## What Goes Up Must Come Down, or Not

Ideas more or less related to teaching and learning physics at Luther College.

Over the past week I have posted several graphs related to changes we observe in our semi-regular (SR) pulsating variable stars. These stars are classed as SR largely because they have relatively small amplitudes of variation. Still, most of the sixty or so SR stars we have discovered in the field we have studied for the past 12 years change brightness by 20 to 30%. When we discovered such a large population of these stars we began to wonder how they might evolve. Are they getting brighter or dimmer on average? Are their amplitudes of variation growing or shrinking? Are their periods of oscillation changing? Are their colors changing? Student David Pfotenhauer and I will be trying to answer some of these questions over the next year. The graphs I have posted this past week represent a tentative first step in the process.

We looked at four stars and tried to estimate their “typical” brightness or “mean magnitude” and their amplitude of variation each observing season since 2006. We have data from 2003 and 2005 but initially at least, we are not using it because it spans insufficient time within the year. Back then we were just learning what we were doing and this SR project wasn’t even on our radar. Brightness versus time graphs (light curves) for two SR stars from the 2012 and 2013 observing seasons are shown below.

The star with the light curve on the left has a typical period of variation of less than 100 days, while the star with the light curve on the right has a typical period of variation near 350 days. For the work we are doing here we limit ourselves to the stars with shorter periods. Because we did not see the top and bottom of the light curve regularly we simply can’t tell how much the brightness of the star on the right changed. If we catch it at different points on its cycle in different years our results will be seriously biased. Of course we can’t simply average all of our measurements in a given year for the star on the left either because we won’t sample the brightness evenly throughout the cycle. To make the graphs below we averaged the three brightest measurements each year to estimate the brightest the star was in that year and we averaged the three faintest measurements to estimate the faintest the star was. Averaging the averages yielded “mean magnitude” and taking the difference of the two averages yielded the amplitude. Is there a better way to do this? Surely. Will we keep working on it? Surely. Only about 25 to 40 of our SR stars have typical periods short enough to allow us to do the work just described but that should keep us busy for a while.

This very first simple try at the data yielded intriguing results. Two stars may be getting brighter and two dimmer. These changes might be periodic instead of monotonic. There might be sub-classes of stars within our population. The amplitudes of variation might be largely stable (although spikes in single years do seem common) or they might be growing or changing periodically. The ultimate goal is to understand what states these stars evolve through but we need to get a handle on the data first. We will keep at it.