OUTBURST OF COMET 17P/HOLMES OBSERVED WITH THE SOLAR MASS EJECTION IMAGER

Data from SMEI are routinely photometrically calibrated using bright stars distributed around the sky. However, because the passband of this filterless instrument is very broad and different from the standard astronomical filters, we elected to calibrate the data against our own measurements of 17P/Holmes taken nearly simultaneously. For these, we used the University of Hawaii 2.2-m telescope to image 17P/Holmes on UT 2007 October 26.33 (DOY = 299.33) in order to photometrically calibrate the SMEI data. The spectral response of the SMEI imager is very broad, exceeding 10% in the optical wave band (4500–9500 Å) and >40% over the 6000 Å ⩽λ⩽ 7500 Å wavelength range. The central wavelength corresponds approximately to the astronomical R band. Accordingly, an R-band filter was employed at the 2.2-m telescope and calibrated in the Kron–Cousins photometric system (Landolt 1992). The comet was imaged using a Tektronix 2048 × 2048 pixel CCD camera placed at the f/10 Cassegrain focus, where the plate scale is 0219 pixel⁻¹ and the field of view is 450''×450''. We used aperture photometry with circular projected apertures and experimented to determine the optimum aperture radius for 17P/Holmes photometry. We found that an aperture radius of 800 pixels (175'') was sufficient to capture >99% of the light from the comet on this date. Such a large aperture could not be used to measure the (∼60,000 times fainter) standard star without incurring unacceptable errors from uncertainty in the sky background. Instead, an aperture 20 pixels (44) in radius, with sky determined from the median of data numbers in a surrounding annulus extending to 70 pixels (153) radius, was used to measure the Landolt (1992) standard star SA95-98. Again, we checked to be sure that this aperture captured >99% of the light from the star.

The particular circumstances of 17P/Holmes demand special mention here. The high surface brightness of the coma on UT 2007 October 26 forced the use of unusually short integrations. Normally, the Tektronix CCD camera is not used with exposures <5 s and, at shorter integration times, the linearity of the shutter (a spring-triggered leaf shutter) is in question. Spatial non-uniformity of the shutter open time with position on the CCD degrades, as does knowledge of the exact duration of the open time. To measure the importance of these effects, we compared exposures of 0.1, 0.5, 1.0 and 5.0 s to estimate possible photometric errors arising from the forced use of short integrations on 17P/Holmes. We find that systematic shutter errors are less than ∼10% for the 17P/Holmes data. This is small enough to be of no significance in the interpretation of the SMEI data.

The brightness of 17P/Holmes was measured within projected, circular apertures centered on the photocenter of the object. Use of small apertures is precluded by the large point-spread function produced by SMEI, while large apertures suffer excessive contamination by background sources. Accordingly, we employed a standard photometry aperture radius of 12 pixels (12) for our measurements, with sky subtraction determined from a contiguous annulus extending to an outer radius of 30 pixels (30; see Figure 2). We used the median of the pixel values within the sky annulus to define the sky brightness, since the median confers some protection against contamination of the sky brightness by imperfectly removed field stars.

The photometry is shown in Figure 3 as a function of time, with measurements from Cameras 1 and 2 identified. Only Camera 1 measurements were calibrated against (nearly) simultaneous observations from the University of Hawaii telescope. However, the two SMEI cameras provide overlapping coverage in the period 366 <DOY< 371, allowing us to calibrate Camera 2 against Camera 1. Based on this overlap, we have normalized the photometry by subtracting 0.08 mag from the Camera 2 measurements. Gaps in the light curve in Figure 3 appear where field stars have irreversibly compromised the comet data leading to their removal. Remaining excursions in the light curve in Figure 3 (e.g., near DOY 340) result from residual contamination of the photometry by the wings of bright, distant stars.

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To see the effects of viewing geometry on the light curve, we correct the apparent magnitudes, R, from Figure 3, to absolute magnitudes, R(1, 1, 0), using

$$\begin{equation} R(1,1,0) = R - 5 \log_{10} (r \Delta) - 2.5 \log_{10} \Phi (\alpha), \end{equation} \tag{ 1 }$$

where r and Δ are the heliocentric and geocentric distances, in AU, and Φ(α) is the scattering phase function of the comet at the phase angle α. The phase functions of active comets are difficult to measure because the phase changes are difficult to isolate from simultaneous changes in R and Δ. However, published phase functions are broadly consistent in showing a large forward scattering peak and a more modest back-scattering peak (Millis et al. 1982; Meech & Jewitt 1987; Schleicher et al. 1998). For this work, we fitted the phase function of Schleicher et al. 1998 (for 0 ⩽α⩽ 70^o) to obtain

$$\begin{equation} 2.5 \log_{10} \Phi (\alpha) = 0.045 \alpha - 0.0004 \alpha ^2. \end{equation} \tag{ 2 }$$

Near opposition, Equation (2) gives a phase coefficient of order 0.04 mag deg⁻¹, close to the characteristic values measured for the macroscopic surfaces of low albedo asteroids and cometary nuclei (Li et al. 2009 and references therein). This suggests that the back-scattering properties of the dust are dominated by particles that are optically large (2πa/λ⩾ 1, or a⩾ 0.1 μm, given λ∼ 0.6 μm). This, in turn, is compatible with the optical continuum colors, which are slightly redder than sunlight (Lin et al. 2009), and with inferences from the coma of comet P/Halley, in which particles with a< 0.1 μm were found to contribute negligibly to the integrated scattering cross-section (Lamy et al. 1987). We note that the selection of the particular form of the phase function given by Equation (2) is not critical, since the range of phase angles over which 17P/Holmes was observed was modest (85 ⩽α⩽ 19°) and the effects of phase in Figure 3 are small compared to the effects of the varying geocentric distance.

The resulting absolute magnitudes are shown in Figure 4. Comparison with Figure 3 reveals that the steep decline by about 2.5 mag in apparent brightness observed for DOY >320 is largely a geometric artifact. The fading portion of the light curve in Figure 4 is comparatively gentle, dimming by only ∼0.6 mag over the same period. This fading is dominated by the escape of dust particles from the region of the coma sampled by the photometry aperture. Figure 2 shows the change in appearance of the comet in SMEI images resulting from the partial resolution of the expanding coma by the end of 2007 December. Evidence from other observers using smaller apertures confirms this conclusion. For example, Mugrauer et al. (2009) used small aperture photometry and found fading of the apparent magnitude by ∼8 mag in the 100 days after the outburst, whereas our integrated light photometry shows fading by ∼2 mag over the same period (Figure 3), almost all of which is due to the changing observing geometry.

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The absolute magnitudes can be used to measure the effective scattering cross-section of 17P/Holmes, C_e (m²), from

$$\begin{equation} p_R C_e = 2.24 \times 10^{22} \pi 10^{0.4(R_{\odot } - R(1,1,0))}, \end{equation} \tag{ 3 }$$

where p_R is the geometric albedo measured in the R band and R_☉ = −27.11 is the apparent red magnitude of the Sun (Russell 1916). We take the geometric albedo of cometary dust to be p_R = 0.1 (Lisse 2002; Hadamcik & Levasseur-Regourd 2009). Effective cross-sections computed in this way are plotted in Figure 5, where we also show photometry taken in the hours preceding the first SMEI observation by Hsieh et al. (2010). The cross-sections are very large, rising to C_e = 5.5 × 10¹³ m² by DOY = 299.25, and equivalent to a circle of diameter 8.4 × 10⁶ m, considerably larger than the diameter of the Moon. We note that the SMEI light curve in Figure 5 is qualitatively similar to the light curve compiled by Sekanina (2008) from visual and other data taken using a wide range of instruments and techniques. However, the latter author derived a peak magnitude H₀ = −0.53 ± 0.12 from naked-eye observations, whereas SMEI data give R(1, 1, 0) = −1.8 ± 0.1 (see Figure 5). Part of the difference (perhaps ∼0.5 mag) can be attributed to the continuum color of the comet (Lin et al. 2009) and the different effective wavelengths of the two measurements. The remainder probably reflects difficulty in using the naked eye to measure the brightness of a diffuse but centrally condensed source.

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The rate of change of the cross-section, dC_e/dt (m² s⁻¹), is plotted in Figure 6, for a three day period containing the start of the outburst. Figure 6 shows that area production peaks at 11.0 × 10⁸ m² s⁻¹ on UT 2007 October 24.54 ± 0.01 (DOY = 297.54 ± 0.01), about 0.5 days before the comet attains peak brightness (and cross-section), as seen in Figure 5. The peak rate of brightening follows the estimated start of the outburst event (UT 2007 October 23.3 ± 0.3, or DOY = 296.3 ± 0.3, Hsieh et al. 2010) by 1.2 ± 0.3 days.

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To what extent is the light curve in Figures 4–6 influenced by optical depth effects in the coma? The mean scattering optical depth is given by

$$\begin{equation} \overline{\tau }(t) = \frac{C_e(t)}{\pi r_o(t)^2} \end{equation} \tag{ 4 }$$

where r_o(t) is the instantaneous radius of the coma. We write r_o(t) = V(t − t₀), where V = 550 m s⁻¹ is the expansion speed of the coma and t₀ = DOY 296.3 is the time of the start of the outburst (Hsieh et al. 2010; Reach et al. 2010). The spatially averaged optical depth computed from Equations (3) and (4) is plotted in Figure 7, where we see that the peak value in the interval of observations, $\overline{\tau }$ = 3 × 10⁻³, was attained at DOY 297.8, about 1.5 days after the start of the outburst. This does not rule out the possibility that the coma was globally optically thick before it was first observed.

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Figure 7 shows that the coma was optically thin, on average, even when at peak brightness, in agreement with the conclusion of Hsieh et al. (2010). Nevertheless, it is still possible that the coma was optically thick when measured along a line to the nucleus, a possibility that we address here with a simple model. As a reference point, we assume a spherically symmetric coma in which the number density of dust grains varies with the inverse square of the distance from the nucleus. The line-of-sight optical depth, in the optically thin limit, then varies as τ(p) ∝ p⁻¹, where p is the angle between a given line of sight through the coma and the direction to the nucleus. We write

$$\begin{equation} \tau (p) = \tau _n \left[\frac{p_n}{p}\right] \end{equation} \tag{ 5 }$$

where p_n = r_n/Δ is the angle subtended by the nucleus radius as observed from Earth and τ_n is the optical depth along a line to the center of the nucleus. We assume r_n = 1.7 km (Lamy et al. 2009) to find, at Δ = 1.6 AU, p_n = 1.5 × 10⁻³ arcsec. The average optical depth across the coma is

$$\begin{equation} \overline{\tau }= \frac{\int _{p_n}^{p_o}2 \pi p \tau (p) dp}{\int _{p_n}^{p_o}2 \pi p dp} \end{equation} \tag{ 6 }$$

where p_o = r_o(t)/Δ is the angular radius of the coma at the instant when $\overline{\tau }$ is computed. After substitution and rearrangement, Equations (5) and (6) give

$$\begin{equation} \tau _n = \frac{r_o(t)}{2 r_n} \overline{\tau }, \end{equation} \tag{ 7 }$$

provided p_n ≪ p_o.

Equation (7) is a crude approximation in that it assumes spherical symmetry and a p⁻¹ coma. Still, to order of magnitude, Equation (7) gives a useful estimate of the likely peak optical depths toward the nucleus. Figure 8 shows that, whereas the average $\overline{\tau }$ is always very small compared to unity, the coma may be optically thick along a line to the nucleus. The nucleus received no direct sunlight as a result of the outburst, proving that the energy driving the expansion was either stored or derived from another source.

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The projected angular radius of the optically thick region of the coma is obtained by setting τ(p) = 1 in Equation (5), giving p = τ_np_n. At the peak τ_n∼ 65 (DOY 297.8 from Figure 8), with p_n = 00015, we find that the optically thick region subtends an angle p = 01 as seen from Earth. This is comparable to the (∼006) angular resolution offered by the best adaptive optics systems on large telescopes, or by the Hubble Space Telescope. It is also so small that the integrated photometric characteristics of 17P/Holmes are dominated by scattering from the much larger optically thin region of the coma. Our conclusion that the coma was optically thick only in a miniscule central region is supported by the optical observations from the UH 2.2-m telescope on UT 2007 October 26 (DOY 299) that were used to photometrically calibrate the SMEI data. They show stars undimmed through the coma and a coma surface brightness increasing smoothly with decreasing projected distance from the nucleus. On the other hand, a detection of extinction was reported by Montalto et al. (2008) two days later, on UT 2007 October 28 (DOY 301). They observed the fading of stars, at 3σ levels of confidence, separated from the nucleus by 25'' < p< 180''. Our data indicate immeasurably small optical depths 3 × 10⁻⁴ < τ< 2.5 × 10⁻³ at these large projected distances and thus cannot be reconciled with the observations of Montalto et al. (2008).

The above considerations show that optical depth effects play a negligible role in shaping the overall photometric properties of 17P/Holmes in outburst. Instead, the light curve results from both the time dependence of the rate of release of mass (and cross-section) from the nucleus into the coma and the possible evolution of the scattering properties of particles once ejected. Near-infrared spectral observations of the inner coma in late October and early November revealed water ice whose sublimation in sunlight would provide a natural mechanism for disaggregating composite grains (Yang et al. 2009). Imaging observations show sub-structure suggestive of the breakup or fragmentation of centimeter- and decimeter-sized objects ejected from the nucleus of 17P/Holmes (Stevenson et al. 2010). Hsieh et al. (2010) attempted to fit the early portion of the light curve with a model assuming exponential fragmentation of dust particles and obtained fits with decay timescales of 1000 s and 2000 s. However, fits to data from their limited (∼4 hr) observing window do not match the more extensive SMEI data set presented here, and any simple model of the light curve in terms of dust fragmentation cannot be supported. All we can say based on the light curve is that the brightening reflects the combined effects of the time-dependent nucleus mass production function (assumed to be impulsive by Hsieh et al. 2010) and evolutionary changes in the dust scattering properties. The data offer no way to separate these two effects.

The conversion between the derived scattering cross-section and the particle mass is model dependent and very uncertain. The principal unknown is the dust size distribution, but the particle density is also unmeasured and its value must be assumed. The simplest model is to assume that the particles are all spheres of one effective radius, a_e, and density, ρ. Then, the total dust mass is given by

$$\begin{equation} M = \frac{4}{3} \rho a_e C_e. \end{equation} \tag{ 8 }$$

Solid spheres scatter electromagnetic radiation most efficiently when a ∼ λ (Bohren & Huffman 1983). With a_e = λ = 0.65 μm and ρ = 400 kg m⁻³, the peak C_e = 5.5 × 10¹³ m² (Figure 5) gives mass M = 1.9 × 10¹⁰ kg. The mass of the nucleus, taken to be a sphere of radius 1.7 km and having the same density, is M_n = 8 × 10¹² kg, so that M/M_n∼ 0.2%.

However, this simplest case is likely to underestimate the dust mass, because the real particles will occupy a size distribution in which large particles might contain significant mass while presenting negligible cross-section. Optical data alone provide little or no evidence concerning such particles but we can estimate an upper limit to the dust mass as follows. The spectral energy distribution from optical (0.5 μm) to mid-infrared (20 μm) wavelengths has been modeled in 17P/Holmes in terms of power-law distributions of dust particles size in which the number of particles having radius between a and a + da is proportional to a^−qda (Ishiguro et al. 2010). The models indicate q > 3 over the radius range 0.3 μm to 100 μm. Measurements in other disintegrating comets show that, while the size distribution is not precisely described by a power law of any index, the data are broadly compatible with power-law models 3 <q< 4 (Fuse et al. 2007; Jewitt et al. 2010; Vaubaillon & Reach 2010). We consider a middle value, q = 3.5, with minimum and maximum particle radii, a₁ and a₂, respectively. The effective radius is then a_e = (a₁a₂)^1/2. With a₁ = 0.1 μm (particles much smaller than this have negligible interaction with optical photons and so present no cross-section for scattering) and a₂ = 10⁻² m (Grün et al. 2001), we obtain a_e = (a₁a₂)^1/2 = 30 μm. The mass computed from Equation (8) then rises to M = 9 × 10¹¹ kg, or M/M_N∼ 10%. The range of inferred dust masses, 2 × 10¹⁰ kg <M< 90 × 10¹⁰ kg, may be compared with the best estimate from mid-infrared thermal observations, namely M = 1.0 × 10¹⁰ kg (Reach et al. 2010).

Masses near the upper limit, 2 × 10¹¹ kg, have been claimed based on millimeter wavelength radio-continuum measurements (Altenhoff et al. 2009). We have reinterpreted these measurements according to the formalism described in Jewitt & Luu (1992). The principal uncertainty is the opacity. With λ = 1 mm opacities in the range 1–10 m² kg⁻¹, we estimate dust masses from the radio-continuum in the range 10⁹–10¹⁰ kg on UT 2007 October 27.1 within a 57 × 73 beam. These masses are one to two orders of magnitude smaller than derived by Altenhoff et al. (2009), but consistent with a reanalysis of the same radio-continuum data by Reach et al. (2010) and with the range of masses allowed by the SMEI photometry alone. Unfortunately, even the earliest reported radio-continuum measurements sample only a tiny central region in the expanding coma. For example, the first radio-continuum measurement on UT Oct 27.105 used an elliptical 57 × 73 beam at a time (∼4 days after the outburst) when the angular diameter of the dust coma was already 300''. Therefore, the radio-continuum data on 17P/Holmes offer only a lower limit to the total dust mass.

For the rest of the discussion, we use 2 × 10¹⁰ kg <M< 90 × 10¹⁰ kg as the best estimate of the dust mass. From Equation (8) the rate of dust production by mass is dM/dt = 4/3ρa_e(dC_e/dt), giving dM/dt∼ (3–140) × 10⁵ kg s⁻¹ at the maximum on UT 2007 October 24.54 ± 0.01 (DOY 297.54 ± 0.01). No contemporaneous measurements of the gas production rate are available. The earliest reported gas production rate is by Combi et al. (2007), who measured Q(H₂O) = 1.4 × 10³⁰ s⁻¹ on UT 2007 October 27 (DOY 300), corresponding to 0.4 × 10⁵ kg s⁻¹. Some four days after the start of the outburst and three days past its peak, the dust production at this time was already negligible (Figure 6). Schleicher (2009) extrapolated narrowband photometry data to infer peak water production rates Q(H₂O)∼ 7 × 10²⁹ s⁻¹, or 0.2 × 10⁵ kg s⁻¹.

The ejected dust mass is equivalent to a cube having a side length (M/ρ)^1/3 = 370–1300 m, where ρ = 400 kg m⁻³ is the assumed bulk density of the nucleus. However, this is an unlikely description of the outburst geometry, for three reasons. First, the sky-plane morphology of 17P/Holmes was initially circularly symmetric, with global deviations from circularity only appearing on timescales of a week after radiation pressure had begun to deflect coma dust (Stevenson et al. 2010). Eruption of material from a localized surface source would more naturally produce a jet or a cone, not a spherical debris cloud or one that appeared symmetric in projection onto the sky. (It is sometimes argued that projection effects would hide deviations from circular symmetry because of the small phase angles of observation but, in fact, with an average phase angle ∼0.2 radian, (see Figure 1) any strong asymmetries would easily have been detected if present). Second, the collimated ejection of mass from a spatially localized source would impart significant recoil to the motion of the nucleus. Very roughly, the velocity impulse on the nucleus is given by ΔV = (M/M_N)V, where V = 550 m s⁻¹ is the ejecta velocity. Substituting 0.2% <M/M_N< 10% gives ΔV = 1.5–70 m s⁻¹. In one month, an impulse of this magnitude would lead to a displacement of the nucleus from its pre-outburst-predicted position by 3900 km to 180,000 km, and this could scarcely have escaped detection. (At our request, Dr. Brian Marsden examined the reported positions of 17P/Holmes before and after the outburst to search for evidence of a change in the fitted non-gravitational parameters, but found none). Lastly, on physical grounds it is difficult to imagine a process that would drive mass loss many hundreds of meters deep into the nucleus against the expected radial gradient of temperature from the hot surface to the cold interior.

At the other extreme, the ejected mass could be contained in a surface layer on the nucleus having thickness

$$\begin{equation} \ell = \frac{M}{4\pi r_n^2 f \rho }, \end{equation} \tag{ 9 }$$

where f is the fraction of the surface area of the nucleus that is ejected. Substituting f = 1 gives 1.4 m <ℓ< 60 m. Shell-like models have been championed for comets including 17P/Holmes for many years (Sekanina 1982, 2008, 2009b). In these models, the rapid increase in brightness and scattering cross-section would be caused by disaggregation of the shell, presumably driven by sublimation of ices acting as glue in aggregated structures when freshly exposed to solar radiation and by collisions between disaggregated pieces moving at different speeds under gas drag near the nucleus. Sekanina's model is not contradicted by any aspect of the SMEI photometry. In this scenario, the 1.2 ± 0.3 day lag between the start of the outburst and the peak rate of area production (Figure 6) provides a measure of the timescale of the disaggregation.

We compare ℓ with the distance over which heat can be transported in the nucleus by conduction. From solution of the heat diffusion equation, this distance is δr = (κP/π)^1/2, where κ is the thermal diffusivity of the surface materials and P is the period of time over which conduction acts. The thermal diffusivity of porous dielectrics is roughly κ∼ 10⁻⁷ m² s⁻¹. For example, setting P = 6.88 yr, the orbital period of 17P/Holmes, we find, δr = 2.5 m. Periodic forcing of the insolation as the nucleus moves around its eccentric orbit drives a wave of conducted heat into the nucleus that damps over a length scale δr∼ 2.5 m. In the ∼100 yr that has elapsed since the outbursts of 1892/93, conducted heat would reach δr∼ 25 m beneath the initial surface. Regions with depth ≫δr will be largely immune to surface heating effects driven by recent surface events and thus are candidate locations for the survival of amorphous and trapped supervolatile ices. An important conclusion is that, within (considerable) uncertainties, ℓ ∼ δr. This approximate equality suggests that the outburst of 17P/Holmes in 2007 could have been triggered by heat conducted from the surface first exposed to space and direct sunlight by the outbursts of 1892/93.

A plausible trigger is the crystallization of amorphous water ice, which is exothermic and which is expected to result in the release of trapped supervolatile gases capable of driving the outburst (Prialnik et al. 2004; Bar-Nun et al. 2007; Reach et al. 2010). Amorphous ice has not been directly detected, but provides a self-consistent explanation for the activity observed in comets (Meech et al. 2009) and Centaurs (Jewitt 2009) located beyond the orbit of Jupiter (where temperatures are too low for crystalline water ice to sublimate). Crystallization models of comets necessarily assume values for many unknown or poorly constrained physical parameters (e.g., the thermal diffusivity, the ice/rock ratio, the nucleus spin properties, the mass of trapped gas, even the orbital evolution in the recent past is important in determining the subsurface temperature structure). As a consequence, crystallization models are very flexible but also very difficult to reject based on observations. One feature that is largely independent of the many unknowns is the stepwise progression of the crystallization front into the nucleus. Thermal runaways triggered by crystallization near the surface propagate downward into colder ice. Eventually, the heat released by crystallization is insufficient to drive additional ice to crystallize, and the runaway stops. The vertical distance is related to the thermal skin depth impressed on the nucleus by sunlight added at the surface and is typically measured in meters. Crystallization is therefore at least qualitatively consistent with a scenario in which a disintegrating dusty surface shell is launched from the 17P/Holmes nucleus.

Kossacki & Szutowicz (2010) computed thermal models of 17P/Holmes and reached the opposite conclusion, namely that runaway crystallization is unlikely to have been responsible for the outburst. However, their conclusion relied, in part, on the very high ejected mass estimates of 10¹²–10¹⁴ kg by Montalto et al. (2008). As noted earlier, the latter mass estimates are based on a reported detection of extinction in the coma which sits uncomfortably with the large-aperture SMEI data presented here. In fact, the upper end of the Montalto et al. (2008) mass estimate considerably exceeds our best guess as to the mass of the entire nucleus of 17P/Holmes, and therefore cannot be correct. For this reason, and because our own mass estimates (see also Sekanina 2008; Ishiguro et al. 2010; Reach et al. 2010) are considerably smaller, we consider that to reject crystallization as the energy source for the 17P/Holmes outburst would be premature.

If the particles all travel with characteristic speed V = 550 m s⁻¹, their total kinetic energy is E = (3–140) × 10¹⁵ J, equivalent to about 0.7–33 megatonnes of TNT (1 MT = 4.2 × 10⁹ J). This, in turn, is equal to the total solar energy falling on the 1.7 km radius nucleus in 7–350 days. While sunlight might be needed to trigger the outburst of 17P/Holmes, it clearly cannot supply enough energy to drive it. The crystallization of amorphous water ice releases ΔE∼ 9 × 10⁴ J kg⁻¹. Curiously, this is close to the energy per unit mass of the 17P/Holmes coma, E/M∼ 10⁵ J kg⁻¹. Therefore, crystallization of a subsurface layer of amorphous ice with the associated release of trapped supervolatile gases could supply the mass, energy, and momentum of the ejecta responsible for the remarkable outburst of comet 17P/Holmes. However, why 17P/Holmes should be uniquely afflicted by three such extraordinary outbursts, whereas most other comets show none, remains a complete mystery.