Refining Your Technique

Repeated estimates over many days or weeks will provoke a desire for greater accuracy. If your observations show a scatter of 0.5 magnitude, you'll soon be burning with curiosity about whether the star really changes that much or whether it's all in your eye. As elsewhere in science, the most interesting data usually show up right where the errors of measurement begin to hide everything. Here are some methods that, when good comparison stars are available, will help you reduce your average error to 0.1 magnitude or even a little better. Do them well, and you'll get a feeling for issues of measurement accuracy and error analysis that are central to every branch of science.

Face the star without preconceptions. Wipe your mind clean of what the variable "ought" to be doing; record exactly what the eye sees. If you brood on the fact that the star can't possibly have jumped 0.5 magnitude since last night, you may try to "correct" your impression of it. This is the worst thing you can do to your accuracy, and it's worth understanding why.

Error in scientific measurement falls into two categories, random and systematic. Random error tends to cancel out in a predictable way after a while, just the way a coin will come up closer and closer to 50 percent heads the more times it's flipped. Systematic errors are those that never cancel out — for instance, if one side of the coin is weighted — and therefore they are more insidious. In the case of variable-star observing, systematic error corresponds to bias in the observer's eye and brain. So if you record exactly what you see without bias, your errors are more likely to be only random, and you can have faith that they will actually average out closer to the truth than any "improvement" you fudge.

Of course, be quick to throw out any estimate that you think results from some actual mistake or carelessness.

Center the stars in the field of view. Place the two you're comparing an equal distance from the field's center, or if this brings them near the edges, move each one to the center and examine it in turn. This is needed because some instruments don't fully illuminate the edges of the field — an effect known as vignetting — so stars near the edge are slightly dimmed. Vignetting is most likely at a telescope's low power, where variable-star work is usually done. Another reason for doing this is that the same star might look subtly different when it's near or far from the black edge of the eyepiece's barrel.

Keep your eyes moving. Scan back and forth between the stars you're judging, constantly checking and revising your impressions. If the variable seems to be a third of the way in brightness from star A to B, try to convince yourself that it's a quarter of the way, then halfway. Is it equally easy to talk yourself into each opinion? Then the truth probably lies between them. If one seems more plausible than the other, shift the assumption you started with and test on either side of it again. This testing of the uncertainty limits is called bracketing an observation, and you should try to make it a habit.

Use the out-of-focus method. It's easier to compare the brightnesses of disks than pinpoints, so twist the focus knob. The brighter the stars, the farther out of focus you can take them.

Choose variables of optimum brightness for your instrument. Stars within about a magnitude of a scope's limit all tend to look alike. Conversely, very bright stars won't have good comparisons nearby; in this case you'll have to go to a smaller instrument with a wider field. The naked eye is the best viewing system down to about magnitude 4, binoculars or a good finderscope down to 7 or 8.

Quirks of the human eye. Beware of three potential sources of error. (1) The Purkinje effect in the retina makes red stars grow brighter (compared to white ones) the longer you stare at them, another reason to keep your eyes moving. (2) Moonlight and light pollution also make red stars look too bright; against a gray background they stand out more than white stars do. Use extra caution under bright skies and mention the observing conditions in your notes. (3) Viewing angle. A star looks brighter in the lower part of your vision than in the upper part. Tilt your head so the line joining your eyes is parallel with the line joining the two stars you're comparing.

All this may seem like a lot to keep in mind. But with time it becomes automatic. Devoted variable-star observers become so familiar with their procedures that they cover dozens of stars a night, swinging from one to the next while hardly looking at their charts.

There's one issue you can't do anything about: your age. The human eye lens yellows over the years, making red stars seem increasingly brighter compared to white ones. This effect may be responsible for a lot of the scatter appearing in AAVSO light curves that combine estimates by many observers. Each person's estimates, however, will be self-consistent for many years at a time, and the potential exists for sorting out effects of different observers' changing eyes (given enough archived observations) and correcting the data base accordingly. As is so often the case in science, good data gathered now may be used far in the future in ways that no one yet imagines.