ISOCAM Imaging of Comets 103P/Hartley 2 and 2P/Encke

Icarus 149, 339–350 (2001) doi:10.1006/icar.2000.6546, available online at http://www.idealibrary.com on ISOCAM Imaging of Comets 103P/Hartley 2 and 2P/Encke1 E. Epifani Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy; and Università degli Studi “Federico II,” P.le V. Tecchio 80, I-80125, Naples, Italy E-mail: [email protected] L. Colangeli Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy M. Fulle Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131, Trieste, Italy J. R. Brucato Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy E. Bussoletti Istituto Universitario Navale, Via A. De Gasperi 5, I-80133, Naples, Italy M. C. De Sanctis IAS-CNR, Via del Fosso del Cavaliere, I-00133, Rome, Italy V. Mennella Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy E. Palomba Osservatorio Astronomico di Capodimonte, Via Moiariello 16, I-80131 Naples, Italy; and Observatoire de Haute Provence de CNRS, F-04870 Saint Michel l’Observatoire, France and P. Palumbo and A. Rotundi Istituto Universitario Navale, Via A. De Gasperi 5, I-80133, Naples, Italy Received April 5, 1999; revised September 5, 2000 We present the results of ISOCAM observations performed on Comets 2P/Encke and 103P/Hartley 2, on 31 October 1997 and 1 January 1998, respectively. Images were obtained in the broadband filters LW3 (centered at 15.00 µm) and LW10 (centered at 11.50 µm). Tail models have been applied to the images to analyze the evolution of the dust coma environment and to derive infor- 1 Based on observation with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, the Netherland, and the United Kingdom) with the participation of ISAS and NASA. mation about the velocity of the grains. The image of 2P/Encke presents a sunward spike interpreted as a Neck-Line. Thanks to the model, the time evolution of the comet dust environment during 3 months preceding the observation has been reconstructed. 2P/Encke presents a strong maximum in the dust velocity, a broad maximum of the dust mass loss rate, and a dip of the size distribution power index around perihelion. Model results indicate that the largest grains in the tail can reach sizes from centimeters to decimeters. This has important implications for the source of the Taurid meteoroids. For Comet 103P/Hartley 2 the numerical model suggests an anisotropic dust ejection with a tail composed of grains smaller than those in 2P/Encke. Both dust ejection velocity and 339 0019-1035/01 $35.00 c 2001 by Academic Press Copyright ° All rights of reproduction in any form reserved. 340 EPIFANI ET AL. dust mass loss rate reach a maximum about 2 weeks before perihelion. The power law best fitting the time-averaged size distribution of both comets has an index of about −3.2, indicating that the released dust is strongly dominated in mass by the largest ejected grains. °c 2001 Academic Press Key Words: comets; infrared observations. 1. INTRODUCTION The dust environment of short-period comets plays a key role in the whole complex of interplanetary dust. Dust trails (Sykes and Walker 1992) and the zodiacal dust cloud evidence that short-period comets are characterized by significant dust losses during their perihelion passages. IR images, dominated by the dust thermal emission, are the best data to deeply analyze, by means of modeling, aspects of the cometary dust environment such as the size distribution of cometary grains, the dynamical processes that may explain the presence of small grains in trails (Sykes et al. 1990), the size dependence of grain ejection velocity, and the relative amount of submicrometer and of millimetersized particles. The latter dominate the dust mass production rate of 1P/Halley and 26P/Grigg-Skjellerup (McDonnell et al. 1991). In this perspective, ISO represents a unique opportunity to have a spectral coverage and a detectability threshold much better than those available from ground-based telescopes. In the present work we report the results of wide-band imaging by ISOCAM (Cesarsky et al. 1996) of the two short-period comets 2P/Encke and 103P/Hartley 2. Comet 2P/Encke is thought to be the parent of the Taurid meteoric stream (Klacka and Pittich 1998). Its dust coma and tail were observed in the past (e.g., Sekanina and Schuster 1978) and analyzed by means of an inverse numerical model (Fulle 1990). This approach allows the determination of the contribution of large grains ejected by the nucleus to the replenishment of the zodiacal cloud. Moreover, IRAS images have evidenced the presence of a trail (Sykes and Walker 1992). Comet 103P/Hartley 2, a bright member of the Jupiter family, was poorly observed before the advent of HST and ISO. UV spectra and images through the F785LP filter (approximately the I band) were obtained by the Faint Object Spectrograph and the Wide Field Camera (Weaver et al. 1994) of HST. The campaign with ISO has provided spectra obtained by SWS (Crovisier et al. 1999) and ISOPHOT (Colangeli et al. 1999) and images by ISOCAM (Crovisier et al. 1999) when the comet was close to perihelion. The analysis of images by appropriate tail models (e.g., Fulle 1989, Fulle et al. 1992) is useful to describe the time evolution of dust grains in the coma. Physical parameters, such as size distributions, mass loss rates, and ejection velocities, are estimated. This kind of information is highly useful to point out main pecularities and common features among short-period comets, and also in the perspective of future in situ cometary missions, such as Rosetta (e.g., Bar-Nun et al. 1993, Schwehm and Schulz 1999). In Section 2 we describe the observations and the data reduction. Section 3 is devoted to the description of the inverse tail model applied to the images obtained in the ISO continuum LW3 filter, while in Sections 4 and 5 we report the results of the application of the model. Finally, in Section 6 we draw our conclusions, also based on comparison with similar results obtained for 65P/Gunn and 46P/Wirtanen, which were previously observed by ISOCAM (Colangeli et al. 1998). 2. OBSERVATIONS, DATA REDUCTION, AND ANALYSIS Orbital characteristics and elements of the target comets are summarized in Table I. The observational approach used for the present program is similar to that described by Colangeli et al. (1998), to which we refer the reader for further details. ISOCAM was used in the standard CAM01 AOT mode, with the broadband filters LW3 and LW10, centered at 15.00 and 11.50 µm, respectively. The LW3 filter was selected to image the comet in a spectral region where no significant emission feature should occur and, thus, to monitor the continuum emission. The LW10 filter, centered on the typical features of silicate grains, was used to sample the distribution of this dust component. A PFOV of 6 arcsec was chosen to obtain a total FOV of about 3′ × 3′ (32 × 32 pixels), adequate to cover the whole coma. 2P/Encke and 103P/Hartley 2 were observed on 31 October 1997 at 16:04:08 UT and 01 January 1998 at 21:48:08 UT (starting times), respectively. Comet 2P/Encke was observed about 5 months after perihelion, when the Earth was very close to the comet orbital plane. The exposure time was 730 s for each filter and comet. The “micro-scanning” observation technique was adopted to obtain the best sensitivity. A raster map TABLE I Orbital Characteristics and Elements of the Target Comets Comet τ (ET) q (AU) e r (AU) 1 (AU) λ (◦ ) α (◦ ) T (K) B (T ) (Jy arcsec−2 ) 2P/Encke 103P/Hartley2 23.611 May 1997 22.017 Dec 1997 0.332 1.032 0.85 0.70 2.429 1.043 2.548 0.824 4 14 23 62 180 275 1360 8810 Note. τ = perihelion time; q = heliocentric distance at perihelion; e = orbital eccentricity. The other parameters refer to ISO observation time: r = heliocentric distance; 1 = geocentric distance; λ = Earth cometocentric latitude on the comet orbital plane; α = phase angle; T = black-body equilibrium temperature; B(T ) = flux expected at 15 µm from a black body at the comet position and its equilibrium temperature. ISOCAM IMAGING OF 103P/HARTLEY 2 AND 2P/ENCKE 341 of M × N = 9 images was obtained by taking M = 3 adjacent images along each of N = 3 lines, with a pointing displacement of 6 arcsec (i.e., one pixel). For each sky position, after several “stabilization” acquisitions, 10 to 15 frames were acquired. The image processing was performed by our own routines built using the IDL software. The starting data were the raw images (CISP files) provided by ISO before any automatic pipeline elaboration. To clean glitches and transient effects from images, the time evolution of the intensity in each pixel and for each sky position was analyzed. The median intensity (MED) was calculated for each pixel. Pixel values exceeding MED by ±1% were set equal to MED and the acquisitions averaged. We decided to use the median as the representative value of the intensity in each pixel, as the average was strongly affected by the glitches. Moreover, we chose ±1% as a limiting value, as this was the best value to obtain proper cleaning of our images. The nine “averaged” images obtained were dark subtracted, flat-fielded, and converted from engineering units to Jansky/pixel using the same procedure as in Colangeli et al. (1998), i.e., by the relation (see also Siebenmorgen et al. 1996) corrected ima(i, j) = µ ima(i, j) − dark(i, j) flat(i, j) ¶Á spec, (1) where “dark” is the dark current, “flat” is the flat-field, “spec” is the conversion factor from engineering units to Jy, and the indices i = 1, . . . , 32, j = 1, . . . , 32 run over the number of pixels. In Eq. (1), “ima,” “dark,” and “flat” data are normalized per unit time and gain. The calibration factors (“spec” values) used in the present work were provided by ESA in the OLP 7.0 version of data and are 1571 and 3192 (ADU/s)/Jy for LW3 and LW10 filters, respectively. The final step of the image reduction was the composition of the raster from the nine images, taking into account both the pointing displacement and the proper motion of the comet. To compute the sky background we considered all the pixels far enough for the contribution of the coma to be small compared to the sky background, in order to have a rather uniform signal. The average sky background value was then subtracted from the composed frame. The final images of the comets are shown in Figs. 1 and 2. This method allowed us to obtain a signal-to-noise ratio about 15 times higher than the value resulting from the standard ISO pipeline processing. Despite the poorly defined appearance of the 2P/Encke coma, we can estimate an extension of ∼4.4 × 104 km from the images in Fig. 1. The difference in coma morphology between the two filters could be due to the presence of a non-negligible fraction of small silicate grains contributing to the silicate band and, thus, in the LW10 filter. This effect must be further studied in detail. The geometric conditions at time of observations are favorable to the observation of a Neck-Line, a bright and thin dusty structure (Kimura and Liu 1977, Fulle and Sedmak 1988). Actually, the 2P/Encke image shows a spike. The syndyne–synchrone diagram, plotted in Fig. 3 for the time of 2P/Encke observation, can help us to understand the actual nature of the observed fea- FIG. 1. Images in the LW3 (a) and LW10 (b) filters of 2P/Encke. The images are 34 × 33 and 34 × 34 pixels, respectively, and the actual scale is ∼3.7 × 105 km along each axis (1.1 × 104 km/pixel). The Sun (⊙) direction is indicated. ture. The trail and the Neck-Line are expected to lie close to each other, but with a position angle difference of about 10◦ . It is possible to attribute the observed spike to a Neck-Line, as its observed position angle (166◦ from the prolonged radius vector) perfectly matches the predicted feature. Moreover, a numerical dust tail model must fit the Neck-Line, as it is part of the dust tail, whereas a trail is not (see Section 4). The contrast on the background of the 103P/Hartley 2 images is higher than that for Comet 2P/Encke (see Fig. 2). The 342 EPIFANI ET AL. coma extends up to at least 6 × 104 km in the continuum and it is brighter than expected, so that the inner 2 × 2 pixels of the LW3 image are saturated. The LW10 image shows an intensity increase in some pixels close to the comet optocenter; this effect is negligible with respect to the radial intensity gradient. Moreover, the coma image is broader in the LW10 filter than in the continuum. Also for this comet, this evidence might suggest that the grains contributing to the silicate band have a wider spatial distribution. FIG. 3. Sky-projected synchrones (dashed lines) and syndynes (continuous lines) for Comet 2P/Encke at the time of observation. The dotted line is the sky projection of the comet orbit, i.e., the theoretical trail axis. The predicted NeckLine is the dot–dashed line, with a position angle of 166◦ from the prolonged radius vector. The synchrones, following clockwise the trail axis, correspond to different ejection times: 100 days before perihelion and from perihelion to 140 days after it, with 20-day steps. The syndynes correspond to different dust sizes: from 0.03 mm (for the almost radial syndyne) to sizes 0.1, 0.3, 1, 3, 10, and 30 mm moving counterclockwise. 3. APPLICATION OF INVERSE TAIL MODELS The model adopted to derive information about the dust physical parameters from our images has been extensively described by Fulle (1989) and Fulle et al. (1992), to which we refer the reader for more details. The approach consists of two main steps: (i) computing the model dust tail and (ii) fitting it to the observed tail and deriving the dust loss rate and the grain size distribution. The whole process is performed automatically via a multidimensional least-squares fit, by approximating the integral relation between the dust tail model and the data to an overconditioned linear system. The solution of the system gives sampled values of the parameters dust loss rate, Ṁ(t), and size distribution, n(d, t). Other parameters appear in non-linear equations and must be determined by trial-and-error procedures: FIG. 2. Images in the LW3 (a) and LW10 (b) filters of 103P/Hartley 2. Both images are 34 × 34 pixels, and the actual scale is ∼1.2 × 105 km along each axis (3.5 × 103 km/pixel). The Sun (⊙) direction is indicated. (i) The dust ejection velocity, v(t, d0 ), describes the time evolution of the dust ejection. Here t is the time of dust ejection from the inner coma and d0 is a reference diameter (here assumed to be 1 mm). (ii) The power index, u = ∂ log v(t, d)/∂ log d, characterizes the power-law dependence of the dust velocity on the diameter, d : v(t, d) = v(t, d0 )(d/d0 )u . Model computations have shown ISOCAM IMAGING OF 103P/HARTLEY 2 AND 2P/ENCKE that u is size-independent for spherical grains larger than 10 µm with constant density (e.g., Crifo 1991). Actually, no information is available on this index behavior. Tests on several comets have shown that the dust tail shape and the brightness distribution are most sensitive to the dust ejection anisotropy and velocity from the inner coma. (iii) The dust ejection anisotropy parameter, w, is the half width of the sun-pointing dust ejection cone. We select the possible directions of the dust ejection velocity vector inside this cone by means of a uniform sampling. The quality and the stability of the automatic least-squares linear fit can be improved by tuning the second set of parameters of the model. They must be varied in the whole range of possible values to ensure a unique determination of their best values. Starting from the dust ejection velocity vector we are able to compute the rigorous Keplerian orbit of each sample grain, building up the model dust tail by means of a Monte Carlo procedure involving about 107 particles. The dust dynamics depends on the ratio between the solar radiation pressure and gravity forces, 1 − µ = C Q(ρd)−1 , where C = 1.19 × 10−3 kg m−2 is independent of the dust chemistry and physics (Burns et al. 1979). The quantity 1 − µ is converted to sizes by adopting the scattering efficiency Q = 1 (large absorbing grains) and the dust bulk density ρ = 103 kg m−3 . Different values for these parameters can be introduced by a simple scaling of the model outputs, without changing the dust dynamics and the model inversion procedure. By the adoption of the 1 − µ variable, the dust ejection velocity is parametrized as v(t, 1 − µ) = v(t, 1 − µo )[(1 − µo )/(1 − µ)]u , where 1 − µo = 1.2 × 10−3 . The second step concerns the automatic fit of the model tail to the observed one, which is performed by solving the oversampled linear system AF = I , where A is the kernel matrix containing the model dust tail, F is the output vector, and I is the data vector containing the surface brightness of the input image. F depends on t and 1 − µ and is given by the grain number loss rate times the dust 1 − µ distribution. F normalized to 1 − µ provides the dust loss rate and the 1 − µ distribution. A contains the surface density of the sampling particles in the model dust tail integrated over t and 1 − µ, so that it has units of s m−2 . The integration time interval ranges back from the observation time to a starting time, which is determined as follows: the earlier the dust ejection time, the more diluted the ejected dust shell on the sky, and the smaller its brightness contribution to the dust tail. Before the starting time the brightness contribution of the dust shell to the total tail brightness is negligible. The 1 − µ integration interval depends on the syndyne–synchrone network (Fig. 3) and therefore it is time-dependent. Along each synchrone (i.e., for each dust ejection time), the largest 1 − µ value [namely (1 − µ)2 (t)] is provided by the syndyne crossing the synchrone at the image edge. Syndynes are not circles (which would provide the same (1 − µ)2 for all times), but spirals, so that the older the synchrone, the smaller (1 − µ)2 . The smallest 1 − µ value [namely (1 − µ)1 (t)] is simply given by (1 − µ)2 divided by the number of tail model size samples (usually 100). 343 From the output F we can compute the dust mass loss rate from Ṁ(t) = 2C Q S(M, N , T ) 3 I (M, N )B(T ) Z (1−µ)2 (t) × (1 − µ)−1 F(t, 1 − µ)d(1 − µ), (2) (1−µ)1 (t) where S(M, N , T ) is the surface monochromatic IR flux (in Jy arcsec−2 ) produced by grains emitting at the temperature T in the sky pixel (M, N ) and B(T ) (in Jy arcsec−2 ) is the Planck distribution computed at 15 µm. The grain temperature T (see Table I) is assumed to be independent of the grain size. In Eq. (2), the surface brightness data I (M, N ) used as input to solve the linear system are dimensionless and F(t, 1 − µ) is the related solution vector (m2 s−1 ). Therefore, the ratio S(M, N , T )/[I (M, N )B(T )] is a constant dimensionless normalization factor of the input vector I . The time-dependent integration limits (1 − µ)1 and (1 − µ)2 give the size range to which all the solutions are related. It follows that the dust loss rates provided by any tail model have to be considered as lower limits, as they are computed over a subset of the sizes of the ejected grains. Equation (2) points out that the mass loss rate computed by means of tail models is independent of the poorly known dust bulk density ρ and depends linearly on the scattering efficiency Q, assumed here to be 1. The normalization of F(t, 1 − µ) described above allows us to obtain the 1 − µ distribution, from which we obtain the dust size distribution (Finson and Probstein 1968). Due to the inverse procedure adopted, the model provides the time evolution of the 1 − µ distribution sampled in ten 1 − µ values. We fitted a power law to the obtained size distribution, so that its behavior with time is described by the time evolution of the power index. This approach (which is not required by the model) allows us to show the model output in a form that can be compared with available information on cometary dust size distribution. For instance, Fulle et al. (1995) have demonstrated that a powerlaw size distribution is perfectly consistent with the fluences collected by the Giotto DIDSY experiment during the Halley fly-by (McDonnell et al. 1991). All the physical quantities which can be deduced by the inverse dust tail analysis depend on the solution vector F, whose determination is affected by three causes of errors (Fulle et al. 1992): (1) the error e1 due to the propagation of errors affecting the data via the kernel matrix A; (2) the bias e2 introduced by the regularization of the solution; and (3) the error e3 introduced by the combination of the free parameters u and w. In general (e1 , e2 ) < e3 . In the case of the faint 2P/Encke the error is about 45% of the values of the solution F. 4. RESULTS FROM 2P/ENCKE The model dust tail, reconstructed by the inverse Monte Carlo approach (Fulle 1989) is compared with the 2P/Encke LW3 observation in Fig. 4. The comet was at high heliocentric distance 344 EPIFANI ET AL. FIG. 4. Observed (continuous lines) and computed (dashed lines) isophotes of the LW3 image of 2P/Encke. The innermost level corresponds to a flux of 0.30 mJy arcsec−2 ; the other levels decrease in steps of a factor of 2. The nine panels refer to different (u, w) combinations. The sunward spike is well fitted by the dust tail model. at the time of observations (see Table I). Nevertheless, the observation geometry was such that the dust tail covered about half the image plane (see Fig. 3). These conditions are the most favorable for obtaining, by applying the dust tail model, information on the comet dust environment over the months preceding the observation and for disentangling time-dependent from size-dependent quantities. The fits reported in Fig. 4 refer to nine different combinations of the u and w parameters. For multi-parameter models it is hard to describe the likelihood of the fitting procedure by using canonical statistical methods. In our case, we considered the residuals (data − model). We assume as acceptable the fits with residuals smaller than 2σ , where σ = 0.016 mJy arcsec−2 is the background noise. Some combinations (u = −1/6 and w = 180◦ ; u = −1/4 and w = 45◦ ; u = −1/2 and w = 45◦ ) do not satisfy this requirement in the inner isophotes and are not considered further. To check the validity of our selection we computed for each (u, w) combination the reduced χ 2 and the correlation index κ, defined as the scalar product of the data and the computed tail vectors (see Table II). Since the model has 800 degrees of freedom, it is not appropriate to give an absolute meaning to these parameters. However, it is possible to judge the quality of the fits in a relative way, to reject the worst cases. The above listed combinations plus (u = −1/2 and w = 180◦ ) show the worst χ 2 and κ values and are then rejected. In Fig. 5 the residuals for the selected solutions are reported. The sunward spike of the coma is perfectly fitted by the model, further confirming its attribution to a Neck-Line. The dust forming the Neck-Line was ejected close to perihelion (0.33 AU from the Sun; see Table I). This result demonstrates that a synthetic numerical dust tail model can allow us to distinguish the contribution to the sunward spike brightness from ISOCAM IMAGING OF 103P/HARTLEY 2 AND 2P/ENCKE TABLE II χ2 and κ Values of the Tail Fits Target u w (◦) χ2 Correlation index κ 2P/Encke −1/6 −1/6 −1/6 −1/4 −1/4 −1/4 −1/2 −1/2 −1/2 −1/6 −1/6 −1/6 −1/4 −1/4 −1/4 −1/2 −1/2 −1/2 45 90 180 45 90 180 45 90 180 45 90 180 45 90 180 45 90 180 2.08 1.69 7.09 2.70 1.57 2.24 12.49 2.09 3.71 6.19 14.69 46.48 6.06 33.62 112.88 144.88 54.28 128.01 0.957a 0.960a 0.943 0.945 0.961a 0.966a 0.875 0.940a 0.944 0.990a 0.979 0.967 0.990a 0.964 0.951 0.907 0.950 0.937 103P/Hartley 2 a Accepted solution. the Neck-Line dust dynamics and the dust loss rate increase at perihelion. It is interesting to observe that the four acceptable solutions span values from 45◦ to 180◦ for the cone angle w. This means that w cannot be further constrained by our model. 345 The selected outputs of the inverse numerical model are plotted in Fig. 6. The results show that the grains in the tail reach the decimeter sizes. In particular, close to perihelion, we have a rare opportunity to observe meteoroids ranging from 1 mm to 0.1 m, which replenish the Taurid stream. The dust velocity peaks at perihelion, where we also observe a broad maximum of the dust mass loss rate. Both quantities show a continuous decrease from perihelion to the observation time. The dust mass loss rate after perihelion is well approximated by the power law 70 r −3 kg s−1 , where r is the heliocentric distance in AU, while the time evolution of the dust size distribution shows a steep drop at perihelion of its power index α. We observe that all the (u, w) combinations provide a similar trend, thus supporting the reliability of such a time evolution. Moreover, the change is strongly correlated to the velocity and the loss rate behaviors. The drop of α could be due to a dependence of the power index on size, as we actually observe different sizes at different times. This hypothesis can be ruled out since the power index of the size distribution is approximately the same pre- and post-perihelion, despite the difference in size being very strong. In more detail, both before perihelion and after 20 days after perihelion the power index is larger than −4; i.e., the released meteoroid population is dominated in mass by the largest grains. In contrast, at perihelion, the index is very close to −4; i.e., the meteoroid population is dominated in mass by much smaller grains. In Fig. 7 we plot the time-averaged size distribution for the (u, w) combinations providing the best fits. This time average FIG. 5. Residuals of the fits of the dust tail of 2P/Encke for the selected solutions. An example of a rejected case (u = −1/6 and w = 180◦ ) is also shown for comparison. The plots show the difference between the data and the model. The levels show the residuals of 0.01, 0.02, 0.04, . . . mJy arcsec−2 from the darkest to the lightest gray levels. 346 EPIFANI ET AL. FIG. 6. Dust environment of 2P/Encke derived from the modeling of the LW3 ISO image. Dust ejection velocity (top left), power index of the differential size distribution (top right), size interval to which all the shown outputs are related (bottom left), and mass loss rate (for a dust temperature of 180 K) (bottom right). The line styles refer to different sets of parameters: u = −1/6 and w = 45◦ (dotted line); u = −1/6 and w = 90◦ (short dashed line); u = −1/4 and w = 90◦ (dotted and dashed line); u = −1/4 and w = 180◦ (three dots and dashed line); u = −1/2 and w = 90◦ (long dashed line). The continuous line is the average of the solutions. considers the size distributions provided by the model, rather than the power-law fits of these distributions, whose power indices are plotted in Fig. 6. Moreover, since we deal with the time-averaged differential size distribution, we weighted it by the grain number released per unit time. It follows that the powerlaw index fitted to the data in Fig. 7 can hardly be compared with the one plotted in Fig. 6. The power law in Fig. 7 has an index of −3.2 ± 0.2. The uncertainty takes into account the 1σ dispersion for each of the five fits and the different slopes of the distributions. The determined value implies that, on the average, the dust released by 2P/Encke is strongly dominated in mass by the largest ejected grains. In general this happens for a population of grains with a size distribution power index larger than −4. On the other hand, the main contribution to the brightness is given by the smallest released grains if the size distribution power index is smaller than −3. We are close to this limit and we must conclude that the largest released grains provide a significant contribution to the reflected and IR emitted radiation from 2P/Encke. This is not surprising for the sunward part of the tail, where the synchrone–syndyne diagram shows centimeter-sized grains, which are usually considered large. However, taking into account the obtained time-averaged dust size distribution, the same consideration is true for the coma, where it is usually assumed that the brightness distribution is due to micrometer-sized grains only. 5. RESULTS FROM 103P/HARTLEY 2 FIG. 7. Time-averaged differential size distribution of 2P/Encke derived from the modeling of the LW3 ISO image. Different line styles refer to the following sets of parameters: u = −1/6 and w = 45◦ (dotted); u = −1/6 and w = 90◦ (short dashed); u = −1/4 and w = 90◦ (dotted and dashed); u = −1/4 and w = 180◦ (three dots and dashed); u = −1/2 and w = 90◦ (long dashed). The power law best fitting the shown distributions has an index of −3.2 ± 0.2. The model dust tail fitted to the 103P/Hartley 2 image is shown in Fig. 8. The strong asymmetry with respect to the antisolar direction is due to the great age of the right-hand part of the observed tail. Synchrone computations show that this tail is almost 1 year old, so that we can infer the time evolution of the ISOCAM IMAGING OF 103P/HARTLEY 2 AND 2P/ENCKE 347 FIG. 8. Observed (continuous lines) and computed (dashed lines) isophotes of the LW3 ISO image of 103P/Hartley 2. The innermost level corresponds to a flux of 7.56 mJy arcsec−2 ; the other levels decrease in steps of a factor of 2. The nine panels refer to different u and w combinations. FIG. 9. Residuals of the fits of the dust tail of 103P/Hartley 2 for the selected solutions. An example of a rejected case (u = −1/2 and w = 45◦ ) is also shown for comparison. The plots show the difference between the data and the model. The levels show the residuals of 0.2, 0.4, 0.8, . . . mJy arcsec−2 from the darkest to the lightest gray levels. 348 EPIFANI ET AL. FIG. 10. Dust environment of 103P/Hartley 2 derived from the modeling of the LW3 ISO image. Dust ejection velocity (top left), power index of the differential size distribution (top right), size interval to which all the shown outputs are related (bottom left), and mass loss rate (for a dust temperature of 275 K) (bottom right). The line styles refer to different sets of parameters: u = −1/6 and w = 45◦ (continuous line); u = −1/4 and w = 45◦ (dotted line). dust environment over a long period preceding the observation. In this case, only two (u, w) combinations, corresponding to a strongly anisotropic dust ejection, allow us to satisfactorily fit the observed tail, namely w = 45◦ and u = −1/6 or u = −1/4. Only these two (u, w) combinations show residuals lower than 2σ (where σ = 0.13 mJy arcsec−2 is the background noise). For more isotropic ejection models, the fit of the observed sunward IR flux along the tail axis is poor. The fit to the sunward coma becomes impossible with u = −1/2 (a fact commonly encountered in tail fits) and the reconstructed anti-sunward tail remains very far from the observed contour. The selected combinations are those with the lowest χ 2 and the largest κ (see Table II). In Fig. 9 the residuals for the selected solutions are reported. The outputs related to the two (u, w) combinations providing the best fits are shown in Fig. 10. The dust size range constrained by the synchrone–syndyne diagram reaches smaller sizes than in the 2P/Encke case: in the case of Hartley 2 we observe grains up to some tens of millimeters. Moreover, this range rapidly varies around perihelion, a shortcoming that usually introduces large instabilities in the model outputs. The dust velocity shows an intense peak about 2 weeks before perihelion, after a long period of almost constant trend. This rapid change in the velocity behavior may be triggered by the constant increase of the nucleus surface temperature and/or by seasonal changes shortly before perihelion (Crifo and Rodionov 1997). The mass loss rate shows a much more regular increase during the approach to perihelion, reaching a maximum well correlated with that observed for the velocity. The dust mass loss rate before peri- helion can be approximated by the power law 100 r −2 kg s−1 , where r is the heliocentric distance in AU. The rapid loss rate decrease just after perihelion may be an artifact of the fact that the model considers smaller and smaller grains. The instability of the model outputs around perihelion is confirmed by the behavior of the power index of the size distribution, which shows unrealistic large variations around perihelion. Before perihelion FIG. 11. Time-averaged differential size distribution of 103P/Hartley 2 derived from the modeling of the LW3 ISO image. Different line styles refer to the following sets of parameters: u = −1/6 and w = 45◦ (continuous); u = −1/4 and w = 45◦ (dotted). The power law best fitting the shown distributions has an index of −3.2 ± 0.1. ISOCAM IMAGING OF 103P/HARTLEY 2 AND 2P/ENCKE the power index remains almost constant, as does the dust ejection velocity, with values between −4 and −3.8. However, the power index of the differential time-averaged size distribution is −3.2 ± 0.1 (Fig. 11). As for 2P/Encke, the dust mass released by 103P/Hartley 2 is dominated by the largest ejected grains. 6. CONCLUSIONS In this paper we have presented ISOCAM images of Comets 2P/Encke and 103P/Hartley 2 in two filters centered at 11.50 and 15.00 µm. The two images in the “continuum” filter have been used as input in a numerical model to derive information about the cometary dust environment. The physical outputs of the model describing the dust environment of 2P/Encke are strongly correlated. To interpret this evidence we consider the results obtained by Sekanina (1988) based on the analysis of the same comet. According to this author, a sudden change of the surface exposed to the Sun (seasonal change) occurs around the perihelion due to the comet nucleus spin axis orientation. This “perihelion season” lasts only a few weeks, due to the short heliocentric distance and the large orbit eccentricity. For the rest of the time (“aphelion season,” lasting some years) the comet surface mantains a rather stable geometrical configuration with respect to the Sun. In this scenario we cannot disentangle the contributions of the close approach to the Sun and of the seasonal effects to the dust velocity and the loss rate variation (Crifo and Rodionov 1997). However, the strong change of the size distribution around perihelion seems consistent with seasonal changes. In fact, the change lasts exactly as long as the polar night duration of the main nucleus active spot found by Sekanina (1988), i.e., from 3 days before perihelion to 23 days after. Within this hypothesis, the time evolution of the dust size distribution we find implies that only the main nucleus active spot releases large grains, while all the others release much smaller grains. The steep drop of the size distribution power index implies that Comet 2P/Encke releases numerous meteoroids mainly far from perihelion. In fact, Fig. 6 points out that, up to 10 days before perihelion and from 30 days afterward, the mass loss rate is dominated by the release of meter-sized boulders at a rate of tons per second. This rate is largely sufficient to replenish both the Taurid meteoric complex and a significant fraction of the zodiacal dust cloud. This result must be considered also in combination with the conclusion by Durda and Dermott (1997) that the entire asteroid population is responsible for at least one third of the dust in the entire zodiacal cloud. The meteoroid supply from 2P/Encke rapidly drops during the 2 weeks around perihelion, when the dust mass loss rate (although larger) is dominated by grains smaller than 1 millimeter. This fact suggests that most of the present dynamical models of the Taurid complex must be updated, since they assume that 2P/Encke releases meteoroids at perihelion only (e.g., Klacka and Pittich 1998). 349 The scenario depicted above is fully consistent with previous results. Fulle (1990) applied the same numerical dust tail model to completely independent data, i.e., visible images of the dust tail of 2P/Encke taken in 1976 (Sekanina and Schuster 1978). He obtained results covering two months centered on the comet perihelion. Although the observation geometry was different, so that the Neck-Line was ejected weeks before perihelion, all the model outputs perfectly agree with both the time evolution and the absolute values of the dust velocity, mass loss rate, and size distribution power index obtained here. Such an agreement induces us to conclude that the dust environment is very well modeled and that the dust release of 2P/Encke is very similar during these two perihelion passages. We point out that the size distribution power index showed the same drop around perihelion, so that the implications for the Taurid complex models are confirmed. In addition, the dust albedo assumed by Fulle (1990) is consistent with the present results. In fact, the absolute mass loss rate values, extracted from the analysis of optical data, coincide with those obtained here from the analysis of IR data. We can conclude that the albedo of 2P/Encke dust is close to 3% for a phase angle of 55◦ . We can perform a comparison among the dust environments of the four short-period comets observed by the same approach with ISOCAM and so far analyzed by means of the same inverse tail model, i.e., Comets 46P/Wirtanen, 65P/Gunn (Colangeli et al. 1998), 2P/Encke, and 103P/Hartley 2. Despite its low brightness, 2P/Encke is by far the most active comet: at perihelion, it releases more than 103 kg s−1 of particles, so that we confirm that this faint comet is one of the main sources of zodiacal dust and seems to account by itself for all the mass in the Taurid meteoroid complex. Comets 65P/Gunn and 103P/Hartley 2 reach a loss rate 10 times lower. However, taking into account the large heliocentric distance of 65P/Gunn at its perihelion, it turns out that this comet also is very active. In fact, two of the brightest trails are associated with 2P/Encke and 65P/ Gunn (Sykes and Walker 1992). Comet 46P/Wirtanen has the lowest dust production rate of the sample. The dust velocity depends on both the heliocentric distance and the nucleus topographic characteristics (e.g., the surface icy fraction), which remain unknown. In general, the more active the comet, the higher the dust ejection velocity, although it is very difficult to find clear correlations. For instance, 65P/Gunn ejects dust with the same velocity as that of 46P/Wirtanen at half heliocentric distances. However, at 1 AU from the Sun, 2P/Encke ejects dust with the same velocity as that of 103P/Hartley 2, which is 10 times less active. Comets 46P/Wirtanen, 65P/Gunn, and 103P/Hartley 2 show random variations of the size distribution power index between −4 and −3.5. In contrast, 2P/Encke shows a clear time evolution, possibly related to nucleus seasons. In this case a relation between the comet dust tail and the nucleus seasons seems possible. The power index larger than −4 implies that all the released dust mass is dominated by the largest ejected meteoroids. This is confirmed by the timeaveraged size distributions, whose power index is −3.2 for both 350 EPIFANI ET AL. Comets 2P/Encke and 103P/Hartley2. It was impossible to compute the time-averaged size distribution for 46P/Wirtanen and 65P/Gunn, as the data concerned very short time intervals. 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