelihood of 311P being hit repeatedly within eight months is low. However, we cannot exclude the possibility that an initial impact-driven event on 311P destabilized the structure of the nucleus and triggered the subsequent activities.

It has been suggested by Jewitt et al. (2013a, 2015) that disruption due to rotational instability of the nucleus is a possible origin for the emission activities of 311P. There is no strong evidence against this activation process. Besides, the indices of the dust size distributions of the tails (Figure 6) are close to that of the power-law distributions of self-organized critical sandpiles (Laurson et al. 2005). We speculate that 311P may have been initially activated by rotational instability or impacts in 2013 March, and several avalanches of the dust distributed on the surface were triggered and part of the avalanched dust debris was eventually detached from the nucleus.

311P/PanSTARRS experienced several mass-loss events during 2013. To derive the dust environment around the nucleus, we analyze observational images of the dust tails of 311P obtained from MAST. The main conclusions of this paper are listed as follows:

• 1.  
  The position angles of 311P's tails ranged from 64° to 238°. The longest dust tail is Tail H observed on 2013 December 31, with a length of 414 (∼71,000 km). The shortest dust tail is Tail F observed on 2013 September 10, with a length of 182 (∼15,000 km).
• 2.  
  A syndyne–synchrone diagram analysis shows that the estimated upper limits of the durations of the mass-loss events ranged from 2 days (Tail F) to 8 days (Tail A). The upper limit of the grain radius that dominates the dust in tails is 38.9 mm and the corresponding lower limit is 6 μm.
• 3.  
  For all tails, the brightness profiles followed a power-law distribution with an index that ranged from approximately −1.81 to 0, and the size distribution indices ranged from −2.29 to −1.45. The masses of particles in the different tails ranged from 0.5 to 8 × 10⁶ kg, and the total mass of dust is m ∼ 3 × 10⁷ kg. The average mass-loss rate is approximately 1.59 kg s⁻¹.
• 4.  
  Analysis of the activities of 311P shows that the possibilities of sublimation, continuous impacts, or tidal forces of planets as the origin of the activities can be ruled out. Activation by rotational instability remains a possibility without strong evidence against it.

This work was supported by the National Natural Science Foundation of China (No. 12002397 and 12311530055), the National Key R&D Program of China (No. 2020YFC2201202 and 2020YFC2201101), grants from The Science and Technology Development Fund, Macau SAR (File No. 0051/2021/A1), and by the Shenzhen Science and Technology Program (grant No. ZDSYS20210623091808026). We thank Man-To Hui for helpful discussions and suggestions. We thank Yijun Zou for her productive suggestions. The data used in this work can be found in the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute via doi:10.17909/59gh-3310.

The data used in this work are generated as detailed in the text and will be shared on reasonable request to the corresponding author.