DETECTION OF REMNANT DUST CLOUD ASSOCIATED WITH THE 2007 OUTBURST OF 17P/HOLMES

Figure 2 shows a composite image taken on UT 2014 September 22 after background objects and instrumental artifacts were subtracted. The figure shows not only a cometary tail near the nuclear position (a whitish cloud in the lower left corner) but also a long structure extending from the lower left (southeast) to the upper right (northwest). It spreads to both sides beyond the FOV of the KWFC (>22). We hereafter analyze these cloud morphologies as shown below.

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3.1.1. Near-nuclear Dust Tail and Coma

Figure 3 shows a close-up of the contours of the near-nuclear dust tail. It extended between the negative heliocentric velocity vector (at a position angle, P.A. = 2754) and the antisolar direction (P.A. = 2601). In Figure 3, we show sets of synchrones (loci of positions of particles having a wide range of sizes released at given times, T_ej) and syndynes (loci of positions of particles of a given size, a_d, having a wide range of ejection epochs). Although these lines are not separated well, we roughly estimated the dust ejection epoch and particle size. We determined the locus of the maximum brightness of the dust tail using least-squares fitting with a Gaussian function in every 1' bin and found that the dust tail extended to P.A. = 270° ± 05, which corresponds to the synchrone of T_ej ∼ 180–360 days before the observation. Because the comet was observed 179 days after the perihelion passage, it is likely that the near-nuclear dust tail consisted of particles ejected during the perihelion passage in 2015. From comparison with the syndynes, we estimate an effective particle radius of 10 μm−1 mm for the near-nuclear tail.

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We visually set the sunward extent of the dust coma to ∼40'', which corresponds to the distance projected on the sky plane, l = 6 × 10⁷ m, at the position of the comet. Considering l as the turnaround distance of dust particles ejected toward the solar direction while being pushed by solar radiation pressure, we placed a limitation on the ejection velocity, V = $340\sqrt{\beta }$ m s⁻¹, where β denotes the ratio of the solar radiation pressure with respect to the solar gravity (Jewitt & Meech 1987). In the possible size range (10 μm−1 mm, or β = 5.7 × 10⁻²–5.7 × 10⁻⁴), we estimated an ejection velocity V of 8 m s⁻¹ for 1 mm particles and 80 m s⁻¹ for 10 μm particles. Although we understand that these are very crude estimates, the derived velocity is typical of dust emission from Jupiter-family comets (JFCs) at r_h ∼ 2.5 AU (Ishiguro et al. 2007; Ishiguro 2008). Thus, 17P/Holmes changed from its peculiar appearance just after the 2007 outburst to an appearance typical of JFCs in only one orbital revolution.

We measured Afρ values with differential aperture size from 5000 km (33, equivalent to 1× FWHM) to 50,000 km at intervals of 5000 km, and we obtained almost constant values of Afρ = 139–141 cm within 10,000 km but found significant drops due to the radiation pressure. The Afρ value is typical of general comets listed in A'Hearn et al. (1995) (≈10²–10³ cm around 2.5 AU).

3.1.2. Long Extended Structure

The prominent feature is the long narrow structure. There could be four possibilities to create such long extended structure: (1) dust tail (i.e., dust particles ejected during the current return), (2) ion tail, (3) dust trail, and (4) neck line. We measured a position angle of 2746 ± 01, which deviates significantly from that of the antisolar direction (P.A. = 2601) but is very close to that of the negative heliocentric velocity vector (P.A. = 2754). It also coincides with the direction of the synchrone of the 2007 outburst epoch (i.e., T_ej = −2526 days in Figure 3), although the time resolution of the synchrone analysis is not sufficiently accurate to specify the exact ejection epoch. This fact indicates that the long narrow structure is associated with neither (1) the dust tail nor (2) the ion tail, but with either (3) the dust trail or (4) the neck line (i.e., a swarm of dust particles ejected during the last perihelion passage or even before). It is interesting to consider why the comet has this spectacular long extended structure, although the near-nuclear dust tail looks typical of JFCs, as we mentioned above (Section 3.1.1).

We examined the surface brightness and width. Figure 4 shows the surface cut profiles perpendicular to the long extended structure, where we averaged the brightness along the extended direction (P.A. = 2746) in the bin length of 6'. The structure was unclear at the distance +3' < l < +9' because the bright near-nuclear dust tail overlapped the faint extended structure. We fitted the background sky brightness by third-order polynomials and obtained the peak brightness and FWHM. Figure 5 shows the result. The FWHM clearly increased as the peak brightness decreased from west to east. The peak brightness is in the range of 26.2–27.0 mag arcsec⁻², which is equivalent to those of some bright cometary dust trails such as 67P/Churyumov–Gerasimenko (Ishiguro 2008) and 22P/Kopff (Ishiguro et al. 2002). It is, however, important to notice that the shape and brightness distributions differ from general dust trails. As shown in some papers (see, e.g., Sykes 1990; Ishiguro et al. 2002, 2003), dust trails show narrowing toward the nuclei. In addition, the fading toward the nucleus is inconsistent with the dust trail structure of 17P/Holmes detected by Spitzer observation, where the brightness increased toward the nucleus (Reach et al. 2010). Thus, the long extended structure in our 17P/Holmes image could be unlike the typical dust trail structures seen to date.

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To determine the surface brightness profile of the long extended structure, we summed up the signal from the extended structure. We set a rectangular aperture box of 2' × 22. After subtracting the sky background, which was determined at 1'–3' from the trail center on both the north and south sides, we obtained the total R_C magnitude of m_R = 12.3 ± 0.2 in the KWFC FOV. The observed R_C magnitude was converted to the absolute magnitude (i.e., corrected to unit heliocentric and geocentric distances at zero phase angle) using

$$\begin{eqnarray}&&{H}_{{\rm{R}}}={m}_{{\rm{R}}}-5\;{\mathrm{log}}_{10}({r}_{{\rm{h}}}{\rm{\Delta }})-2.5\;{\mathrm{log}}_{10}({\rm{\Phi }}(\alpha )),\end{eqnarray} \tag{ 1 }$$

where the term ${\mathrm{log}}_{10}({\rm{\Phi }}(\alpha ))$ characterizes the scattering phase function of dust grains. Using a commonly used formula, ${\mathrm{log}}_{10}({\rm{\Phi }}(\alpha ))$ = 0.035α, and substituting r_h = 2.464 AU, Δ = 2.094 AU, and α = 237, we obtained H_R = m_R − 4.4 = 7.9 ± 0.2. The absolute magnitude is converted into the cross section by the following equation (Russell 1916):

$$\begin{eqnarray}&&{C}_{\mathrm{FOV}}=\displaystyle \frac{2.24\pi \times {10}^{22}\times {10}^{0.4({m}_{\odot }-{H}_{{\rm{R}}})}}{{p}_{{\rm{R}}}},\end{eqnarray} \tag{ 2 }$$

where m_⊙ = −27.1 is the R_C magnitude of the Sun (Drilling & Landolt 2000, p. 381) and p_R is the geometric albedo in the R_C band. Assuming p_R = 0.04, which is often used for cometary grains, we obtained C_FOV = (2.3 ± 0.5) × 10¹⁰ m².

The grain mass can be derived as ${M}_{\mathrm{FOV}}=\frac{4}{3}{C}_{\mathrm{FOV}}\;{a}_{{\rm{d}}}{\rho }_{{\rm{d}}}$, where a_d and ρ_d are the grain radius and mass density, respectively. From the synchrone analysis (see Figure 3), the long extended structure extended to the upper right (along the negative velocity vector, −v), which is consistent with dust particles of ${a}_{{\rm{d}}}\gtrsim 1\;{\rm{mm}}$ but inconsistent with a_d ≲ 100 μm. Assuming ρ_d = 10³ kg m⁻³, we obtained M_FOV = 3 × 10¹⁰ kg (when a_d = 1 mm) or M_FOV = 3 × 10¹¹ kg (when a_d = 1 cm). It is important to note that the derived mass is the lower limit because the dust particles extended beyond the FOV. Nevertheless, we can use the M_FOV value to identify the origin of the long extended structure. The dust production rate of 17P/Holmes was ∼3 kg s⁻¹ around its perihelion before the 2007 outburst (Ishiguro et al. 2013). Supposing that a comet loses most of its mass at a constant rate within 2.5 AU, which corresponds to a duration of about a year, 17P/Holmes was expected to lose about 10⁸ kg in total during the last perihelion passage, except for the outburst. The mass is significantly (more than two orders of magnitude) smaller than the mass of the long extended structure in the KWFC FOV. In contrast, the total mass of the outburst ejecta was derived as 10¹⁰–10¹³ kg (Montalto et al. 2008; Altenhoff et al. 2009; Ishiguro et al. 2010; Reach et al. 2010; Boissier et al. 2012). The mass of the long extended structure is equivalent to or smaller than the total ejecta mass of the 2007 outburst. Together with the position angle and morphology we mentioned above, we conclude that the long extended structure is a part of the dust cloud ejected during the 2007 outburst but is tentatively detected by our observation because of the convergence effect (i.e., the neck-line effect). In Section 4, we further investigate the physical properties of the long extended structure, regarding it as a remnant dust ejecta during the 2007 outburst.

As a first step, we considered a simple impulsive dust ejection model in which the dust cloud consists of dust particles with a uniform size and ejection velocity. Assuming ρ_d = 10³ kg m⁻³ and isotropic dust ejection (i.e., particles are ejected equally in all directions), we simulated a_d = 100 μm particles and a_d = 1 cm particles in a possible velocity range of V = 5–500 m s⁻¹. The upper limit of V is comparable to the highest dust velocity in the outburst envelope (i.e., 554 m s⁻¹, Lin et al. 2009), whereas the lower limit is close to the escape velocity (V_es = 1.5 m s⁻¹) from the nucleus with R_N = 2080 m (Stevenson et al. 2014) and a bulk density of 1000 kg m⁻³. Figures 6 and 7 show the resultant simulated images. In Figure 6, the width and length of the neck-line structure increase as V increases. The convergent point appears about 27 rightward of the nucleus, showing the strongest intensity enhancement (i.e., neck-line structure). These models qualitatively reproduce the observed narrowing and brightening from east to west. A visual comparison yielded an order-of-magnitude estimate of the ejection velocity of V ≈ 50 m s⁻¹ for 1 cm particles. For 100 μm particles with low V < 50 m s⁻¹, the dust cloud was blown off westward beyond the FOV, because such small dust particles are susceptible to solar radiation pressure and are strongly accelerated toward the negative velocity vector (i.e., western direction) (Figures 7(a) and (b)). The increase in ejection velocity would enlarge the dust cloud in every direction, having the cloud appear in the FOV of the KWFC. However, we noticed that 100 μm is too small to be detected in the KWFC FOV. If we increase V to be observable in the FOV, it should have a width much wider than what we observed (e.g., Figure 7 (c)). To summarize the uniform size model, we applied constraints of a_d ≳ 100 μm and V ≈ 50 m s⁻¹.

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Second, we employed a more realistic model having a power-law size distribution and velocity distribution for the neck-line structure. We assumed that the number of dust particles was

$$\begin{eqnarray}&&N({a}_{{\rm{d}}})\;{{da}}_{{\rm{d}}}={N}_{0}{\left(\displaystyle \frac{{a}_{{\rm{d}}}}{{a}_{0}}\right)}^{q}\;{{da}}_{{\rm{d}}}\end{eqnarray} \tag{ 3 }$$

in the size range a_min ≤ a_d ≤ a_max, where a_min and a_max are the minimum and maximum particle sizes detectable in the KWFC FOV, respectively. Further, a₀ is the reference size of dust particles (we set a₀ = 1 cm and a_min = 100 μm following the result of the uniform size model above). We use the following function for the ejection terminal velocity of dust particles:

$$\begin{eqnarray}&&V={V}_{0}{\left(\displaystyle \frac{{a}_{{\rm{d}}}}{{a}_{0}}\right)}^{u}v,\end{eqnarray} \tag{ 4 }$$

where v is a random variable having an average of 1 and a standard deviation σ_v (see, e.g., Ishiguro et al. 2014). We set σ_v = 0.1, which was the value obtained from a similar outburst at P/2010 V1. Note that v makes a minor contribution to the spatial distribution of dust particles when ${\sigma }_{v}\ll 1$. Now we have five variables (N₀, a_max, q, V₀, and u). Among them, N₀ can be determined by scaling the simulation intensity to the observed one once the other four parameters are fixed. We thus created a number of simulation images to find the best-fit parameter set assuming a_max = 1 cm, 10 cm, and 1 m in −4.5 ≤ q ≤ −3.0 at the interval of Δq = 0.1, $1\leqslant {V}_{0}\leqslant 70\;{\rm{m}}$ s⁻¹ at the interval of ΔV₀ = 1 m s⁻¹, and 0.1 ≤ u ≤ 0.9 at the interval of Δu = 0.1, respectively.

The simulation revealed several trends. The width of the neck-line structure increases as V₀ increases. Further, q is also sensitive to the width. The width increases when q is small, because small particles with higher velocity are efficient scatterers for smaller q. We compared the width and intensity distribution with respect to the distance from the nucleus with those of the model simulation. We found that the leftmost data point does not match any model probably because the data were contaminated by an unconsidered error source (such as the remnant of background stars or imperfect flat-fielding), and thus we ignored it. We obtained the best-fit parameters via the χ² test, q = −3.4 ± 0.1, V₀ = 50 ± 10 m s⁻¹, and u = 0.3 ± 0.1. We appended the errors of these parameters when simulation results matched the observed results to an accuracy of the measurement. In the parameter range above, a_max is less determined (although we got the constraint of a_max > 1 cm) because such large particles are supposed to stay near the comet nucleus while such a signature from the biggest particles was obscured by the bright dust tail and coma.

An unexpected result is the high ejection velocity for 1 mm–1 cm particles in the neck-line structure. Before this observation, we predicted an ejection velocity of several meters per second for various reasons. First, we predicted the low ejection velocity as an analog of cometary dust trails. They consist of 1 mm–1 cm particles with an ejection velocity of several meters per second, which is marginally larger than that of the escape velocities from kilometer-sized bodies (Sykes & Walker 1992; Ishiguro et al. 2002). In addition, the velocity of the smallest (probably 0.1–1 μm) particles for the 2007 outburst was estimated to be 554 m s⁻¹ (Lin et al. 2009). If we extrapolate the velocity of 1 cm particles using the inverse square law of the grain size, we would have 2–6 m s⁻¹. Figure 8 shows the velocity of the dust particles with respect to the grain size. For comparison, we show the velocity predicted using the classical model developed by Whipple (1951). The model has been widely applied to characterize the velocity–size law. The velocity in the classical model is found to be in good agreement with that of fresh dust particles in the coma (see Section 3.1.1) but more than one order of magnitude smaller than those of dust particles in the neck-line structure. The discrepancy may suggest that dust ejection in the 17P/Holmes outburst differed from ejection due to normal sublimation by solar heating.

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To compensate for the large discrepancy in the ejection velocity, we reviewed the formula in the Whipple model. In the generalized formula of the Whipple theory, it is written as (Ryabova 2013)

$$\begin{eqnarray}&&V=\sqrt{\displaystyle \frac{{k}_{\mathrm{drag}}{\rm{\Delta }}M\bar{{v}_{{\rm{g}}}}}{2\pi {R}_{{\rm{N}}}}\displaystyle \frac{A}{m}-\displaystyle \frac{2{{GM}}_{{\rm{N}}}}{{R}_{{\rm{N}}}}},\end{eqnarray} \tag{ 5 }$$

where k_drag is a drag coefficient, usually assumed to be k_drag = 26/9, and m and A are the mass and cross-sectional area, respectively, of the dust particles. For spherical particles, they are written as m = $4/3\pi {\rho }_{{\rm{d}}}{a}_{{\rm{d}}}^{3}$ and A = $\pi {a}_{{\rm{d}}}^{2}$. M_N is the mass of a nucleus having a radius R_N. Assuming a spherical body with a mass density ρ_N, it is written as M_N = $4\pi {\rho }_{{\rm{N}}}{R}_{{\rm{N}}}^{3}/3$. Note that the second term in the square root makes a minor contribution when V is significantly larger than the escape velocity V_es, where V_es is 1.5 m s⁻¹ for 17P/Holmes (R_N = 2080 m and ρ_N = 10³ kg m⁻³ are assumed). ΔM is the mass-loss rate of the gas. Assuming that dust particles are accelerated by water molecules, we can write ${\rm{\Delta }}M={\mu }_{{{\rm{H}}}_{2}{\rm{O}}}\;{Q}_{{{\rm{H}}}_{2}{\rm{O}}}$. $\bar{{v}_{{\rm{g}}}}$ is the velocity of the water vapor outflow.

In this model, there are several unknown parameters. We adopted $\bar{{v}_{{\rm{g}}}}$ = 550 m s⁻¹, which corresponds to the maximum velocity of dust particles in the outburst envelope (Lin et al. 2009) and is also equivalent to the assumed gas velocity in Dello Russo et al. (2008). The water production rate, ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$, was determined by several authors; the obtained values include ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ = (1.2–1.4) × 10³⁰ mol s⁻¹ on UT 2007 October 25–27 (Combi et al. 2007), ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 4.5 × 10²⁹ mol s⁻¹ on UT 2007 October 27.6 (Dello Russo et al. 2008), and ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 5 × 10²⁹ mol s⁻¹ on UT 2007 November 01.2 (Schleicher 2009). We adopted ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ = 1 × 10³⁰ mol s⁻¹. Assuming the mass densities of the dust particles ρ_d = 10³ kg m⁻³, we obtained the size–velocity law (thick dashed line in Figure 8). Although there are uncertainties in ${Q}_{{{\rm{H}}}_{2}{\rm{O}}}$ and $\bar{{v}_{{\rm{g}}}}$, the model velocity coincides with the observed velocity to within a factor of <2. We guess that this trivial difference can be explained by the simplifications in the model. For example, the term 2π in the denominator of Equation (5) was obtained assuming hemispherical dust emission. It can be <2π in a realistic case when the dust particles were ejected from limited active areas on the surface, increasing the ejection velocity (also described in Hughes 2000). In addition, the gas velocity would be increased via adiabatic expansion into space. These effects may result in a dust velocity higher than that in the generalized Whipple model. We thus conclude that a sudden sublimation of a large amount of water-ice (≈10³⁰ mol s⁻¹) would be responsible for the high ejection velocity of the remnant dust debris in our observed image.

The total mass of the outburst ejecta has been derived by many researchers using different techniques. It differs substantially depending on the author, i.e., 10¹⁰–10¹⁴ kg (Montalto et al. 2008; Altenhoff et al. 2009; Ishiguro et al. 2010; Reach et al. 2010; Li et al. 2011; Boissier et al. 2012; Ishiguro et al. 2013). As discussed in many papers, there is an intrinsic problem in the determination of the mass of cometary dust because the scattering cross section is dominated by the smallest particles, whereas the mass of the largest particles in the differential size frequency distribution has a power index of −3 < q < −4. The dust cloud of 17P/Holmes may be no exception. Zubko et al. (2011) studied the polarimetric property of 17P/Holmes outburst ejecta and found that the size distribution has the power index q ∼ −3.5.

From our dynamical model, we found that the total cross section of the dust grains in the KWFC FOV is about 5%–10% of the total dust cloud in the size range of a_d = 100 μm–1 cm. Considering the size distribution with an index of q = −3.4 ± 0.1 in the size range a_d = 100 μm−1 cm, which were obtained by the dynamical model in Section 4, we obtained a mass of ${M}_{\gt 100\mu {\rm{m}}}$ = (3.6–7.2)  × 10¹¹ kg for the neck-line particles (i.e., big remnant particles). If we integrate down to submicron particles (i.e., a_min = 0.6 μm; Zubko et al. 2011), we derive a total mass of M_TOT = (3.8–7.7) × 10¹¹ kg for the 2007 outburst ejecta, which is almost the same as ${M}_{\gt 100\mu {\rm{m}}}$ because largest grains make up most of the mass. The mass also shows good consistency with several previous studies, such as a radio continuum observation by Boissier et al. (2012), and is consistent with the upper limit in Li et al. (2011). The kinetic energy of large dust particles (a_d = 100 μm−1 cm) is estimated to be ${E}_{\gt 100\mu {\rm{m}}}$ = (7–14) × 10¹⁴ J. Similarly, if we integrate down to 0.6 μm-sized particles, we get E_TOT = (1–6) × 10¹⁵ J. The energy per unit mass is less than 20% of the energy released during the crystallization of amorphous water-ice. As already described in Li et al. (2011), our results may imply that the outburst can be caused by the crystallization of buried amorphous ice.

It is interesting to notice that a large amount of big dust particles was injected into the interplanetary space by a single outburst event and survived for >7 yr without melting or disintegrating the structure and observed as the neck-line structure. The cometary dust particles will probably disperse in the interplanetary field via planetary perturbations and constitute a portion of the zodiacal cloud (Vaubaillon et al. 2004). There is a long-standing question about the origin of the zodiacal dust cloud because it erodes by the Poynting–Robertson effect and mutual collision among particles. We estimated the contribution of cometary dust particles via 17P-like outbursts. It is not clear how often such big cometary outbursts occurred. We assumed the frequency of 0.1–1 per century because the comet exhibited similar (but slightly weaker) outburst in the nineteenth century (Reach et al. 2010). Multiplying the frequency by M_TOT, we obtained a crude estimate of 12–240 kg s⁻¹. Although there should be a large uncertainty in the rate, ejecta by 17P-like outburst would account for (0.1%–2.4%) of the required mass to sustain the zodiacal cloud (i.e., 10⁴ kg s⁻¹; Mann et al. 2006). Therefore, we speculate that some fraction of zodiacal dust might be generated by 17P-like outbursts and remain in the interplanetary space for a long time to be observable as zodiacal light.