from VSSC93

Analyses of Variable Star Observations

Tony Markham

Light curves that are published are usually the ones that look the best. In reality, not all light curves are so photogenic.

If all of the estimates made of a large amplitude variable are plotted in a single light curve then, even though there will be some scatter, it is usually quite straightforward to see the general pattern of variation.

The same is not true, unfortunately, for lower amplitude variables. Plotting one observers estimates of a low amplitude variable will hopefully show up some pattern of variation. However, combining the observations of more than one observer can be more complicated.

The SPA VSS programme includes several relatively low amplitude variables (e.g. Gamma Cas, Mu Cep, Zeta Gem, Alpha Her, etc). The following notes illustrate some of the factors that I have to allow for when analysing the observations of such variables.

Systematic Differences

These are most common in red variables. Typically, each observer will see the variable consistently several tenths of a magnitude brighter or fainter than will other observers. This is not the fault of the observers ! In some cases the systematic differences between observers may be larger than the observed amplitude of variation.

Experience has shown that I often see red variables as being fainter than other observers. A few years ago Melvyn Taylor sent me a comparison of BAA VSS estimates of TX Piscium (cat range 4.8-5.2). Whereas most observers were reporting it as around mags 5.2/5.3/5.4, my estimates were 5.9/6.0/6.1. Fortunately, systematic differences, once quantified, are easy to correct for. Experience shows, however, that the corrections required for a given observer do sometimes drift over a number of years. Various factors could account for this - changing light pollution, moving house, changing which comparison stars are used.

Although these effects are most common for red variables, they can show up in estimates of other variables. For example, whereas most SPA VSS observers see Gamma Cas as mag 2.2/2.3, one reports 2.0/2.1 and another reports 2.4/2.5.

Reporting the results of analyses

Someone who is new to variable star observing will probably not be aware of the above problem. If the observer has seen R Lyrae varying between mags 3.9 and 4.3, they may well be disheartened if it is subsequently stated in print that R Lyrae was varying between mags 4.4 and 4.8. It is much better to quote a range of 0.4 mag and, if possible, avoid quoting specific magnitudes.

Observed Amplitude

Although systematic differences are fairly easy to correct for, complications arise if different observers observe different amplitudes of variation. For example, one observer of Mu Cep might observe a range of 3.8-4.3 (0.5 mag) whilst another is observing a range of 4.2-4.4 (0.2 mag).

Comparison Stars

Systematic Differences and differing Observed Amplitudes can be influenced by the choice of comparison stars when making an estimate.

Everyones eyes respond slightly differently to the different colours of light. Thus we will never all agree as to the exact magnitude differences between comparison stars. Thus there is no guarantee that two observers will make the same estimate of a variable when both use comparisons A and B, let alone if one of them uses A and C !

For historical reasons, the SPA VSS sequences for the brighter variables use V magnitudes. For Delta and Mu Cephei, these place Zeta Cep somewhat brighter than either Eta and Iota. In contrast, the BAA VSS sequence for Mu Cephei attempts to convert these to a closer approximation to visual magnitudes. This places Zeta fainter than Eta, but brighter than Iota. Personally, I would agree with the BAA VSS order of Eta, Zeta, Iota - but no SPA VSS members have reported problems.

In the SPA VSS sequence for Zeta Gem, the V magnitudes for Nu Gem and 1 Gem are only 0.01 mag apart. This does get queried. However, taking into account the other comparison star magnitudes, some observers would prefer a brighter magnitude for Nu Gem whereas other observers suggest a fainter magnitude for 1 Gem.

The most troublesome comparison is comparison G in the U Orionis sequence. Originally, the SPA VSS sequence used the same comparison star magnitudes as used in the BAA VSS sequence, with G=7.17, H=7.61, etc. However, this led to problems since, in reality, G seems to be slightly fainter than H. When U Orionis was similar in brightness to G and H, observers who used comparison G typically reported magnitudes half a magnitude or more brighter than those who used comparison H. However, some observers who used both G and H did report it as fainter than G and brighter than H ! (I believe that this is also true of BAA VSS estimates).

Comparisons close to other stars

These can be troublesome in that they can affect the apparent brightness of the comparison. Most of the comparisons in the Lambda Tauri sequence are so afflicted. This probably accounts for the large systematic differences between observers. Typically, one observer will see a range of 3.4-3.8 whereas another will see 3.8-4.2. Thus, if an observer reports an isolated estimate of mag 3.8, I don't know whether or not Lambda Tauri was seen in eclipse by that observer !

Problems also occur when Mira is near minimum. The faintest comparison in the SPA VSS sequence is very close to Mira and when estimates only use the next brighter comparison there is uncertainty as to whether the estimate is really of Mira itself or of the comparison.

Altitude Effects

These are a particular problem for naked eye variables, especially those for which the comparisons are located some distance from the variable. Although variables such as Beta Pegasi and Alpha Herculis are sometimes affected in this way, the problem tends to be greatest for Betelgeuse. Estimates made during August and September when Aldebaran is much higher than Betelgeuse, and Procyon is either very low or has not risen, typically show enormous scatter.

Distribution of Estimates

Inevitably, variables tend to be much better covered when well placed in the evening sky than when they are only visible in the morning sky. In addition, the summer months tend to get better coverage than do the winter and spring months - a consequence of both the holiday season and the better weather.

Cepheid and Eclipsing variables, for which observations from many different cycles may be combined into a single light curve covering just one cycle, generally do not need an even spread of observations throughout the year - but an even spread throughout the cycle of variation does help, otherwise some parts of the light curve will be based on more estimates than are other parts.

However, when 300 estimates of a variable are split into 30 divisions of equally sized phase ranges, it is not unusual for some of the phase ranges to have as few as 2 estimates whilst others have as many as 20 ! As an example, Beta Lyrae has a period of approx 12.913 days. In practice, because the period is fairly close to a whole number of days, this means that it will not be observable in a dark sky at certain phases for many weeks during the summer. Certain phases will occur near Full Moon when observers are less likely to be out observing. And then there is the weather .... These factors lead to some phases being poorly represented in the data. On the other hand, if it is clear across the UK on a moonless Saturday night in August, many observations will be received for a particular narrow range of phases.


We all sometimes make mistakes.

Some are introduced when transcribing estimates from the log book to the report form. Some occur when converting the light estimate into the deduced magnitude. Some occur when making the estimate itself.

No-one seems to be immune. Even the most experienced observers occasionally report class 1 estimates whereby, for example, they see Beta Lyrae at maximum when everyone else sees it at minimum.

But, as has been illustrated earlier, just because the estimates of two observers do not agree does not necessarily mean that one observer is right and the other is wrong. Although it is generally accepted that, under good conditions, visual estimates can be accurate to +/- 0.1 mag, we have to be careful in how we interpret this accuracy.