By Doug Welch 
(Editor's Note: Doug Welch is the 2011 Janet A. Mattei Research Fellow , a program to fund visiting researchers to spend time at AAVSO HQ working with on variable star research of mutual interest. Dr. Welch is a past AAVSO Council Member and a professor of Physics and Astronomy at McMaster University .)
It is ironic. I'm sure. That we had to launch a satellite observatory called "Kepler" - designed to find planets around other stars - to learn that we are on the wrong planet ... for understanding certain variable stars. Truth be told, Mars isn't much better and so we kind of "struck out" in our own solar system. But great mysteries don't last forever in science. This one took over a hundred years to sort out, longer than it should have ... mainly because we were are on the wrong planet.
The story of this puzzling class of variable stars began in 1907 when Sergei Nikolaevich Blazhko reported a long-period modulation of the lightcurve of the near-circumpolar RR Lyrae star, RW Draconis. Subsequent to this discovery, he became head of the Moscow Observatory, was awarded *two* "Orders of Lenin" and had a crater named after him on the Moon, which - almost everyone will agree - is better than a poke in the eye with a sharp stick. Harlow Shapley later reported a similar modulation of RR Lyr itself (although he credits Mrs. Fleming for being the first to actually notice it).
RR Lyrae stars in Messier 3 changing brightness over time (images and animation copyright J. Hartmann, Harvard U., and K. Stanek, Ohio State U.).(Click for a larger version.)
Fast forward to the modern era. "Kepler" was launched in 2009. Its primary mission was to detect the photometric signatures of planets transiting stars in order to establish the frequency of planetary systems. In order to do this, it has a HUGE mosaic of CCD detectors and the spacecraft itself has been put in an Earth-trailing orbit where essentially continuous observations of its target patch are possible. Robert Szabo (reference below) analyzed Kepler data taken of Blazhko-afflicted RR Lyrae stars and reported a remarkable, but previously completely undetected and unsuspected behavior: period-doubling . There is a two-cycle modulation of the lightcurve of Blazhko RR Lyrae stars. And it isn't a small effect. In many cases, every other peak brightness is different from the previous one by *10%*! Such a clue!
How did we miss this? Our excuses are a story in themselves - even several stories! First, we are on the wrong planet. Seriously. RR Lyrae stars typically pulsate with a period near 0.5 days. Okay - seems well-matched to the length of a night, right? Sort of. In a way, our night and the pulsation period of many RR Lyrae stars are too well-matched! So many of them pulsate with a period close to 0.5 days that, if you go out the next night and take observations at the same time, you see ... pretty much the same thing ... as the night before. It is kind of a "Groundhog Day" for observers - you wake up to observe pretty much the same thing over and over again! The period-doubling means that the brightness maximum that occurs during the day is significantly different than the one that occurs during the night - but we only get to observe during the night! Treachery! But of course, only if you are stuck on Earth (or Mars) and the day-night cycle is 24 hours in length. The RR Lyrae stars don't know that - they are just doing their thing!
This is a light curve of RR Lyrae data from Kepler. Note how the amplitude sometimes changes between two cycles. The cycle of this star just happens to be 1/2 of a day. So if an observer watches it at the same time every night, they will only see every other cycle of the star. The cycles in between would be missed. (The light curve was made with the VStar open-source software , which has a plugin to automatically load Kepler  data files.)
Clever observers like Blazhko and Shapley *did* notice that something else was going on. They reported a much longer modulation of the shape of the lightcurve. Weeks to months to years, depending on the star. They even noticed it in RR Lyr itself - the prototype - where the long-term modulation was said to be 41 days in length. Strangely, this is *another* unfortunate timescale for us! Not only is the rotation period of our planet an issue - so, too, is the orbital period of the Moon (about 29 days). Allocations of observing time at facilities frequently have "dark time" (between the lunar phases of "Last Quarter" and "First Quarter"), which is devoted to deep, faint, extragalactic work, and "bright time" - less competed for in historical times and now the province of everyone else (including infrared astronomers where it is *always* bright time!) And so it fell to a band of hardy souls who could control their own observing time, with their own facilities, to attempt to fill in the blanks with respect to the "Blazhko Effect". Needless to say, this type of research had neither the panache nor the guaranteed results of studying, say, supernovae.
Three close-up sections of the Kepler light curve of RR Lyr at the same phase of the Blazhko-modulation. In each case the amplitude of the pulsation is increasing because of the Blazhko modulation. Theses sections are part of a 127-day long Kepler lightcurve. In the leftmost two sections of the panel adjacent maxima sometimes differ by as much as 0.10 mag. But the effect of period-doubling is not always evident (as seen in the rightmost panel. (From Szabo et al, 2010  - used with permission).
The first troops to the front, professional and amateurs, did their best. In hindsight, they both made their own fatal decisions which concealed the discovery of RR Lyrae Blazkho period-doubling. For many decades amateurs decided that keeping and sharing the brightness measurements for every observed maximum was just too much hassle. After all, they reasoned, it was the time of maximum which informed the *only* obvious use of these measurements - the change in pulsation period with time - hopefully due to the slow but steady change in stellar structure due to stellar evolution. Of course, times of maximum light did not preserve the brightnesses of maximum light. So, here was a case where the data taken by amateurs was cut off at the knees and the opportunity to detect period-doubling was lost due to poor decisions. The few professionals studying the Blazhko Effect had dilemmas of their own. Partly publish or perish - partly no opportunity to realistically follow the long-term behavior of even the brightest RR Lyrae for any significant period of time. Certainly there was no suspicion of period-doubling so there was no incentive to plan observations to detect it!
Then came the photometric surveys - OGLE (Optical Gravitational Lensing Experiement) I-IV, inclusive, EROS, MACHO, ASAS-3, SuperWASP. But they all shared the same handicap - being on Earth at a single location. Yes - they were very good at seeing the long-term modulation of the Blazhko Effect in many stars. But the scientific and political geography of these surveys resulted in a lack of desire - and/or ability - to easily combine results from different longitudes. The MACHO Project's bandpasses were "non-traditional", OGLE's were V and/or I and SuperWASP's were unfiltered. Since the law of the funding jungle was to make sure that your project continued, little merging of datasets occurred or was seen as especially desirable. Since no one knew that every-other-period modulations occurred in many RR Lyrae, no one bothered to look for them.
However, there were still some efforts to obtain "multi-site" (i.e. "multi-longitude"), near-continuous photometry of some Blazhko RR Lyrae. Why did they fail to detect the period-doubling? In some cases, the data was collected and never analyzed. In some cases, the Blazhko target was too faint and too few amateurs could or wanted to participate. In some cases, the target was too close to the ecliptic and inevitably suffered interference from the (very predictable) passages of the Sun and Moon! There was a kind of a Drake Equation (in the most negative sense) at work to prevent all but the most motivated campaigns from discovering anything new!
And what about all those RR Lyrae stars in globular clusters? Why didn't we notice something there? Well, the same day/night selection bias exists but the difficulty of discovering and following possible Blazhko RR Lyrae stars in globular clusters is greatly exacerbated by the need to use large telescopes at sites with stable seeing for long periods of time. There are some Blazhko RR Lyrae now known in globular clusters (M3, M5 M53), but not many. While this fact may still be the result of the strong selection biases against their discovery, it may also be a clue that the Blazhko Effect is not strong or possible at the metallicities of most globular cluster RR Lyrae.
In hindsight, what was the right thing to do to have discovered this additional and photometrically-obvious behavior? One strategy was to choose stars with apparent Blazhko signature's whose pulsation periods were as far removed from 0.5 days as possible. A star with a 0.47-day period is less desirable than one with a 0.42-day period or a 0.60-day period where the observer won't be trapped observing the same portion of the lightcurve for an entire observing season. (Indeed, there are near-one-third day Blazhko variables which *would* reveal period-doubling effect on subsequent nights!) A star in a circumpolar region (north or south) is obviously preferable to a star on the ecliptic. (Stars in circumpolar regions can be observed year-round.) Given the large number of RR Lyrae in the sky, one also had the luxury of selecting relatively bright Blazhko variables where the largest possible number of observers could contribute with the highest signal-to-noise measurements. Blazhko discovered things with RW Dra - he made a good choice about the right star to study - or possibly the fact that it was the right star made the Blazhko Effect easier to find there!
Another reason we may have missed the period-doubling in Blazhko RR Lyrae stars for so long is that so few people had access to the computational tools - both hardware and software - that would allow for the timely exploration of the available time-series. It will be interesting to now delve back into the most promising ground-based campaigns and time-series to see if they could have revealed this period-doubling effect much earlier.
It is now very likely that the correct explanation for the Blazhko Effect is at hand. Certainly, the hard work of many groups, especially the Konkoly Blazhko team, have found that several (most!) of the proposed explanations for Blazhko behavior are not consistent with the findings of detailed studies of Blazhko stars. The remaining few viable models involve interactions between radial (and possibly non-radial) modes of oscillation. The key element of the probably-correct solution appears to be a coupling between a high-order radial mode (the 9th!) and the fundamental radial mode of pulsation.
The people associated with the Kepler mission who first discovered this behavior in one of brightest and most common types of variable stars in the sky deserve great credit and there is nothing that trumps high-precision, uninterrupted measurements from space. Still, I wonder how things might have been different had we lived on a planet with a different rotation period. It is likely that we would have noticed the period-doubling of these very common, luminous, and important pulsators much sooner after their discovery as a class. Would the Eddingtons and Chandrasekhars of the day have decided that this was a well-characterised mystery in need of solution? Would the modelling of stellar evolution and pulsation been accelerated as a result? Would the success of understanding this phenomemon have been a catalyst in a scientific revolution on another planet? Instead of Neptune's discovery, would a defining historical achievement in early astrophysics have been understanding the period-doubling of Blazhko RR Lyrae stars?
I can't say - I'm on the wrong planet.
I'd like to thank the AAVSO for inviting me to be the third Janet A. Mattei Research Fellow . I'd also like to thank Katrien Kolenberg and Robert Szabo for deciding to visit AAVSO headquarters despite the 40 deg C heat at the time. While I was aware of the period-doubling of some RR Lyrae stars from Kepler, their visit and my subsequent attendance at Robert's talk at CfA galvanized me to write about their work. In the words of George Peppard  of the "A Team" - "I love it when a plan comes together."
Benko, J.M., et al, 2010, MNRAS, 409, 1585 "Flavours of variability: 29 RR Lyrae stars observed with Kepler" http://arxiv.org/abs/1007.3928 
Buchler, J.R., and Kollath, Z., 2011, ApJ, 731, 24 "On the Blazhko Effect in RR Lyrae Stars" http://arxiv.org/abs/1101.1502 
Jurcsik, J., et al, 2011, MNRAS, 411, 1763 "Long-term photometric monitoring of Messier 5 variables - II. Blazhko stars" http://arxiv.org/abs/1010.1119 
Kolenberg, K., et al, 2011, MNRAS, 411, 878 "Kepler photometry of the prototypical Blazhko star RR Lyr: an old friend seen in a new light" http://arxiv.org/abs/1011.5908 
Shapley, H., 1916, ApJ, 43, 217 "On the changes in the spectrum, period, and lightcurve of the Cepheid variable RR Lyrae" http://adsabs.harvard.edu/abs/1916ApJ....43..217S 
Szabo, R., et al, 2010, MNRAS, 409, 1244 "Does Kepler unveil the mystery of the Blazhko effect? First detection of period doubling in Kepler Blazhko RR Lyrae stars" http://arxiv.org/abs/1007.3404 
The Blazhko Project
The Konkoly Blazhko Team (make sure to check out the list of publications)
A reasonably well-maintained list of Blazhko RR Lyrae in the Milky Way field and globular clusters can be found here: http://www.univie.ac.at/tops/blazhko/Blazhkolist.html  (This list does not include the objects reported in the various microlensing survey catalogs, but those tend to be significantly fainter in any case.)
The AAVSO Variable Star of the Season entry on RR Lyr.
The Kepler Mission homepage:
ASAS-3 http://www.astrouw.edu.pl/asas/ 
EROS Experiment http://eros.in2p3.fr/ 
MACHO Project http://macho.anu.edu.au/ 
OGLE http://ogle.astrouw.edu.pl/ 
SuperWASP http://www.superwasp.org/