3. Discussion

Table 1 (click here) lists the observed values of polarization in the three continuum filters along with the apertures used and the phases at which the observations were carried out. The heliocentric and geocentric distances at the time of observation are also given. There are six observing runs before perihelion passage (1st April 1997) and seven during the post-perihelion period.

The observations are mostly made with an aperture of 26.5 arcsec diameter. However the Earth-Comet distance being different for different observations, sampled area of the comet is different. This might cause some change in the degree of polarization. The inner coma region of comets has been found to be quite heterogeneous in spatial distribution of polarization by various researchers (Renard et al. 1996). In the case of Halley phase curves for the inner coma (radius 5000 km) and the outer region (radius 10000 km) appear different (Dollfus et al. 1988). This maybe due to either a difference in the microtexture of the dust grains (Dollfus 1989) or a difference in dust size distribution. But in the case of Halley, a fair degree of agreement was noticed among all the observers, as long as the polarization was estimated over the whole coma with a large aperture (which averages out the effect of the heterogeneity of the inner coma) aimed at the photometric center. In all our observations the linear scale sampled on the comet is greater than 13000 km radius which is much larger than the inner coma region. In order to check the polarization behaviour with respect to the area sampled on the comet, we observed the comet through two different apertures on 1st March 1997 (cf. Table 1 (click here)). We note that within the errors of observation there is no significant difference for the two apertures. The linear scales corresponding to apertures of 26.5 and 52.4 arcsec are respectively 14318 and 28313 km radius. This means that the comparison of polarization observations on different dates is meaningful as long as the sampled linear size is in the range 14000 to 28000 km radius. On the other hand, during the October, November, 1996 observations the area sampled is much larger (linear scale > 55000 km radius) and light from the tail region also contributes to the observed polarization. During these (October, November, '96) observations, the phase angles are between and the observed polarization is found to have the position angle parallel to the plane of scattering i.e. the polarization is negative. The comet being fainter during this period, the observed errors in polarization measurements are large, especially in the u-band (3650 Å) observations. In the other two continuum bands, the S/N ratio is better than three and therefore the numbers are significant. The polarization values measured on November 1 and November 2, 1996 differ significantly though the phase angles and comet distances from Sun and Earth are nearly same. This could be due to different levels of activity on the above two dates.

 

UT date r phase Aperture Wavelength Polarization

AU AU deg arcsec(dia.) Å %P

1996 October 16.64 2.70 3.04 18.8 52.4 3650 -3.11 2.40 78

52.4 4845 -3.13 0.85 105

52.4 6840 -3.85 1.16 102

1996 November 1.60 2.52 3.05 17.2 52.4 3650 -2.69 2.17 119

52.4 4845 -1.26 0.27 70

52.4 6840 -2.01 0.22 81

1996 November 2.6 2.50 3.05 17.1 52.4 4845 -0.55 0.37 48

52.4 6840 -1.12 0.27 68

1997 February 13.02 1.23 1.77 32.6 26.5 3650 3.94 0.25 60

26.5 4845 4.40 0.07 53

26.5 6840 5.67 0.08 53

1997 February 28.02 1.08 1.50 41.1 26.5 3650 7.87 0.11 61

26.5 4845 9.33 0.04 62

26.5 6840 12.16 0.04 63

1997 March 1.01 1.07 1.49 41.7 26.5 3650 7.83 0.28 58

26.5 4845 9.43 0.07 59

26.5 6840 11.63 0.05 59

52.4 3650 8.08 0.10 60

52.4 4845 9.57 0.05 60

52.4 6840 11.73 0.07 60

1997 April 2.59 0.91 1.36 47.0 26.5 3650 10.82 0.30 120

26.5 4845 12.20 0.06 116

26.5 6840 14.63 0.04 110

1997 April 3.62 0.92 1.37 46.6 26.5 3650 10.84 0.50 121

26.5 4845 12.22 0.03 120

26.5 6840 14.56 0.10 119

1997 April 4.59 0.92 1.38 46.2 26.5 3650 10.38 0.20 127

26.5 4845 11.86 0.05 121

26.5 6840 14.15 0.06 121

1997 April 10.61 0.93 1.44 43.1 26.5 3650 8.82 0.13 133

26.5 4845 10.24 0.04 132

26.5 6840 12.27 0.06 131

1997 April 28.6 1.03 1.72 31.4 26.5 3650 4.50 0.25 165

26.5 4845 4.50 0.05 168

26.5 6840 5.67 0.07 161

1997 April 29.6 1.04 1.74 30.8 26.5 3650 3.15 0.40 167

26.5 4845 3.98 0.09 164

26.5 6840 5.05 0.09 166

1997 May 4.6 1.08 1.83 27.7 26.5 3650 2.30 1.00 144

26.5 4845 2.73 0.10 165

26.5 6840 3.75 0.10 160

 

In Fig. 1 (click here), we have shown the observed polarization for all the three wavelengths as a function of the phase at the time of observation. The solid line is a theoretical curve adopted from Sen et al. (1991b) for refractive index and dust distribution estimated for Halley's comet. It is clear from the figure that there is a significant deviation between the observed polarization values of Comet Hale-Bopp and the phase curves for Halley, especially at the larger phase angles. On the basis of their study of observations of various comets, Levasseur-Regourd et al. (1996) have suggested the existence of two classes of comets: low polarization and high polarization classes. Comparing our observations with Figs. 3a and 3b of their paper, it is evident that at phase angles above 30 the polarization observed in Comet Hale-Bopp is the highest observed till now. If the classification suggested by Levasseur-Regourd et al. (1996), is applied, the comet Hale-Bopp will belong to high polarization class of comets.

  
Figure 1: The observed percentage polarization as a function of phase angle for the three continuum bands. Filled circles represent the data for Comet Hale-Bopp, open triangles and open squares are for comet Halley, taken from two sources: Sen et al. (1991b) and Kikuchi et al. (1987) respectively. The solid line is the best fit model curve for Halley data (Sen et al. 1991b). Dotted curve is a polynomial fit to the present data

A polynomial fit to the observed data (with the boundary conditions of zero polarization at 0 and 180 phase angles) gives the values of the inversion angle and the slope at inversion and these are listed in Table 2 (click here) for the three continuum wave bands. The values of the slope at inversion, h, for the 3650 Å  and 4845 Å  wavelengths obtained for this comet are close to those for Halley ( Å) while for the 6840 Å  wavelength the slope for this comet is clearly larger. The parameter h is a direct indicator of the albedo (see Fig. 1 in Dollfus 1989). The albedo of the dust grains in this comet is similar to that of Halley for the shorter wavelengths. The albedo is very low i.e. the comet grains are dark. The total brightness of the comet Hale-Bopp was far below the expected brightness - the presence of darker dust grains may be one of the reasons. The inversion angle is related to the fluffiness of the dust grains - fluffier the particle, larger the phase angle at which inversion occurs. In the present case the inversion angle is found to be dependent on the wavelength. This may be due to the fluffy nature of the grains.

 

Wavelength Inversion angle Slope at inversion

in Å @(phase) V₀ h 3650 4845 6840

 

Figure 2 (click here) displays the wavelength dependence of polarization at different phase angles. Shown with a dotted line is the wavelength dependence of Comet Halley (Kikuchi et al. 1987) for one phase angle. This figure shows that continuum polarization in Comet Hale-Bopp has a very strong wavelength dependence. The degree of polarization increases with increasing wavelength which is a marked difference from Comet Halley whose wavelength dependence is more flatter. This wavelength dependence is found to increase with increasing phase angles. This is expected for smaller (compared to Halley) sized dust grains.

  
Figure 2: Wavelength dependence of polarization for Comet Hale-Bopp, as observed at different phases; Phase angles are mentioned adjacent to the respective curves. Comet Halley data (Kikuchi et al. 1987) for one phase (46.1) close to observations of Hale-Bopp at phase 46.2 is also plotted in the figure (dotted line)