Comet Hale-Bopp Recovers


by Mark Kidger

During the next few months the eyes of tens of thousands of amateur astronomers and hundreds of professionals, not to mention the general public, will be centered on Comet Hale-Bopp. After the rather depressing news of the last few months, which warned that the comet could turn out to be one of the greatest disappointments of the century, the situation has changed once again. Although it is not very likely that Hale-Bopp will be as bright as we, perhaps naively thought, its development over the last two months has confirmed that this really is one of the great comets of the last few centuries. The study of the light curve which is presented here seems to confirm that this is the third greatest comet in the last five centuries. The hopes that a negative magnitude will be reached remain on their feet, although the comet will have to continue evolving favourably during the next two months to maintain this course.

The light curve

This light curve study is based on the ICQ archive and consists of the observations made by the most expert observers in the world. The archive shows that the comet was increasing rapidly in brightness for the first few months after the solar conjunction at the start of January 1996. From magnitude 8.5 at the middle of March, the comet's evolution was so fast that the first naked eye sightings happened in the second half of May, with the comet now at magnitude 6.5. However, this rate of increase only continued for a few more weeks: in late June the comet was at a magnitude between 5.5 and 6 and stayed there, with virtually no increase in brightness, until October.

During the period when the magnitud was virtually unchanged, the geocentric distance hardly changed, but the heliocentric distance decreased from 3.9 to 2.9 AU, which should have produced a correspondingly large increase in brightness. For a typical comet this increase in brightness would have been around 1.3 magnitudes whilst, if Hale-Bopp had maintained the trend established at large heliocentric distances, the brightness increase would have been 1.6 magnitudes. In fact, the increase was actually less than half a magnitude and, at one point, the comet actually got slightly fainter as it came closer to the Sun.

However, from the start of October we see a new jump in the brightness of the comet. The magnitude has gone from 5.0 (approximately) at the end of Octuber to 4.2 at the start of December and the observations seem to show that this rate of increase is being maintained.

Light curve analysis

The observations made up to the end of 1995 appear to follow an inverse fifth power law:

m1 = -2.70 + 5 log Delta + 12.6 log r

The absolute magnitude at large distances (m0 = -2.7) is the second brightest ever recorded for comets observed in the last five centuries (before the year 1500 it is almost impossible to estimate the light curve parameters because of the poor quality of the observations). Only Comet Sarábat, of 1729, with its absolute magnitude of m0 = -3.0 was brighter.

However, it is the behaviour at lower distances, closer to perihelion, which dominates the maximum magnitude of the comet, in combination with its minimum distance from the Earth. From March 15th 1996 to early December, the light curve has been much more conservative in its behaviour. The light curve can be fitted with a formula of:

m1 = -0.18 + 5 log Delta + 6.6 log r

Extrapolating this relation through to perihelion we obtain a maximum brightness of magnitude + 0.4, which, although more optimistic than some of the more pessimistic extrapolations, is rather disappointing, being slightly fainter than Comet Hyakutake (C/1996 B2). The reason for this improvement in the extrapolation is the rapid increase on brightness during the Autumn: from March through to September the mean values were of n ~ 3, an absolute magnitude around one magnitude fainter than given above and a maximum magnitude of around + 2 to + 3.

However, since mid-October the absolute magnitude is, once again, almost a magnitude brighter and "n" has increased quite significantly. The observations carried out since October 11th fit a relationship of:

m1 = -1.04 + 5 log Delta + 8.9 log r

What is more important, there is some evidence that "m1" and "n" are continuing to improve. With this relation the comet should reach negative magnitude: the relation predicts a maximum of m1 = -0.5, although, for an observation with the naked eye this translates to m1 ~ -1 because naked-eye observations are giving magnitudes typically half a magnitude brighter than those made with binoculars. The absolute magnitude calculated here is the third brightest of the last few centuries after Comet Sarábat and the Comet of 1577.

Why does Comet Hale-Bopp behave this way?

There have been various estimates of the size of the nucleus of the comet. Observations by the Hubble Space Telescope point to a diameter of the nucleus of some 40 km, while Zdenek Sekanina estimates 15 km from the activity of the nucleus. The former would put Hale-Bopp firmly in the Giant Comet class, while the second estimate would make it just 50 % larger than Comet Halley, making it a big and hyperactive comet, although not a giant one.

Since its discovery, Comet Hale-Bopp has maintained a high level of activity. Through the summer and autumn of 1996 the activity of the gas jets produced by the nucleus was quite remarkable and the comet has, according to observations taken at the Observatorio Astronómico de Mallorca, shown as many as 8 jets at the same time. This activity is almost unprecedented in a comet so distant from the Sun and only Comet Humason (of 1962) has shown, in the last few years, similar behaviour: Humason, although not as bright intrinsically as Hale-Bopp, was a giant comet, with an absolute magnitude of m0 = + 1.5 (a factor of 100 brighter than average for new comets).

Thus it seems that Hale-Bopp really is a giant and/or highly active comet and is thus a worthy candidate to become an important object. So, why has its photometric behaviour changed so many times?

The best clues that we have about the behaviour of Comet Hale-Bopp appear to be the jumps in the light curve and their relation to the sublimation of volatiles. Far from the Sun the activity appears to have been driven by the sublimation of CO. So far from the Sun water ice sublimation is totally negligible. However, the crucial moment in a comet's evolution is when the dominant volatile passes from being CO, to being water. This point tends to occur, depending on the comet, between about 1.5 and 3 AU from the Sun. Very disappointing comets are the ones which liberate only small quantities of water at 1.5 AU and less from the Sun (eg: Austin), the point where water vapour sublimation should really kick-in strongly.

It seems, however, that water ice sublimation started at an extraordinarily large distance in Comet Hale-Bopp: more than 5 AU from the Sun. When water started to sublime it seems that CO became inactive, or stopped subliming efficiently. However, at such a large heliocentric distance the sublimation efficiency for water is very low and, because of this, the light curve showed a marked knee. For several months the comet was literally being suffocated due to the inactivity of the water ice. Only at the end of the summer, when the comet reached a distance of around 3 AU from the Sun could water sublimation start-up with greater effect. That was one of the critical points in the light curve: had the rapid increase in brightness not happened at around r = 3 AU it is certain that the comet would not have reached even magnitude + 3 at maximum.

Right now, we are approaching another critical date as water sublimation should have started to occur vigorously, more or less exactly at the point that was initially expected. Around the second half of January the comet will cross the orbit of Mars and reach a heliocentric distance of 1.5 AU. At this distance water sublimation should start to take off as the comet will have reached a distance at which the temperature of the surface of the nucleus can reach 0 degrees Centigrade. For the comet to be brilliant (a significantly brighter maximum than magnitude 0), the activity has to remain high from mid-January onwards. A half magnitude increase in brightness during those two weeks would be positive, whilst the most optimistic predictions require an increase in brightness of a full magnitude at this time.

In other words, if the comet goes from magnitude + 3 at the start of January to + 1.5 at the end of the month, we are on track for a magnitude between 0 and - 1. If the increase is greater, the maximum could reach - 1 to - 2. A lesser increase would leave the comet around 0 to + 2 according to the degree of slow-down seen in the light curve.

Conclusions

It seems that Comet Hale-Bopp really is one of the largest comets of all time, although the poor observing conditions around perihelion, with the comet on the opposite side of the Sun to the Earth, will make its observation more difficult. Despite these poor conditions, which make the comet 5 magnitudes fainter than Comet Halley and almost 6 magnitudes fainter than Comet Hyakutake, it is still possible that Comet Hale-Bopp could turn out to be one of the ten brightest comets of the last three centuries.