Well, I’ve held off on posting this one because it isn’t very good.  Part of that is the creeping noise problem (looks like brush strokes) that I was battling back then.  Limited integration time (1.5 h) didn’t help at all and, to boot, M33 is a difficult target and this was my first ever try at it.  I tried to accent the spiral structure in the processing.  I’m posting the image despite the problems because a main goal was to find and measure variable stars in this field of view (see panel B).  As it turned out, I got really nice data on two eclipsing variable stars, v TRI and BC Tri (panels D and E show their light curves).  But there was another adventure that popped up involving a star named AR Tri.  This was a new denizen of the variable star zoo for me:  a pulsating star that has both radial and non-radial pulsations of varying frequency; AR Tri is a member of the Delta Scuti class of variable star, which have very short periods and an entire cycle can be captured in an hour or so.  These stars have very small changes in brightness due to the pulsations, generally in a magnitude range of less than 0.1.  The mechanism for the pulsations is quite interesting.  The atmosphere of the stars is rich in helium and they are generally hot and bluish, falling in spectral classes A through F.  A pulsation starts when heat from the core starts ionizing some of the helium, thus causing this layer to become opaque.  Since radiant energy is now prevented from escaping, the brightness of the star diminishes and the temperature of that layer builds.  This, in turn, creates a pressure buildup that forces the layer radially outward.  The outward movement lowers the pressure, so the gas expands and cools.  Now the helium ions are cooled enough to capture electrons and become neutral again.  The gas becomes transparent and the radiant energy can escape, making the star brighter.  Without trapped thermal energy, the hydrostatic forces in the atmosphere bring the expanded gas inward, which then initiates the start of a new cycle.  Notably, the period of these cycles is directly correlated to the absolute magnitude of the stars, just as in Cepheid variables, making them useful as standard candles.  By measuring the period of a Delta Scuti-type variable, astronomers can then know the intrinsic brightness of the star.  By comparing this to the apparent brightness of the star in the sky, the astronomers can determine the distance to the star. The noise in the original images of AR Tri really clobbered the precision of the magnitude data for the star and the light curve came out really wacky (Panel F).  What sense could I make of this?  Well, light curves for variable stars are generally up and down curves that can be modeled with sine and cosine curves.  So, I built a cosine curve model in which the period could be varied.  Using an Excel spreadsheet, I plugged in a series of possible values for the period and calculated predicted brightness variations over time.  I then found the deviations from the predicted values from the observed values for each trial period.  The period with the smallest deviations would be the estimate of the actual period.  As Panel G shows, the result was 0.051 day (73 min), which is surprisingly close to a literature value of 0.045 day.  Panel H shows the data fitted with the cosine model using a period of 0.051 d.  Order out of chaos thanks to cool math! 

DATA:180 30" images, OSC, total integration of 1.5 hr, variable star analyses by ASTAP