6. Properties of the nucleus
The geometric cross-section of the nucleus may be calculated from V(1,1,0) using a standard relation (c.f., Keller, 1990; Jewitt, 1992) and assuming a geometric albedo of 4%. From the equivalent circular cross-section, an effective radius can be computed (Table 1). The uncertainty of ts mag translates into an uncertainty of 2.3% in the size of the nucleus, while a brightening of the nucleus of 0.25 mag, for example, increases the radius by 12%. Using an albedo of only 3.5% would increase the radius by 7%.
The above derivation assumes that the nucleus is spherical, which is clearly contradicted by the observed lightcurve (Fig. 8). The observations strongly suggest that we are seeing the apparent cross-section of a rotating elongated nucleus. In principle, albedo variations on the nucleus could produce the observed lightcurve variations, but this hypothesis is contradicted by the simultaneous visible and infrared observations of several cometary nuclei (cf., Millis et al., 1988). We searched for periodicity in the lightcurve by constructing a Fourier decomposition limited to the first sine and cosine terms due to the limited number of data points. The coefficients of these two terms were first found using a gradient method, and the period was searched in the interval from 5 to 40 hr. A least-square fit to the data yielded hr. This value was then introduced as the initial guess in a full, non-linear parameter fit, which produced the same value for the period hr, as well as an accurate determination of the Fourier coefficients.
In order to reconstruct the shape of the nucleus, we assumed that it was a prolate spheroid with semi-axes a and b, that it was in rotation around one of the minor axes, and that its brightness was proportional to its geometric cross-section (the so-called geometric scattering law). Under these assumptions, the amplitude of the lightcurve becomes a function of the aspect angle and the ratio . The aspect angle was calculated adopting the orientation of the spin axis found by Sekanina (1979). The ecliptic longitude and latitude of the north pole are and , respectively (for 1950.0), implying a retrograde rotation. The viewing geometry on 28 November 1994 resulted in an aspect angle of ("equatorial view"), with the spin axis being practically perpendicular to the line-of-sight. After imposing a rotational period of 25.02 hr, we find that the best fit synthetic lightcurve (Fig. 8) gives a ratio .
The viewing conditions of the nucleus, depicted in Fig. 8, were such that nearly the full cross-section was seen at the maximum of the lightcurve. We calculated the fraction of illuminated area (0.95) and introduced this correction to derive the true elliptic cross section assuming a geometric albedo of 4%. We obtained km and km. The errors are derived from the propagation of the photometric uncertainties within the framework of the above model.
We tested other solutions for the orientation of the spin axis by randomly selecting any direction within of the direction found by Sekanina. Any deviation from this nominal solution, for which the aspect angle is at a maximum, results in a decrease of the amplitude of the light curve as illustrated in Fig. 9. The uncertainty in the observed lightcurve amplitude translates into a wide range of solutions for the ecliptic longitude and latitude of the spin axis, typically . Similarly indeterminate solutions are well-known in the study of asteroidal lightcurves having limited data, as applies to our case also.
From an analysis of the non-gravitational forces on the nucleus of 19P/Borrelly, Rickman et al. (1987) derived that the mass of the nucleus is kg. Combining the latter with our result on the shape of the nucleus leads to a bulk density of kg m-3, a somewhat low value but still within the range of presently accepted values. The nucleus of 19P/Borrelly is stable against centripetal disruption since the critical density (Jewitt and Meech, 1988) is much lower, kg m-3. Finally, from the active area of 6.6 km2 obtained by A'Hearn et al. (1995), and the total area of the equivalent spheroidal nucleus, we calculated a fractional active area of 8%, comparable to that of comet 1P/Halley (10%).
© European Southern Observatory (ESO) 1998
Online publication: August 27, 1998