THE EXTRAORDINARY MULTI-TAILED MAIN-BELT COMET P/2013 P5

For photometry of the nucleus, we used apertures 5 pixels (02) and 25 pixels (10) in radius, with sky subtraction determined from the median signal computed within a contiguous annulus having outer radius 50 pixels (20). We used the HST exposure time calculator to convert the measured count rate into an effective V magnitude, finding that a V = 0 G2V source gives a count rate of 4.72 ×10¹⁰ s⁻¹ within a 02 radius photometry aperture. The results are summarized in Table 2.

The smaller aperture gives our best estimate of the nucleus brightness. We examined the six images from each orbit individually to search for temporal variation that might result from rotation of an irregular nucleus. No such variation was observed on either date, consistent with a nucleus rotation period that is long compared to the ∼40 minute observing window per HST orbit, or a rotation axis that is close to the line of sight, or both. The mean apparent magnitudes on September 10 (V = 20.92 ± 0.01) and 23 (21.01 ± 0.01), are very similar, given that the observing geometry changed between the two dates of observation (Table 1).

We compute the absolute magnitude (i.e., corrected to unit heliocentric and geocentric distances, and to zero phase angle) using the inverse square law and an assumed phase function from Bowell et al. (1989). We use a phase function parameter g = 0.25, consistent with an S-type asteroid spectral classification, since most inner-belt asteroids are S-types. The phase corrections on September 10 and September 23 are −0.37 and −0.59 mag, respectively. If we had instead assumed g = 0.15, corresponding to the phase function of a C-type asteroid, the corrections would have been −0.42 and −0.67 mag. Our lack of knowledge of the phase function renders the derived absolute magnitudes uncertain by 0.05–0.1 mag. Regardless, the estimated values H_V = 18.69 (September 10) and 18.54 (September 23) are very close. The 0.15 mag brightening in H_V could be due to rotational variation of an elongated nucleus between the two dates, to phase function uncertainties or to an increase in the amount of near-nucleus dust. There is no evidence for fading that might be expected if the dust were ejected impulsively before the first observation.

The absolute magnitude is related to the effective nucleus radius, r_n (in km), and to the geometric albedo, p_V, by

$$\begin{equation} r_n = \frac{690}{p_V^{1/2}}10^{-H_V/5}, \end{equation} \tag{ 1 }$$

where p_V is the V-band geometric albedo. The orbit of P5 is close to the Flora asteroid family (the family center lies near (a, e, i) = (2.254, 0.141, 5.5)). The mean geometric albedo of Flora family members is p_V = 0.29 ± 0.09 (Masiero et al. 2013), which we take as the albedo of P5 pending a future measurement. Substitution into Equation (1) then gives r_n = 0.24 ± 0.04 km, where the uncertainty reflects only the ∼30% uncertainty in p_V. The Floras are thought to be a principal source of near-Earth asteroids and meteorites, and a particular association with the LL chondrites has been claimed (Nesvorný et al. 2002; Dunn et al. 2013). The average mean density of LL chondrites is ρ_LL = 3300 ± 200 kg m⁻³ (Consolmagno et al. 2008; Wilkison & Robinson 2000). With this density and radius, the approximate gravitational escape speed from the nucleus is V_e = 0.3 m s⁻¹. Strictly, both r_n and V_e are upper limits to the true values, since even the small aperture photometry must include some near-nucleus dust contamination for which we have made no correction.

The position angles of the tails are summarized in Table 3, together with best estimates of their uncertainties based on repeated measurements at different positions along the tails. Tail A changed least between the visits, in terms of its direction, length and brightness. The tail A position angle is closest to, but significantly different from, the projected orbital velocity vector, marked -V in the figure. This observation suggests that A contains larger, slower, possibly older particles than those in the other tails. Tails B, C and D splay apart between September 10 and 23, and also fade in surface brightness. Their large angular motion is presumably related to the ∼36° change in the projected antisolar position angle, θ_☉ (Table 1), but the tails rotate by larger angles and are not antisolar. The fading might suggest dissipation of the tails under the action of radiation pressure. While B, C and D fade, tail E grows in length and brightens between the two visits suggesting that fresh material is being supplied to it.

We calculated the positions of particles of a wide range of sizes and released over a wide range of dates, assuming that the initial velocity of the particles is negligible compared to the combined action of solar radiation pressure and gravity (Finson & Probstein 1968). All particles ejected at a given time lie on a straight line emerging from the nucleus (a synchrone), the orientation of which (described by the position angle) is diagnostic of the date of ejection. For any given observation date, there is a unique relation between position angle and ejection time. We find, for a given tail, an excellent agreement between the ejection date derived from the observations on September 10 and the ejection date derived from the September 23 data (Figure 2 and Table 3). This result shows that the individual tails follow synchrones and that splaying of the tails between the two panels of Figure 1 is caused by projection effects, not by evolutionary changes in the tails. The synchrone models indeed show that tail A is the oldest, with ejection on April 15 ± 2. The youngest is tail E, with ejection occurring only days before the September 10 observation. We speculate that the ejection of bright tail D on August 8 may have been responsible for the discovery of P5 on August 18. From the lengths of the tails and their best-fit synchrone ages, we estimate particle sizes up to ∼10 μm to ∼100 μm, with the largest particles being those in tail A.

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The complicated morphology and low surface brightness of P5 make photometry of the dust very difficult. We used large circular apertures 40 and 60 in radius, with sky subtraction from a surrounding annulus extending to 120, to measure the integrated light from the dust. The principal uncertainties on the large aperture magnitudes are systematic and difficult to quantify, but are at least several tenths of a magnitude. The total magnitudes (Table 2) provide an estimate of the total dust cross-section in P5. On both dates, ΔV = V_0.2 − V_6.0 ∼ 2.8 mag, showing no relative fading between the two. If the dust in the tail has the same albedo and phase function as the nucleus, then the dust cross-section can be estimated from C_d = $\pi r_n^2 10^{0.4\Delta V}$. We find C_d = 2.7 ± 0.4 km².

The total dust mass, M_d, and cross-section of an optically thin assemblage of spherical particles are related by $M_d = 4/3 \rho \overline{a} C_d$, where ρ is the material density and $\overline{a}$ is the cross-section weighted mean grain size. With mean grain size $\overline{a}$ = 10 to 100 μm and density ρ = 3300 kg m⁻³, for instance, the dust mass implied by C_d is M_d ∼ 10⁵ to 10⁶ kg, about 10⁻⁴ to 10⁻³ of the mass of the nucleus, assuming the same density.