7 Coma morphology

The emission pattern of the coma at radii $r<80\,000\ \rm km$ was highly heterogeneous with respect to r and $\theta$ on all dates. In the general solar direction, a system of shells at regularly spaced radii was visible. Five shells were seen by temporal derivative processing, each separated by $\Delta r\sim20\,000\ \rm km$, and spiralling towards the photo-centre with decreasing radii in the direction of the evening terminator. The relative intensities of the photo-centre and the brightest regions of the three innermost shells were 1.00, 0.24, 0.07 and 0.04 on $\lambda\, 830$ nm images obtained on April 24, subjected to basic reduction only.

An (r, $\theta$)-coordinate system with origin at the photo-centre and the sub-solar direction of the respective image was introduced to facilitate interpretation of coma features. Features following (i.e. having smaller PA values), in the sense of rotation, the sub-solar direction have $\theta\in[-180, 0]$. A point on a hypothetical spherical nucleus with axis of rotation perpendicular to radius vector would be located at the morning terminator when $\theta=-90\hbox{$^\circ$}$. Features preceding the sub-solar direction are characterised by $\theta\in[0, 180]$. A point at the evening terminator would have $\theta=90\hbox{$^\circ$}$.

On sharp images, the shell system was consisting of two superposed components, having similar mean radii, curvatures and intensities, and lagging each other by $\Delta \theta\sim55^\circ$. This effect was visible out to the third shell at $r\sim47\,000\ \rm km$ on April 24. The two-system shell morphology was not apparent in the outermost shells. The shells are characterised by sharp outer boundaries and more diffuse inner boundaries.

The sharpest and highest quality (in terms of S/N) images were obtained April 21 and 24. Unsharp masking, azimuthal renormalisation and rotational gradient processing effectively revealed low-contrast detail in the near-nucleus coma on images from these dates (Fig. 6). The effect of these processing methods is to remove the diffuse underlying coma emission from the image, thereby increasing the relative brightness of small-scale details. The first two methods produce output images with unaltered feature locations with respect to the input image. Characteristics of coma features are measurable with respect to location for unsharp masking and to location and size for azimuthal renormalisation, but not to relative intensity. Diffuse and large-scale features are well detected with azimuthal renormalisation and rotational gradient techniques, which are well removed by unsharp masking. Rotational gradient processing enhances regions of intensity gradients and may therefore be used to detect the presence of small-scale intensity variations, given that the angle of rotation of the subtracted image component is kept small. As most of the flux of the resulting image is removed, its S/N is low, requiring that the data intensity range of the input images covers a significant portion of the dynamic range of the CCD chip.

The effect of the convolution with the seeing disk effective during the exposure is well seen in Fig. 6, where the general features of the April 21 and 24 images are still detectable at the poor seeing conditions of April 25, but more diffuse and with lower S/N. For absolute characterisation of features in the following morphological description, measurements were made on images subject of basic reduction only, to assure a linear relative intensity scale.

  

Figure 6: Processed images of the near-nucleus region of Hale-Bopp on April 21 (21:24.6 UT), 24 (20:45.5 UT) and 25 (20:42.9 UT). In the leftmost a) frames, unsharp masking processing is shown, emphasising the innermost filament and shell structure. Amplification factors in the range A=1.0-1.3 and high-pass filters of n=13 were used. The middle column b) display azimuthal renormalisation processing and the rightmost column c) rotational gradient processing with $\Delta\theta=10\hbox{$^\circ$}$ in order to enhance morphology more distant from the photo-centre. A linear intensity grayscale map from black to white indicates increasing brightness for b) and c) frames, while the intensity scale is inverted in a) frames. Frames are oriented with celestial south up and west to the right. The slanted lines mark the direction of the projected radius vector, which in c) frames is relative to the unrotated image component. Scale bars are 10000 km; the field size corresponds to $73\,000$ km at the distance of the comet

7.1 April 21

April 21 images show an inner shell forming near the nucleus on the sub-solar hemisphere. It consists of two curved components, "subshells'', at different radii, where the inner subshell is directly connected to the photo-centre by dust outflow on the morning hemisphere. It is of homogeneous intensity out to a distance of $r\sim5\,200\ \rm km$ from the photo-centre, where the intensity abruptly decreases. The subshell disappears into the background noise at (r, $\theta)\sim(8\,500\ \rm km$, $-31\hbox{$^\circ$}$).

The outer subshell at $r=4\,500-12\,000\ \rm km$ has a very irregular intensity and stretches to the evening terminator. It disappears into the background on the morning hemisphere at (r, $\theta)\sim(12\,000$, $-12\hbox{$^\circ$}$).

There is further a very faint and small jet-like feature visible on the anti-solar hemisphere, apparent as a narrow coma elongation passing through the point (r, $\theta)\sim(2\,000$,$-130\hbox{$^\circ$}$).

The second shell has a mean radius of $25\,000-30\,000\ \rm km$ and is more diffuse than the inferior shell with a similar general structure. The shell has two superposed components. The preceding one starts at a radius just outside of the inner shell spiral on the evening hemisphere at $\theta\sim100^\circ$ as a wide diffuse arc emanating from the inner coma. It is curved towards the following hemisphere and connects to the second shell main dust trajectory. The following component of the shell is superposed on the preceding, emanating from a similar wide but slightly fainter diffuse arc discernible just outside the inner shell at $\theta\sim20^\circ$. The shell components have intensity maxima at $\theta\sim75^\circ$ and $\theta\sim25^\circ$, coinciding with the points of connection of the wide arcs to the main trajectory of the shell.

The third and fourth shells have too low S/N to show any associated diffuse arcs connecting them towards the nucleus, and are seen only as single-component shells with intensity maxima at $\theta\sim38^\circ$. Rotational gradient processing reveals only a steeper curvature of the third shell towards the photo-centre, at the assumed position of the aforementioned diffuse arc with origin at smaller radii.

7.2 April 23

April 23 images have low resolution due to bad seeing. They do not show small-scale features other than the major filament complex of the inner shell, at a time approximately four rotation periods later than those of April 21.

7.3 April 24

Morphology of the inner shell on April 24 is even more complex than on April 21, due to very stable seeing.

A major very bright and wide jet-like feature on the dayside at $\theta=20\hbox{$^\circ$}$ near the photo-centre dominates the flux of the inner shell. It starts curving at $r\sim3\,000\ \rm km$. There is a rather sharp decrease in intensity at the outer boundary at $r=15\,000-18\,000\ \rm km$ as it separates into three filaments. The very bright and narrow filament on the following side of the major jet-like feature is visible on the morning hemisphere and reaches sky intensity at (r, $\theta$) = ($12\,000$, $-45\hbox{$^\circ$}$). It shows an extended intensity maximum at (r, $\theta$) = ($8\,900$, $-15\hbox{$^\circ$}$). Following this filament is a diffuse isolated patch at (r, $\theta$) = ($4\,300$, $-20\hbox{$^\circ$}$).

Two fainter, more diffuse filaments precede the inner filament at larger radii and have endpoints at (r, $\theta$) = ($14\,000$, $0\hbox{$^\circ$}$) and (r, $\theta$) = ($12\,500$, $25\hbox{$^\circ$}$) at the outer boundary of the first shell. At (r, $\theta$) = ($7\,500$,$70\hbox{$^\circ$}$) there is an enhancement in intensity, relating to a region of locally higher dust opacity or the end of another filament. This point is located on the extreme preceding edge of the major jet-like feature.

A small jet-like feature is visible on the anti-solar hemisphere at $\Delta\theta=-105\hbox{$^\circ$}$ close to the photo-centre. It starts curving in the following direction at $r\sim2\,500\ \rm km$ and forms a spiralling filament stretching into the sub-solar hemisphere, apparently joining the inner shell.

The second shell from the photo-centre shows a double aspect as on April 21, with two main superposed components separated by $\Delta r=6\,000\ \rm km$, diffusing in the following direction.

The third and fourth shells show only a single aspect with intensity maxima at $\Delta\theta\sim30\hbox{$^\circ$}$. As on April 21, the third shell is curved towards the photo-centre at the apparent location of the wide arc connecting to the inner coma. The feature is most apparent on images of long exposure times, processed with the rotational gradient method.

7.4 April 25

April 25 images have lower resolution and S/N ratio than those of April 24 but still show signs of similar activity. Only the first and second shells are prominent.

The morphology of the coma was thus very complex during the period of observation, with small-scale patches apparent both within and separated from the filaments. On April 21 images, unsharp masking processing (Fig. 6) reveals that the outer subshell of the inner shell was outlined by five diffuse light patches with sizes of $\sim$1000 $-2\,000$ km. From the mean dust outflow velocity and distance to the photo-centre, this matter was emitted from the nucleus at least $\sim$8 h before the image was obtained. If the size of the patches is directly correlated with increased intermittent activity of the nucleus emission region and not due to gas and dust grain interaction processes within the coma, these periods had durations of $\sim$1 h or less. Similar patches were apparent on April 24. The contrast of the brightest of these patches is $\sim$1% relative to the brightness of the neighbouring filament trajectory, as measured on images from April 21 and 24 subjected to basic reduction only.

The inner and bright filaments apparent in the inner shell of April 24 contain each $0.09\pm0.01$ of the flux within radii of $4\,000-14\,000$ km, corresponding to the area of first shell outside of the point where the filaments are separable. Thus, the filaments within the otherwise diffuse emission of the first shell visible on April 24 carry a non-insignificant amount of the projected dust column density, and may carry a significant part of the total dust emitted. It seems clear from these figures also that a major part of the dust flux is attributable to structures with spatial sizes below the resolution limit of the present observations.

Regarding the global shape of the shell spiral pattern, analysis of images from April 24 subjected to a $\Delta\theta=10\hbox{$^\circ$}$rotational derivative processing (Fig. 6) shows that the steepness of the spiral, $\Delta r /\Delta \theta$,is dependent on $\theta$. The geometric centre of the pattern is close to the photo-centre position and the magnitude of $\Delta r /\Delta \theta$ is small, indicating that the angle of the rotational axis to the line of sight $\psi$ is not very large. An estimation of the value of $\psi$ requires a more rigorous treatment of the data.