MONITORING OBSERVATIONS OF THE JUPITER-FAMILY COMET 17P/HOLMES DURING ITS 2014 PERIHELION PASSAGE

A summary of the observations is given in Table 1. In order to monitor the time variation in the activity as described above, we made observations of 17P/Holmes over about two years around the time of the perihelion passage on UT 2014 March 27 at five observatories, namely, the Ishigakijima Astronomical Observatory (hereafter, IAO), the Okayama Astrophysical Observatory (OAO), the Nishi-Harima Astronomical Observatory (NHAO), the Siding Spring Observatory (SSO), and the Bohyunsan Optical Astronomy Observatory (BOAO). In total, we obtained valid data at thirty-six epochs from UT 2013 May 4 to UT 2015 March 16. All telescopes were operated in a comet-tracking mode. Detailed information about the instruments and telescopes is shown below.

Table 1.  Journal of 17P/Holmes Monitoring Observations

UT Date	Telescope (Instrument)	Filter	Exptime	N	ϕ ['']	rh	Δ	α	${\theta }_{{\rm{T}}}$
2010/10/14.25	Aphelion	...	...	...	...	5.19	...	...	180.0
2013/05/04.67	SSO050 (FLI-PL6303E)	RC	120	10	5.86	3.09	2.35	14.7	263.8
2013/05/10.75	SSO050 (FLI-PL6303E)	RC	120	5	6.06	3.06	2.27	13.8	264.9
2013/05/20.54	SSO050 (FLI-PL6303E)	RC	120	10	6.39	3.02	2.16	12.0	266.7
2013/07/13.58	SSO050 (FLI-PL6303E)	RC	120	6	7.17	2.78	1.92	13.4	277.6
2013/07/31.58	SSO050 (FLI-PL6303E)	RC	100	5	6.94	2.71	1.99	17.7	281.6
2014/03/27.56	Perihelion	...	...	...	...	2.05	...	...	0.0
2014/07/02.79	IAO105 (MITSuME)	RC	180	7	5.19	2.19	2.66	21.6	37.3
2014/07/04.79	IAO105 (MITSuME)	RC	180	7	5.21	2.20	2.64	21.8	37.8
2014/07/05.75	IAO105 (MITSuME)	RC	180	12	5.23	2.20	2.64	22.0	38.0
2014/07/17.75	IAO105 (MITSuME)	RC	180	12	5.37	2.23	2.57	23.1	42.2
2014/07/18.76	IAO105 (MITSuME)	RC	180	14	5.38	2.24	2.56	23.2	42.5
2014/07/24.81	IAO105 (MITSuME)	RC	180	13	5.46	2.25	2.52	23.7	44.5
2014/08/04.76	IAO105 (MITSuME)	RC	180	18	5.63	2.29	2.45	24.4	48.1
2014/08/06.79	IAO105 (MITSuME)	RC	180	12	5.66	2.30	2.44	24.5	48.8
2014/08/20.80	IAO105 (MITSuME)	RC	180	22	5.90	2.34	2.34	25.0	53.2
2014/08/22.79	IAO105 (MITSuME)	RC	180	2	5.93	2.35	2.32	25.0	53.8
2014/08/31.72	IAO105 (MITSuME)	RC	180	18	6.11	2.38	2.26	25.0	56.5
2014/09/03.71	IAO105 (MITSuME)	RC	180	9	6.17	2.39	2.24	24.9	57.4
2014/09/05.80	IAO105 (MITSuME)	RC	180	19	6.21	2.40	2.22	24.8	58.0
2014/09/10.73	IAO105 (MITSuME)	RC	180	12	6.32	2.42	2.18	24.6	59.5
2014/09/11.70	IAO105 (MITSuME)	RC	180	26	6.34	2.42	2.18	24.6	59.8
2014/09/13.67	IAO105 (MITSuME)	RC	180	16	6.38	2.43	2.16	24.4	60.4
2014/09/14.74	IAO105 (MITSuME)	RC	180	14	6.41	2.43	2.15	24.4	60.6
2014/09/15.70	IAO105 (MITSuME)	RC	180	15	6.43	2.44	2.15	24.3	60.9
2014/09/16.33	OAO188 (KOOLS)	RC	120	12	6.44	2.44	2.14	24.3	61.3
2014/09/20.75	OAO188 (KOOLS)	RC	120	71	6.54	2.46	2.11	23.9	62.3
2014/09/23.76	IAO105 (MITSuME)	RC	180	40	6.61	2.47	2.08	23.6	63.2
2014/09/26.75	IAO105 (MITSuME)	RC	180	25	6.68	2.48	2.06	23.3	64.0
2014/10/29.68	IAO105 (MITSuME)	RC	180	16	7.37	2.61	1.87	17.2	72.7
2014/11/19.54	IAO105 (MITSuME)	RC	180	19	7.55	2.70	1.83	12.0	77.7
2015/01/29.58	IAO105 (MITSuME)	RC	180	19	5.67	3.00	2.43	17.0	92.5
2015/01/30.46	NHAO200 (MINT)	RC	180	7	5.64	3.01	2.45	17.1	92.7
2015/01/31.53	OAO050 (MITSuME)	RC	120	43	5.60	3.01	2.46	17.2	92.9
2015/02/19.58	IAO105 (MITSuME)	RC	180	28	4.96	3.10	2.78	18.4	96.4
2015/02/20.54	IAO105 (MITSuME)	RC	180	47	4.93	3.10	2.78	18.4	96.5
2015/02/24.37	BOAO180(4kCCD)	RC	180	5	4.83	3.11	2.86	18.4	97.2
2015/03/16.51	OAO188 (KOOLS)	RC	180	36	4.28	3.20	3.22	17.8	100.7

Note. The header shows Exptime, the exposure time of each image in seconds; N, the number of images on a given date; r_h, the heliocentric distance in AU; Δ, the geocentric distance in AU; α, the median phase angle; and ${\theta }_{{\rm{T}}}$, the true anomaly in degrees. ϕ is an aperture diameter in arcseconds to measure the area within the circle of radius 5000 km from the center of the nucleus. We utilized the JPL Horizon Ephemeris program³ based on the Web interface to obtain the median UT at the given observation date. The abbreviations of the telescope names denote the Siding Spring Observatory 50 cm telescope (SSO050), the Ishigakijima Astronomical Observatory 105 cm telescope (IAO105), the Okayama Astrophysical Observatory 188 cm (OAO188) and 50 cm telescopes (OAO050), the Nishi-Harima Astronomical Observatory 200 cm telescope (NHAO200), and the Bohyunsan Optical Astronomy Observatory 180 cm telescope (BOAO180).

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2.1.1. IAO Observations

2.1.2. OAO Observations

2.1.3. NHAO Observation

2.1.4. SSO iTelescope Observations

2.1.5. BOAO Observation

We exploited only R_C-band data because this band is sensitive to the scattered light from cometary dust grains, but is mostly uncontaminated by gaseous emissions at the circumnucleus. The observed raw data were preprocessed in a standard manner using dark (or bias if the CCD was cooled enough) and dome flat frames. To subtract background stellar objects and make composite images, we basically followed the method developed by Ishiguro (2008), tuning some parameters to neatly erase the background sources. We calibrated the pixel coordinates into celestial coordinates using WCSTools (Mink 1997) or Astrometry.net software¹² In order to perform aperture photometry, we utilized the APPHOT package in IRAF. We conducted flux calibration using field stars listed in the UCAC-3 catalog (Zacharias et al. 2010). We considered the calibration error of 0.1 mag for the UCAC-3 catalog, as well as photon noises from objects and sky background and readout noise in the CCDs. As a consequence, we could select thirty-six reliable epoch data sets with reasonable photometric errors (<0.15 mag).

Figure 1 shows selected R_C-band images taken at IAO and OAO; the circumnuclear coma was clearly detected in the center of all images. In addition, a feeble tail extended between the anti-solar direction (${{\boldsymbol{r}}}_{\odot }$ vector) and the negative velocity vector projected on the celestial plane ($-{\boldsymbol{v}}$). Note that the dust tail is not clearly seen in Figures 1 (h)–(i) because it extended along the line of sight (in fact, the vectors between the anti-solar direction and the negative velocity nearly aligned with the observer–comet vectors in these images). Unlike the images in Paper I and Stevenson et al. (2014), we could not detect a lingering dust tail oriented along $-{\boldsymbol{v}}$. We interpret this invisibility as being due to the fact that the exposure times were not long enough to detect such a faint structure. In fact, our group succeeded in the detection of the lingering dust cloud by using a much deeper imaging observation at the Kiso Observatory (Ishiguro et al. 2015). We will report that result in a separate paper and concentrate here on the analysis of fresh dust particles in the coma.

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Figure 2 shows the surface brightness profiles of the near-nuclear coma with respect to the radial distance ϱ. We binned the radial-distance logarithmically spaced bins over 10 < ϱ < 100, calculated the average values within each bin, and plotted normalization at ϱ = 325 in which the data points are vulnerable to the seeing effects. For comparison, we show power functions with the indices of m = −1 (solid lines) and m = −1.5 (dashed lines). It is found that our data show profiles lying between these two power functions, but strictly speaking, closer to the power function with m = −1.5 (except for the later stages at which the comet was located nearly 3 AU from the Sun).

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It is known that a steady-state dust cloud expanding with an initial velocity, but no acceleration, shows a surface brightness profile with m = −1. The application of the ${Af}\rho$ parameter (where A denotes the albedo of dust particles and f denotes their packing density within a considered aperture, ρ) was contrived assuming a simple steady-state dust coma. In this case, the flux within the aperture, multiplied by ρ, should be a constant regardless of the size (A'Hearn et al. 1984). However, this is not the case for general cometary dust comae, where dust particles are supposed to be accelerated by the solar radiation pressure. Jewitt & Meech (1987) considered a more realistic case of a cometary dust cloud, that is, a steady-state flow of dust particles under the solar radiation field, and noticed that the surface brightness follows a power function with an index of m = −1.5. Thus, the surface brightness profiles of 17P/Holmes can be explained by continuous dust ejection from the nucleus under the solar radiation field. Since the solar radiation pressure made a non-negligible contribution to the surface brightness profile of 17P/Holmes, we chose a small physical distance, ρ = 5000 km (428–755 depending on the distance from the comet), for the aperture photometry below. This value is large enough to diminish the nightly atmospheric effect while small enough to reduce the influence of solar radiation pressure.

We deduced the absolute magnitudes of the comet, which correspond to the magnitude at a hypothetical point in space, namely, a heliocentric distance of r_h = 1 AU, an observer distance of Δ = 1 AU, and a solar phase (Sun–comet-observer's) angle of α = 0°. This magnitude is given by

$$\begin{eqnarray}&&{m}_{{\rm{R}}}(1,1,0)={m}_{{\rm{R}}}-5\;{\mathrm{log}}_{10}({r}_{{\rm{h}}}{\rm{\Delta }})-2.5{\mathrm{log}}_{10}{\rm{\Phi }}(\alpha ),\end{eqnarray} \tag{ 1 }$$

where m_R denotes the observed R_C-band magnitude. Since the comet was observed in a moderate phase angle range (α = 12°–25°), we need to correct the phase darkening of the dust cloud as written in the third term of Equation (1). We adopted a commonly used empirical scattering phase function, $2.5{\mathrm{log}}_{10}$Φ(α) = βα, where $\beta =0.035$ mag deg⁻¹ is assumed (see, e.g., Lamy et al. 2004, p.223). Figure 3 shows the absolute magnitudes after UT 2008 December 24 with respect to r_h. In Figure 3, there is a general trend of the magnitude decreasing (i.e., the brightness increasing) as the comet approaches the perihelion. The trend can be explained naturally by extra-solar heating making the comet more active. A temporal increase in the brightness (i.e., a minor outburst) was detected on UT 2015 January 26 at r_h = 2.99 AU. Except for the data during this minor outburst, the outbound data (in 2014–2015) appear to be about 1–2 mag fainter than the inbound data (in 2013), though they were taken around the same distance from the Sun.

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We derived ${Af}\rho$ as well, which is given by

$$\begin{eqnarray*}&&{Af}\rho =K\quad {\left[\displaystyle \frac{{\rm{\Delta }}}{\mathrm{AU}}\right]}^{2}{\left[\displaystyle \frac{{r}_{{\rm{h}}}}{\mathrm{AU}}\right]}^{2}{\left[\displaystyle \frac{\rho }{\mathrm{cm}}\right]}^{-1}\times {2.512}^{(-{m}_{\odot }+{m}_{{\rm{R}}})},\end{eqnarray*}$$

where ${m}_{\odot }$ is the R_C-band magnitude of the Sun at r_h = 1 AU. ${\rm{K}}$ is a constant of 8.95 × 10²⁶, used for unitary transformation of distances. We adopted ${m}_{\odot }$ $=\quad -27.11$ (Drilling & Landolt 2000). We tabulated the derived ${Af}\rho$ values and absolute magnitudes in Table 2.

Table 2.  ${Af}\rho$ and Dust Mass-loss Rate Values of 17P/Holmes

UT Date	${Af}\rho$ (cm)	${\dot{M}}_{d}$ (kg s−1)
2013/05/04.67	67	0.61
2013/05/10.75	97	0.86
2013/05/20.54	103	0.87
2013/07/13.58	116	1.1
2013/07/31.58	121	1.3
2014/07/02.79	179	2.4
2014/07/04.79	177	2.4
2014/07/05.75	160	2.2
2014/07/17.75	126	1.8
2014/07/18.76	140	2.0
2014/07/24.81	185	2.6
2014/08/04.76	104	1.5
2014/08/06.79	99	1.4
2014/08/20.80	117	1.7
2014/08/22.79	95	1.4
2014/08/31.72	112	1.6
2014/09/03.71	89	1.3
2014/09/05.80	103	1.5
2014/09/10.73	96	1.4
2014/09/11.70	111	1.6
2014/09/13.67	102	1.4
2014/09/14.74	94	1.3
2014/09/15.70	92	1.3
2014/09/16.33	103	1.4
2014/09/20.75	88	1.2
2014/09/23.76	87	1.2
2014/09/26.75	87	1.2
2014/10/29.68	77	0.83
2014/11/19.54	56	0.50
2015/01/29.58	364	3.6
2015/01/30.46	344	3.4
2015/01/31.53	352	3.5
2015/02/19.58	74	0.75
2015/02/20.54	73	0.75
2015/02/24.37	55	0.56
2015/03/16.51	35	0.35

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Figure 4 shows the r_h-dependence of ${Af}\rho$ between 2013 and 2015. In this figure, the notations of all symbols are the same as those in Figure 3. At the given heliocentric distance, ${Af}\rho$ values in the 2014 data (after the perihelion passage) are at least 2.5 times below those in 2013 (before the perihelion passage). We appended the trend lines with a slope in the single logarithmic plot (a) to signal the differences in ${Af}\rho$ between the inbound and outbound orbits. By fitting data with a function, ${Af}\rho \propto {10}^{{{ar}}_{{\rm{h}}}}$, we obtained a = −0.16 cm AU⁻¹ for inbound data and −0.20 cm AU⁻¹ for outbound data. We did not detect any change in ${Af}\rho$ at the exact position of the 2007 outburst (see the dashed vertical line). In contrast, a sudden but minor brightening was observed on UT 2015 January 26 (at r_h = 2.99 AU ), increasing the flux by a factor of ∼10. Soon after the minor outburst, ${Af}\rho$ was higher than the trend line for about one month and came back again to follow the original decreasing trend, although the trend lines do not have any physical implications.

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As suggested in A'Hearn et al. (1984), ${Af}\rho$ can be used as an index to characterize the dust-production rate. It is also possible to derive the dust-production rate from photometric magnitudes. We first calculated the mean optical cross-section of the dust coma by adapting the same manner as Luu & Jewitt (1992) whose equations are defined as

$$\begin{eqnarray}&&{p}_{{\rm{R}}}\;{C}_{{\rm{c}}}=2.25\times {10}^{22}\pi \;{r}_{{\rm{h}}}^{2}\;{{\rm{\Delta }}}^{2}\;{10}^{0.4({m}_{\odot }-{\bar{m}}_{{\rm{R}}})},\end{eqnarray} \tag{ 2 }$$

where p_R is the geometric albedo (p_R = 0.04 was assumed) for 17P/Holmes, and C_c is the optical cross-section of dust particles within the aperture. Next, we obtained a parameter η, defined as the ratio of C_c to the cross-section of a nucleus, C_n (i.e., η = C_c/C_n). Applying an effective nuclear radius of r_obj = 2.07 ± 0.31 km derived by an infrared observation (Stevenson et al. 2014), we obtained C_n = 1.34 × 10⁷ m². Except for the sudden brightening at r_h = 2.99 AU, η has decreased from 5.38 to 1.11, which is even smaller than the value measured at r_h = 4.15 AU on UT 2008 December 26 in Paper I.

We derived the dust mass-loss rate with η in the same manner as Paper I, using an equation in Luu & Jewitt (1992),

$$\begin{eqnarray}&&\dot{{M}_{{\rm{d}}}}=\displaystyle \frac{1.1\times {10}^{-3}\pi {\rho }_{{\rm{d}}}\bar{a}\eta {r}_{\mathrm{obj}}^{2}}{\phi {r}_{{\rm{h}}}^{1/2}{\rm{\Delta }}}.\end{eqnarray} \tag{ 3 }$$

where ${\rho }_{{\rm{d}}}$ is the mass density of dust particles, $\bar{a}$ is the averaged small particle size, and ϕ is for the aperture size for photometry in arcseconds, respectively. In estimating $\dot{{M}_{{\rm{d}}}}$, we assumed $\bar{a}$ = 1.0 × 10⁻⁶ m and ${\rho }_{{\rm{d}}}$ = $1000\;{\rm{kg}}$ m⁻³. The effects of different aperture sizes can be cancelled by the denominator in Equation (3).

Figure 5 shows the result for the dust-production rate. The change of the dust mass-loss rate appears to be explained in a similar way to those of the absolute magnitude and of the ${Af}\rho$, in that it has been declining with increasing heliocentric distance. The dust-production rates around the 2014 perihelion passage were about five orders of magnitudes lower than the maximum value during the 2007 outburst (3 × 10⁵ kg s⁻¹, Li et al. 2011), while they were comparable to that of the pre-outburst data at r_h = 2.23 AU (i.e., 2.8 kg s⁻¹ in Paper I). The peak around r_h = 3.0 AU is in accordance with the sudden explosion of 17P/Holmes.

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It is true that the derivation of the above dust mass-loss rate is crude because we have not considered the dust average particle size ($\bar{a}$) seriously. In fact, the ejection of large particles has been confirmed from a variety of comets, including 17P/Holmes (see Paper I). Our estimate for $\dot{{M}_{{\rm{d}}}}$ would be significantly (two to three orders of magnitude) lower than in the case of big particles ($\bar{a}$ = 100 μm−1 mm). However, we suggest that the mass-loss derivation still yields valuable information for monitoring the activity of the comet. It would not be unreasonable to assume that the size distribution would be constant over the period in a steady state. In this case, the relative values of $\dot{{M}_{{\rm{d}}}}$ are reasonable for comparing the activity at different solar distances.

It is interesting to notice that the dust-production rate became equivalent to the level before the 2007 outburst when the AKARI infrared telescope happened to observe the comet (see Paper I). Note that almost the same model was applied to derive $\dot{{M}_{{\rm{d}}}}$ using the AKARI infrared data, although there is a subtle difference in conversion from flux to the cross-section between optical and infrared data. This similarity suggests that the activity was restored to its former state, though the comet has shown lingering activity for years when it was around its aphelion. It is probable that the area excavated by the 2007 outburst was mostly covered with an insulating dust mantle.

Now, we show our derivation of the active area fraction of the nuclear surface. The overall methodology is the same as that of Paper I (presented in Section 3.4 therein). We consider an instant thermal equilibrium between the incident solar influx, thermal radiation from the nucleus, and latent heat of water ice sublimation to calculate the gas production rate at given heliocentric distances. The energy balance equation of a spherical body is given by

$$\begin{eqnarray}&&\displaystyle \frac{{S}_{0}}{{r}_{{\rm{h}}}^{2}}(1-{A}_{{\rm{p}}})\mathrm{cos}\;z={\epsilon }_{{\rm{E}}}\sigma {T}^{4}+{L}_{{\rm{w}}}(T)\displaystyle \frac{{dZ}}{{dt}}\;\;\end{eqnarray} \tag{ 4 }$$

where S₀ is the solar flux at r_h = 1 AU, z is the zenith distance of the sunlight (the angle between the sunlight and normal vector of the local surface), ${\epsilon }_{{\rm{E}}}$ is the emissivity, σ is the Stefan–Boltzmann constant, T is the equilibrium temperature of the nucleus, ${L}_{{\rm{w}}}(T)$ is the latent heat of water ice sublimation, and ${dZ}/{dt}$ is the sublimation rate of water ice. A_p is the R_C-band geometric albedo identical to p_R. Since ${L}_{{\rm{w}}}(T)$ and ${dZ}/{dt}$ (as well as the sticking coefficient and the Clausius–Clapeyron equation) are dependent on the equilibrium temperature (T), we can rearrange Equation (4) into a function of equilibrium temperature. Integrating ${dZ}/{dt}$ over the sunlit hemisphere with the calculated temperature and assuming a water/gas ratio of κ, we can compute the dust mass-loss rate:

$$\begin{eqnarray}&&{\dot{M}}_{{\rm{d}}}=\displaystyle \frac{2\pi {r}_{\mathrm{obj}}^{2}f}{\kappa }{\displaystyle \int }_{0}^{\pi /2}\left(\displaystyle \frac{{dZ}}{{dt}}\right)\mathrm{sin}z\;{dz},\end{eqnarray} \tag{ 5 }$$

where f is the active area fraction on the cometary surface. We adopted κ = 0.6, which provided reasonable results from observations (Paper I) and a theoretical thermal model of the 17P/Holmes nucleus (Hillman & Prialnik 2012).

Comparing the derived dust mass-loss rates in Equation (3) with theoretical ones in Equation (5), we could derive the fractional active area of the cometary nucleus, f. In Figure 6, f is plotted with respect to the true anomaly, ${\theta }_{{\rm{f}}}$. Since the true anomaly of a comet changes slowly around the aphelion, but rapidly near the perihelion, this figure efficiently shows the time evolution of the fractional active area. Crosses and filled squares are quoted from Paper I to compensate for the fractional active area soon before and after the 2007 outburst event. After the 2007 outburst, the ratio of active-to-inert surface area had significantly increased, even around the aphelion, probably because the excavated area had been sufficiently preserved under low temperature to quench the water sublimation rate. During the inbound orbit, however, the f value significantly decreased by nearly two orders of magnitude and became equivalent to the level of activity before the 2007 outburst. Although the fractional active areas were tentatively induced by the sudden brightness enhancement of UT January 26 at 2.99 AU, it fell to the original level within a month. From this evidence, we conjecture that adiathermic materials (sublimation-driven dust particles) spread over the surface and prevented the sublimating icy volatile materials from being ejected outward from the nucleus.

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In the previous sections, we have shown a rapid dormancy for 17P/Holmes, due to the formation of an insulating dust mantle, despite the expectation in Paper I. To sum up the major finding of this research, we consider whether the period is enough to develop such a dust mantle on the comet.

Rickman et al. (1990) implied that the formation of a stable dust mantle is preferred when the spin axis is on the comet's orbital plane and when the perihelion distance is r_h ≥ 2 AU. Jewitt (2015) suggested that solar heat penetrates only a few diurnal thermal skin depths into the surface, about 10–20 cm on 67P/Churyumov–Gerasimenko (Jupiter-family comet, a dynamical analog to 17P/Holmes). In that regard, it is noteworthy that 17P/Holmes has shown saliently dormant features over intervals far shorter than the dynamical lifetime (≈1×10⁴ years; Levison & Duncan 1997). Since a large fraction of the fresh surface of 17P/Holmes was exposed by the 2007 outburst, this would provide a unique opportunity for researchers to estimate the formation timescale of the dust mantle. 17P/Holmes spends more than half a revolution period beyond the heliocentric distance of 3 AU. Taking into account the persistent activities of the comet around its aphelion (Paper I), it should have had favorable conditions in developing the dust mantle with continuously outward sublimating volatiles over quite large portions of its orbit.

We performed an order-of-magnitude estimate following a method by Jewitt (2002; Section 4.7 therein). Regarding the ballistic redeposition of resurfacing of a comet and restricting the activity to within a limited active area, we considered a rotational period of P_rot = 7.2–12.8 hr (Snodgrass et al. 2006), a nuclear density of ${\rho }_{n}$ = 1000 kg m⁻³, a capture fraction of f_B = 10⁻³, an active area fraction of the comet's surface (ψ in Jewitt (2002)) of f = (2–3) $\times \;{10}^{-3}$, and a mass-loss rate of ${\dot{M}}_{{\rm{d}}}$ (see Section 4.2). As a result, we obtained a diurnal skin depth of the dust mantle of L_D = 5–7 cm, thick enough to quench subsurface ice sublimation, and found that the timescale for growing up to L_D was ${\tau }_{B}$ = 5–10 years. Although there may be uncertainties in this estimate, our result (i.e., a mantle growth timescale of $\lesssim 7$ years) is consistent with the estimate by the ballistic mantle model.

There are several examples of in situ observations on similar comets that support the rapid formation of a dust mantle on Jupiter-family comets. The nucleus of 9P/Tempel 1 has been investigated by two flyby spacecraft missions, Stardust-NExT and Deep Impact, separated by one orbital period of 5.5 years (Kobayashi et al. 2013; Thomas et al. 2013). From the topographical changes that took place between the missions and observations of the jet plume, it was suggested that 9P/Tempel 1 has a dust mantle consisting of micron-scale dust grains. In addition, Schulz et al. (2015) investigated data for 67P/Churyumov–Gerasimenko, taken with the Cometary Secondary Ion Mass Analyser (COSIMA) on board the ESA Rosetta spacecraft, and suggested that ice-free dust would have accumulated on the cometary surface, quenching the subsurface icy volatile sublimations and restricting the activity within the localized active area.

Rosenberg & Prialnik (2009) studied a numerical model of 67P/Churyumov–Gerasimenko and found that the dust mantle thickness varies over the surface in the range of 1–10 cm, which is slightly thinner and thicker than the diurnal skin depth of solar radiation at a given heliocentric distance. In addition, a state of low activity can exist ubiquitously over cometary surfaces, mainly due to thermal effects that help active regions to keep opening up again (Rickman et al. 1990). In these regards, if the thickness of 17P/Holmes's surface coverage was shallow enough for sunlight to penetrate the refractory layers or for inner sublimation pressure to crack and come to the dust–ice interface, certain regions could suddenly manifest minor outbursts. Therefore, a minor brightness enhancement of 17P/Holmes on UT 2015 January 26 can be explained in terms of an unstable nucleus and inhomogeneous dust mantle coverage.

We also note that the post-outburst activity of 17P/Holmes in 1892 showed a trend similar to our results. The flux dropped rapidly by two orders of magnitude in the following return in 1899, but slowly decreased by a factor of two to five over one century (Sekanina 2009a). This suggests that the rapid drop could be explained by the rapid development of a dust mantle, as we discussed above, while the prolonged hibernation of the cometary activity can be attributed to the additional accumulation of refractory materials and/or lost of near-surface ice. From the repetitive evolutionary pattern of 17P/Holmes over one century, it is reasonable to think that the activity of the comet is highly controlled by the formation and evolution of dust mantle.