DISINTEGRATING ASTEROID P/2013 R3

Figure 1 shows three groups of objects (labeled A, B, and C) initially distributed along a line at position angle 40°, corresponding neither to the projected orbit nor to the anti-solar direction. This is unlike split comets, where the major components are spread along the projected orbit (Ishiguro et al. 2009; Reach et al. 2009) and the minor ones along the anti-solar direction (Weaver et al. 2001, 2008). The number of components (by December 13 we detect 10 distinct components, most formed by the disintegration of A and B), the sky-plane separations between them, L (scaled to 1 AU), and their brightnesses all change with time. We measured, L and dL/dt for the components taken pair-wise, and calculated nominal ages, τ = L/(dL/dt). The separations projected to zero over dates in the range 140 ⩽DOY ⩽ 270 (2013 May to September), where DOY is the day of year in 2013. One object (component "D") not shown in Figure 1 was detected 364 from component B in position angle 2419, on UT 2013 October 1. The object was also identified at 373 and 2390 in data from the Magellan telescope on UT October 29, kindly provided by Scott Sheppard and was reported in a press release by J. Licandro et al. The age for object D is τ ∼ 8 months (DOY 50). We consider these estimates preliminary pending acquisition of further astrometric data from which proper orbits and possible non-gravitational accelerations can be constrained.

The position angles of the dust tails (2437 ± 05 on October 1 and 2432 ± 06 October 28) correspond to discordant synchrone dates (September 4 ± 7 and July 10 ± 13, respectively).

Each discrete component appears embedded in a dust coma having steep surface brightness gradients in the central arcsecond. We experimented with schemes to inwardly extrapolate the coma surface brightness, in order to isolate the brightness contribution from the embedded nuclei. However, we found these schemes to be critically dependent on the extrapolation method, yielding highly uncertain results. Here, we elect to present robust upper limits to the embedded nuclei based on photometry obtained within circular projected apertures 02 in radius with background subtraction from a contiguous annulus extending to 04 (Table 2). Large aperture measurements were taken to assess the integrated dust cross-section.

Absolute magnitudes of the nuclei were computed from

$$\begin{equation} H_V = V - 2.5 \log _{10}[R^2 \Delta ^2] + 2.5 \log _{10}[\Phi (\alpha)]. \end{equation} \tag{ 1 }$$

Here, Φ(α), is the ratio of the brightness at phase angle α to that at phase angle 0°, estimated from Bowell et al. (1989). We used the phase function parameter g = 0.15 as applicable to C-type asteroids.

The absolute magnitudes are related to the geometric albedo, p_V, and the radius, r_e (km), of a circle having a scattering cross-section equal to that of the object by

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

We take p_V = 0.05 to compute effective radii as listed in Table 2. The largest components, A1, A2, B1, and B2, all have r_e ∼ 0.2 km. Because of dust contamination we only know that the nucleus radii are r_n ⩽ r_e and we cannot determine which, if any, of the components in R3 is the primary (mass-dominant) one. However, the photometric limits to r_n are sufficient to show that mutual gravitational interactions are negligible. The angular scale of the Hill sphere of a body having radius r_n is θ_H ∼ r_n/(3R_☉), where R_☉ is the radius of the Sun. With r_n = 200 m, we find θ_H ∼ 002 (∼20 km), which is beneath the resolution of HST. The components in Figure 1 can be safely assumed to move independently.

We used LRIS images and a photometry aperture 60 in radius to determine the global colors of the object on UT 2013 October 1. Photometric calibration was obtained from separate observations of nearby standard stars (Landolt 1992). We obtained B − V = 0.66 ± 0.04, V − R = 0.38 ± 0.03, and R − I = 0.36 ± 0.03 mag., while the solar colors in the same filters are B − V = 0.64 ± 0.02, V − R = 0.35 ± 0.01, and R − I = 0.33 ± 0.01 mag (Holmberg et al. 2006). Evidently, R3 is a neutral C-type object, as are ∼50% of asteroids beyond 3 AU (DeMeo & Carry 2013). Note that the scattering cross-section in our data is dominated by dust, not by the embedded parent nuclei.

We also used LRIS to obtain a spectrum of R3 on UT 2013 October 2, in search of gaseous emission bands. The cyanide radical (CN) band-head at 3888 Å (e.g., A'Hearn et al. 1995) is the brightest optical line in comets and is used here as a proxy for water. We obtained a 2000 s spectrum using a 10 wide slit, oriented along position angle 50° (the approximate tail axis) and a 400/3400 grism, obtaining a dispersion of 1.07 Å pixel⁻¹ and a wavelength resolution of 7 Å, FWHM. Wavelength calibration and spectral flat fields were obtained immediately following the R3 integrations. We also observed the G-type stars SA 115-271 and SA 93-101 for reference. The former star provided better cancellation of the H and K lines of calcium at 3933 Å and 3966 Å, and so we used this star to compute the reflectivity (Figure 2).

Zoom In Zoom Out Reset image size

We extracted the spectrum from a 39 long section of the slit. We determined a 3σ upper limit to the flux density from CN by fitting the flanking continuum (wavelengths 3780 Å to 3830 Å on the blue side and 3900 Å to 3950 Å on the red side) and taking into account the scatter in the data. The resulting upper limit to the flux density is f_CN = 1.3 × 10⁻¹⁶ erg cm⁻² s⁻¹.

To calculate the production rate, Q_CN, we adopted a Haser model with parent and daughter scale lengths ℓ_p = 1.3 × 10⁴ km and ℓ_s = 2.1 × 10⁵ km, respectively, both at R = 1 AU (A'Hearn et al. 1995) and a fluorescence efficiency at 1 AU, g(1) = 10^−12.5 (Schleicher 2010). We integrated the Haser model over the 10 × 39 slit, projected to the distance of the object, and assumed a gas outflow speed of 500 m s⁻¹. The non-detection of CN then corresponds to an upper limit Q_CN < 1.2 × 10²³ s⁻¹. The ratio of water to CN production rates in comets is $Q_{{\rm H_2O}}/Q_{{\rm CN}} \sim$ 360 (A'Hearn et al. 1995). If this ratio applies to R3, then we deduce $Q_{{\rm H_2O}} <$ 4.3 × 10²⁵ s⁻¹, corresponding to dM/dt < 1.2 kg s⁻¹. At R = 2.25 AU, a perfectly absorbing, spherical, dirty ice nucleus sublimating from the day-side would lose F_s ∼ 2 × 10⁻⁵ kg m⁻² s⁻¹, in equilibrium. The limit to the area of ice on the nucleus is A = (dM/dt)/F_s ∼ 6 × 10⁴ m², corresponding to a hemisphere of radius ∼100 m. However, the cometary ratio of $Q_{{\rm H_2O}}/Q_{{\rm CN}}$ might not apply to ice in a main-belt object and so the significance of the inferred $Q_{{\rm H_2O}}$ is unclear.

All images of R3 taken after October 1 show both a tail of months-old particles in the direction of the negative velocity vector (west of the nuclei), and tails of new material in the anti-solar direction (east). The simultaneous presence of tails in both directions is a strong indication that activity is ongoing (>2–3 months).

In order to study the distribution of the dust, we calculated synchrones (locations of particles ejected at constant time) and syndynes (locations of particles having fixed dimensionless radiation pressure factor, β) for each observation date (Finson & Probstein 1968). The position angles of the eastern tails of different fragments correspond to synchrone dates from late September to early October. The largest detectable value of β was 0.7, 0.02, and 0.007 at the three HST epochs, corresponding to radii of 1, 30, and 100 μm. The smallest of these particles were quickly removed by radiation pressure and therefore are not observed in the later images.

Each component of R3 resembles a typical active comet, with a roughly spherical coma being blown back by radiation pressure. This suggests that the initial velocity of the particles was not negligible and, therefore, that the Finson-Probstein approach is not strictly valid. The sunward extension of the largest coma (A2) was about s = 2000 km. Following Jewitt et al. (2011), we connect s, the turn-around distance in the sunward direction, to u, the initial sunward particle speed from

$$\begin{equation} u^2 = 2 \beta g_{\odot } s, \end{equation} \tag{ 3 }$$

where g_☉ is the gravitational acceleration toward the Sun. Substituting for g_☉, we obtain

$$\begin{equation} \beta = \frac{u^2 R^2}{2 G M_{\odot } s}, \end{equation} \tag{ 4 }$$

where G is the gravitational constant, R the heliocentric distance and M_☉ the mass of the Sun, which gives β = 2 × 10⁻⁴u². The characteristic travel time from the nucleus to the apex of motion is τ = 2s/u. Assuming that the observed dust is on average 2 months old (as inferred from the tail position angles), we obtain ejection speeds of u = 0.8  m s⁻¹, and hence a typical β = 1.3 × 10⁻⁴ (radius of 5 mm).

Integrated light photometry was extracted from KAIT data using a 6'' radius circular aperture centered on the optocenter, with calibration from field stars (Figure 3). Curves in the figure show the brightness variation expected from the changing observing geometry (Equation (1)). We plot two estimates of Φ(α), applicable to C-type (blue line; low albedo, primitive composition) and S-type (red line; high albedo, thermally metamorphosed composition) asteroids. Figure 3 shows that the apparent fading of R3 by ∼2 mag is largely a result of the changing observational geometry and that the dust cross section remains nearly constant from October to December. Near-constancy of the cross section over 2.5 months is consistent with a large mean particle size in the coma.

Zoom In Zoom Out Reset image size

The KAIT photometry corresponds to an effective radius r_e ∼ 2.6 to 3.0 km (Table 2), and to cross-section $C_e = \pi r_e^2$ = 21 to 28 km². As may be seen by comparing the 6'' versus the 02 photometry in Table 2, almost all of this cross-section lies in coma dust structures in R3, not in the embedded nuclei. The mass and cross section of an optically thin dust cloud are related by $M_d \sim 4/3 \rho \overline{a} C_e$, where ρ is the dust mass density and $\overline{a}$ is the weighted mean dust grain radius. For $\overline{a} \gtrsim$ 5 mm and ρ = 10³ kg m⁻³ we estimate peak dust masses (on October 29) M_d ≳ 2 × 10⁸ kg, equivalent to a ∼35 m radius sphere having the same density.