3 The data

3.1 The sources

About half of the magnitudes included in this catalog have been taken from the compilation of cometary magnitudes collected by Kamél (1991) (the "Comet Light Curve Catalogue'' - CLICC). Kamél mainly used two sources for references: Astronomischer Jahresbericht for the period 1899-1968 and Astronomy and Astrophysics Abstracts for the period 1969-1989. A large part of his data set comes from Green's (1988) Archive of Cometary Photometric Data. The ending date for CLICC was December 31, 1989. Although for sure it is not complete, CLICC is the largest data set for cometary magnitudes available for that period of time.

We have added magnitude measurements for the period January 1, 1990 to August 1998 taken from the Minor Planet Center (MPC) data base. We downloaded the observations for all the JF comets from the Extended Computer Service of the MPC. It should be borne in mind that the MPC data base is mainly for astrometric purposes, and the reported magnitudes are not of homogeneous quality. There is a distinction between total and nuclear magnitudes, but no information is given on how the nuclear magnitudes were estimated. Furthermore, the passband of the measurement is not mentioned, and the only information about the observer and his/her instrument is the observatory code.

We have added a few extra observations that were not included in the MPC data base but appeared in the IAU Circulars or International Comet Quarterly. Data from a few papers devoted to particular comets, published after 1990, have also been included (Mueller 1992; Meech et al. 1993; Chen & Jewitt 1994; Lamy & Toth 1995; Mueller & Ferrin 1996; Lamy et al. 1996; Lamy et al. 1998a; Lamy et al. 1998b) as well as our own set of nuclear magnitudes (Licandro et al. 1999a).

From these data sources, we have taken all the nuclear magnitudes and total magnitudes observed at heliocentric distances r > 3 AU observed after 1950. The cometary activity, on average, is a strong function of the heliocentric distance. The inner coma brightness in the visual is largely due to the presence of a dust cloud surrounding the nucleus. The sublimation of volatile species (mainly H₂O) drives the ejection of dust from the nucleus. At r > 3 AU, cometary activity is expected to be very low because the H₂O sublimation rate is tiny due to the low surface temperature. Total magnitudes at those heliocentric distances might thus be close estimates of the true nuclear magnitudes. Yet, this cannot be taken as an absolute rule: some comets keep very active at heliocentric distances well above 3 AU, presumably due to outgassing of species more volatile than H₂O (e.g., CO and/or CO₂). Therefore, we cannot take for granted that magnitudes measured at r > 3 AU never have strong coma contamination.

We find that 59% of the data points are magnitudes reported as nuclear, though there are different criteria among the observers to define a nuclear magnitude (see Sect. 3.2). The number of pre-perihelion observations is similar to that of post-perihelion observations.

From thermal lag considerations, one might expect some asymmetry between the outbound and inbound branches of the comet's orbit, such that after passing aphelion, the JF comets might be at a lower level of outgassing activity (i.e., closer to showing the bare nucleus). Yet, the photometric data is still too sparse to confirm this theoretical presumption. A better photometric coverage of JF comets along their orbits is necessary before reaching any conclusion regarding the part of the orbit at which JF comets reach their lowest level of activity (or complete inactivity).

Some considerations are presented in Sect. 3.3 to justify the deletion of some data. Table 1 presents a summary of the sources and a general classification of the data. The numbers listed correspond to the data remaining after the deletions mentioned in Sect. 3.3.

Another piece of very valuable information would be the negative observations, i.e., in case the comet was not found, an estimation of the limiting magnitude on the sky-field where one would expect to find the comet. This would give a lower limit to the brightness that in many cases could be lower than a positive detection. There are two reasons why we do not intend to collect these data: i) most of the authors, do not publish the negative observations, e.g. though we have a large data set of negative detections from our observing runs, we do not include them in our paper (Licandro et al. 1999a); ii) the negative observations could be due to a cometary magnitude fainter than our detection limit, but also could be due to ephemeris uncertainties. Remember that comets are subjected to non-gravitational forces that are, generally, poorly known; they could produce differences between the real and expected position larger than several arc-minutes. With CCD fields of a few arc-minutes, the comet could easily be out of the field or far from the center. Our own experience tells us that it is very hard to find a moving object close to the detection limit that it is not close to the field center. Many negative reports could reflect uncertanties in the computed orbit rather than a faint magnitude.

 

 

Table 1: Statistics of our data sets

Number of observations(1)	3990
Data taken from CLICC	1474
Data taken from MPC	2392
Data taken from other sources(2)	124
Observations pre-perihelion	1968
Observations post-perihelion	2022
Reported nuclear magnitudes(3)	1952
Total magnitudes at r > 3 AU(3)	1073
Scotti's total magnitudes at $r \le 3$ AU(4)	514
Scotti's total magnitudes at r > 3 AU(4)	553
Scotti's nuclear magnitudes(5)	412
Roemer's magnitudes	700
CCD nuclear magnitudes(6)	312

⁽¹⁾ For consistency with other observers, the observations by J. Scotti reported as total but taken at $r \le 3$ AU are not included in these numbers.
⁽²⁾ Observations taken from the ICQ after 1990 that did not appear in the MPCs (25), personal communication by C. Hergenrother (6), our own observations (48), data taken from the literature (45).
⁽³⁾ Observations by J. Scotti are not included.
⁽⁴⁾ Magnitudes reported as total.
⁽⁵⁾ Magnitudes reported as nuclear, in most cases Scotti has applied a coma reduction method.
⁽⁶⁾ Only the observations with medium and large aperture telescopes are included. This number may be underestimated, because for many observers we do not know which telescope was used.

   
3.2 Main categories of observers

There are four data sets that deserve a detailed analysis: long-focus photographic observations by Elizabeth Roemer; James Scotti's Spacewatch observations; recent data taken by other professional astronomers using CCD cameras attached to medium- and large-size telescopes; and, finally, amateur observations with small-size telescopes. There is finally a fifth data set that is rapidly increasing in importance: we refer to the recently published observations of cometary nuclei using the Hubble Space Telescope.

Elizabeth Roemer started her observations in 1950. Almost every comet to appear in the following 25 years was photographed by her. She used a 1.4-m and a 2.3-m telescopes at Catalina Station and Kitt Peak, respectively. The trend at that time was to estimate the nuclear magnitude by visual inspection of the plates, where the sharp concentration of the inner coma was actually measured. Roemer argued that long-focus instruments and photographic techniques were best suited for the observation of quasi-stellar comets, where little or no traces of the coma were recorded. The plates, originally taken for astrometric purposes, were used for photometric estimates of the nuclear condensations. The photometry (often around 20$^{\rm th}$ magnitude) could not be done accurately with the aid of nearby photoelectric sequences. The apparent photographic magnitudes observed were hence reported only in terms of whole or half magnitude units.

Contributing 18% of the entries in our data base, Roemer's material is obviously of great interest. During the Roemer era, her observations were generally the faintest, indicating that she indeed came closest to measuring the actual nuclei, whereas other observers were more influenced by coma contamination. However, when viewed from a present-day perspective, it is clear that there is no guarantee that her stellar sources would represent the bare nuclei, and generally speaking, CCD frames offer much better opportunities. This is especially true in the many cases when they have reached 2-3 magnitudes deeper than Roemer's plates and caught the comets closer to their aphelia.

The second large data set from a single observer corresponds to James Scotti's observations with the Spacewatch telescope. This is a 91-cm Schmidt telescope at Kitt Peak dedicated to the discovery and follow-up of Near-Earth Objects. Scotti started his cometary observations with T. Gehrels, but since the late 80's he has conducted his own program for cometary photometry. 24% of the entries in our data base corresponds to his observations (we do not take into account the reports of total magnitudes at r < 3 AU). During the 90's he has recovered many comets at large heliocentric distances (in the sense of the first observation after aphelion passage).

Scotti has developed a tentative method to face the problem of nuclear magnitude determination in active comets. Though a detailed description of the method has yet to be published, we asked Scotti for a brief sketch of it. As described in Sect. 1, the brightness profile of an active comet is the addition of the brightness profile of the coma plus a stellar-like nucleus. Assuming an optically thin coma, the typical width of the nucleus contribution is on the order of two times the Full Width at Half Maximum of the PSF (the seeing). At a distance a few times the radius of the seeing disk from the photometric centre of the comet, the contribution to the profile mainly comes from the coma. Scotti then takes a thin annulus of this radius and computes the mean surface brightness ($\sigma$). He assumes a constant coma surface brightness inward of that annulus. From the total flux of a disk centered on the brightest pixel he subtracts a coma flux corresponding to: $\sigma \times A$ (A - the disk area). The remaining flux supposedly corresponds to the contribution of the nucleus. A nuclear magnitude can thus be computed.

Since 10% of our data correspond to coma-corrected observations thus derived by Scotti, let us scrutinize these a little closer. Several drawbacks may question the validity of this coma-correction method:

i) The assumption of an optically thin coma, in particular in the region very close to the nucleus. A few observed near stellar occultations suggested that extinctions ranging from a few percent to a few tens of percent of the starlight were present in stars passing at distances of a few hundred km from the comet nucleus (Larson & A'Hearn 1984; Eritsyan & Akhverdyan 1987; Ninkov 1994; Fernández et al. 1999). However, other occultations of stars by JF comets have not shown any appreciable extinction. Licandro et al. (1999b) have studied several occultations of stars by the inner coma of comets 81P/Wild 2, 69P/Taylor, and 78P/Gehrels 2. They concluded that no extinction is detected even for stars that passed very close to the nucleus (a few hundred km). They also discussed methodological problems involved in such studies, which may produce spurious drops of the star brightness. In any case the assumption of an optically thin coma, supported by model predictions (see Appendix A), seems to have observational support. Thus, we do not expect any significant trend for overcorrections due to coma extinction.

ii) The assumption of a constant coma surface brightness ($\sigma$) inside the annulus. It is observed that $\sigma$ is a function of $1/\rho$ ($\rho$ is the angular distance from the center) for intermediate distances to the nucleus, but it should level off as $\rho \to 0$. However, a monotonic increase is expected as $\rho \to 0$. Since Scotti assumes a constant coma surface brightness inside the annulus, he tends to underestimate the true coma contribution inside the small disc. The amount of the underestimation would depend on the size of the coma and the radius of the annulus. Grosser underestimations could be expected for small apparent comae, typical of JF comets with large perihelion distances, since the annulus would fall near the coma's edge.

iii) The background "sky''. There may also be problems with unresolved background objects contaminating the "sky'' level underlying the coma. Sometimes the annulus may contain a significant extra brightness from such objects, and then the coma contribution may be overestimated and the nuclear magnitude obtained after the coma substraction may be fainter than the real one. However, it may also happen that the background is more contaminated in the interior of the annulus than within it, and thus the expectation is relatively few cases of gross overcorrections compensated by a larger number of slighter undercorrections.

iv) The difference between the total and coma fluxes inside the small disc may be close to the noise level. Let us consider a difference of 4 magnitudes between the total and corrected nuclear magnitudes. If the surface brightness varies as $\sigma \propto 1/\rho$, the coma flux inside a disc of radius $\rho$ is directly proportional to $\rho$. Assuming a coma diameter of 1', the coma brightness inside a central disc of 10'' diameter would be seven times the nuclear brightness. The actual photometric measurement would be given by the coma and the nucleus fluxes plus the sky background and the read-out. By Poisson statistics, the noise in the measurement would be on the order of the square root of the value. Applying Scotti's method, the nuclear flux would be computed from the difference of two similar quantities that are many times larger than this difference, and the statistical uncertainties of each would be on the order of the square root of the value. We may expect a significant random scatter in such situations.

v) The color of the magnitude. Scotti's CCD frames are taken without filters. He uses solar analogs as standards to estimate his magnitudes, so these resemble the standard visual magnitudes, though some small color corrections may be involved to define them in the Bessel or Kron-Cousins systems. Conceivably, a systematic error of $\sim 0.1 - 0.2$ magnitudes may be involved, but this is not very important compared with other sources of errors. A larger non-systematic error (may be even more than 1 mag) could be foreseen if the observer does not calibrate the observations on a nightly basis, a fact we do not know.

From the previous discussion we can conclude that Scotti's coma subtraction method may be rather uncertain, at least in the cases of very active comets, as shown by the wide spread of the estimated nuclear magnitudes in some cases; for low-active comets it may give more useful estimates of the nuclear magnitudes (see Sect. 8.2 for a more detailed analysis).

The majority of Scotti's reports are taken from the MPCs. We have already mentioned the drawbacks of these data for photometric purposes. It is only mentioned that the observed magnitudes were total or nuclear, but nothing is said e.g. if a total magnitude corresponds to a comet with stellar appearance (in which case it can be considered as a typical nuclear magnitude), or if the coma subtraction method was applied to the reported nuclear magnitude. In many cases, for similar observing days, Scotti reported total as well as nuclear estimates. We decided to include all his nuclear as well as total reports (even those at r < 3 AU); in that way we were able to analyse the relative contribution of the nucleus and the coma to the total magnitude and the validity of the coma subtraction method. Note that almost half of the observations in our data base correspond to Roemer or Scotti.

Professional astronomers using medium and large telescopes (say, larger than 1.5 m aperture) with CCDs constitute another important group of observers to be discussed. The pioneer in this field was David Jewitt, who started in 1984 a photometric program of distant comets, first with Karen Meech and later with Jane Luu. During the 90's several other groups have engaged in the difficult task of detecting comets close to their aphelia; e.g., Larson & Hergenrother, Meech et al., Mueller et al. and our group (Licandro et al. 1999a). These groups use high quality CCDs attached to large telescopes in sites with good seeing conditions; the detection of even a weak coma is much easier and the distinction between nuclear and total magnitudes more clear. The members of these groups define the nuclear magnitude as the total magnitude of the comet when it has a stellar appearance. If there is no coma, this magnitude would correspond to the definition of nuclear magnitude we have adopted in Sect. 2.

Finally, we have the contribution of many amateur astronomers. The amateur data is very inhomogenous. Some consider a magnitude as nuclear only if they see the comet inactive (no detectable coma), but most of them define the nuclear magnitude as the magnitude of the central brightness. In the past, they may even have tried some methods for "better'' estimates of nuclear magnitudes from visual observations, such as different defocussing methods (see e.g. Kamél 1991). Though we have taken away all the visual observations from the CLICC data set, it was not possible to do the same for MPC data due to the lack of information. Nevertheless, the number of visual reports of nuclear magnitudes has been very low in recent years.

Though the amateur contribution has been of great value in the analysis of total magnitudes, in particular perihelion comet lightcurves, the quality of the amateur nuclear magnitudes is very poor, which makes their reports of little use, unless the comet is far from the Sun and inactive, but "professional-like'' amateurs with large telescopes and CCDs, like William Offutt, are then required.

The data taken from the HST observations included in our catalog correspond to only 4 comets: 4P/Faye, 22P/Kopff, 9P/Tempel 1 and 46P/Wirtanen. There are observations of 19P/Borrelly and 45P/Honda-Mrkos- Pajdu $\breve{\rm s}$áková, but they were taken at large phase angles (38$^\circ$ and 90$^\circ$, respectively). As explained below, these large phase angle observations are discarded from our catalog.

   
3.3 The screening procedure and the reduction

As mentioned, we have discarded all magnitudes determined visually from the CLICC data set since they are too unreliable. We could not do the same for the MPC data, but there are likely very few visual observations there anyway. Total magnitudes of comet 29P/Schwassmann-Wachmann 1 were also deleted. This comet has a quasi-circular orbit with a semimajor axis of 6 AU. The reasons to include total magnitudes at r > 3 AU are not valid in this case because the comet is well known to intermittently exhibit major activity ("outbursts'') by an as yet unknown mechanism. It has been well observed all around its orbit; total magnitudes are generally many units brighter than the large set of more than 200 nuclear estimates.

Following Kamél, we have corrected all the photographic magnitudes (P) for color, introducing the color correction: P - V = 0.6. Concerning red magnitudes, observations show that the coma-subtracted nuclei are slightly redder than the Sun in that part of the spectrum (a gradient of the reflectivity of about 10% per 1000 Å at optical wavelengths). While the Sun has a color in the Kron-Cousins system of V - R = 0.36, observations of 28P/Neujmin 1, 10P/Tempel 2 and 46P/Wirtanen show an average $V - R \sim 0.5$ (e.g. Jewitt & Meech 1987; Jewitt & Luu 1989; Lamy et al. 1998a). Some of the red magnitudes were obtained with the Mould R filter, which is close enough to the Kron-Cousins R magnitude to consider the difference as negligible at the expected level of accuracy. Therefore, we will apply a standard color correction V - R = 0.5.

From comparison of MPC reports and IAUC (where more information is given on the magnitude estimates), we have seen that the following observers always report magnitudes in R: S. Larson and C. Hergenrother (from many telescopes at Kitt Peak and Whipple Observatory - Mt. Hopkins); D. Jewitt, K. Meech and collaborators (from Mauna Kea); H. Boehnhardt (from ESO); A. Fitzsimmons & I. Williams (from La Palma). In case no information is provided about the color, we then assume that they report R-magnitudes and the proper color correction is applied.

The observed apparent magnitudes V are then transformed into absolute magnitudes V(1,1,0) by:

$$V(1,1,0) = V - 5 \times \log(r \ \Delta) - \beta \ \alpha$$ (2)

where r and $\Delta$ are the heliocentric and geocentric distances at the instant of the observation and $\alpha$ is the phase angle. $\beta$ is the phase coefficient, for which we have assumed a common value of 0.04 mag/degree for all the comets (Jewitt & Luu 1989). Since the phase coefficient might depart significantly from the adopted value in individual cases (Scotti, private communication), we have discarded magnitudes measured at phase angles greater than 30$^\circ$ in order to avoid gross errors in the phase correction.

For each data point we compute ephemeris to calculate the values of r, $\Delta$ and $\alpha$ and apply the correction from apparent to absolute magnitudes.