Forums / The Science / Data Analysis / Looking at the Light Curve: Has the Eclipse Begun?
Looking at the Light Curve: Has the Eclipse Begun?
Visual reports are starting to come in suggesting that the eclipse may finally be starting. So I took a look at the data to see if it backs up the discussion. First, I went to the AAVSO Quick Look file to look at the raw data we've received, displayed in an HTML table. The table to the right is a screen shot. (It's too big to put the whole thing in this post.) Older observations are at the bottom. As you can see, a quick glance with the naked eye does suggest that it began to dim from 3.0ish to 3.2ish. But can we believe this?
Over in the Visual Observing forum I recently posted a topic discussing how visual observations can be pooled together to get accuracy greater than a single observation. So let's apply some of what we talked about there with some of what is discussed in this tutorial about reading light curves.
Let's look at a light curve of the most recent 30 days of visual observations (below). Each dot is a visual observation. The blue crosshairs denote one of my observations. (If you want to see yours observations highlighted, just type in your observer code into the "observer code" box of the light curve generator interface.) The red line is a mean curve of the visual data averaged into 2 day bins. That is, all of the observations in a two day bin were averaged together. A red dot was placed at this point and a red line connects the dots. Note the vertical lines. These are 1-sigma error bars. Statistically, that means that 68% of the data should fall within the range of these error bars. It's a quick and dirty way to look at the noise in the data set.
Looking just at the last three bins in the red mean curve, it appears as if the star is indeed becoming dimmer. The eclipse may actually be starting! But, as they say on TV, there's more! Take a look at the error bars on the last three means. You can easily draw a horizontal line between those three means. In order for the final mean point to be outside of the error bars of this light curve, it would need to be about a tenth of a magnitude or more fainter. Remember the error bars mean (generally) that there is a 68% chance a measurement is somewhere within those bars. It's not actually in the very middle. Use your imagination and you can easily draw a red line from the bottom of the previous mean point to the top of the last mean point. That would mean the star is actually getting brighter! All of this means that, statistically, we cannot say the star is getting fainter based on this light curve analysis alone. The eyeballs see something there, but the data doesn't back it up yet.
Now we come to the scientists creed: We need more data! More data may be submitted of observations taken during these two day bins. If so, then the error bar may shrink - if the data is of quality. Also, a few more days of fainter observations or a further drop by a tenth of a magnitude may bring the center of the new mean curve bins outside of the existing error bars. But it's also possible that the eclipse isn't actually beginning and we may be seeing nothing more than noise in the light curve. We'll know, soon enough.
So lets look for confirmation of our result (that the eclipse is not beginning according to this data) and go back to the light curve generator and make a plot that includes our photometric data:
Now we have greater precision. In fact, the error bars for the photometric data are so small that you can't see them at this scale (you'd have to "zoom in" with the light curve). The green V band data is closest to what the human eye sees. Notice the last few observations do not show any dimming, rather the data is flat or possibly even brightening. But these are very few data points, so they are not enough to make a definitive statement based on this photometric data alone. However, it is clear that they do not back up the visual mean curve's suggestion of a dimming. The other photometric bands don't have enough recent data to make any type of conclusion. It takes longer to reduce and submit photometric data, so it's likely many of our photometric observers have taken data but not yet submitted them.
The sum total of this investigation is that there is not enough data right now to conclude that the eclipse has begun. So hang on to your hats for just a little while longer. And now you know how to use the tools to follow the data for yourselves.
Aaron
*** You can make your own light curves instantly using the AAVSO light curve generator. For starters, just type "epsilon Aurigae" into the star name box and click "Plot Data" for a fast plot using all the defaults. You can go back later and start tweaking settings. Important Note: We are going to build a much easier to use version of that light curve generator into the Citizen Sky web site. It's very high on our TODO list. So if you don't want to mess with the current program, just kick back a few more weeks and we'll have an easier one for you to use.
Hello Gary, Your explanation is good. What I recommend for both visual and photometric observers is at this time of the season to observe as close to twilight in the morning as you can. Epsilon is actually fairly high up now and exticntion will be minimized. Back in July and early August, people were looking through tremendous air mass and getting anything of value was super human effort. BTW, I am curious how you observed epsilon close to the zenith? It does not even get close to the meridian yet before sunrise happens. You will not see it at the meridian before sunrise until October. Also, if you observe close to the horizon and then higher up I would expect an even greater difference in magnitudes. Right now (31 August) epsilonAurigae rises about 10:15 PMat my location in Phoenix. Of course you cannot see it as it is attenuated too much. Eta Aurigae rises above the horizon about 15 minutes later. Again it cannot be seen either. Even at midnight the stars are still pretty low and at high air mass. Right now here in Phoenix, for photometric observations 4:00 AMMST (11:00UT)is very good. For visual one could even wait another 45 minutes and still get even better data from a higher altitude. Jeff
Indeed, there are loads of other factors to consider. The original post was more about what the light curve offers. I'm not sure that extinction is a big factor at this stage. The main reason is that most people are using the 32 and 38 comp stars. While being 2.5 degrees away, much of that is lateral movement across the horizon. For example, from my location (Boston) and when epsilon Aurigae is about half way up the sky the difference in airmass between both the 32 and 38 comp stars and epsilon aurigae is just 0.08 airmasses. I don't think that is much extinction for the visual observer. Of course your core point is still valid - and especially so if they are using the 26 comp star. I mentioned this in an earlier post about my first observation. I don't think most people will be using the 26 right now. If you check the Quick Look file you'll see that there are few people using the 26.So, yes, the effect you describe is real. But I don't think it's a major factor in the data at this point. Of course, it will be easy enough to statistically look for once we have a few months of data. As long as we have the observer's rough location we can determine the azimuth at the time of the observation and, once we remove the overall slope of the eclipse, look for leftover trends in the data. That would be a fun project for a cold, cloudy night in the winter!
The error bars mentioned above at the begin of this post by Aaron, are average error of single estimate!Standard error of the mean is- see below and http://en.wikipedia.org/wiki/Standard_error_(statistics).So the error of observations in group together is smaller, naturally without bias, because we may say that error of mean is weighted average of all estimates in group.Let say, we have 15 estimates in 10 days group which are dispersed 0.15 magnitude, than is error of the mean 0.04 magnitude. And we can say that average error of single estimate is 0.15 magnitude. Note that observations can be biased! But that is another story.
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An interesting discussion, Aaron. As is so often the case, there might be even more layers to the problem. It could be that the reported visual observations are NOT reflecting what is really happening with the star, but at the same time they demonstrate just how ACCURATE visual observations are! How can this be? Well, imagine two stars, at the zenith (straight up), that are the same brightness. Just for fun, let's call one Eps, and the other will be our comparison star, Eta. So, our trusty visual observer would report that Eps has the same magnitude as Eta. All is good. Now, let's assume those two stars are down near the horizon in the evening, with, say, Eta about 2.5 degrees lower than Eps. Well, now the light from Eta goes through a lot more of our atmosphere than Eps (when they were overhead, they went through the same amount of atmosphere). You might think 2.5 degrees doesn't seem like much, but if the stars are really low, it does make a difference. Our observer carefully follows her training, and reports Eps is perhaps 0.3 magnitudes brighter than Eta. Her observation is correct! But to determine what is actually happening with the stars, we would need to compensate the difference between how the light of Eps and Eta were attenuated in the atmosphere. This is called 'correction for atmospheric extinction'. If our observer kept observing each night at the same time, they'll both be higher each night, and the differences in the atmospheric extinction will decrease. So, when she starts observing, with the stars really low, she'll report Eps as 0.3 mags brighter than Eta. A month later, at the same time of night, she might be reporting Eps as 0.2 mags brighter than Eta. Since we assume the comparison star is constant, we'd think that Eps has decreased 0.1 magnitudes. An observer using a photoelectric photometer (PEP) would be doing calculations to remove these effects, so a PEP lightcurve would not show this effect. I hope I've made this understandable -- it is a bit intricate! It came to me because I'm observing these stars a different way: I'm using a lens from an old 35 mm camera lens as a telescope, a 15 year old ST-7 CCD camera, and a "V" filter. I've put this on a telescope mount that tracks the stars. So, I can start it all up, and get some sleep while it shoots images all night. When I get up and measure the relative brightness of epsilon Aurigae, compared to eta Aurigae, all through the night, I'm finding that the relative brightness changes by 0.28 magnitudes from when epsilon Aurigae rises to when it gets close to the zenith! With my 'first cut' of extinction calculations, Ican explain 0.23 of the 0.28 mags. I'm sure the whole effect is due to extinction, because I see the same trend every night: I'm sure eps Aur is not actually rebrightening every day, just so I can see it decline again every night! Cheers, g.