Wirtanen

ICARUS

134, 35–46 (1998) IS985944

ARTICLE NO.

ISOCAM Imaging of Comets 65P/Gunn and 46P/Wirtanen1 L. Colangeli,* E. Bussoletti,† C. Cecchi Pestellini,* M. Fulle,‡ V. Mennella,* P. Palumbo,† and A. Rotundi† *Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy; †Istituto Universitario Navale, Via A. De Gasperi 5, 80133 Napoli, Italy; and ‡Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34131 Trieste, Italy E-mail: [email protected] Received April 9, 1997; revised April 20, 1998

our Solar System originated. Thus, they are considered the link between the diffuse interstellar medium and the Solar System. This is why they have been and will continue to be a primary target for studies of astronomers and planetologists. In particular, the ESA Rosetta space mission (BarNun et al. 1993) will rendezvous with Comet 46P/Wirtanen and will study in depth its environment and nucleus. The main goal of the NASA Stardust space mission is to return to Earth samples from Comet 81P/Wild2 to be analyzed in the laboratory. From this perspective, it is of major relevance to perform remote observations of comets and to characterize their properties, both to improve our general knowledge of these objects and to properly prepare for the success of space missions. So far, analysis and modeling of visible and IR groundbased observations have provided average estimates of physical cometary dust parameters, such as size distributions, loss rates and ejection velocities, as well as grain albedo, thermal properties, and chemical composition (Newburn et al. 1991). Although the analysis of groundbased photometry and imaging data has provided important results, it has also raised questions that remain so far open. Relevant aspects to be clarified are: (a) the size distribution of grains (e.g., Fulle et al. 1995), (b) the relative amount of sub-micrometer- and millimeter-sized particles (e.g., McDonnell et al. 1991), (c) the velocity distribution as a function of grain size (e.g., Gombosi 1986, Fulle et al. 1993a). The Infrared Space Observatory, ISO (e.g., Kessler et al. 1996), represents a unique opportunity to explore comets, and in particular their solid component, at wavelengths not easily accessible from the ground. In the present work we report the results of wide-band imaging by ISOCAM (e.g., Cesarsky et al. 1996) of Comets 65P/Gunn and 46P/ Wirtanen (obtained within the ISO project CONTRAST: Cometary Nucleus and Trail Study), aimed at analyzing the coma and tail dust environment. Appropriate models (i.e., Fulle 1989, Fulle et al. 1993a) have been applied to the images to describe the evolution in time of comets. This approach has already been applied to images of other

In this paper we present images of Comets 65P/Gunn and 46P/Wirtanen obtained by means of ISOCAM in the broadband filters at 9.62 (LW7) and 15.00 mm (LW3). The observations were performed on 23 March 1996 and on 9 November 1996, respectively. The aim of this work is to analyze the coma and tail dust environment of the targets. The application of tail models to the comet images allowed us to derive several interesting parameters about the dust ejection and dynamics. The tail of 46P/Wirtanen is symmetric with respect to the prolonged radius vector and a strong anisotropy characterizes the dust emission (most probable value of the power index describing the size dependence of the dust ejection velocity u . 2As). Estimates of the dust ejection velocity (from 14 6 3 m s21 at a heliocentric distance R 5 2.5 AU to 23 6 2 m s21 at R 5 2.0 AU, for 0.1-mm-sized grains), the power index of the differential size distribution (between 23.5 and 24), and the mass loss rate (from 1.5 6 0.5 kg s21 at R 5 2.5 AU to 2 6 1 kg s21 at R 5 2.0 AU) have been obtained. We conclude that the most probable dust-to-gas ratio is close to one, within a heliocentric distance from 2.5 to 2.0 AU. The dust tail of 65P/ Gunn is strongly asymmetric. The fitting process indicates a dust ejection cone axis defined by the argument F 5 1108 and the obliquity I 5 808. The dust ejection velocity (from 16 6 1 m s21 at R 5 2.9 AU to 24 6 2 m s21 at R 5 2.6 AU for 0.1-mm-sized grains), the power index of the differential size distribution (around a value of 24), and the dust mass loss rate (between 100 and 300 kg s21) have been determined. Dust mass loss rates determined by IR tail models depend on the scattering efficiency and the temperature of grains, but are independent of poorly known parameters, such as dust bulk density and albedo  1998 Academic Press Key Words: comets, dust; comets, dynamics; infrared observations; image processing.

1. INTRODUCTION

It is commonly accepted that comets contain a significant fraction of proto-solar unprocessed material, from which 1

Based on observations 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. 35

0019-1035/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

36

COLANGELI ET AL.

TABLE I Orbital Characteristics and Elements of the Target Comets Comet

Period (years)

t (ET)

q (AU)

e

g at 2000.00

V at 2000.00

i at 2000.00

R (AU)

D (AU)

a (deg)

l (deg)

T (K)

Bv(T) (Jy arcsec22)

65P/Gunn 46P/Wirtanen

6.8 5.5

24.40 July 1996 14.18 March 1997

2.4619268 1.0637276

0.316313 0.656748

196.81730 356.34444

68.51903 82.19883

10.37993 11.72307

2.574 1.854

2.044 1.675

21.2 32.1

4.6 4.0

175 205

1170 2620

Note. t, Perihelion time; q, heliocentric distance at perihelion; e, orbital eccentricity; g, perihelion argument; V, nodal line argument; i, orbital plane inclination. The other parameters refer to ISO observation time: R, heliocentric distance; D, geocentric distance; a, phase angle; l, Earth cometo-centric latitude on the comet orbital plane; T, blackbody temperature; Bv(T), Planck distribution at 15 em.

comets observed at various visible and near-IR wavelengths. The extension to the longer infrared region, covered by ISO, sets constraints on model parameters, offers the opportunity to derive some unique information about the observed comet environments and, thus, allows us to improve our capabilities of simulating and understanding comet evolution. In Section 2 the applied observational method will be reported, as well as the approach used to reduce the images. In Section 3 we will describe the modeling approach. Section 4 is devoted to the discussion of the results obtained from the model fits, while Section 5 includes our conclusions in the perspective of future comet observations and space missions. 2. OBSERVATIONS AND DATA ANALYSIS

The two target comets were selected for the following main reasons. Comet 46P/Wirtanen is the target of the Rosetta mission and a better understanding of its properties is highly desirable. For this reason, a number of groundbased and space observing programs have considered this comet as a primary target. Comet 65P/Gunn appeared to be a suitable comet for observations by ISO since it had already been observed by IRAS and a trail was detected (Sykes et al. 1986). The main orbital characteristics and elements of the comets are summarized in Table I. ISOCAM was used in one of the standard (CAM01) observing modes (Siebenmorgen et al. 1996) to image the comets in selected wavelength bands. We chose filters LW3 and LW7, centered at 15.00 and 9.62 em, respectively. The use of the LW3 filter was aimed primarily at detecting the contribution of the continuum emission. The LW7 filter was chosen to look for the contribution of silicate grains. A PFOV (pixel field of view) of 6 arcsec was used to have a FOV (field of view) of about 39 3 39 per frame (32 3 32 pixels). This FOV allowed us to achieve a compromise between sufficient resolution of the coma and tail and coverage of a good portion of sky, for background correction. The log of observations is given in Table II; the sky coordinates were determined by standard ephemeris computation codes.

For each observation, the micro-scanning option was applied to achieve the best sensitivity for our expected faint targets. In our case, the micro-scan was a raster map consisting of (M 3 N) 5 9 images on M 5 3 points along N 5 3 lines, with displacement in the two directions DM 5 DN 5 6 arcsec (i.e., just the PFOV). This oversampling was used to have enough data for a good flat fielding of the array. After some (15 to 20) ‘‘stabilization’’ exposures, 10 to 15 exposures were taken for each fixed position of the raster map at an integration time 5 5.04 s and with a gain 5 1. These exposures form a ‘‘data cube’’ for each fixed position (Fig. 1). To obtain a composite image from the raster, some routines were built under the IDL (Interactive Data Language) software and applied to the raw data in the ‘‘standard processed’’ form provided by ESA, which are not treated by any ‘‘automatic routine’’ (Siebenmorgen et al. 1996). Our first processing step was aimed at cleaning images from glitches and transient effects and was applied to each series of exposures acquired at each fixed position of the micro-scanning raster. To do this, we have analyzed the intensity temporal evolution for each pixel in the map, along all the acquisitions at a fixed position. We have applied the following criteria; (a) the ‘‘stabilization’’ acquisitions, which are affected by significant transient effects, have been neglected in the data analysis; (b) in order to eliminate glitches, for each pixel we have computed (from the intensity temporal evolution) the median intensity, MED, and we have imposed that the pixel intensity equals MED for all the pixels outside the range 61% of MED. After this first processing, we have built an ‘‘average’’ image, ‘‘sky,’’ for each of the nine positions of the raster map. To obtained the normalized image, ‘‘corrected – sky,’’ in Jy, we used the relation (see also Siebenmorgan et al. 1996) corrected –sky(i, j) 5

sky(i, j) 2 dark(i, j) · spec, flat(i, j)

(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 5 1 . . . 32, j 5 1, . . . 32 run over the

37

ISOCAM IMAGING OF COMETS 65P/GUNN AND 46P/WIRTANEN

TABLE II Log of Observations Target

Observation time

RA (J2000)

Dec. (J2000)

Filters

65P/Gunn 46P/Wirtanen

23 Mar 1996 02:26:46 UT 09 Nov 1996 12:14:22 UT

16h 43m 32.4s 21h 10m 53.4s

218d 109 30.00 229d 449 24.00

LW3, LW7 LW3, LW7

number of pixels. In Eq. (1), ‘‘sky,’’ ‘‘dark,’’ and ‘‘flat’’ data are normalized per unit time and gain. The quantities ‘‘dark,’’ ‘‘flat,’’ and ‘‘spec’’ were provided by ESA (CCGLWDARK, CCGLWDFLT, and CCGLWSPEC files) on the basis of data acquired during the instrument performance verification phases. For the LW3 filter we used a ‘‘flat’’ derived from other images taken within our observing program. Actually, to search for the trails of our target comets, we used the micro-scanning method and took three adjacent images, at right angles with respect to the expected trail central path, 18 behind (for 65P/Gunn and 46P/Wirtanen) and 0.58 ahead (for 46P/Wirtanen only) of the comet position, in mean anomaly. The results of the trail search will be the subject of a forthcoming paper (Colangeli et al. 1998, in preparation). To build the LW3 flat-field we applied the following procedure: (a) we put all the images, except the stabilization frames, in a single sequence; (b) the ‘‘dark’’ was subtracted from all images; (c) for each pixel, any data points deviating more than 2% from the average were eliminated; (d) the remaining data for each pixel (around 400 for 46P/Wirtanen and 200 for 65P/Gunn) were averaged to obtain the mean brightness observed during the entire raster. The flat-field was then

FIG. 1. The data cube for each position of the raster map is formed by several exposures (temporal coordinate t). For each pixel in the map (i, j coordinates) the processing was: (a) the first ‘‘stabilization’’ acquisitions were cut; (b) the intensity of all pixels deviating from the median for more than 61% was set equal to the median.

computed under the assumption that the potential contribution of the trail flux is negligible in the dominating background and, anyway, would be blurred by the micro-scanning. This ‘‘flat’’ was used in Eq. (1) for the LW3 images. The final step was to build the final image of the comets from the nine ‘‘corrected – sky’’ images of the raster map. In principle, it should have been sufficient to compensate for the raster motion (6 arcsec for each step in the 3 3 3 map) and to average over the nine frames in order to obtain the final image. In practice, for the position of both comets we noticed sometime a little deviation (of the order of 1 pixel) from the expected apparent shift of the target on the raster frames. We attribute this effect to the proper motion of the comets. Actually, according to the ISO characteristics, observations of Solar System targets in raster mode are forbidden, as tracking would be needed both to follow the target and to perform the raster. Thus, in order to apply the micro-scanning mode to our comets we had to consider them as extended targets, so that tracking of the sources was not required. Of course, this choice has implied that, even in the relatively short time of our observations and despite the high ISO pointing accuracy, the target could slightly move during the raster acquisition. In order to eliminate this drawback, the frame composition was done by imposing that the pixel of maximum intensity for each of the nine images is at the same location in the final image. Finally, the background level was determined as the median over all the pixels of the images not affected by the cometary flux. By applying the procedure described above, the final images reported in Figs. 2 and 3, for Comets 65P/Gunn and 46P/Wirtanen, respectively, were obtained. The maximum fluxes measured for the comets in the two filters are reported in Table III. To compute the errors reported in Table III for each comet and filter, we applied the following approach: (a) we considered the standard deviation of the maximum fluxes obtained in the nine frames of the raster; (b) we computed the standard deviation of the flux values on all the pixels used for the determination of the background level; (c) we assumed as error on the maximum flux the sum of the two standard deviations. 3. DISCUSSION AND MODELING

The IR flux for comets is difficult to estimate with accuracy, as groundbased data refer mainly to bright objects

38

COLANGELI ET AL.

FIG. 2. ISOCAM images of Comet 65P/Gunn in the LW3 (a) and LW7 (b) filters.

and IRAS observations are limited to a reduced comet sample. Fulle (1989) developed numerical codes to simulate the behavior of cometary comae. These models were applied to IRAS data to get information on the relation

between dust densities and observed IR fluxes. We have applied the results of these models to our targets by scaling for the proper Planck function at the relevant heliocentric and geocentric distances at the time of observation and

FIG. 3. ISOCAM images of Comet 46P/Wirtanen in the LW3 (a) and LW7 (b) filters. The comet is not centered probably due to a poor correction of parallax effects with ISO observations.

ISOCAM IMAGING OF COMETS 65P/GUNN AND 46P/WIRTANEN

TABLE III Measured and Estimated Cometary Fluxes Maximum flux (mJy arcsec22) Target

LW3

LW7

Computed flux of outer coma at 12 em (mJy arcsec22)

65P/Gunn 46P/Wirtanen

4.2 6 0.3 0.7 6 0.1

1.4 6 0.1 0.4 6 0.1

1 3 1022 5 3 1022

by adopting a dust environment similar to that of 26P/ Grigg–Skjellerup (dust production of at least 200 kg s21; Fulle et al. 1993a). The estimated coma fluxes are reported in column 3 of Table III. We notice that the aim of the ISO coma observations was the analysis of the spatial brightness distribution by means of coma models. Thus, the predicted values refer to the outer coma regions, where the surface brightness is about 10 times lower than in the inner regions. Therefore, for 46P/Wirtanen, the predicted values are consistent with observations. For 65P/Gunn, the measured flux is much higher than expected and implies a high dust loss rate at 3 AU (as the inverse tail model application suggests, see Section 4). In order to analyze the coma and tail images obtained with ISOCAM, we applied an inverse tail model (see Fulle (1989) for a more detailed description). In the present paper we apply such models to the images taken at 15 em only. In fact, at this wavelength no significant band emission from dust is expected and some simple assumptions can be applied, such as a blackbody emission. This assumption cannot be valid for images at 9.62 em, where the silicate emission should be dominant. Several tests have shown that the inverse tail model is able to fit to the surface brightness distribution of comet dust tails by adopting the minimum number of free parameters. In particular, the model accounts for: (a) size and time dependence of the velocity; (b) size distribution and mass loss rate of the ejected dust. Moreover, the dust emission from the inner coma is modeled by an anisotropy parameter, which determines the opening angle of the dust ejection cone. In the case of axisymmetric coma, all the information coming from dust tail images is contained in the parameters mentioned above (e.g., Finson and Probstein 1968, Fulle 1987, 1989). In other words, all the quoted parameters are needed to obtain good tail fits and no other parameter (e.g., describing the dust ejection from the inner coma) could be efficiently constrained from the fits. Only in particular cases of nonaxisymmetric tails it is possible to constrain a further parameter: the pointing axis of the dust ejection cone (Fulle 1994, 1996). While for axisymmetric tails this direction must necessarily point toward the Sun (the mean direction of maximum dust production on long time scales), for

39

nonaxisymmetric tails the cone axis must be turned toward other directions, possibly related to the nucleus spin direction (see Fig. 4). Moreover, the inverse method allows us to rigorously approach the problem of the uniqueness of the physical output in the multi-parameter tail and coma models. When the number of free parameters increases, the frequently used time and error procedures do not ensure the uniqueness of the solution. The inverse tail approach minimizes the number of parameters to be found. Their uniqueness is ensured by covering all the possible values (usually by means of hundreds of trials) and searching for the values which provide the best and most stable tail fits. The values of other parameters are determined by an inverse least square fit to the dust tail data. Actually, in the inverse tail procedure the least square fit approach is extended to an N-dimensional (with N 5 number of parameters) space and is comparable to the usual least square straight line fit in the 2-D space. However, the inverse approach allows us to extract from the data physical information on the cometary dust consistent with the adopted functional form of the parameterization. For example, it would be hard to quantify the error of the solutions if the dust bulk density, assumed here to be constant, should be heavily time and/ or size dependent. Details about the tail model, adopted to analyze the ISO images, are reported in Fulle (1996), where it is applied to IRAS images of 10P/Tempel 2. The image analysis method consists of two main steps: (i) computation of the model dust tail, (ii) automatic fit of the model tail to the observations. The first step of the process depends on many nonlinear input parameters, which must be determined by means

FIG. 4. Geometry of dust tail orientation. The argument, F, and obliquity, I, define the dust ejection cone axis, g. The point q indicates the comet perihelion position; Q lies in the comet orbital plane and is oriented according to the comet orbital velocity vector.

40

COLANGELI ET AL.

of a trial-and-error procedure in order to reach the most stable model outputs. These nonlinear parameters are: (1) the dust ejection anisotropy, which is modeled by means of a Sun-pointing cone with half opening angle w; (2) the power index, u 5 ­ log v(t, d)/­ log d, describing the sizedependence of the dust ejection velocity, which should be constant for dust diameters d . 10 em (Crifo 1991); (3) the time dependence of the dust ejection velocity, v(t, do), which is referred to an arbitrary diameter, do , so that the time- and size-dependent dust ejection velocity becomes v(t, d) 5 v(t, do)(d/do)u. The model dust tail is computed by means of a MonteCarlo procedure involving about 107 particles. The dust ejection velocity and anisotropy allow us to compute the rigorous keplerian orbit for each sample grain. The dust dynamics depends on the ratio between solar radiation pressure and gravity forces, 1 2 e 5 CQ(rd)21, where C 5 1.19 3 1023 kg m22 is independent of the dust chemistry and physics (Burns et al. 1979). The quantity (1 2 e) is converted to dust sizes by adopting a scattering efficiency of large absorbing grains Q 5 1 and a dust bulk density r 5 103 kg m23. Changes of such parameters imply a simple scaling of the model physical outputs without modification of the dust dynamics and model inversion. The automatic fit of the tail image is performed by solving the over-sampled linear system AF 5 I, where A is the kernel matrix containing the model dust tail and the regularising constraints, F is the solution vector containing the physical model outputs, and I is the data vector containing the surface brightness of the tail. The quantity A contains the surface density of the sampling particles in the model tail integrated over t and (1 2 e), so that its units are s m22. The integration time interval ranges from the observation time back to a time to . The dust shells ejected before to are so diluted on the sky to give no appreciable brightness contribution to the model tail. The integration interval of (1 2 e) is computed by means of the classical synchrone–syndyne network (see Fig. 5) and, therefore, is a time-dependent quantity. Along each synchrone (i.e., for each ejection time), the largest (1 2 e) value [namely (1 2 e)2(t)] is provided by the syndyne crossing the synchrone at the image edge. Syndynes are not circles (which would provide the same (1 2 e)2 for all times), but spirals, so that the older the synchrone, the smaller (1 2 e)2 . The smallest (1 2 e) value [namely (1 2 e)1(t)] is simply given by (1 2 e)2 divided by the number of tail model size samples. The emissivity of sub-micrometer grains is proportional to the dust size, so that the emitted flux depends on the dust volume (Ney 1982). However, ISO images in the continuum concern grains much larger than 1 em, so that their emissivity does not depend on their size. In this case Sv(M, N, T ) is the IR intensity (in Jy arcsec22) produced by grains

FIG. 5. Sky projected synchrones (dashed lines) and syndynes (continuous lines) for Comet 46P/Wirtanen at the ISO observation. The synchrones shown are related to different ejection times: from 150 days before perihelion (for the almost radial synchrone) to older ejection times, with 50-day steps moving clockwise. The shown syndynes are related to different sizes: from 0.02 mm (for the almost radial syndyne) to sizes 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, and 10.0 mm, moving clockwise. The dotted line is the sky projection orbit of the comet nucleus.

emitting at the temperature T in the sky pixel (M, N) and the dust mass loss rate is given by Sv(M, N, T ) ˙ (t) 5 2CQ M 3 I(M, N) · Bv(T )

E

(12e)2(t)

(12e)1(t)

(1 2 e)21 (2)

· F(t, 1 2 e) · d(1 2 e),

where Bv(T ) (in Jy arcsec22) is the Planck distribution: Bv(T ) 5

F

G

2hv3 hv · exp 21 c2 kT

21

.

(3)

ISOCAM IMAGING OF COMETS 65P/GUNN AND 46P/WIRTANEN

In Eq. (2), the IR flux data, I(M, N), used as input of our linear system are dimensionless, and F(t, 1 2 e) (m2 s21) is the solution vector. Therefore, the ratio Sv(M, N, T )/ [I(M, N) Bv(T )] is a constant, dimensionless, normalization factor. We point out that the IR dust tail data allow us to obtain the mass loss rate independent of both the dust bulk density and dust albedo, which are parameters by far more uncertain than the dust scattering efficiency and temperature. In Eq. (2), we account for the sensitivity of the mass loss rate to the grain size distribution through the F function. In the majority of comet models, this function is fixed a priori, a very dangerous assumption, as the size distribution may vary not only from comet to comet, but also in time for the same comet. In our modeling, instead, it is obtained as a time-dependent quantity from the tail fit. This ensures a complete self-consistency between mass loss rate and grain size distribution and between mass loss rate and observational data. Actually, the mass loss rate is independent of the dust bulk density, r, because it is derived by observing a surface brightness, which depends on the number loss rate. The observed tail brightness, B, is proportional to the number loss rate and the dust scattering area, and, in order to consider the (1 2 e) quantity, can be written as ˙ (t) · BYN

k(rd)2l , r2

(4)

where kxl is the average of the quantity x, weighted by the dust size distribution. The mass loss rate is proportional to the dust bulk density, the dust grain volume, and the number loss rate; i.e., 3 2 k(rd)3l ˙ (t) Y rk(rd) l · B r . M 3 2 5B r k(rd) l k(rd)2l

(5)

These equations clarify why the dust bulk density disappears in the relation between mass loss rate and tail brightness. The ratio in Eq. (5) (which is related to 1 2 e and is independent of r) contains all the information on the dust size distribution required by the computation of the mass loss rate and is exactly taken into account in Eq. (2). Therefore tail models provide the most accurate estimates on the dust mass loss rate from comets, because they properly take into account its dependence on both the dust bulk density and the dust size distribution. 4. MODEL RESULTS

Data on the observation geometry are reported in Table I. We recall that we have applied the tail model to the LW3 images in the continuum. The blackbody temperature was assumed for the dust (Hanner and Newburn 1989).

41

This assumption is justified a posteriori by the fact that the dust grains in the observed dust tail are much larger than 1 em, as confirmed by tail modeling (see discussion below). The fits of the 46P/Wirtanen dust tail are shown in Fig. 6 for each combination of the u and w parameters. These fits allow us to select u and w values consistent with the observed tail brightness distribution. The best fits are obtained for w 5 458 (strongly anisotropic dust ejection) and u . 2As. For u 5 2As, the sunward coma fit becomes impossible, as the coma envelope is not as sharp as predicted by the fountain model, a result common to many comets (Combi 1994). This behavior was often interpreted in terms of dust fragmentation, which implies u . 2As (see also Fulle et al. 1993b). However, other mechanisms, such as a decrease of dust sintering (Delsemme 1987) or a contribution from different nucleus areas to the dust release, might explain this result. For hemispherical dust ejection (w 5 908) the tail fit is unstable, whereas for isotropic dust ejection (w 5 1808) the tail fit is acceptable for all the u values, although less satisfactory than for strongly anisotropic ejection. We conclude that inverse tail model fits suggest strongly anisotropic dust ejection with u . 2As. Isotropic dust ejection cannot be excluded (although less probable). In Fig. 7 we show the solutions related to the acceptable fits discussed above. As mentioned above, the time dependent size interval concerns sizes much larger than 1 em, so that the assumption of dust at the blackbody temperature is fully justified. The time interval to which the physical outputs are related corresponds to an heliocentric distance, R, ranging from 2.5 to 2.0 AU. The velocity increase is perfectly consistent with the R22 dependence predicted by Crifo and Rodionov (1997a,b) and is probably due to seasonal changes of the 46P/Wirtanen nucleus. However, the absolute velocity values are from two to three times larger than those predicted by Crifo and Rodionov (1997a,b): this fact points out the need for a proper link between velocities provided by detailed coma models (depending on the nucleus spin and topography) and global observations. Only coma in situ measurements during the Rosetta mission will give definite information on this subject. The dust size distribution power index shows random variations between the values 23.5 and 24.0, which are due to the residual inversion instability. This power index range is fully consistent with the values provided by the DIDSY-GIOTTO experiment (23.5 6 0.2 for 1P/Halley; Fulle et al. 1995) and illustrates that the dust mass loss rate of this short period comet is dominated by the largest released grains. The dust mass loss rate increases from 1.5 6 0.5 kg s21 at 2.5 AU to 2 6 1 kg s21 at 2.0 AU. In order to estimate the dust-to-gas ratio of 46P/Wirtanen, these values can be compared to the gas loss rate predicted by Jorda and Rickmann (1995): from 1.5 kg s21 at 2.5 AU

42

COLANGELI ET AL.

FIG. 6. Observed (continuous lines) and computed (dashed lines) isophotes of the LW3 ISO image of 46P/Wirtanen. The panels cover the image portion where the comet is observed. The innermost level corresponds to a flux of 0.35 mJy arcsec22; the other levels decrease by a factor 2. The u parameter (u 5 ­ log v(t, d)/­ log d) is the power index of the dust ejection velocity size dependence and w(deg) is the anisotropy parameter (half opening angle of the dust ejection cone pointing toward the Sun). The best fits offering the most stable outputs are for u 5 2Ah and w 5 458 and u 5 2Af and w 5 458.

to 15 kg s21 at 2.0 AU. The first value is very close to our determination, pointing out that the most probable dust to gas ratio is close to one. In order to explain the apparent much lower dust-to-gas ratio at 2.0 AU, we must consider the dust size interval to which the dust loss rate is related. As discussed in Section 3, the synchrone–syndyne network determines the size ranges to which the tail brightness is sensitive. It turns out that, at 2.5 AU, the largest size considered in our model is about 1 cm, very close to the largest size that the gas drag is able to eject, whereas at 2.0 AU the largest considered dust size is only about 1 mm, much smaller than the largest ejectable diameter. Since the mass loss rate certainly depends on grains larger than 1 mm, as implied by the dust size distribution, we must conclude that our determination of the dust mass loss rate at 2.0 AU is a lower limit. In particular, since the largest observed size decreases by a factor 16, if the power index of the size distribution is 23.5, the actual mass loss

rate at 2.0 AU is four times larger than the value plotted in Fig. 7, so that our results are fully consistent with a dust-to-gas ratio close to one over the whole heliocentric distance range from 2.5 to 2.0 AU. We point out that, by forcing the model to consider 1-cm-sized grains at 2 AU, we would have introduced an arbitrary extrapolation of the results not constrained by the data. These do not provide information on grains larger than 1 mm ejected at 2.0 AU, due to the synchrone–syndyne network. The fits of the 65P/Gunn dust tail are shown in Fig. 8. In this case, the dust tail is strongly asymmetric with respect to the Sun direction, so that it is impossible to fit with dust ejection pointing toward the Sun (e.g., the 46P/Wirtanen case). A very similar asymmetry was shown by Comet 10P/ Tempel 2, whose tail was best fitted by assuming a dust ejection cone axis pointing toward a fixed direction in space (Fulle 1996). Due to the short orbit arc covered by 65P/ Gunn during the release of its tail, it is impossible to

ISOCAM IMAGING OF COMETS 65P/GUNN AND 46P/WIRTANEN

43

FIG. 7. Dust environment of 46P/Wirtanen derived from the modeling of the LW3 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 205 K) (bottom right). Different line styles are for the following sets of parameters: u 5 2Ah and w 5 458 (continuous); u 5 2Ah and w 5 908 (dotted); u 5 2Ah and w 5 1808 (short dashed); u 5 2Af and w 5 458 (long dashed); u 5 2Af and w 5 1808 (three dot and dashed); u 5 2As and w 5 1808 (dotted and dashed).

FIG. 8. Observed (continuous lines) and computed (dashed lines) isophotes of the LW3 ISO image of 65P/Gunn. The panels cover the image portion where the comet is observed. The innermost level corresponds to a flux of 2.3 mJy arcsec22; the other levels decrease by a factor 2. The u parameter (u 5 ­ log v(t, d)/­ log d) is the power index of the dust ejection velocity size dependence and w(deg) is the anisotropy parameter (half opening angle of the dust ejection cone). The asymmetric tail is fitted by means of a dust ejection cone axis pointing toward a fixed position in space defined by F 5 1108 and I 5 808. All the considered combinations of u and w offer stable outputs.

44

COLANGELI ET AL.

FIG. 9. Dust environment of 65P/Gunn derived from the modeling of the LW3 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 175 K) (bottom right). Different line styles are for the following u values: u 5 2Ah (continuous); u 5 2Af (dashed); u 5 2As (dotted line). The dust ejection cone is defined by w 5 458, F 5 1108, and I 5 808.

uniquely relate the axis direction to the nucleus spin. The dust tail is best fitted with a cone axis pointing toward the direction defined by argument F 5 1108 and obliquity I 5 808 (see Fig. 4). In the fan shaped coma scenario, the direction of the dust ejection cone axis coincides with the nucleus spin axis, which is defined by the same argument and obliquity. An alternative scenario for interpreting the tilt of the cone axis is based on a time lag of the largest dust production with respect to the local noon of the active spot on the nucleus surface. In this context, the active spot would have a latitude of about 108 north of the comet orbital plane and the nucleus would have to co-rotate with its orbital motion, as the cone axis points to the left of the Sun (from a cometo-centric point of view) during the release of the dust tail. In Fig. 9 we show the solutions related to the fits plotted in Fig. 8. The time interval to which the physical outputs are related corresponds to an R range from 2.9 to 2.6 AU.

Inside this range, the dust velocity shows a steep increase very similar to that of 46P/Wirtanen. The dust size distribution power index shows a significant increase from values smaller than 24 to values larger than 24, i.e., from a dust mass dominated by the smallest ejected grains, to a dust mass dominated by the largest ejected grains, so that large underestimates of the dust mass loss rates at 2.6 AU are probable. The dust mass loss rate shows a decrease, which may reflect the decrease of the observed dust sizes more than a real decrease of the nucleus activity. As it was discussed for 46P/Wirtanen, the decrease of a factor 16 of the largest observed size corresponds to an increase of a factor 4 of the plotted masses, in the case of a size distribution power index close to 23.5. It turns out that the model outputs are fully consistent with a dust mass loss rate between 100 and 300 kg s21 within the heliocentric distance range from 2.9 to 2.6 AU. Thus, 65P/Gunn appears to be one of the main sources of the interplanetary dust cloud,

ISOCAM IMAGING OF COMETS 65P/GUNN AND 46P/WIRTANEN

since it ejects more dust not only than 46P/Wirtanen (a quite inactive object), but also than 10P/Tempel 2, one of the brightest short period comets. 5. CONCLUSIONS

In this paper we have presented ISOCAM images of Comets 65P/Gunn and 46P/Wirtanen in two filters centered at 9.62 and 15.00 em. Tail models have been applied to images in the 15.00-em filter, which should be mainly related to continuum dust emission. The fits of the 46P/ Wirtanen tail image suggest anisotropic dust ejection with a power index describing the size dependence of the dust ejection velocity, u . 2As, although isotropic dust ejection cannot be excluded. The dust ejection velocity of 0.1-mmsized grains increases from 14 6 3 m s21 at 2.5 AU to 23 6 2 m s21 at R 5 2.0 AU. The dust mass loss rate increases from 1.5 6 0.5 kg s21 at R 5 2.5 AU to 2 6 1 kg s21 at R 5 2.0 AU. The obtained dust size distribution power index (ranging from 23.5 to 24.0) and the considered dust diameter interval allow us to conclude that the most probable dust-togas ratio is close to one. The dust tail of 46P/Wirtanen appears symmetric with respect to the prolonged radius vector, so that it does not contain information on the spin of the comet nucleus. In contrast, the dust tail of 65P/ Gunn is strongly asymmetric, so that its fit requires anisotropic dust ejection, not pointing toward the Sun. The fits constrain the dust ejection cone axis toward the direction defined by argument F 5 1108 and obliquity I 5 808. The fits are almost insensitive to the u parameter (the power index of the size-dependence of the dust ejection velocity). The dust ejection velocity of 0.1-mm-sized grains increases from 16 6 1 m s21 at R 5 2.9 AU to 24 6 2 m s21 at R 5 2.6 AU. The dust mass loss rate is about constant at 200 6 100 kg s21, when we take into account the decrease in the observed dust size range. The dust mass loss rates obtained do not depend on the poorly known dust bulk density and albedo, but only on the scattering efficiency (assumed equal to one for the large dark absorbing grains) and the temperature (assumed equal to that of a blackbody). The results can be compared with the output of the same inverse tail model applied to other short period comets: 26P/Grigg–Skjellerup (Fulle et al. 1993a) and 10P/Tempel 2 (Fulle 1996). Groundbased optical images of the short and faint dust tail of 26P/Grigg–Skjellerup contain information on the dust released close to perihelion only (between 1.14 and 0.99 AU), whereas the 10P/Tempel 2 dust tail was observed by IRAS (Campins et al. 1990): it provides information on all the dust environment, starting from the activity onset at 2.9 AU up to perihelion at 1.4 AU. The comparison of the dust ejection velocities shows that, in the range between 2 and 3 AU, relevant for Comets

45

46P/Wirtanen and 65P/Gunn, it is impossible to find a relation common to all comets between heliocentric distance and dust velocity. The dust velocity at perihelion of 26P/Grigg–Skjellerup is similar to that of 46P/Wirtanen at 2.5 AU and to that of 65P/Gunn at 2.9 AU, which, however, show a clear increase during the approach to the Sun. Similarly, the dust velocity of 10P/Tempel 2, between 2.9 and 2.0 AU, is lower than 15 m s21. Therefore, although all comets show a dust ejection velocity increase as they approach the Sun, it is impossible to find a dust velocity law common to all comets. This result is probably due to seasonal effects, which influence the dust ejection velocity (Crifo and Rodionov 1997a,b) and strongly depend on the actual nucleus that one deals with. A similar conclusion can be drawn for the dust size distribution. Close to perihelion, 26P/Grigg–Skjellerup provides a most probable value of the size distribution power index close to 23.3, larger than the 24 found for 46P/Wirtanen. 65P/Gunn shows a clear time dependence of the power index, passing from values smaller to values larger than 24 during the approach to the Sun. This fact may reflect an increase of comet activity, with consequent ejection of larger grains. A similar behavior was shown by 10P/Tempel 2, with a power index smaller than 24 at the comet activity onset and larger at perihelion. However, at the activity onset the model was able to provide information on centimeter-sized grains only, so that a direct comparison with the results obtained for 65P/Gunn is dangerous: the size distribution power index may depend not only on time, but also on size. After the previous considerations, the comparison among the dust loss rates is even less significant, as it depends on the former quantities, as well as on the intrinsic comet activity. As already pointed out, the mass loss rate of 65P/Gunn at R . 2.5 AU is similar to that of 26P/Grigg–Skjellerup at perihelion, and about one-half than for 10P/Tempel 2 at perihelion. In any case, it is larger than the loss rate of about 50 kg s21 found for 10P/Tempel 2 at 2.9 AU. Among the comets here considered, 46P/Wirtanen is clearly the less active, with a mass loss rate an order of magnitude lower than those of the others. ACKNOWLEDGMENTS We thank the ISO staff for help during observation planning and execution and for support during data analysis. We express our thanks to Dr. J. F. Crifo for providing us the results of his comet simulations and for the stimulating discussion and suggestions about cometary grain dynamics. This work has been supported under ASI, CNR, and MURST contracts.

REFERENCES Bar-Nun, A., and 20 colleagues 1993. Rosetta Comet Rendezvous Mission. ESA SCI(93)7. Burns, J. A., P. L. Lamy, and S. Soter 1979. Radiation forces on small particles in the Solar System. Icarus 40, 1–48.

46

COLANGELI ET AL.

Campins, H., R. G. Walker, and D. Lien 1990. IRAS images of Comet Tempel 2. Icarus 86, 228–235. Cesarsky, C. J., and 65 colleagues 1996. ISOCAM in flight. Astron. Astrophys. 315, L32–L37. Combi, M. R. 1994. The fragmentation of dust in the innermost comae of comets: Possible evidence from ground-based observations. Astron. J. 108, 304–312. Crifo, J. F. 1991. Hydrodynamic models of the collisional coma. In Comets in the Post-Halley Era (R. L. Newburn Jr., M. Neugebauer, and J. Rahe, Eds.), pp. 937–990. Kluwer, Dordrecht. Crifo, J. F., and A. V. Rodionov 1997a. The dependence of the circumnuclear coma structure on the properties of the nucleus. I. Comparison between a homogeneous and an inhomogeneous spherical nucleus, with application to P/Wirtanen. Icarus 127, 319–353. Crifo, J. F., and A. V. Rodionov 1997b. The dependence of the circumnuclear coma structure on the properties of the nucleus. II. First investigation of the coma surrounding a homogeneous, aspherical nucleus. Icarus 129, 72–93. Delsemme, A. H. 1987. Diversity and similarity of comets. In Diversity and Similarity of Comets (E. J. Rolfe and B. Battrick, Eds.), pp. 19–30. ESA SP-278. Finson, M. L., and R. F. Probstein 1968. A theory of dust comets. I. Model and Equations. Astrophys. J. 154, 327–352. Fulle, M. 1987. A new approach to the Finson–Probstein method of interpreting cometary dust tails. Astron. Astrophys. 171, 327–335. Fulle, M. 1989. Evaluation of cometary dust parameters from numerical simulations: Comparison with an analytical approach and the role of anisotropic emissions. Astron. Astrophys. 217, 283–297. Fulle, M. 1994. Spin axis orientation of 2060 Chiron from dust coma modelling. Astron. Astrophys. 282, 980–988. Fulle, M. 1996. Dust environment and nucleus spin axis of Comet P/Tempel 2 from models of the infrared dust tail observed by IRAS. Astron Astrophys. 311, 333–339.

Fulle, M., S. Bosio, G. Cremonese, S. Cristaldi, W. Liller, and L. Pansecchi 1993b. The dust environment of Comet Austin 1990V. Astron. Astrophys. 272, 634–650. Fulle, M., L. Colangeli, V. Mennella, A. Rotundi, and E. Bussoletti 1995. The sensitivity of the size distribution to the grain dynamics: Simulation of the dust flux measured by GIOTTO at P/Halley. Astron. Astrophys. 304, 622–630. Fulle, M., V. Mennella, A. Rotundi, L. Colangeli, E. Bussoletti, and F. Pasian 1993a. The dust environment of Comet P/Grigg–Skjellerup as evidenced from ground-based observations. Astron. Astrophys. 276, 582–588. Gombosi, T. I. 1986. A heuristic model of the Comet Halley dust size distribution. In Exploration of Halley’s Comet, ESA SP-250, Vol. 2, pp. 167–171. Hanner, M. S., and R. L., Jr. Newburn 1989. Infrared photometry of Comet Wilson (19861) at two epochs. Astron. J. 97, 254–261. Jorda, L., and H. Rickman 1995. Comet P/Wirtanen, summary of observational data. Planet. Space Sci. 43, 575–579. Kessler, M. F., and 10 colleagues 1996. The Infrared Space Observatory (ISO) mission. Astron. Astrophys. 315, L27–L31. McDonnell, J. A. M., P. L. Lamy, and G. S. Pankiewicz 1991. Physical properties of cometary dust. In Comets in the Post Halley Era (R. L. Newburn Jr., M. Neugebauer, and J. Rahe, Eds.), pp. 1043–1073. Kluwer, Dordrecht. Newburn, R. L., Jr., M. Neugebauer, and J. Rahe 1991. Comets in the Post Halley Era. Kluwer, Dordrecht. Ney, E. P. 1982. Optical and infrared observations of bright comets in the range 0.5 em to 20 em. In Comets (L. L. Wilkening, Ed.), pp. 323–340. Univ. of Arizona Press, Tucson. Siebenmorgen, R., J-L. Starck, D. A. Cesarsky, S. Guest, and M. Sauvage 1996. ISOCAM Data Users Manual. ESA SAI/95-222/Dc. Sykes, M. V., D. M. Hunten, and F. J. Low 1986. Preliminary analysis of cometary dust trails. Adv. Space Res. 6, 7, 67–78.