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Astron. Astrophys. 337, 945-954 (1998)

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5. Discussion of errors

As mentioned in Sect. 2, the two images of the sixth observation were processed separately because they differed in the sub-pixel location of the nucleus. We find that the magnitudes derived from these two images differ by only 0.01 mag, which lends further credibility to our technique.

The uncertainties in the coefficients involved in the transformation of the instrumental to absolute magnitudes (zero-points, color coefficients) lead to an error of 0.014 mag.

The model PSF generated by the TinyTIM software is a potential source of error, as it does not exactly represent the actual PSF of the telescope. One point of particular concern is the jitter of the spacecraft, which is not known when the telescope is tracking a moving target. A direct measure of the jitter could be determined by analyzing star trails, but there were no bright stars in the 19P/Borrelly field. However, variable amounts of jitter can be introduced in the TinyTIM calculation in order to estimate its effect. In essence, the jitter makes the PSF slightly "fatter", thus decreasing the contribution of the coma in the central pixels and making the nucleus brighter. The jitter is usually characterized by the rms value of the fluctuations of the pointing direction in milliarcsec (mas). A reasonable estimate of 10 mas led to a brightening of the nucleus by 0.014 mag while an extreme value of 20 mas increased the nuclear magnitude by 0.047 mag.

Scattering of light by the CCD electrodes has an effect on the PSF that is similar to that produced by jitter, so we do not consider that effect separately here.

In summary, we adopt a conservative value of [FORMULA] mag for the error in the nuclear magnitudes due to the effects discussed above.

Turning now to the systematic errors, we first discuss our key assumption that the gradients of the coma can be extrapolated within 140 km of the nucleus. The only data relevant to this issue are the high resolution images of 1P/Halley obtained by the Giotto/HMC camera. Analyses of those images indicate that the spatial brightness profile has a constant gradient between 200 and 600 km - very much like what we found for 19P/Borrelly - and a conspicuous flattening inside 200 km, which is possibly explained by the fragmentation of dust grains in the coma (Thomas and Keller, 1990; Keller, Marconi, and Thomas, 1990). Note that this latter effect is small; for example, the intensity at a radial distance of 20 km is depressed by only [FORMULA] % compared to that predicted by the constant gradient model. In order to estimate the effect on our photometry of 19P/Borrelly's nucleus, we generated flattened coma models by introducing a "flattening" function derived from the 1P/Halley profiles (Figs. 1 and 2 of Thomas et al., 1988). The contribution of the coma in the central pixels was consequently reduced, resulting in a brightening of the nucleus by 0.25 mag.

Our adopted reddening of 17%/103Å is another potential source of systematic error. Using a value of 11%/103Å, as observed for P/Encke (Luu and Jewitt, 1990), decreases the R magnitude by 0.007 and the V magnitude by 0.06.

Another source of systematic error is the unknown phase law for the nucleus. Our adopted phase coefficient of 0.04 mag/deg is consistent with that estimated for some other cometary nuclei. Using a coefficient of 0.034 mag/deg, as found for P/Neujmin 1 (Jewitt and Meech, 1987), makes the nucleus fainter by 0.23 mag.

As expected, the error in the determination of the magnitude of the nucleus is dominated by systematic effects. However, these errors do not affect our results on the relative brightness variations of the nucleus.

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© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998