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Astron. Astrophys. 333, 746-752 (1998)

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4. Discussion

4.1. Absolute magnitude and nuclear diameter

Assuming that the comet does not display any cometary activity, its brightness should strictly follow an inverse square law which can be expressed as:

[EQUATION]

where [FORMULA] is the magnitude normalized to [FORMULA] AU and the phase angle [FORMULA]. The [FORMULA] term is an empirically determined correction of the phase effect (Meech and Jewitt, 1987). This relation may of course be modulated by brightness variations due to the unknown rotation of the comet. In Table 3 we present the photometry for all of the runs (average [FORMULA] magnitudes), and in addition have presented the [FORMULA] values calculated from the data. The photometry was measured in a very small aperture (typically 2 [FORMULA] the seeing) in order to minimize the sky noise contribution to the measurement. The data do not show any systematic deviation from an inverse square law, thus we interpret this to mean that the comet was not active, even at r = 3.5 AU. The [FORMULA] magnitude reduced to [FORMULA] = r is plotted in Fig. 2 a, and Fig. 2 b shows the [FORMULA] magnitude. A photometric measurement of 55P/Tempel-Tuttle was obtained by Weissman and Buratti (1997) at the Palomar [FORMULA] telescope on June 16, 1996, while the comet was at [FORMULA]  AU. The magnitude [FORMULA] is compatible with our results. This data point has been plotted together with ours for comparison.

The weighted mean value of [FORMULA] may be used to compute the radius, [FORMULA], of 55P/Tempel-Tuttle (Russell, 1916):

[EQUATION]

where [FORMULA] is assumed for the geometric albedo and [FORMULA] is the red solar magnitude. The radii derived from this equation are shown in Table 3. Although these values correspond to a small nucleus, they are consistent with what is being found for other comet nuclei (Meech, 1998). The average value of the nucleus radius is

[EQUATION]

A comparison of the sizes of cometary nuclei measured so far is shown in Fig. 3.

[FIGURE] Fig. 3. Comparison of nucleus sizes for 24 nuclei - after Meech (1998); 55P/Tempel-Tuttle is highlighted.

The amplitude of any observed lightcurve caused by rotation of the nucleus may be used to obtain a minimum axis ratio for the comet. None of the runs have sufficient time base coverage to constrain the rotation; however, on several runs (1996 May, 1997 March and 1997 June) more than 1 image was taken, and in all cases the difference between the magnitudes obtained from the images was greater than the errors (i.e. significant). In order to estimate the axis ratio, we make the assumption that these differences are entirely caused by the rotation, and not at all by the photometric errors, nor by possible albedo variations. We also assume that the bare nucleus can be modeled as a tri-axial ellipsoid with axis dimensions [FORMULA]. If the comet is rotating along the shortest axis, then the area of the nucleus projected on the plane of the sky would vary from [FORMULA] to [FORMULA] (if the aspect angle is [FORMULA] ; or [FORMULA] for an aspect angle of [FORMULA]). The measured lower limit to the amplitude of the lightcurve can then be interpreted as a lower limit

[EQUATION]

where [FORMULA] is the full range of the lightcurve in magnitudes. Using this equation, we obtain a lower limit to the axis ratio for the comet of [FORMULA] = 1.5, corresponding to the largest change in brightness, which occurred during the 1996 May run.

4.2. Cometary activity

Although observations of deviations from the inverse square law on the heliocentric lightcurve is the most sensitive way to detect any cometary activity (this was the method by which activity was first detected on comet 1P/Halley; Meech et al. (1986)) we have computed the radial surface brightness profile of the comet compared to field stars to see if there is any evidence of image extension indicative of a coma. This is done by computing the sky subtracted total counts in concentric annuli centered on the peak pixel and using the photometric transformations to place this on an absolute scale. As shown in Fig. 4, the profile is consistent with a bare nucleus.

[FIGURE] Fig. 4. Radial surface brightness profile of 55P/Tempel-Tuttle (filled circles) compared to a stellar profile from the 1997 March 4 Keck run.

4.3. Future plans

We intend to continue to observe this comet as often as possible in order to study the onset of the dust production and also to monitor the further development. During the fall of 1997, in collaboration with M. A'Hearn and Y. Fernandez, we will be observing the comet simultaneously in the optical and IR from Mauna Kea, in an attempt to directly measure the nucleus size and albedo.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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