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Astron. Astrophys. 349, 649-659 (1999)

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4. Discussion

4.1. Nuclear radii estimates

The nuclear radii estimates for the inactive comets listed in Table 3 may well be extremely close to the actual values 2 as no evidence for activity was found. Strictly speaking however, the majority could be upper limits as the presence of an unresolved faint coma cannot be ruled out when one considers that these comets were observed at heliocentric distances within the water sublimation region. Also the CLICC Atlas of Cometary Lightcurves (Kamél 1992) shows that at these distances most cometary lightcurves do not correspond to those of point source objects of constant scattering cross-section (i.e. inert cometary nuclei). For the active comets listed in Table 6, the upper limits derived for the cometary nuclei without using the PSF subtraction technique discussed in Sect. 3.3.1 may be regarded as firm. For the smaller upper limits obtained using PSF subtraction, in some cases the 3[FORMULA] upper limit is the same as or exceeds the more simple analyses. More realistic modelling might be achieved by convolving the PSF with a steady state coma model and adjusting it to the data (Lamy & Toth et al. 1995), but unfortunately to be successful requires a higher signal to noise ratio than was available to us. We note that the nuclear radii estimates listed in Tables 3 & 6 are typical for Jupiter family comets. The nuclear radii estimates derived in this paper significantly increase the number of such estimates for short period comets published to date. A more statistically useful sample is therefore obtained.

Column 3 of Table 7 lists previously measured nuclear radii estimates and lower limits along with lower limits derived in this paper using published H2O production rates and active nuclear areas. The lower limit estimates for 9P/Tempel 1 and 81P/Wild 2 stated in Osip et al. (1992) were derived by assuming a spherical nucleus and 100% of the surface area of the nucleus is active to produce the measured OH production rates. For 87P/Bus, 74P/Smirnova-Chernykh, 69P/Taylor and 43P/Wolf-Harrington the amount of active area required to produce the measured OH production rates given in A'Hearn et al. (1995) were used to derive lower limits to their nuclear radii. Again a spherical nucleus and 100% active surface area is assumed. A value of 0.46 km2 for the amount of active area normal to the sun at 205 K required to produce the observed water (Newburn & Spinrad 1989) was used to calculate a lower limit to the nuclear radius of 86P/Wild 3. A spherical nucleus is assumed but this time 100% of the area normal to the sun is assumed to be active. For 26P/Grigg-Skjellerup a lower limit of [FORMULA] 0.38 km was derived using the published H2O production rate (Jockers et al. 1993; Johnstone et al. 1993). The amount of active area required to produce the measured H2O at a heliocentric distance of 1.01 AU was calculated using a Sublimating Nucleus Model based on the equations of Meech et al. (1986). By assuming a spherical nucleus and the entire surface is active the lower limit value was reached.


Table 7. Comparison of nuclear radii estimates with previous values.
[FORMULA]) The lower limits are either directly given, or based on other information, in the respective references. See text. [FORMULA]) The minimum percentage of active nucleus area at the time of previous measurements, [FORMULA] & [FORMULA]) Equatorial & Polar radii respectively. Based on nucleus precession model by Whipple & Sekanina (1979).
A'Hearn et al. (1995), [2] Osip et al. (1992), [3] Meech (1998), [4] Newburn & Spinrad (1989), [5] Sekanina (1985), [6] Johnstone et al. (1993), [7] Jockers et al. (1993)

The lower limits listed in Table 7 derived by these methods are less than, or as in the case of 87P/Bus equal to, our estimates. A value of 2.0 [FORMULA] 0.3 km for the radius of 81P/Wild 2 is in excellent agreement with the previous value of 2.0 km (Meech 1998). However, the radius estimates for 86P/Wild 3 & 26P/Grigg-Skjellerup of 1.1 [FORMULA] 0.2 km and [FORMULA] 1.2 [FORMULA] 0.1 km respectively are considerably smaller than the previous estimates of 3.10 km & 2.9 km (Meech 1998). Recently the nucleus of 9P/Tempel 1 was detected with the Hubble Space Telescope at a heliocentric range of 4.48 AU (Lamy 1998). The nucleus is elongated with semi-axes [FORMULA] km and [FORMULA] km (for an assumed albedo of 4%). This is in excellent agreement with the value obtained here of [FORMULA] km within the measurement error. In our observations 9P/Tempel 1 displayed coma activity and therefore its nuclear radius upper limit was obtained by the method described in Sect. 3.3.1. The agreement with Lamy (1998) shows that the method of refining the nuclear radii upper limits mentioned in Sect. 3.3.1 can be effective in achieving a radius value extremely close to the actual value.

4.2. Fractional active area

The lower limits to the nuclear radii listed in Column 3 of Table 7 were used to derive lower limits to the percentage of active nucleus area (F) at the time the observations of previous studies were taken. Taking 9P/Tempel 1 as an example, a lower limit of [FORMULA] km for the nucleus radius was found by Osip et al. (1992). As mentioned earlier this previous value was originally derived from the amount of active area required to produce the measured OH production rates. The amount of active area is compared to the maximum nucleus surface area possible derived from our value of [FORMULA] km for the nuclear radius. By assuming a spherical nucleus a lower limit for F of [FORMULA] is derived. Similarly the F values for 81P/Wild 2, 86P/Wild 3, 26P/Grigg-Skjellerup, 87P/Bus, 74P/Smirnova-Chernykh, 69P/Taylor and 43P/Wolf-Harrington were also calculated and are given in Table 7. The values obtained for 9P/Tempel 1, 81P/Wild 2 and 87P/Bus are unusually high compared with the distribution of percentage active areas presented if Fig. 6 of A'Hearn et al. (1995). Of the comets studied by A'Hearn et al. the percentage of active areas ranged from [FORMULA] 0-16.5% for periodic comets. It is therefore apparent that estimates of fractional active areas are continuing to increase as more nuclear radii estimates emerge.

4.3. [FORMULA] measurements

Roughly 50% of the comets observed here displayed coma activity. This is a significantly large fraction for comets in the heliocentric range of 3 AU [FORMULA] Rh [FORMULA] 6 AU even with a sample of just 15 comets. Fig. 2 illustrates the difference in activity for 2 of these 15 comets at similar heliocentric distances. Fig. 3 is plot of the [FORMULA] values given in Table 5 vs. heliocentric distance. The plot reveals that many comets may maintain large [FORMULA] values out to 5 AU. Any nucleus contribution to the [FORMULA] values for the active comets is considered negligible after comparison of the R magnitudes measured within the [FORMULA] radii with (a) the derived [FORMULA] measurement for each comet within the [FORMULA] radii, and (b) the scaled PSF R band magnitudes listed in Table 6. Taking 74P/Smirnova-Chernykh as an example, its scaled PSF R magnitude was [FORMULA] and the R magnitude measured within the [FORMULA] radius was [FORMULA]. Therefore a maximum of [FORMULA] 20% of the total flux within the [FORMULA] radius could be due to the nucleus. As an unresolved coma may indeed be present for the comets of Sect. 3.2 Fig. 3 also includes upper limits to their dust production rates using the [FORMULA] values listed in Table 3. Although some of these [FORMULA] upper limits are quite high they can only be regarded as evidence for possible activity as the flux observed from the comets of Sect. 3.2 could be due to the bare nuclei only.

[FIGURE] Fig. 2. R band CCD Images of 74P/Smirnova-Chernykh (left) and 81P/Wild 2 (right) at heliocentric distances of 4.61 AU and 4.25 AU respectively, illustrating the range of activity possible for comets at large heliocentric distances.

[FIGURE] Fig. 3. A plot of [FORMULA] [cm] vs. Heliocentric distance [AU] for the comets of Sect. 3.2 (open circles) & 3.3 (filled circles). The open circles are upper limits.

Table 8 compares the present [FORMULA] values with those listed in A'Hearn et al. (1995) derived at different heliocentric distances. 9P/Tempel 1 shows a dramatic decrease in dust production over a change in Rh of [FORMULA] 1.73 AU. 74P/Smirnova-Chernykh undergoes a shallower rate of change of dust production with heliocentric distance which is typical of dynamically new comets (A'Hearn et al. 1995). If 74P/Smirnova-Chernykh was a recent arrival to the inner solar system, compared to most other Jupiter family comets, this might explain how it can maintain its high degree of activity throughout its orbit given the high mass loss rate due to continuous sublimation of surface volatiles. 74P/Smirnova-Chernykh also displays the highest degree of activity observed by us with an [FORMULA] value [FORMULA] cm at 4.61 AU. With an aphelion distance of 4.81 AU it is apparent that this comet probably remains highly active throughout its entire orbit. Another candidate for continuous substantial outgassing throughout the orbit is P/Helin-Lawrence with an aphelion distance of 5.85 AU. A reasonably high [FORMULA] measurement of [FORMULA] cm (at Rh [FORMULA] AU) was obtained.


Table 8. Comparison of [FORMULA] values with previous values listed in A'Hearn et al. (1995).
[FORMULA] Pre-perihelion, [FORMULA] At perihelion, [FORMULA] Post-perihelion

An [FORMULA] value of [FORMULA] cm was measured for 87P/Bus at a post-perihelion distance of 3.38 AU. [FORMULA] measurements for previous apparitions were 16.2 cm at a pre-perihelion distance of 2.23 AU and 251.2 cm at a post-perihelion distance of 3.15 AU. A'Hearn et al. (1995) found that for the majority of comets the production of dust as a function of position in an orbit remains the same from one orbit to the next, but this is clearly not the case for 87P/Bus. The post-perihelion [FORMULA] values measured on different orbital passages are extremely different even though the comet is in approximately the same orbital position in each case. The post-perihelion dust production rate at Rh [FORMULA] 3.15-3.38 AU has decreased dramatically with each new orbital passage. As no recent gravitational perturbation of the comets orbit has occurred, the previous high post-perihelion activity may have been due to an outburst on the surface of the nucleus. Future [FORMULA] measurements are necessary to further understand the erratic behaviour of 87P/Bus. Finally, we note that 81P/Wild 2 and 43/Wolf-Harrington show a huge decrease in dust production with increasing heliocentric distance, similar to 9P/Tempel 1.

4.4. Dust colours

From the (B-V) and (V-R) values listed in Table 4 it is apparent that the dust comae of 119P/Parker-Hartley, 32P/Comas-Solá, 74P/Smirnova-Chernykh and 89P/Bus show red colours relative to the sun. The [FORMULA] and [FORMULA] values are 0.67 (Tedesco et al. 1982) and 0.36 (Meech et al. 1995) respectively. Previous (B-V) measurements for 74P/Smirnova-Chernykh are [FORMULA] at Rh = 3.559 AU and [FORMULA] at Rh = 3.56 AU (Remillard & Jewitt 1985). These are in excellent agreement with our measurement of [FORMULA] and shows that there is no significant change in the colour of the ejected dust coma after several perihelion passages. The colour indices for 9P/Tempel 1 are similar to those of the sun, within the measurement error. P/Helin-Lawrence shows a blue colour at short wavelengths but is much redder at longer wavelengths when compared to the sun. A (V-R) value of [FORMULA] was obtained for 87P/Bus. The fact that the V band magnitude is less than the R band magnitude for this comet may have been due to contamination by C2 emissions within the passband of the V filter. Finally, no correlation of dust colour with heliocentric distance, phase angle or [FORMULA] value was found. The lack of correlation of colour with heliocentric distance is consistent with previous studies by Jewitt & Meech (1986) and Jewitt & Meech (1988).

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Online publication: September 2, 1999