6 Terminal dust outflow velocity

The projected outflow velocity of the dust emission was estimated from the radial distances of shell trajectories from the photo-centre. From each high S/N image, subjected to basic reduction only, 45 radial profiles at $\Delta\theta = 5^\circ$angular separations were subtracted by the averaged radial profile extracted from the corresponding azimuthally renormalised image. The range of $\theta$ values included the complete span of measurable shell position angles. The profiles thus extracted ideally contains only signal from light scattered and reflected from dust in the shells, and the radial "continuum" should be close to zero. This was true for all radii but those closest to the elongated photo-centre, where the subtraction was incomplete or excessive, depending on the position angle relative to the direction of the major axis of isophote elongation.

The locations of maximum shell intensities for each $\theta$ were identified, and the mean radius of each shell, over the available range of position angles, was calculated. A projected radial velocity was obtained from a least squares linear fit of positions versus time. An error estimate was obtained from the radial scatter of data points. Extracted radial intensity profiles and shell positions obtained from an April 21 image is shown in Fig. 4.

  

Figure 4: Radial intensity profiles extracted at 5 degree intervals in PA from an image obtained on April 21 at 21:24.6 UT, subsequent to subtraction by the azimuthally averaged intensity profile. The image is shown in the April 21 (b) column of Fig. 6. Points of maximum brightness of two shells used in the derivation of the dust outflow velocity are indicated on the profiles by squares and diamonds. The brightness scale of the profiles is relative and arbitrary. The ordinate gives the radius in pixels from the photo-centre of the image along the radial profile. Selected profiles are labelled with the PA in which they were extracted. The PA of the sun for this observation was $243.1^\circ$ relative to the nucleus

  

Figure 5: Least-squares linear fits (solid lines) of the position angle and the rotational phase of fitted ($r_{\rm max}$, $\theta$)-data, shown for six radii within the radius interval where isophote elongations were measured on the images. The rotational phase is defined as the fraction of the full rotation period P elapsed since the first image obtained on April 21. Best-fit rotation periods P and corresponding radii (r, in pixels) are given in the lower right-hand corner of each panel. Extrapolation of the P(r) curve thus obtained to zero radius gives the nucleus rotation period of $11\hbox{$.\!\!^{\rm h}$}46\pm0\hbox{$.\!\!^{\rm h}$}25$. The dotted lines define a 50% error confidence interval of the fit

An initial estimate on the outflow velocity was obtained from temporal derivative processing of navigated single-night images, from the multi-pixel relative motion of a well-defined edge of an inner shell filament. April 24 images, obtained at the best seeing conditions, showed a spatial movement of $\sim$4 pixels during a $0\hbox{$.\!\!^{\rm h}$}48$ interval, due to rotational and expansional motion of the dust. Based on the expected amount of shell motion resulting from the $\dot{\theta}=31\hbox{$.\!\!^\circ$}4\ h^{-1}$ rotational angular velocity at the nuclear distance in question, the radial component of motion was calculated to $\dot{r}\sim0.5\pm0.1\ \rm km\ s^{-1}$.

Assuming (on the basis of the regular coma spiral pattern) that the activity of the nucleus was periodic and showed similar outflow behaviour at each revolution during the period of observation, a given shell on a given night will be located two shell positions further from the nucleus the nest night. This is due to a time lapse between observations of nearly $24\ \rm h$ ($\sim$2P). From shell positions on April 23, 24 and 25 images a least-squares straight line fit to the radius data points gives a mean projected outflow velocity of $\dot{r}=0.41\pm0.02\, \rm km\ s^{-1}$ over a range $r=5\,000-45\,000\ \rm km$. The largest velocities measured from the width of the shells are $\dot{r}_{\rm max}=0.55\ \rm km\ s^{-1}$.