Disintegrating Inbound Long-period Comet C/2019 J2

No point-source nuclei are evident even in our deepest image, the 3600 s R-band integration from UT 2019 August 2 (Figure 1, bottom panel). The limiting magnitude of this composite is estimated as R = 25.0 (3σ), which compares with R = 25.5 from the ALFOSC exposure time calculator (http://www.not.iac.es/observing/forms/signal/v2.8/index.php) for 11 seeing under dark sky conditions. The modest difference reflects the irregular background to J2 evident in the real data. Equation (1) gives the corresponding limit to the absolute magnitude of any point-like nucleus as H ≥ 21.6 and, by Equation (2), the maximum allowable nucleus radius is r_n = (C_e/π)^1/2 ≤ 0.1 km, again assuming p_V = 0.1 (the radius limit may be scaled to other assumed albedos in proportion to (0.1/p_V)^1/2). The imaging data thus show that no nucleus fragment larger than about 100 meters remains in early August.

The position angle (PA) of the tail center line in our August 2 data is θ_PA = 52° ± 5°. We computed synchrones for a range of dates to find that the synchrone PA reaches the observed value for ejection on DOY ${146}_{-18}^{+17}$ (UT 2019 May ${26}_{-18}^{+17}$). While the tail is too broad to be consistent with a single synchrone, the center line gives an approximate indication of the mid-time of the ejection.

An independent estimate of the ejection timescale is obtained from the photometry listed in Table 2 and plotted in Figure 2. A weighted least-squares parabola fitted to the photometry gives the time of peak absolute magnitude as DOY = 144 ± 12, corresponding to UT 2019 May 24 ± 12. We take this date, which is ∼2 months before perihelion, as our best estimate of the time of disintegration and note that the comet was then at r_H = 1.87 au. The dates deduced independently from the tail PA and from the photometry are in agreement, within the uncertainties of measurement. Furthermore, images posted online (http://aerith.net/comet/catalog/2019J2/pictures.html) show a change from centrally condensed on 2019 May 13 to diffuse with a fading core on 2019 June 4 and thereafter, which is consistent with a major physical change in the comet between these dates, and again consistent with the inferred disruption time.

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If contained in particles of mean radius $\overline{a}$, the mass of material implied by scattering cross-section C_e is

$$\begin{eqnarray}&&{M}_{d}=\displaystyle \frac{4}{3}\rho \overline{a}{C}_{e}\end{eqnarray} \tag{ 3 }$$

where we have assumed ρ = 500 kg m⁻³ as the grain density. We obtain a crude measure of the size of the particles from the length of the dust tail, assuming that radiation pressure is the driving force. For a constant applied acceleration, βg_⊙, where β is the radiation pressure efficiency and g_⊙ is the local gravitational acceleration toward the Sun, the distance traveled by a grain released from the nucleus with zero relative speed is L = βg_⊙ Δt²/2, where Δt is the time since the dust particle release. Writing g_⊙ = ${g}_{1}/{r}_{H}^{2}$, where g₁ = 0.006 m s⁻² is the acceleration at r_H = 1 au, we obtain

$$\begin{eqnarray}&&\beta =\displaystyle \frac{2{{Lr}}_{H}^{2}}{{g}_{1}{\rm{\Delta }}{t}^{2}},\end{eqnarray} \tag{ 4 }$$

with r_H expressed in au. Consider the observation on UT 2019 July 24, for which Δt = 61 days (5.3 × 10⁶ s) from May 24 and C_e = 3.5 ± 0.7 km² within the photometry aperture of radius L = 10⁷ m. Substitution into Equation (4) gives β = 4 × 10⁻⁴. For dielectric spheres, the particle radius expressed in microns is approximately equal to the reciprocal radiation pressure factor, a ∼ β⁻¹ (Bohren & Huffman 1983), giving a ∼ 2.5 mm. Smaller particles should have been swept out of the aperture by radiation pressure, while larger ones are retained within it. Setting $\overline{a}\,\geqslant$ 2.5 mm in Equation (3) gives M_d ≥ 6 × 10⁶ kg. This is a minimum mass because all the particles in the aperture must be larger than 2.5 mm in order not to have been swept out by radiation pressure. To obtain a better estimate of M_d we must consider the size distribution of the ejected particles.

Observations from other split and disintegrating comets show that the debris size distribution approximates a power law, such that n(a)da = Γa^−qda is the number of particles with radius in the range a to a + da, where Γ and q are constants. The index is typically q ∼ 3.5 (Moreno et al. 2012; Ishiguro et al. 2016b; Jewitt et al. 2016; Kim et al. 2017) although smaller (e.g., q = 1.7, Kleyna et al. 2019) and larger indices (e.g., q = 3.8, Ishiguro et al. 2016a) have been reported. If the particle radius range extends from minimum a_min to maximum a_max, the average radius in a q = 3.5 distribution is $\overline{a}={({a}_{\min }{a}_{\max })}^{1/2}$. Setting a_min = 2.5 mm (from Equation (4)) and a_max = 100 m (from the absence of a point-source nucleus), we find $\overline{a}=0.5$ m. Then, Equation (3) gives M_d = 1.2 × 10⁹ kg for the debris mass in the aperture on 2019 July 24. This is equivalent to a sphere of the same density having radius ${r}_{n}={[3{M}_{d}/(4\pi \rho )]}^{1/3}$ or r_n ∼ 10² m. The mass in power-law distributions with q < 4 is dominated by the largest particles in the distribution. For example, in a q = 3.5 distribution initially extending from a_min = 10⁻⁷ to a_max = 10² m, particles larger than 2.5 mm contain 99.5% of the total mass. Because these larger particles have not left the 10⁴ km photometry aperture, we can be confident that r_n ∼ 10² m is a good estimate of the equivalent radius of the disrupted body, unless the fragment size distribution is much steeper (q larger) than that assumed.

Suggested mechanisms for cometary disintegration are many and varied. In the case of J2 at r_H ∼ 1.9 au, however, some of these mechanisms can be rejected. Tidal disruption can be rejected, for instance, because J2 was not close to any major solar system body. Impact disruption is implausible, because the comet was >1 au above the ecliptic at the time of disintegration as a result of the highly inclined orbit of J2 (i = 1051). The number density of asteroids and other bodies drops precipitously with height above the mid-plane and the likelihood of a disruptive collision at >1 au is vanishingly small.

Ice sublimation can potentially lead to disintegration through distinctly different processes. We first calculated the rate of sublimation of exposed water ice using the energy balance equation and assuming equilibrium. At r_H = 1.9 au, the maximum rate, found at the hotspot sub-solar point on a nucleus having Bond albedo 0.05 and emissivity of unity, is f_s = 1.0 × 10⁻⁴ kg m⁻² s⁻¹, and the ice temperature (depressed relative to the blackbody temperature by sublimation) is T = 195 K. The gas outflow speed is approximately given by V_th = 420 m s⁻¹, the thermal speed of water molecules (molecular weight 18) at this temperature. The resulting back pressure on the nucleus caused by sublimation is then Ψ = f_sV_th ∼ 0.04 N m⁻². The same calculation repeated for supervolatile CO gives f_s = 1.2 × 10⁻³ kg m⁻² s⁻¹, and a free sublimation temperature of only T = 28 K, leading to V_th = 160 m s⁻¹ and a back pressure that is only slightly larger, Ψ = 0.2 N m⁻². These back pressures can be compared to the best available estimates of the compressive strength of cometary material, set at S = 30–150 N m⁻² in the nucleus of 67P/Churyumov–Gerasimenko by Groussin et al. (2019). With Ψ ∼ 10⁻²S to 10⁻³S, we reject free sublimation as a likely cause of nucleus cracking or disintegration.

Sublimation at specific rate f_s leads to recession of the sublimating surface at rate $| {{dr}}_{n}/{dt}| =({f}_{s}/\rho )$ m s⁻¹. With f_s = 1.0 × 10⁻⁴ kg m⁻² s⁻¹ and ρ = 500 kg m⁻³ we find $| {{dr}}_{n}/{dt}| =2\times {10}^{-7}$ m s⁻¹. Even a very modest nucleus of radius r_n = 100 m could sustain sublimation at this rate for ${r}_{n}/(| {{dr}}_{n}/{dt}| )\sim 10$ yr, showing that devolatilization on a timescale of weeks is unlikely. Devolatilization on a timescale of months would only be possible if the ice on the nucleus of J2 were confined to a thin (≪1 m) surface skin, but this geometry seems contrived.

A more promising mechanism is spin-up of the nucleus by sublimation torques, potentially driving the nucleus to rotational instability. The e-folding timescale for spin-up due to sublimation, τ_s, is a strong function of nucleus radius, r_n, given by

$$\begin{eqnarray}&&{\tau }_{s}=\left(\displaystyle \frac{16{\pi }^{2}}{15}\right)\left(\displaystyle \frac{{\rho }_{n}{r}_{n}^{4}}{{k}_{T}{V}_{\mathrm{th}}P}\right)\left(\displaystyle \frac{1}{\overline{\dot{M}}}\right),\end{eqnarray} \tag{ 5 }$$

where ρ_n is the density, k_T is the dimensionless moment arm, V_th is the speed of the sublimated material, P is the starting rotation period of the nucleus, and $\dot{M}$ is the mass-loss rate. While the numerical multiplier in this equation is geometry dependent and therefore uncertain (see Jewitt 1997; Samarasinha & Mueller 2013), the key factor is the strong dependence of τ_s on the nucleus radius, ${\tau }_{s}\propto {r}_{n}^{4}$, if all other factors are equal.

The physical quantities in Equation (5) are not measured for J2, but we can use evidence gleaned from the study of other comets to at least consider the possibility that spin-up might be effective in this object. Accurate measurements of cometary densities are few and far between. Those that exist are consistent with ρ_n = 500 kg m⁻³ (Groussin et al. 2019). As above, we take V_th = 420 m s⁻¹. The median dimensionless moment arm in comets is k_T = 0.015 (D. C. Jewitt 2019, in preparation). We take P = 10 hr (3.6 × 10⁴ s) as a nominal nucleus rotation period (Kokotanekova et al. 2018). Jorda et al. (2008) determined an empirical relationship between the apparent magnitude of a comet and its hydroxyl production rate, Q_OH, namely log(Q_OH) = 30.68 − 0.25m_H, where m_H is the apparent magnitude reduced to unit geocentric distance by the inverse square law. Taking the UT 2019 April 27 magnitude, V = 18.19 ± 0.07 (Table 2), we estimate m_H = 16.02 and find Q_OH = 10^26.7 s⁻¹, corresponding to $\dot{M}$ = 15 kg s⁻¹. Substituting into Equation (5) gives ${\tau }_{s}\sim 1\times {10}^{9}{r}_{n}^{4}\,{\rm{s}}$, with r_n expressed in km. If r_n = 0.1 km, we find τ_s ∼ 10⁵ s.

To judge the importance of spin-up, we compare τ_s with the characteristic timescale for change of the heliocentric distance, given by $\tau ={r}_{H}/| \dot{{r}_{H}}|$. We reason that pre-perihelion spin-up is likely when τ_s < τ. At the time of the disintegration in mid-May 2019, J2 had r_H ∼ 1.9 au and $| \dot{{r}_{H}}| \sim 10$ km s⁻¹, giving τ ∼ 3 × 10⁷ s. The requirement τ_s < τ is satisfied for r_n < 0.4 km, meaning that J2 could have been torqued to break-up if its nucleus was initially smaller than about 400 m in radius, which is consistent with the ∼0.1 km scale obtained above. As another consistency check, we note that the specific sublimation rate, f_s = 1.0 × 10⁻⁴ kg m⁻² s⁻¹ and the Jorda-derived mass-loss rate, $\dot{M}$ = 15 kg s⁻¹, imply a sublimating area $C=\dot{M}/{f}_{s}$ = 1.5 × 10⁵ m² (0.15 km²), which is equal to the surface area of a sphere 0.11 km in radius.

Again, while the available information is insufficient to prove that rotational instability caused J2 to disintegrate, the above considerations show that the data are consistent with this possibility. Disintegrations have been described in several comets having small perihelia. Notable examples include C/1925 X1 (Ensor) with q = 0.323 au (Sekanina 1984); C/1999 S4 (LINEAR) with q = 0.765 au (Weaver et al. 2001); C/2012 S1 (ISON) with q = 0.013 au (Keane et al. 2016); and C/2010 X1 (Elenin) with q = 0.482 au (Li & Jewitt 2015). These objects all displayed a diffuse, elongated appearance that is similar to that of J2. The nuclei of comets ISON and Elenin had radii r_n ∼ 0.5 km (Keane et al. 2016) to 0.6 km (Li & Jewitt 2015); the radius of comet LINEAR is uncertain, but estimated as 0.1 km or larger (Weaver et al. 2001), while the size of the nucleus of comet Ensor is not known.

We suggest that the rotational disruption of comet J2 is possible, even at a heliocentric distances as large as 2 au, because of its diminutive nucleus and the strong radius dependence of the e-folding spin-up time (Equation (5)). We further surmise that rotational break-up of long-period nuclei may contribute to, or even account for, the "fading problem," i.e., the long-recognized inability of purely dynamical models to account for the measured distribution of cometary orbital binding energies (Oort 1950; Wiegert & Tremaine 1999; Levison et al. 2002). Lastly, we observe that the strong size dependence of the rotational break-up e-folding time should lead to the preferential depletion of small nuclei, and to a flattening of the size distribution of small long-period comets. While reliable measurements of sub-kilometer nuclei are few, flattening of the distribution has indeed been inferred in a study by Fernández & Sosa (2012).