Comets are notorious for not following predictions, but even judging the magnitude of a bright comet that's right in front of you is not straightforward.
Stellar magnitude estimates made by long-time variable-star observers often agree to within 0.1 or 0.2 magnitude. These observers are comparing stars with stars. But a comet's coma or head may be anywhere from a few arcminutes to a degree or more in size. Because comets appear radically different from the pointlike stars used for brightness comparisons, determining a comet's integrated (total) magnitude is far more difficult.
For centuries the reported magnitudes of naked-eye comets were very ambiguous. Often they seem to refer to the brightness of the intense nuclear condensation — the strong, sometimes starlike feature seen at the heart of the coma. As such, the total brightness of the comet's head was usually underestimated. Not until the turn of the century were satisfactory visual methods developed for determining the brightness of extended objects.
As with variable stars, ascertaining a comet's brightness requires two comparison stars of known magnitude — one slightly brighter than the comet and the other slightly fainter. It helps greatly if they are all in the same field of view and at a similar altitude above the horizon to avoid errors caused by atmospheric extinction.
Listed on the next page are five widely recognized methods used by amateurs to estimate a comet's integrated brightness. Each has its faults, but all (except perhaps the last one) will give acceptably accurate results if carefully employed.
Five Methods to Estimate a Comet's Brightness
In order of common usage, the five methods are:
Sidgwick's method. This is the most widely used procedure, popularized by J. B. Sidgwick within the British Astronomical Association in the 1950s. Here the observer carefully memorizes the brightness and size of the in-focus comet. The instrument is then racked out of focus until the images of the comparison stars have the same diameter as that of the in-focus coma. The observer then judges the recalled brightness of the comet relative to the defocused stars. Typically, you need several tries before arriving at a definite brightness value. This method works very well for diffuse comets. However, it is difficult to apply to those comets (like Hale-Bopp) that appear strongly condensed (concentrated toward the center). Defocused stars look "flat," while the brightness of an in-focus comet changes markedly from the pseudonucleus outward.
Bobrovnikoff's method. This is usually credited to Nicholas T. Bobrovnikoff but apparently was devised decades earlier. The comet and comparison stars are defocused simultaneously to such a large extrafocal diameter that they can be compared directly with one another. In the case of a bright naked-eye comet, eyeglass wearers can often simply remove their glasses to create the desired effect. Bobrovnikoff's procedure is certainly the easiest to master. It also works best for highly condensed objects like Hale-Bopp, since it smooths out the coma's steep brightness gradient. Very diffuse objects, on the other hand, can be significantly underestimated in brightness using this method.
Beyer's method. Devised by Max Beyer, one of the foremost amateur astronomers of the 20th century, this method is similar to Bobrovnikoff's but takes the extrafocal procedure to a more extreme level. To work effectively, the comet's head must be defocused to many times its in-focus diameter. The instrument is racked out of focus until the comet and stars begin to disappear into the sky background. Their order of disappearance is then noted. If a given star disappears before the comet does, it must necessarily be fainter, and vice versa. Measuring disappearance increments between the stars and comet as you turn the focuser allows you to obtain a magnitude value. Beyer's method works best for highly condensed objects of fairly small diameter but is unsuited to very diffuse comets.
Morris's method. Independently formulated by Charles Morris and Stephen James O'Meara in the early 1970s, this procedure was developed to bridge the perceived gap between the Sidgwick and Bobrovnikoff methods when the coma appears moderately condensed. The comet is put slightly out of focus, just enough to "flatten" the brightness profile and make it easier to determine the comet's average surface brightness. This brightness is then memorized, as well as the out-of-focus diameter. The comparison stars are then defocused to the same out-of-focus diameter. Some observers consider this procedure more difficult to master than the others.
The in-focus method was used for centuries. With the unaided eye one simply attempts to compare the brightness of the comet with the surrounding stars, all in focus. As noted earlier, unless the coma is extremely compact and starlike, this will underestimate its brightness. However, if done in conjunction with one of the other, more appropriate methods, it will provide a magnitude value roughly comparable to those obtained for pre-20th-century comets. Thus it helps calibrate the true brightnesses of earlier, historically interesting objects.
As readers can imagine, the visual measurement of cometary brightness has a highly convoluted history. For a most interesting and detailed account of its development, see the article by Green in the October 1996 International Comet Quarterly. An explanation on how to correct magnitude estimates for atmospheric extinction and how to estimate the coma's degree of condensation are given in the July 1992 and July 1995 ICQ, respectively.