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

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7. Properties of the coma

7.1. Calibration of the surface brightness

Holtzman et al. (1995) gives the physical zeropoint of the WFPC2 magnitude system for an object having a Vega-type spectrum with [FORMULA] and observed through the F675W filter: [FORMULA] erg sec-1 cm- 2 Å-1. Their Eq. 7 allows one to relate the WFPC2 magnitude to the observed signal S in DN sec-1:


where [FORMULA] and [FORMULA] is the zeropoint for the F675W filter. As recommended, we added 0.1 mag to the zeropoint to correct to an infinite aperture. The flux expression:


can now be rewritten as:


The standard flux calibration factor given by the routine processing (FITS keyword "PHOTFLAM" in the image header), which strictly applies to a source with a constant flux per unit wavelength, has been revised in version 2 (December 1995) of the HST Data Handbook to [FORMULA]. The agreement between the two derivations is excellent (3.4%) and, as expected, the calibration factor is practically independent of the spectral type.

The final calibration formula, which relates the pixel value S (DN sec-1) to the absolute surface brightness B in W cm-2 sterad-1 µm-1, involves the solid angle subtended by a pixel of the WFPC2 ([FORMULA] sterad) and is given by:


Based on the previous discussion, the uncertainty is [FORMULA]4 %.

7.2. The radial gradients

Fig. 10 displays the radial surface brightness profiles of the coma averaged over four sectors having [FORMULA] angular extents and centered, respectively, along the solar and anti-solar directions and in the perpendicular directions (the latter almost correspond to the North-South direction; see Fig. 1). The power law exponents of these average profiles are practically constant from [FORMULA] to 1000 km but deviate somewhat from the canonical [FORMULA] value. The largest deviation occurs for the solar sector, where p ranges from -1.08 (5th and 6th obervations) to -0.96 (1st and 2nd observations) with an intermediate value of -1.02 for the 3rd and 4th observations. The situation is much simpler in the anti-solar direction, where the six profiles exhibit nearly the same gradient of -0.97 except for some slight variations inside 160 km. The north and south sectors display intermediate situations; note that beyond [FORMULA] km all the profiles converge but with distinct gradients, -1.03 (north) and -1.07 (south). While these average profiles allow a gross characterization of the inner coma of 19P/Borrelly, they tend to hide a more complex reality, which is best revealed by the angular variations of the parameters [FORMULA] and [FORMULA] introduced in Sect. 2 (Fig. 11). There is a gross anti-correlation between the two parameters as [FORMULA] tends to reach its minimum value when [FORMULA] reaches its maximum value. The first and, to a lesser extent, the second observations are somewhat at odds with this trend. The broad fan is systematically offset from the solar direction by approximately [FORMULA], except for the first observation where there is no offset. Note that the minima of [FORMULA] are further offset, by approximately [FORMULA]. A secondary maximum, or shoulder, is clearly present at about [FORMULA] from the antisolar direction. The power exponent, [FORMULA], is close to its canonical value only in a sector close to the antisolar direction where the amplitudes [FORMULA] roughly reach their minimum value.

[FIGURE] Fig. 10. The average brightness profiles of the coma of comet 19P/Borrelly in the solar and antisolar directions (top) and in the North and South directions (bottom)

[FIGURE] Fig. 11. The angular variations of the parameters [FORMULA] (top) and [FORMULA] (bottom) for the six observations.

7.3. Temporal variations

Fig. 11 indicates that the largest temporal variation of the brightness of the coma takes place in the sunward fan and reaches a factor [FORMULA], which roughly corresponds to the variation of the cross-section of the nucleus illuminated by the Sun. (If the aspect angle is close to [FORMULA] as discussed above, the Sun sees a cross-section almost identical to that seen by the Earth as illustrated in Fig. 8, with a time lag of 2.6 hr corresponding to the solar phase angle of [FORMULA]). However, the situation is more complex as the variation of the maximum value of [FORMULA] does not strictly follow the nuclear lightcurve, especially for the first and second observations. Nevertheless, the emission pattern of dust is clearly determined by the insolation of the sub-solar region of the nucleus.

7.4. [FORMULA] and the dust production rate

Although the quantity [FORMULA], as introduced by A'Hearn et al., (1984) is not strictly applicable to a coma that is not in steady-state, we calculated it for 19P/Borrelly to allow a comparison with ground-based measurements. We first subtracted the contribution of the nucleus, and then integrated the coma signal using an aperture radius of 2400 km ([FORMULA]). The results for the six observations fall in the range 600-620 cm and compare very favorably with the value of 646 cm obtained by A'Hearn et al. (1995) when the comet was at a mean heliocentric distance of 1.38 AU (i.e., slightly closer to the Sun than for the present observations).

The determination of the dust production rate follows exactly the method we used for comet 4P/Faye (Lamy et al., 1996), except that the required parameters were set to the values appropriate for 19P/Borrelly: an effective radius of 2.4 km, a fractional active area of 8 % (derived above), and an OH production rate of [FORMULA] molecules sec-1. The latter value was measured by A'Hearn et al. (1995) at a heliocentric distance of 1.41 AU, which is sufficiently close to the present value (1.401 AU) that no correction is required. We assumed that the gas production was dominated by water with [FORMULA] molecules sec-1. We calculated the dust production rate for two values of the bulk density of the nucleus, the canonical value of 1000 kg m-3 and 140 kg m-3, the value derived above using previous results from a non-gravitational force analysis, and obtained 180 and 215 kg sec-1, respectively. We calculated dust production rates using three different aperture sizes (500, 1000, and 2400 km) and found essentially no difference among them. During the 1981 apparition, at a heliocentric distance of [FORMULA]1.34 AU, Newburn and Spinrad (1989) estimated a dust production rate of about 335 kg sec-1, assuming a nuclear radius of 3.5 km and an active fraction of 10%. During the 1987 apparition at a heliocentric distance of [FORMULA] AU, Singh et al. (1992) obtained 240 kg sec-1 assuming a radius of 4 km and a similar active fraction. In view of the large errors inherent in the method (a factor 2 error is estimated by Newburn and Spinrad, 1985), we conclude that these values are in reasonable agreement.

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© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998