Statistics of Visual Observations

  I want to take a moment and talk about how visual estimates of variable stars can be used to build relatively precise light curves of variable stars. While it is always the case that a well done digital observation will be more precise than a well done visual observation, visual observations still can attain a high level of precision. First, some visual observers simply have a talent for the task. Take a look at the graphs below of two such observers. The two graphs and text are taken from this web page on the AAVSO web site, describing analysis results from a statistician and former AAVSO employee, Grant Foster, when he spent a summer at HQ a few years ago.

This is a Fourier power spectrum from Foster's Cepheid paper (in progress). It is an analysis of around 580 visual observations by Stanislaw Swierczynski (SSW) of TU Cas. The noise level is less than 0.03 magnitudes proving that careful and talented visual observers can make very precise and consistent observations.	This is a light curve of X Cyg with data from another talented visual observer, Wayne Lowder (LX). Around 2400 of his observations are combined and compared with photometric data from the McMaster Cepheid Database. Notice the amount of detail Lowder could detect when his observations are statistically combined, all which is confirmed by the photometric data!

Even if you are not one of the legendary "eagle eyes" like Stanislav or Wayne (both have well established positions in AAVSO lore), you can still contribute to a precise light curve thanks to the nature of statistics. Lots of visual observations can be combined to create a more precise light curve than any of the individual observations, as long as they are honest observations (free from purposeful bias). Basically, any random distribution of independent, natural data will form a distribution profile with a known shape (the central limit theorem - one of the coolest things in nature in my opinion). As long as the shape (Gaussian)  is known, then properties can be derived from it ranging from a simple (yet still precise) mean to more advanced Fourier analysis. Random errors of the observer can be smoothed out by the large number of observations. However systematic errors will become evident, that is why Wayne's data in the above light curve is about a tenth of a magnitude fainter than the photometric data. This is largely due to the basic way the human eyeball and brain perceive light. There is more on this in Chapters 6 and 10 of Variable Star Astronomy.

I would also like to also point people to a poster paper I presented at an AAS meeting where I looked for trends (like the effect of the Moon, location in the sky, etc.) in the precision of visual variable star estimates:

• The Precision of Visual Estimates of Variable Stars (3.6 MB pdf file), A. Price (AAVSO), G. Foster (AAVSO), B. Skiff (Lowell Observatory); AAS Meeting, January 2007.

Again, quality digital observations will be more precise. But visual observations bring some qualitative advantages to the table that digital observations cannot. First, they cost nothing! If you have at least one functioning eyeball then you can make a visual estimate. There is no need to purchase special equipment, computers and software. Second, the learning curve is not nearly as steep as digital observing so it is a great way to get introduced to variable stars while still contributing quality data to the permanent, public archive. Third, the simplicity of a visual estimate means that there are many more of them. The majority of observations the AAVSO receives are from CCD systems. However, they are usually focused on a subset of stars. The majority of stars in the sky are only observed by visual observers. It is the visual observers that keep up the watch and then guide the CCD observers to their targets. For example, some visual observers often monitor cataclysmic variables for outbursts. When they detect an outburst, they notify the CCD observers who then will observe it closely to look for specific properties in the outburst light curve. This is a symbiotic system that works very well for both groups.  Fourth, and perhaps most important, is the social aspect. Many observers form a connection with their favorite stars by visually observing them. I know of many observers who later graduated to CCD observing, but still observe visually simply because it is more fun (I include myself in that group).

The point I'm trying to make is not that one is better than the other. That is a false argument. But that visual observations can contribute valuable observations and due to the other advantages it brings, that a good variable star program will include both visual and digital observations. Use the best of both worlds.

And remember times will change so what is true today won't neccessarily be true tomorrow. So the key is to find what you like and do it and be flexible to change.

Aaron