The light curve of C/1999 S4 (LINEAR)
When this comet was discovered in late September Brian Marsden pointed out that the comet could become a naked eye object in late July. The comet is now well within the asteroid belt and with 4 months of light curve data some conclusions can be drawn about the probable evolution of the comet. The early IAU light curve prediction was based on CCD magnitudes and "predicts" a maximum of magnitude 3.7 in late July. However, at an early stage, Alan Hale pointed out that the magnitude that he was estimating visually was already one full magnitude brighter than the IAU prediction. This has led to some hopes that the comet might do significantly better.
In fact, applying a "fast-slow" model to the light curve typical of fairly new comets (a fifth power law down to 1.5AU and then a third power law to perihelion - in other words, a fast brightening when far from the Sun and a much slower brightening when close) led to a predicted maximum around magnitude 2. However, over the last two months it has become obvious that the brightness was not increasing as rapidly as would be expected if this were the case and the CCD magnitudes have also deviated considerably from the 4th power law used to "predict" the light curve.
Fitting to all visual data, either received from Spanish observers, or available on the Internet, it seems that the light curve is showing a very slow rate of brightening. The nominal fit that is obtained is:
m1 = 7.9 + 5 log Delta + 7.0 log r
The power law is pretty well defined as n=7 gives a much better fit to the data than, for example, n=7.5. Applying this brightening law the maximum, reached on July 23rd, would be magnitude 5.0.
There is a curious detail in this. The latest MPC orbit has now confirmed the earlier Japanese calculations that the orbit is slightly hyperbolic. This means that the comet is dynamically new and is almost certainly on its first pass after falling from the Oort cloud. Oort cloud comets are usually gassy and then to brighten as a 6th-8th-power law at r>2AU before slowing down dramatically closer in. Comets such as Kohoutek and Austin (the latter was more than 5 magnitudes fainter close to the Sun than predicted from its light curve extrapolation at large distances) established this pattern. One exception was C/1956 R1 (Arend-Roland) which was a rare dusty Oort cloud comet with a hyperbolic orbit. It was also a comet that did not increase very rapidly at high heliocentric distance before slowing down, but rather showed sustained brightening through to perihelion.
The light curve of Comet LINEAR is actually brightening faster than C/1995 O1 (Hale-Bopp) did at a similar range of heliocentric distance (it showed n=4.15 from the TA database, see Kidger, Hurst & James, 1997, Earth, Moon & Planets, 78, 169). Hale-Bopp actually brightened at an increasing rate as it approached the Sun, with n=10.3 close to perihelion. Hale-Bopp started to brighten more rapidly at r=2.6AU, corresponding to the switch-on of rapid water ice sublimation. Were Comet LINEAR to duplicate this behaviour (H-B was extremely dusty, although not dynamically new), we would expect the more rapid brightening to start by the end of February - just before we lose the comet in evening twilight. If this happens, we could still get a maximum around magnitude 3-4. It is well worth trying to follow the comet down into the twilight, to see what happens.
Light curve update (February 18th)
The latest CCD observations added to the database appear to show a slight, but definite brightening in the light curve. Although this is just by a very small amount at present (a few tenths of a magnitude), it appears to be more than would be expected given the light curve fit described above. The latest data are highly consistent, with very little scatter and suggest that this trend is real. Unfortunately, we are at Full Moon now and thus there is no contrasting visual data. However, it does appear that the increase in the rate of brightening described above has started to happen already.
There is not enough data yet to be certain and the visual magnitudes obtained over the next two weeks after Full Moon will be required to confirm the effect, although observations will become ever-more difficult as C/1999 S4 (LINEAR) slips into the evening twilight. By the end of the month though it should be possible to make a first estimate as to the current rate of brightening and to give an idea of how it might affect the peak magnitude in July.
At present the visual light curve fit remains as described above. Adding additional data up to February 23rd has not changed the light curve significantly. There is no evidence of a change in the rate of brightening at any stage, nor of an imminent increase in the rate of brightening at this stage.
The CCD light curve (February 26th)
The team at the OAM in
Note that a CCD does not measure the total brightness of the coma. It measures what is often wrongly termed the nucleus - in fact, the nuclear condesnation, or the inner coma. As such, it is a measure of recent activity.
The result of an analysis of the data is rather interesting. It is evident that the light curve brightened as a third power law law initially and then slowed to an inverse square law in mid-January. There is a "jump" in the light curve around January 10th when the central condensation dropped in brightness by about 0.4 magnitudes in a few days.
The light curve fits to date are:
m1 = 8.6 + 5 log Delta + 7.5 log
r (up to
m1 = 10.2 + 5 log Delta + 5.0 log
These numbers suggest that the nucleus has been rather inactive since mid-January and do not auger well for the comet.
Pre-conjunction light curve update (March 23rd)
As of March 23rd the situation with the light curve really has not changed at all. Most of the visual observations fall on the same light curve extrapolation that has been followed since the Autumn. A few recent points fall some way below this line, although these were taken in difficult conditions, with the comet rather low in the sky and must be regarded as somewhat doubtful. In other words, the comet neither brightens neither obviously more rapidly nor more slowly than previously despite closing in considerably on the Sun now - it is heading for magnitude 5 at best unless there is a drastic change.
A recent IAU Circular warns that the total visual magnitude at maximum may be as faint as 7-8. When the comet emerges from conjunction in June it should be close to magnitude 9. If it is not, this worst case scenario may come to be the correct one.
The CCD magnitude continue to show similar behaviour to previously with a light curve parallel to, but fainter than the visual estimates. Once again the CCD light curve shows an important jump in early March.