2007 OUTBURST OF 17P/HOLMES: THE ALBEDO AND THE TEMPERATURE OF THE DUST GRAINS

The Rc-band images of 17P/Holmes were taken at Kiso Observatory (Nagano, Japan, 137°37'422E, 35°47'387N, 1130 m) and Ishigakijima Astronomical Observatory (Okinawa, Japan, 124°08'214E, 24°22'223N, 196.7 m). The observations were carried out using the 2KCCD camera mounted on the 105 cm Schmidt telescope (F/3.1) at Kiso and Apogee U6 1 K × 1 K CCD camera on 105 cm Ritchey–Chrétien telescope (F/12) at Ishigakijima, respectively. The field of views of these instruments are 50' × 50' with a pixel resolution of 15 at Kiso and 66 × 66 with a pixel resolution of 039 at Ishigakijima. The observations were performed by the observatory staff mainly for the public relations. The observed raw data were reduced using bias (zero exposure) or dark frames, plus flat-field data. The flattened images were known to be uniform in sensitivity at the ± 3% level around the area of 17P/Holmes. No photometric standard stars were observed at Kiso, while standard stars were observed at Ishigakijima. We calibrated the flux of the data using the field stars listed in the USNO–B1.0 catalog (Monet et al. 2003) and Carlsberg Meridian Catalog (Morrison et al. 1990) to eliminate the uncertainty of time-variable atmospheric absorption (in fact, the weather conditions were unstable during these optical runs). The photometric error was 0.2–0.3 mag.

The mid-infrared images of 17P/Holmes were taken using COMICS (Kataza et al. 2000; Okamoto et al. 2003) mounted on the 8.2 m Subaru Telescope from 2007 October 25 to 28 UT. The details of the observations were given in Watanabe et al. (2009). The combination of COMICS and Subaru telescope provides an imaging capability of 40'' × 30'' field of view with spatial resolution of 013 pixel⁻¹. We used four different filters, that is, 8.8 μm (Δλ = 0.8 μm), 12.4 μm (Δλ = 1.2 μm), 18.8 μm (Δλ = 0.9 μm), and 24.5 μm (Δλ = 0.8 μm) bands. To eliminate the high sky background at mid-infrared wavelengths, we applied the secondary mirror chopping technique with a 60'' throw. HD21552 was observed for the photometric standard stars. We applied a standard reduction procedure of mid-infrared data taken on the ground-based observatories, i.e., chopping subtraction and flat fielding. Note that the mid-infrared images did not cover the entire dust cloud because of the narrow field of view (see Figure 1). Due to the low chopping frequency, the sky emission was not completely canceled out. In addition, some fraction of the thermal radiation of the dust grains was also subtracted through the chopping subtraction technique. This makes it difficult for us to determine the absolute brightness of the 17P/Holmes dust cloud. Therefore, we do not deal here with the absolute brightness of the entire dust cloud. We examined the brightness of the distinctive features by the aperture photometry. We set the same aperture size and the same location in the sky for the aperture photometry when we compared the optical and this mid-infrared data. The flux calibration error was ∼10% at most.

In addition, we made use of not only our data above but also the near-infrared data. It was acquired on 2007 October 27 using the NASA Infrared Telescope Facility (IRTF) 3 m telescope atop Mauna Kea, Hawaii, with SpeX, when we made observations in both optical and mid-infrared wavelengths (Yang et al. 2009). We compared our data with these to find whether or not our data and those by Yang et al. (2009) are consistent (especially inconsistency in the color temperature). They used 03 × 15'' slit and adopted the point source extraction algorithm using an average extraction aperture box width of 9''. The resultant spectrum appears in Yang et al. (2009). We extracted the data values from the figures in the paper and compared our results. Whereas the detailed observation times of IRTF/SpeX observation are not described in their reference, we ignored small differences in time (<0.5 days).

As noted by the previous studies (Watanabe et al. 2009; Montalto et al. 2008; Lin et al. 2009; Moreno et al. 2008), the morphology of 17P/Holmes was quite different from those of the normal comets. It was composed of (1) a spherically expanding envelope around the nucleus (hereafter SPHE), (2) a detached blob extended toward the southwest (BLOB), and (3) a central condensation (CENT). SPHE was not found in Subaru/COMICS images because of the narrow field of view (Figure 1). Similarly, SPHE and BLOB were not mentioned in the near-infrared observation. It is likely that SPHE and BLOB were out of the field of view of IRTF/SpeX or too broad to be detected by these measurements. Apparently, SPHE expanded radially enclosing both BLOB and CENT. The moving direction of BLOB was exactly in correspondence with the projected direction of the Sun and the comet vector, which leads to a presumption that BLOB was accelerated by the solar radiation pressure or the rocket force (Watanabe et al. 2009). CENT could be mainly composed of dust grains ejected with small ejection velocity by the initial outburst. Therefore, we may conjecture that larger particles were dominant in CENT. In addition, there could be fresh particles injected into CENT and SPHE following the initial outburst. Although it might be still an open question whether the 17P/Holmes dust cloud could be categorized into these three, we use SPHE, BLOB, and CENT in this paper for the sake of convenience.

As we mentioned above, we cannot derive the albedo and the temperature of the entire dust cloud of 17P/Holmes because only the optical data could cover the whole cloud while the mid-infrared could cover CENT and BLOB. Hence, we derived the flux of the distinctive structures, i.e., CENT (within 9'' aperture diameter) and BLOB (within 15'' aperture diameter) by aperture photometry. We set the aperture of CENT to match the IRTF/SpeX measurement The results are shown in Figures 2–4. We found no obvious differences in spectral energy distribution (SED) shape between CENT and BLOB observed on October 24. In Figure 2(a), we also show the near-infrared spectrum taken by IRTF/SpeX. The near-infrared spectrum is smoothly connected to the optical data, implying that the calibration processes of these two data sets are consistent. In the SED, the dust cloud of 17P/Holmes was observable through the scattered sunlight in the optical and near-infrared wavelengths (λ < 3 μm) and observable through the thermal radiation in the mid-infrared wavelength. At shorter wavelengths (λ < 3 μm), the most significant spectral feature of 17P/Holmes is the negatively sloped continuum mainly originated in the solar spectrum. There is a deep absorption band around λ = 3 μm (Yang et al. 2009). As noticed by Yang et al. (2009), a weak but evident increase in flux was seen at λ>3.2 μm. There were strong silicate emission features at 10 μm and 18 μm as shown in Watanabe et al. (2009).

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In estimating the albedo and the temperature of the particles in CENT and BLOB, we first assumed that the dust particle has a graybody property which radiates energy having a blackbody distribution reduced by a constant factor, and fit the optical and mid-infrared data. The emissivity, in this assumption, is considered to be independent of particle size and wavelength, in such a way that the entire dust cloud within the aperture behaves as a graybody. We consider the flux at 12.4 μm and 24.5 μm as the thermal continuum flux (discuss later). The model spectrum is shown by the dashed line in Figures 2–4. The best-fit parameters for the albedo and the color temperature are A_p(α) = 0.12 ± 0.04 and 195 ± 17 K on October 25, A_p(α) = 0.043 ± 0.013 and 186 ± 26 K on October 27, and A_p(α) = 0.032 ± 0.014 and 172 ± 35 K on October 28, respectively. There is no difference in the albedo and the temperature between CENT and BLOB (see Figure 2). The similarity between BLOB and CENT would suggest that optical properties of the dust grains in these different dust clouds are similar. Note that we use the albedo A_p(α) defined by Hanner et al. (1981) as the ratio of the energy scattered by particles at phase angle α to that scattered by a white Lambert disk of the same geometrical cross section. The J-band albedo of the other comets was derived to be 0.02–0.1 around the phase angle of 10°–20° (Hanner et al. 1985; Hanner & Newburn 1989; Hanner 2003), which is consistent with our results obtained after October 27 (i.e., 4 days after the outburst). However, we should point out the albedo obtained on October 25 (∼2 days after the outburst) was slightly larger than those of the other comets. The color temperature of 17P/Holmes is consistent with that of a blackbody at 2.44 AU (i.e., 179 K), as already pointed out by Watanabe et al. (2009). It is not obvious but likely that the albedo and probably the color temperature could decrease over the observed duration. The silicate feature could also decrease over 3 days (Table 2).

In Figure 2(a), we ignored the observed data at 3–4 μm for the graybody fitting because we could not fit both 3–4 μm and 9–25 μm spectra with a single color temperature. The fitted SED decreases monotonically at wavelengths ≲5 μm but the observed SED shows the minimum around 3–4 μm. Yang et al. (2009) attributed the decreased negative slope to the thermal radiation of the dust grains, and derived the color temperature 360 ± 40 K. Since the flux contribution of the graybody at 170–200 K is negligible around 3–4 μm, it is reasonable to think that the temperature of the dust particles in the cloud is not homogeneous. What caused this lack of uniformity in the temperature?

The equilibrium temperature of the dust particles can be computed by considering the thermal equilibrium, i.e., a balance between the input solar energy on a grain (E_a) and the output energy from a grain (E_r) plus sublimation energy (E_s, if it includes volatiles), that is, E_a = E_r + E_s. For the dust particles which have no icy inclusions, we can ignore the sublimation energy E_s. These energies are defined by Mukai (1986) as follows:

$$\begin{equation} E_a = \pi \left(\frac{a}{r_h}\right)^2 \int ^\infty _0 S_\odot (\lambda) Q_{\rm abs}(a,\lambda, m^*) d\lambda, \end{equation} \tag{ 1 }$$

$$\begin{equation} E_r = 4\pi a^2 \int ^\infty _0 \pi B(\lambda,T_{eq}) Q_{\rm abs}(a,\lambda, m^*) d\lambda, \end{equation} \tag{ 2 }$$

$$\begin{equation} E_s = 4 \pi a^2 \rho _w \left|\frac{da}{dt}\right| L_w, \end{equation} \tag{ 3 }$$

and

$$\begin{equation} \left|\frac{da}{dt}\right| = \frac{\mu m_p p_w(T)}{\rho _w \sqrt{2 \pi \mu _w m_p k T_{eq}}}. \end{equation} \tag{ 4 }$$

In Equation (1), S_☉(λ) is the solar flux at 1 AU at the wavelength λ and r_h is the heliocentric distance of the dust particle, which has a radius a and a complex refractive index m*(λ). For the solar spectrum S_☉(λ), we use the data in Mukai (1989). We assume a spherical particle for simplicity in calculation, i.e., the efficiency factor for absorption and emission Q_abs is obtained by Mie theory as functions of a and λ (Bohren & Huffman 1983). We are not concerned in this paper with the application of nonspherical particles due to the difficulty in Mie theory (Bohren & Huffman 1983), although there are challenging methods of calculation of the optical properties of irregularly shaped particles such as the discrete dipole approximation (DDA) and T-matrix method (Draine 1988; Mishchenko et al. 1996). For a heterogeneous material consisting of an icy matrix embedded with small refractory inclusions, the Maxwell–Garnett mixing rule to calculate m* is applied (Mukai 1986). ρ_w and L_w in Equations (3)–(4) denote the mass density of grain material and the latent heat of sublimation of ice. In Equation (2), B(λ, T_eq) means the Planck function at the grain temperature T_eq. The rate of size decrease |da/dt| is shown in Equation (4), where μ is the mean molecular weight of the evaporated molecules and m_p and k are the atomic mass unit and the Boltzmann constant, respectively. Since the water ice is the dominant volatile around 2.44 AU, we consider the sublimation of water ice. We apply a functional form of the latent heat of water ice sublimation in Delsemme & Miller (1971). In Equations (3) and (4), we apply μ_w = 18 and ρ_w = 1 g cm⁻³. In Equation (4), the saturated vapor pressure of water p_w(T) is given by the Clausius–Clapeyron equation.

We solve this energy balance at 2.44 AU for icy heterogeneous grains (what is called, dirty water ice in Mukai 1986), absorbing grains (magnetite, graphite, amorphous carbon; Kelley & Wooden 2009; Ootsubo et al. 2007), and silicate grains (Draine & Lee 1984) as a function of grain radius (Figure 5). We applied the optical constants of magnetite, graphite, and water ice in Mukai (1989) and amorphous carbon in Preibisch et al. (1993). In Figure 5, we also show the color temperature derived by Yang et al. (2009) and ourselves. Strictly speaking, the color temperature of the grain is not the same as its equilibrium temperature, because the emissivity at infrared wavelengths (where the color temperature is estimated) depends on the wavelength. However, we assume that the wavelength dependence of emissivity is weak in the middle infrared wavelengths, except for remarkable silicate features. The temperature of a grain with a ≳ 1 μm becomes almost independent of the radius and close to the blackbody temperature. On the other hand, the temperature of a small grain with a < 1 μm is largely dependent on the compositions. Only small (a < 1 μm) dry absorbing particles without icy inclusion show the equilibrium temperature >300 K. It is, therefore, likely that the hot dust particles derived by IRTF/SpeX observation are attributed to the small (a < 1 μm) absorbing grains while cold dust particles to the large (a ≳ 1 μm) grains. In addition, this computation suggests that pure water ice grains are less dominant in relation to the thermal radiation in the infrared wavelength.

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To duplicate the observed spectrum of 17P/Holmes, we consider the absorbing materials composed of different sizes. We, thus consider the size dependence of the temperature for graphite, magnetite, and amorphous carbon as a representative of absorbing materials. We simplify the computed results of absorbing materials in Figure 5 as follows:

$$\begin{eqnarray} T(a)= \left\lbrace \begin{array}{@{}ll} 420 & (a<0.1 \;\mbox{$\mu $m}) \\ \ms\ms C_1 a^{C_2}+C_3 & (0.1 \;\mbox{$\mu $m}\ \leqq a \leqq 1\;\mbox{$\mu $m})\\ \ms\ms 177 & (a>1\;\mbox{$\mu $m}) \end{array} \right.\!\!\!{,} \end{eqnarray} \tag{ 5 }$$

where C₁ = 14909.9, C₂ = −0.00679919, and C₃ = −14719.4 (Figure 5).

A size distribution of the form

$$\begin{eqnarray} n(a)= \left\lbrace \begin{array}{@{}ll} N a^{q} & (a_{\rm min} \leqq a \leqq a_{\rm max})\\ \ms\ms 0 & (a < a_{\rm min}, a>a_{\rm max})\\ \end{array} \right. \end{eqnarray} \tag{ 6 }$$

was used to fit to the thermal radiation spectrum of 17P/Holmes, where a_min and a_max are minimum and maximum radii of the grains, q the power index of the size distribution, and N the reference number of the particles. Although grains smaller than a_min may be present in the cloud, we assumed that they do not contribute significantly to the observed brightness. The flux density F_λ is computed by integrating over the size distribution at each wavelength:

$$\begin{eqnarray} F_{\lambda } &=& \frac{1}{\Delta ^2} \Bigg\lbrace \frac{S_{\odot }(\lambda)}{r_h^2} A_p(\alpha) \int ^{a_{\rm max}} _{a_{\rm min}} a^2 n(a) da\nonumber\\ &&+ \int ^{a_{\rm max}} _{a_{\rm min}} Q_{\rm abs}(a) B(\lambda, T_{eq}) \pi a^2 n(a) da \Bigg\rbrace. \end{eqnarray} \tag{ 7 }$$

In Equation (7), we assume that the size of the dust particle is large enough to scatter the sunlight (i.e., a ≧ λ_opt/(2π)≈ 0.1 μm) because the dust cloud was reported to be distinctively red (Lin et al. 2009). We simplify the absorption efficiency as follows:

$$\begin{eqnarray} Q_{\rm abs}(a)= \left\lbrace \begin{array}{@{}ll} 1 & (a \geqq \lambda /(2\pi))\\ 2\pi a/\lambda & (a < \lambda /(2\pi)).\\ \end{array} \right. \end{eqnarray} \tag{ 8 }$$

Figure 6 illustrates the model fit to the SED. We derived parameters a_min, a_max, q, and A_p(α) by the simplex method (Press et al. 1992). It is clear that, not only at optical and mid-infrared wavelengths but also at 3–4 μm, our heterogeneous grain size model fit the observed SED. The derived parameters are a_min = 0.3 μm, a_max>100 μm, q = −2.5, and A_p(α) = 0.032 ± 0.010, respectively. As mentioned above, the thermal radiation around 3–4 μm is sensitive to the small grains, that is, a_min and q, but insensitive to a_max. It is, therefore, important to notice that our estimate of a_max is just a lower limit to the maximum size of the particles. It is worth noting that the derived q is larger than generally refereed values (−4 < q < −3). It is likely that large particles were dominant in the vicinity of the nucleus (within 9'' aperture) because small grains expanded rapidly via gas drag while large grains stayed there. Similar discussion is found in the polarimetric study of dust grains in CENT (Zubko et al. 2009). Assuming steady dust ejection with an ejection velocity given by v_ej∝ a^−0.5, q = −2.5 in Equation (6) corresponds to q = −3 in the production size distribution. Considering the fact that the production rate decreased (Schleicher 2009), we expect q < −3 in the production size distribution, which is consistent with the other comets studies (see Section 3.5).

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We can evaluate the total mass of the particles lost by the outburst based on the albedo evaluated above. It was derived by several authors: Montalto et al. (2008) provided an estimate of the ejected dust mass during the outburst through the extinction of stars behind the dust cloud. Assuming small grains (0.005–1 μm), they obtained a mass between 10¹²–10¹⁴ kg. Sekanina (2008) estimated the mass by the optical magnitude of the whole cloud (i.e., SPHE+BLOB+CENT) on the plateau. He supposed the geometric albedo A_p(0°) = 0.04 and concluded the mass was near 10¹¹ kg. Altenhoff et al. (2009) derived the mass using millimeter observation data near the nucleus (i.e., CENT), and deduced a mass of 4.3 × 10¹⁰ (kg) at the time of the initial outburst.

While a huge number of particles was injected into CENT, BLOB, and SPHE during the initial outburst event, a small number of new particles could be resupplied continually from the new active region on the nucleus created by the initial event. Such an aftermath was ensured by the observations of OH (Schleicher 2009) and H₂O (Dello Russo et al. 2008). Nevertheless, we would like to argue that a significant fraction of dust particles was ejected within a couple of days after the outburst because, as Sekanina (2008) asserted, the total magnitude became a constant value around this time. Here, we examine the total mass of CENT, BLOB, and SPHE which are presumably composed of the particles released by the initial event.

First, we derive the total (CENT+BLOB+SPHE) optical magnitude of 2.46 ± 0.20 on the basis of Kiso–Schmidt observation. We assume that the albedo of the dust particles was homogeneous over the entire dust cloud. The magnitude is translated into the cross-sectional area of 6.8 × 10¹³ m² and 1.8 × 10¹³ m² when we apply A_p(α) = 0.03 A_p(α) = 0.12. Hence, we follow the methodology employed by Sekanina (2008) in which he discussed the total mass by assuming the dust size distribution and the albedo. The total mass is given by

$$\begin{eqnarray} M_d &=& \int _{a_{\rm min}}^{a_{\rm max}} \frac{4}{3} \pi \rho _d a^3 n(a) da\nonumber\\ &=&\left\lbrace \begin{array}{@{}ll} \displaystyle\frac{4 \pi \rho N}{3(4+q)} \big(a_{\rm max}^{4+q}-a_{\rm min}^{4+q}\big) & (q\ne -4)\\\ms \displaystyle\frac{4}{3} \pi N \rho _d \log (a_{\rm max} / a_{\rm min}) & (q=-4),\\ \end{array} \right. \end{eqnarray} \tag{ 9 }$$

where ρ_d means the mass density of the dust particles. In Equation (9), a power index of the dust size distribution plays a critical role when we evaluate the total mass of the dust cloud. In the case of q < −4, both the brightness and the mass largely depend on the smallest grains. If q> − 3, both the mass and the brightness depend on the largest grains. The brightness and the mass become decoupled if −4 < q < −3 in which case the dust mass depends on the largest grains, while the brightness depends on the smallest grains. By tradition, it is generally believed that in the comae we see dust particles close to the observation wavelength (i.e., a≈0.1–1 μm). It could be presumed that implications in Montalto et al. (2008) were due to the tradition. Similarly, Sekanina (2008) supposed that the enormous cross-sectional area of the dust cloud resulted from microscopic grains and suggested that the particle-size distribution might be steeper than usual. He derived the mass of the dust particles supposing −4.5 < q < −4.

A near-nuclear dust cloud of 17P/Holmes was, however, detected in the radio wavelength for CENT (Boissier et al. 2008), suggesting that the particle size was large enough to radiate in the radio wavelength. Altenhoff et al. (2009) claimed Sekanina's assumption of grain size because such microscopic particles are too small to detect with radio or millimeter telescopes. It is appropriate to think that only CENT could be detected by their radio observations because the particles near the nucleus are large enough to radiate in the millimeter wavelength range. Moreno et al. (2008) studied the morphology of the dust cloud in terms of the dynamics of the particles, and found that >600 μm particles, which are much less sensitive to radiation pressure than micrometer-sized or smaller particles, could be ejected by the outburst. Evidence of such large particles is found to be ubiquitous in in situ observations (McDonnell et al. 1986; Tuzzolino et al. 2003), by the remote sensing observations of dust tail (Fulle 2004; Moreno 2009; Watanabe et al. 1990) and dust trail (Ishiguro et al. 2007; Ishiguro 2008; Sarugaku et al. 2007; Reach et al. 2000, 2007; Kelley et al. 2008), sub-millimeter and millimeter observations (Jewitt & Matthews 1997; Altenhoff et al. 1999). As a result of these studies, we found that the power index of the size distribution of almost all comets would be in the range of −4 and −3 (Fulle 2004). We would like to emphasize that the power indices for the debris associated with comet outbursts are also in this range, that is, −3.7 < q < −3.3 for 29P/Schwassmann–Wachmann 1 (Moreno 2009) and −3.4 < q < −3.3 for 73P/Schwassmann–Wachmann 3B (Ishiguro et al. 2009). Therefore, we will adopt an assumption of −4 < q < −3. Because q> − 4, the total mass of the fragments strongly depends on the largest fragment, that is, M_d≈ 4πρNa^4+q_max/(3/(4 + q)). Supposing that the mass density of the particles, ρ_d = 1 g cm⁻³, and applying A_p = 0.03 or A_p = 0.12, we can derive the mass of the particles ejected by the outburst.

The result is shown in Figure 7. Although the power index of the size distribution q (probably in the range of −4 and −3) and maximum size of the particles a_max (probably >600 μm; Moreno et al. (2008)) are not still well known, we can safely say that no less than 4 × 10¹⁰ kg of material, corresponding to the >2.5 m surface layer of the 3.42 km diameter body (we assumed the mass density of the nuclear surface layer of 0.45 g cm⁻³), was removed by the initial outburst. Note that the derived mass is a lower limit, although the mass (4 × 10¹⁰ kg) is close to that of previous studies (Sekanina 2008; Altenhoff et al. 2009). If dust emission were to take place on inhomogeneously distributed active areas on the nucleus, the derived depth (>2.5 m) would increase. Since the derived depth is deeper than a typical thickness of the surface inert dust mantle (∼1 m), we can conjecture that internal pristine materials were also ejected by the initial event and thereby the mid-infrared spectrum showed silicate features similar to Hale–Bopp (see the mid-infrared spectrum in Watanabe et al. 2009).

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