Light Curve of CR Bootis 1990–2012 from the Indiana Long-Term Monitoring Program

The 0.41 m Boller and Chivens Cassegrain telescope at the MMO was installed in 1965 and was operated as an attended single-channel photometric telescope, using a photomultiplier detector, until ∼1988. This f/13.5 telescope is on a German equatorial mount and is housed in a 5.0 m steel dome by Ash Dome, Inc. In 1989, the telescope and dome were converted to an automated, unattended system for long-term monitoring of CVs and related objects, and began to be called RoboScope. The telescope conversion involved changing the drive gear trains, and changing the drive motors to computer-controlled stepping motors. A stepping motor also controls the filter wheel. The existing focus motor was retained and the focus reading is provided by a precision LVDT (low-voltage displacement transducer). During campaigns A and B (see Table 1) the focus procedure was to acquire a focus exposure 2–3 times per night and analyze the focus exposure in real-time to find and apply the best focus.

It is highly desirable for an automated telescope to be able to close the dome slit at any dome azimuth, in case of problems. However, there is no dome commutator on the 0.41 m telescope; therefore, we installed a permanent power cable from the support wall of the dome to the dome slit motor. This cable is twisted as the dome rotates, but software and hardware prevent rotating the dome more that 1.5 revolutions either direction, to avoid overtwisting the cable. A Geneva-like mechanism is tripped for each revolution of the dome, and removes the power to the dome rotation motor if the dome tries to rotate beyond its legal limits. We have equipped the dome slit with limit switches and with confirmation switches for both open and closed positions. An absolute encoder supplies the dome azimuth to the computer and a sensor is provided to confirm that the dome is properly positioned for the flat-field screen.

The pointing residuals on the 0.41 m telescope were fitted with a two-dimensional spline, providing a pointing accuracy of ∼30'' over most of the sky. Although this pointing map contains no physical modeling of the flexure or the polar alignment, it has nevertheless been satisfactory for operation of the 0.41 m telescope for 22 years, without updates.

The original CCD was a thinned, backside-illuminated, Texas Instruments device having 800 × 800 15 μ pixels (TI 800). It was cooled in a liquid nitrogen dewar and the dewar was automatically filled twice per day using a custom autofill system (Honeycutt et al. 1994b). Our TI 800 turned out to have been overthinned in an irregular pattern covering about 25% of the area. In these overthinned regions, the photometric response was not reproducible, being subject to hysteresis and memory of past exposures. We were able to map out the bad regions and modify our reduction software to ignore stars falling on those portions of the CCD, allowing us to use much of the data acquired from this chip during Campaign A. Nevertheless, there is a 3 month gap within Campaign A when we interrupted the observing to investigate the problems with the TI 800.

Eventually, we arranged to replace the TI 800 with a thinned, backside-illuminated Tektronix CCD having pixels (Tek 512). This change of detectors resulted in a 5-week gap between Campaign A and B. The Tek 512 was also deployed in a LN2 dewar, serviced by an autofill system. This detector, though small, had excellent quantum efficiency and was our workhorse detector for over 13 years.

In 1992 an experiment in autonomous spectroscopy was conducted on the 0.41 m telescope (Honeycutt et al. 1993). Over a 6 week interval, nearly 100 stellar spectra were automatically scheduled and exposed using a small fiber-fed spectrograph. Using adaptions of the existing autonomous photometry procedures, the spectrographic exposures were intermixed with the regular photometric monitoring program. The 0.41 m telescope has a small collecting area and the spectrograph was inefficient; therefore, we were restricted to bright stars. However, our procedure for automatically placing the program star on the fiber is independent of the brightness of the program star and could therefore be extended to fainter objects, which required a larger telescope. This was one of the motivations for adding the 1.25 m telescope at the MMO. Such an integrated program of automated photometry and spectroscopy was laid out by Honeycutt (1994), including specifications for a spectrograph design that was matched to the autonomous character of the operations.

When RoboScope operation began in 1990, disk storage was very expensive. Therefore, we adopted an approach in which neither the raw nor reduced images were retained. (We did began keeping all images in 2002 September.) The disadvantages of this decision are rather obvious, but without having taken this step the expense of acquiring storage media would have greatly compromised the early operation of RoboScope.

Not having routine access to the original images for much of Campaigns A and B hampers our ability to identify with certainty particular light curve features that might be due to CCD artifacts. We therefore include here a brief discussion of the statistical effect of cosmic rays on the light curves of Campaign B. A series of dark exposures was analyzed for cosmic ray statistics on the Tek512 chip. Most of our program star exposures are 4 minute long, and in a 4 minute dark exposure we find an average of 18 cosmic-ray events. These events show a Landau-like distribution in strength, having a long low-amplitude tail toward high energies. The mode of the distribution corresponds to a star of V ∼ 17.2 for 4 minute exposures. Inclusion of such a characteristic cosmic-ray event in the sky annulus of a star usually has little effect, since the area of the sky annulus is large compared to the cosmic-ray track, and we use the mode of the sky pixel measures to determine sky. However, a cosmic ray in the star aperture with strength corresponding to V ∼ 17.2 will brighten a 14 mag star by 0.03 mag, a 16 mag star by 0.17 mag, and an 18 mag star by 0.8 mag. A typical star aperture occupies ∼10^-4 of the CCD area. Combining this with the average number of cosmic rays per frame, we predict that, on average, about 1 in 500 mag measures will be contaminated by a cosmic ray.

Many light curves of constant field stars in Campaign B were examined for the presence of anomalous deviations. We found that about 1 in 800 measures were clearly anomalous by 0.1 to 0.8 mag. About 90% of the anomalous excursions were brightward and 10% were faintward. Both the rates and amplitudes of the brightward excursions are consistent with cosmic ray events in the star aperture. The amplitudes were about 0.2 mag at V = 16, increasing for fainter stars. We conclude that about 1 in 500 light-curve points from Campaign B will have a nonphysical brightward excursion of 0.1–0.5 mag (due to cosmic rays), and that about 1 in 2500 lightcurve points will have a nonphysical upward or downward excursion of uncertain magnitude due to unspecified CCD artifacts. Therefore, a single isolated excursion from a lightcurve trend is probably not real, but a number of excursions in a single star is probably physical.

Calibration exposures (bias and dome flats) were automatically acquired at the beginning of each night and applied to the stellar images as they were exposed. Another code located all the stars in the reduced image, determined the mean full-width-half-maximum (FWHM) of the stars, and performed aperture photometry on each star using a stellar aperture diameter that was scaled from the mean FWHM. The result of this operation was a modest-size text file, listing for each star the pixel position, FWHM (both x and y), stellar instrumental magnitude, sky aperture magnitude, and a number of other characterizations of the image. This file was sent to campus (originally via phone modem and later by radio modem) for additional automated analysis using more capable computers.

The autonomous on-campus analysis consisted of identifying the star field using the stellar pixel positions and magnitudes, and picking out the variable star of interest. This data was then supplied to an incomplete ensemble photometry code (Honeycutt 1992) in order to build a light curve. This technique uses all of the stars on all of the exposures to make a least squares solution for the instrumental light curve of each star plus the "exposure magnitude" for each exposure (representing the amount by which the brightnesses of the constant stars on an exposure experience a common change in instrumental magnitude due to clouds or other effects). The advantage of this approach over simple differential photometry is that the use of numerous comparison stars renders negligible the error in the comparison, and also averages over any residual photometric field errors. The advantage over conventional ensemble photometry is that the number and identity of the comparison stars are allowed to vary from exposure to exposure. The latter point is particularly important for long-term monitoring because the data can be rather inhomogeneous due to clouds, pointing, detector changes, etc.

The up-to-date light curve from this process was available only a few minutes after the exposure was completed, a feature that we used to advantage for coordinated spectroscopic exposures at Kitt Peak and to automatically trigger a closer spacing of the RoboScope photometric exposures. However, this scheme had a flaw that became apparent after a few years. The incomplete ensemble solution requires inverting a large matrix whose size grows with the number of exposures and the number of stars being analyzed. The number of objects in the solution grows rapidly because all detected objects in each exposure (even defects) must be kept in case they line up with another detected object later in the sequence. Eventually the matrix inversion demands became incompatible with a quick-look capability, and we turned instead to differential photometry with respect to a single comparison star for the realtime light curves. The incomplete ensemble technique has continued to be employed off-line for publication-quality reductions. With the addition of a GUI and other features, this code for incomplete ensemble photometry is now called AstroVar.

The computing environment at the MMO for Campaigns A and B consisted of Fortran and VMS on a MicroVax II computer. This was a highly reliable configuration, but it later became obvious that this system was unsupportable in the long term. Not only was VMS becoming orphaned on campus, it was becoming difficult or impossible to find hardware replacements. In March of 2005 our MicroVax II suffered an unrecoverable failure, which marked the end of Campaign B on the 0.41 m telescope. We always intended to reinstate this program on RoboScope, but by the time of this 2005 failure of RoboScope the 1.25 m telescope was being commissioned, which took priority.

Operation of the 0.41 m telescope in unattended mode was restored in 2011 (Campaign E). By that time, the 1.25 m telescope was using new automation software running under Linux, and this software was retrofitted to the 0.41 m telescope. The top-level commands remain very similar for the two telescopes, but the lower-level software quickly diverges due to the differing hardware.

In 1994 we began the acquisition process for a 1.25 m telescope at the MMO. The science drivers were to (1) photometrically monitor CVs which were too faint for the 0.41 m telescope, and (2) spectroscopically monitor a few brighter CVs on long time scales. The mid-1990s were an unsettled time for acquiring a modest-aperture, research-quality telescope (i.e., Sinnott 1996) and our 1.25 m project became entangled in this disorder. We lost only a relatively small fraction of the direct project costs, but we did lose a large amount of time, and the extreme delays we experienced were very effective in depleting project resources. We will not dwell unnecessarily on these difficulties, but they deserve a brief outline because the situation significantly affected the shape of our science programs at the MMO.

By the time AutoScope defaulted on our original telescope order, the dome and pier needed to accommodate this particular telescope design had been in place for some time. We therefore arranged to acquire the partially-completed telescope from Rettig Machine, Inc. We intended to complete the telescope ourselves, using subcontractors as needed but doing much of the design and construction work at Indiana. This process was ultimately successful, albeit with substantial delays which necessitated a modification of the original instrument configuration and the science programs.

The welded-steel equatorial fork mount was without optics, optical supports, or controls. The mount is an open truss design, with friction drives in both axes. Hextek Corp. was retained to fabricate lightweighted, primary and secondary borosilicate blanks for us, and we contracted the figuring of the Ritchey–Chrétien mirror pair to Torus Optics, Inc. The primary mirror is f/3 and the final focal ratio is f/8. Torus delivered the polished optics (twice) along with measurements certifying that the specifications had been met. In both cases, the telescopic images were far from useable, but the existence of the Torus measurements from their optical shop made us reluctant to blame the optical figuring until we had thoroughly exhausted other possibilities—this approach led to even more delays. It was eventually established conclusively that the Torus measurements were in error, and we had to start over on the optical figuring. The primary mirror was eventually figured successfully by the Optical Sciences Center (OSC) at the University of Arizona. The OSC was to have figured the matched primary/secondary pair, but a problem with the availability of their Hindle sphere prevented this, which led to more delays. The secondary was eventually figured by Brashear LP. The supports for the optics were designed mostly by Optical Perspectives Group, LCC (Parks & Honeycutt 1998), with participation from Indiana, and they were fabricated at Indiana. The control system was designed and implemented at Indiana, using stepping motor control of hour angle, declination, focus, tip-tilt of the secondary mirror, primary mirror covers, etc. This software is in Fortran and C, operating under Linux, and we use Tpoint for the pointing model.

By 2004 we had a working telescope that could be operated on-site via a GUI. However, routine autonomous operation was not achieved until 2006. This was mostly due to the fact that the project delays had depleted project resources and personnel, slowing the work and requiring de-scoping of our original objectives. Because our revised instrumentation now had more limited capabilities than anticipated, we decided to concentrate on a core mission of long-term photometric monitoring of old nova and nova-like CVs, which had run on RoboScope for 14 years. The demise of RoboScope in 2005 meant that if this program were to continue it would have to be transferred to the new telescope.

The 1.25 m installation has a number of improvements over the 0.41 m that have a positive effect on automation. The 6.9 m steel dome (from Ash Dome) is equipped with commutators to supply power to the dome slit. This means that the dome slit can be closed at any dome azimuth, eliminating the need for a cable arrangement such as we use on the 0.41 m. We added confirmation sensors for the slit open and closed positions, absolute encoding of the dome azimuth, a fiducial sensor to confirm that the telescope is pointed at the flat-field screen, and a Geneva-like mechanism to prevent more than 1.5 rotations in either direction. This dome azimuth restriction is needed to avoid rollover of the dome encoder.

The dynamic scheduler used for the 1.25 m automation is the same as on RoboScope, but the focus procedure has been changed somewhat. Under our Linux implementation of the automation software, several focus exposures are still taken each night. However, these exposure are not analyzed in real time and are not used to adjust the focus for that night. Instead, focus during the night is computed from a telescope-temperature/focus relationship, and the acquired focus exposures are used offline to refine and update this relation.

In accordance with the goals outlined in Honeycutt (1994), only a single instrument is deployed on the telescope. This instrument, known as I-FIG (for Integrated Fiber-feed, Filter wheel, Imager, Guider) serves a number of needs. Changing instruments is best avoided for reliable automated operations. Not only do instrument changes invite mechanical and electronic problems, but calibrations also often change when an instrument is removed. I-FIG functions include a fiber feed for the spectrograph, a stepping-motor-controlled stage for an offset guider camera, a nine-position filter wheel, a set of calibration lamps for the spectrograph, and a computer-controlled optics stage that is used to bring into place optics for centering the star in a fiber and to feed calibration light to the fiber. I-FIG is also equipped with a computer-controlled dust cover.

A tip-tilt motion has been designed into the mount for our secondary mirror. Three stepping motor are carried along with the focus motion and are used to control the tilt of the mirror. The motion of these three motors is coordinated in software to provide orthogonal tip and tilt. This installation was designed and implemented at Indiana and was developed to address two needs: (1) ease of collimation of the telescope when the optics are installed, and (2) allow active collimation as a function of telescope altitude in order to preserve image quality. However, only the first capability is currently available. Because our optics were removed and re-installed so many times, ease of collimation has been a major blessing. Using an out-of-focus video star image for feedback, along with our paddle-controlled tip-tilt motion, we can perform this portion of the collimation task in just a few minutes.

The desirable features for a spectrograph intended to operate on an autonomous telescope have been described in Honeycutt (1994). To eliminate grating changes we prefer an echelle design so that all wavelengths are on-blaze. Using prisms for cross-dispersion also avoids configuration changes due to grating blazes, and a fiber-fed design minimizes calibration demands. Honeycutt et al. (1998) describe our implementation of this spectrograph. It has a resolution of ∼5000 and provides simultaneous coverage 390–900 μ using 25 echelle orders. We are using an echelle design to achieve broad wavelength coverage, not for high spectral resolution—therefore the collimator beam size is only 25 mm, resulting in a relatively compact and inexpensive design. We have also incorporated custom white pupil optics (Baranne 1972) in order to improve the throughput near the ends of the echelle orders. This spectrograph is installed in a small room inside the pier of the 1.25 m telescope, and is fed by fibers from I-FIG.

After the telescope had been in autonomous operation for nearly a year, we began noticing that an increasing number of images were doubled in hour angle. From the start we suspected that the bearings on the two hour angle drive capstans might have failed. Because replacing those bearings was such a large job we choose to first eliminate all other possibilities, a time-consuming process. Upon eventually fabricating custom fixtures to lift the telescope and press out the bearings, we found that the races had been scored (brinelling) on three of the four bearings, which bear the full weight of the telescope. It turns out that the bearings provided by AutoScope were underrated for the static load being applied. This problem was solved by replacing the four bearings with units properly rated for the applied load. However, ∼1.5 yr of our archived images are afflicted to varying degrees by the double image problem. The fraction of affected images begins at ∼3% and increases to nearly 20% until the problem was fixed. Our reduction routines are able to handle these double images, but the data are nevertheless degraded in quality.

The LN2-cooled CCD used on the 0.41 m telescope for Campaigns A and B is too small for use on the longer focal length 1.25 m telescope, and depleted project resources did not allow acquiring a new LN2-cooled imager. However, we had on hand a camera from Photometrics, Inc. (later acquired by Roper Scientific), which was intended for use as a guider camera in I-FIG. This Model PXL camera uses a backside-illuminated Tektronix 1024 × 1024 chip with 24 μ pixels, and liquid-assisted thermoelectric cooling. Because the PXL 1024 did not implement MPP operation of the chip, the dark current is quite high at our operating temperature of -25°C. This dark current would have been of little consequence had the PXL been used, as originally intended, for short integrations as a guider camera. However, for our typical 4 minute science integrations, the PXL 1024 dark current constitutes the major noise source. After being used as our science camera for almost 3 years, the PXL system failed in an irrepairable fashion in 2009 May, marking the termination of Campaign C.

After a delay of 16 months, we were able to resume photometric monitoring on the 1.25 m telescope using an SBIG STL-1001E camera, marking the beginning of Campaign D. This thermoelectically-cooled system uses a 1024 × 1024 Kodak chip having 24 μ pixels (SBIG 1024). This CCD is front-illuminated and therefore has somewhat lower quantum efficiency than our earlier back-illuminated devices. However, the SBIG 1024 dark current in our typical 4 minute exposures is nearly negligible, and is very much less than our broadband sky brightness on a moonless night. Later an identical SBIG 1024 camera was installed on the 0.41-m telescope, which begins Campaign E. These SBIG cameras are used with liquid circulation during the summer months, in order to regularly reach -25°C.

We found these SBIG cameras to be subject to window condensation on some of our high-humidity summer nights. Initially, we plumbed dry gas from a nitrogen cylinder to maintain a light flow of gas onto the window. This was effective in preventing condensation on the window, but it took considerable time and expense to keep enough nitrogen gas on hand. Eventually we constructed a dry air supply. An air compressor draws reasonably dry (but cool) air-conditioned air from the workroom. The air compressor tank allows the air to reach ambient temperature and it is then routed through a high-capacity silica gel drier before being vented onto the detector window. This implementation has been fully effective in preventing window condensation.

Midway into the 1.25 m project we made a deliberate decision to set aside, at least for now, a number of our partially completed capabilities in favor of attaining reliable data flow from what we consider to be our core program; that is, the continued collection of data for long-term light curves of accretion-powered stellar sources. As a result of the construction delays, we simply did not have the resources or manpower needed to complete all of the intended capabilities. For example, our spectrograph is completed and working, but its operation is not automated as planned. (However, the spectrograph is sometimes used in attended mode.) Likewise the tip-tilt secondary mirror is completed and working, but unattended active collimation has not been deployed. The tip-tilt is however used for alignment when the telescope optics are installed. We have no autoguiding capability, partly because we have no guider camera. However, the telescope tracks well and we seldom have trailing on our typical 4 minute exposures. Finally, we have not recovered the quick-look and trigger capabilities of the realtime RoboScope reductions used in Campaign B. Instead we employ, for now, offline batch reductions for the images of Campaigns D and E.

The reduction procedures for the 0.41 m data of Campaigns A and B were discussed in § 3.1. These realtime automated reductions were divided between the observatory computer and computers on campus.

Data reduction for Campaigns C, D, and E is performed offline, using IRAF⁴ and SExtractor⁵ packages. The raw images and the calibration frames are automatically sent to campus each morning. As time permits, these images are subjected to a custom reduction pipeline, consisting of IRAF routines called from Fortran that are used to combine and apply the bias, dark, and dome flats. This is followed by SExtractor to perform the aperture photometry. From that point forward the process closely follows the RobosScope process, using our field identification software and AstroVar to generate light curves.

Our reduction pipeline allows choosing any of several types of flats. Twilight flats can be generated and applied if they are available. Median sky flats have also been found to be reliable if there are enough exposures in each filter for that night. Our default flat choice consists of the generation and application of dome flats, followed by application of an illumination correction frame. The illumination correction is generated by a median combine of the dome-flat-corrected images, which is then smoothed with a 40 pixel average.

The illumination correction accounts for differences between illumination by the sky and illumination by the dome flats. Our illumination correction is small. The rms value is ≲0.5% and seldom exceeds ± 1.5% peak-to-peak. Our pipeline allows applying to a particular night's data the calibration data from any nearby night. This is particularly useful for the illumination correction, which we have found to be typically stable for weeks.

The light curve provided by AstroVar has an arbitrary magnitude zeropoint, which must be established using secondary standards in the field. Henden & Honeycutt (1995, 1997) established secondary standards for many of the MMO program stars, and we use a variety of secondary standards for the other fields. Transformation coefficients are evaluated for each campaign. The colors of variables may differ somewhat from epoch to epoch, but we do not measure the color at the time of the observation. In applying the transformation we assume that the color of a CV is B - V = 0.0. This assumption will introduce some error. However, it is better than ignoring the transformation altogether because the CV is almost always bluer than the secondary standards.

The RoboScope target list of Campaigns A and B consisted of ∼100 CVs, which were mostly old nova and nova-like systems, plus a number of SU UMa-type dwarf novae (DN). In addition, about 25 miscellaneous objects were included such as BL Lac objects, X-ray binaries, symbiotic binaries, etc. This target list has evolved somewhat over time, but we tried to keep a core group of old novae and nova-like CVs intact in order to study VY Scl-type low states in a relatively unbiased manner. This target list was transferred over to the 1.25 m telescope for Campaigns C and D, with the addition of some new CVs from published surveys for blue stellar objects and for x-ray sources.

The monitoring data has a typical spacing of 2–3 days, but it is often useful to have much more closely spaced data on particular objects in order to explore shorter time scales. Both telescopes have been routinely used in this mode. At times when the monitoring program is "caught up", we sometimes devote most of a night to continuous exposures of a single object.

We have also conducted occasional temporary observing programs to study variability of types not covered by the regular monitoring program. An example is our study of variability among M dwarfs in the Hyades and Prasepe open clusters. This two-season program is timed to coincide with spectroscopic studies of the Hα emission line strengths in these same stars. The goal is better understand the nature of chromospheric activity as one moves to smaller masses among the M dwarfs.

Our cluster M dwarfs exposures are in the R filter, but the rest of the exposures (on both telescopes) are mostly in V. For the fainter targets, we have sometimes added Clear filter exposures to the mix. On most nights the C exposures reach fainter than V. However, the C exposures are subject to saturation on nights with a bright sky (which is more apparent on the 1.25 m exposures because of that telescope's faster focal ratio), and the C exposures can be difficult to calibrate. Nevertheless, having both V and C exposures for the fainter portion of our program objects has proven to be a useful approach.

Figure 1 shows our full CR Boo light curve, which is made up of data from each of the five campaigns listed in Table 1. The data spacing ranges from ∼0.01 days to ∼1000 days. Table 2 summarizes the reduction process for the 2409 useable V-band exposures of CR Boo. The columns list the campaign (see Table 1), the number of usable exposures, the number of ensemble field stars in the solution, the mean error of the variable from the incomplete ensemble solution, the number of secondary standards used (from Henden & Honeycutt [1997]), and the error in the light-curve zero point using these secondary standards. Note that CR Boo lies in a sparse field at high galactic latitude, limiting the number of ensemble stars and the number of secondary standards. Table 3 shows a sample of the light curve data. The full version appears in Table S1.

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There are few multiyear light curve studies of CR Boo. However, Ramsay et al. (2012) reported on a 2.5 year monitoring program of 16 AM CVn binaries, which included CR Boo. The purpose of that study was to determine how the variability changed with orbital period, finding that the orbital period of the outbursting systems lies in the range 24–44 minutes, consistent with theoretical predictions. CR Boo is very near the short period edge of the instability range and was found to be variable by Ramsay et al. between magnitudes 13.5 and 16 over ∼1.6 yr, 2009–2010. However, the density of the points is not sufficient to reveal details of the character of the variability.

One of the obvious features of Figure 1 is that points with V > 16.3 are missing for 6 observing seasons 1999–2000 to 2004–2005, whereas CR Boo is frequently as faint as 17.2 for later and earlier seasons. For the six seasons 1990–1991 to 1995–1996 CR Boo seemed to alternate between seasons in which mags 17.2 > V > 16.3 are present, and seasons in which data in that magnitude range are absent. The histograms in Figure 2 contrast the magnitude ranges present for the two behaviors.

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In earlier work, SOB separations in CR Boo were found at 46.3 days for two (or possibly three) events in 1996–1997 (Kato et al. 2000), and at 14.7 days for two (or possibly three) events in 2001 (Kato et al. 2001). The recurrence times for normal DN OBs in CR Boo (if they exist) are poorly determined, as are their shapes. Wood et al. (1987) reported a quasiperiodic variation at 4–5 days over the magnitude range 13.6 to 17.2 in CR Boo, which presumably represents intervals of DN OBs as well as excursions to and within the high state. Warner (1995c) showed events over 18 days of monitoring by Provencal (1993) that were interpreted as DN outbursts. These events arise from a common quiescence level at V ∼ 18. They have amplitudes of 1.5–2.5 mag, rise times of ∼0.5 days, durations of 1–2 days, and full decay times of ∼5 days. However, Patterson et al. (1997) reported sinusoidal-like variations with a quasiperiod of about 19 hr and a typical magnitude range 14–15.5.

Figures 3 9 display the CR Boo light curve season by season, providing details on the high-state and low-state patterns. A wide range of behaviors is present. At times the system is "stuck" in a high state with variations of ∼1 mag near V = 14.5 for years, but with occasional excursions to a low state where it lingers for months near V = 16–17, with variations of ∼1 mag. In other years, the high state of CR Boo has frequent excursions to V = 16–17. This does not exhaust the variety displayed in Figures 3–9, but indicates how complex the light curve changes appear. Figures 3–9 lack sufficient expansion for some details to be seen. Therefore Figure 10 displays, as examples, four regions that have been expanded even more.

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In order to explore the nature of the superoutbursts (SOBs) in CR Boo we have accepted as a SOB an event in the CR Boo lightcurve if it has three or more declining points over at least 2 days in the magnitude range 13.7–14.7. Table 4 lists the 32 adopted SOBs, along with some of their characteristics. The table presents a serial designation for each SOB for later reference, along with the JD (with the JD zeropoint adjusted to correspond to that of Figures 1–9), and the detected duration in days (The true duration may be longer due to sampling issues, though we note that most of the tabulated SOBs are terminated by a rapid move toward the low state rather than by missing data.) Also presented are the mean V magnitude for the event, and the number of points detected for the SOB. (The number of points per SOB is typically 3–6 for most of the years of observation. However, over a 2 year interval CR Boo was observed 15–20 times on some nights [see § 4.3], providing up to 50 points per SOB in those cases.) The slope of a straight-line fit to the SOB is listed in mag days^-1, and the error in the slope is given. The final column is the separation of the SOB from the preceding SOB, in days. Typical errors in the separations are ± 2 days, set by the sampling rates.

Because our sampling is often less than ideal, our "definition" of a SOB will not result in a perfectly clean set of SOB detections. There may be a few rogue entries that are not really SOBs, and it is certainly true that we missed some SOBs (especially between observing seasons). However, our expectation is that this sample will be sufficient to reveal the aggregate properties of the SOBs in CR Boo. The correlations we find (see the following discussion) would not be apparent if there was serious contamination of our sample.

Figure 11 shows the SOB decline rate versus the duration using the data from Table 4. The absence of points at large decline rate and long duration is mostly due to the fact that SOBs with these properties cannot appear in our sample because we used a restricted magnitude range (13.7–14.7) for candidate SOBs. Fast declines over long durations would take such events fainter than the 14.7 limit. Even with recognition of this selection bias, it appears that the SOBs come in two varieties: those having a typical decline rate of 0.1 mag days^-1 and others with typical decline rate of 0.035 mag days^-1. It is worth noting that most of the fast declines occur before 2002, while most of the slow declines are found after 2002 (see Table 4).

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We must acknowledge the possibility that the short duration SOBs having rapid declines are in fact the tops of normal DN OBs. We think this is unlikely because we see few (if any) rising groupings of points in Figures 3–9, as might be expected by sampling the tops of sinelike DN OBs. Patterson et al. (1997) found CR Boo sinelike oscillations in the magnitude range 13–15.5, with quasiperiods of ∼19 hr. The tops of these oscillations overlap the magnitude range of the SOBs; however, they would not be expected to linger at this bright level long enough to be confused with SOBs. One might argue that a series of successive tops of such oscillations might resemble a SOB in CR Boo; but again we would expect as many rising SOB-like events as declining ones, which is not seen. Random sampling of sinelike variations will provide more points near the top than during the rise or fall because a sine wave lingers longest at the extremes. But if the tops of sinelike DN OBs served to significantly populate the region having V brighter than 15, then we would expect a similar grouping near the bottom of the DN OB range, which is not seen. For all these various reasons we will assume that the two groupings of events in Figure 11 probably represent two varieties of SOBs in CR Boo.

Figure 12 is a histogram of the separation of the SOBs, which shows a concentration at 46.0 days. This clump of eight separations has a sdso of 2.6 days and a sdm of 0.9 days. If other SOBs with 46 day spacing were missed, we would expect to find additional peaks at multiples of 46 days, which are not seen. Instead we find a rather uniform distribution of additional spacings on either side of 46 days, suggesting that SOBs in CR Boo are mostly irregular in spite of the 46 days peak. A curious phenomenon can be seen in the spacings listed in Table 4. The eight SOBs making up the 46 day peak are themselves found in two sets of SOBs that are adjacent in time. SOBs 14 and 15 are part of an adjacent 3 SOB set with spacings of 49.6 and 43.3 days, while SOBs 30, 31, 32 are part of an adjacent 4 SOB set with spacings of 48.2, 44.6, and 48.5 days. These set are interspersed with events at random spacings, plus occasional groupings such as SOBs 5, 6 and 7 having spacings of 75.9 and 76.8 days, and SOBs 15 and 16 with a spacing of 76.7. These kinds of groupings suggest mathematical chaos at work, in which quasi-periodic behavior switches randomly among several kinds of more periodic repetition.

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Note that the two or three SOBs described by Kato et al. (2000) at 46.3 day spacings in data from 1996 to 1997 are not included in our Table 4 or Figure 12, because our sampling was sparse in 1996–1997. Therefore, in Figure 12, two or three additional points could be added from Kato et al. to the histogram peak near 46 days, which already has eight points. The situation with the two or three SOBs described by Kato et al. (2001) at 14.7 days spacings in data from 2000 to 2001 is more complicated. Only the middle of those three events denoted as SOBs by Kato et al. (2001) met our criteria for a SOB, and it appears in our Table 4 as SOB 15. Our data at the time of the third SOB in Kato et al. (2001) is not inconsistent with a SOB, but does not met our strict criteria. Our data at the time of the first SOB in Kato et al. (2001) is not consistent with a SOB. Note also that the 14.7 SOB spacing provided by Kato et al. (2001) already has a bin in Figure 12 occupied by two events (SOBs 22 and 24 in Table 4) and could therefore also be supplemented by the Kato et al. data. Overall the agreement between the results of Kato et al. and this work with regard to SOB spacings appear quite satisfactory, considering the sampling issues in both data sets. And the agreement in the most common SOB spacings at 15 days and 46 days is very good.

A large amount of time was spent trying to tease information regarding the shapes and intervals of the likely normal OBs from our CR Boo data, with rather disappointing results. First, we examined periodograms of various subsets of our data, using magnitude breakpoints suggested by the inflections in the histograms of Figure 2. We paid particular attention to those quasiperiods reported earlier by various authors. After folding on numerous trial periodogram peaks, none of the weak periodicities in our data seemed real to us, probably because our typical data spacing of 0.5–3 days poorly samples the suggested quasi-periods near 19 hr, and because the lengths of our data intervals were typically 3–10 years, during which time the variability characteristics of CR Boo seems to change. We also used a kind of "runs" test to examine the distribution of the slopes between adjacent points, with somewhat more success. For example, using the magnitude range 13.7–14.7 (where the SOBs occur) we compared the numbers of rising pairs of data points with the declining pairs, restricting ourselves to a maximum pair separation of 0.5 days. We found that the number of fading pairs over the interval 0.02–0.14 mag days^-1 was 89 compared to 48 for the number in the symmetrical window of rising pairs. This confirms our visual impression that there are few, if any, intervals of brightening magnitudes with slopes and durations similar to the events we have noted as likely SOBs. Encouraged by this result, we found that for V fainter than 15 (encompassing the normal OBs?) and separations less than 3 days, the declining pairs (using a range in slope of 0.0–3.0 mag days^-1) exceed those in the symmetrical range of rising brightness pairs by ∼2×. The oscillations described by Patterson et al. had typical variations of 0.1 mag hr^-1, or 2.4 mag days^-1. If, as seems likely, we are sampling similar oscillations, this implies that they systematically have faster rise times than fall times. Such an effect was noted by Warner (1995c) in earlier CR Boo light curves.

Normally one to three exposures per clear night were acquired for CR Boo. However, we desired to have a few sets of more frequent exposures in order to more completely characterize the variability seen in the night-to-night data. Over the interval 1997 Nov to 2000 Apr the scheduling priority for CR Boo was increased on some nights to produce more closely spaced exposures of CR Boo, which were interleaved with the regular nightly exposures of the other program stars. This produced "sparse" sequences of between 8 and 24 exposures (average = 14) on 47 different nights, with an average spacing of 17 minute and an average duration of 4 hr. Figure 13 shows four examples of these sparse sequences, which are described below.

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The extensive CR Boo photometry by Patterson et al. (1997) gives us some idea of what to expect. For their ∼70 nights of photometry 1988–1993 they found quasiperiodic light variations with an amplitude of ∼1–1.5 mag, a typical range ∼14–15, and a quasiperiod of ∼19 hr. This upward and downward ramping in brightness had typical speeds of ∼0.1 mag hr^-1 and, as seen in their Figure 3, is roughly sinusoidal in character. This same behavior was present in the first 10 days of their 1996 data, but became more constant at V ∼ 14.7 for the next 80 days.

Figure 14 plots the mean V magnitude vs. the slope for each of our sparse sequences. For V fainter than 14.55 our results are consistent with Patterson's et al. (1997) finding of ramp speeds typically ± 0.1 mag hr^-1. However, for V brighter than 14.55 the ramp speeds are very much slower, being confined to ± 0.02 mag hr^-1, while on many occasions the variation were too small to be detected (< 0.03 mag over ∼4 hr). This behavior does not appear to have an easily identifiable counterpart in the Patterson et al. (1997) data. These 18 constant or near-constant intervals with V brighter than 14.55 make up 38% of our 47 sparse sequences, a significant effect.

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Note the asymmetry in the sign of the detected slopes in Figure 14. For V fainter than 14.55, there are 14 points in which the slope shows the source fading, but only 8 with the slope brightening. This confirms our conclusions in § 4.4 in which we used all the data (not just the sparse sequences). The full data set includes the sparse sequences, but it is mostly a different set of measurements with different cadences.

The asymmetry of the small slopes found for V brighter than 14.55 is in the same sense, but is somewhat less well-established. A possible explanation for the copious points in the range V brighter than 14.55 in CR Boo is that they are parts of "failed" SOBs that do not stay high long enough to qualify as a true SOB. Note that the decline rates of the SOBs in Table 4 are such that they would fall into the narrow central clumping at bright mean magnitudes in Figure 14, with undetected or barely detected slopes in a sparse sequence. Those slopes should be systematically positive if the "failed" SOB points are mostly fading at SOB decline rates.

SOBs 8, 9, 11, and 12 in Table 4 incorporate one or two sparse sequences in each of their declines. The cadence of our sparse sequences does not allow conventional resolution of SH variations, but is able to distinguish between intervals with and without SHs, if their amplitudes exceed ∼0.04 mag. Of the six sparse sequences found in SOBs, SHs were detected in four of them. Even when detected, the SHs seemed to come and go during a SOBs (see the bottom left panel of Fig. 13 for an example). SH-like variations were also occasionally seen in sparse sequences which did not overlap a SOB in Table 4, but always at a bright magnitude near that of a SOB.

Three of the sparse sequences display ∼1 mag outbursts that are not resolved at our typical 17 m exposure spacings–one of these is shown in the bottom right panel of Figure 13. Patterson et al. (1997) did not report any similar outbursts in their extensive monitoring, and our events are likely due to image artifacts (see § 3.1). However, the rate and amplitude of these events exceed that expected for cosmic ray hits, leaving their reality uncertain. Two of the events are unresolved, being a single-point excursion. However, the outburst in Figure 13 is barely resolved, with the point immediately following the outburst being higher than the underlying declining trend of the sparse sequence.

Examination of the long-term light curve of CR Boo has revealed the following properties:

• 1.  
  The most common SOB spacing is ∼46 days, but other clusters of SOB spacings are found near 15 days and 76 days. Having established a particular SOB spacing, CR Boo often continues this repetition interval for several successive SOBs.
• 2.  
  The decline rates and the durations of the SOBs seem to fall into two groupings: fast decline rates of ∼0.1 mag days^-1 having short durations of 3–5 days, and slower decline rates of ∼0.035 mag days^-1 with durations 5–20 days.
• 3.  
  While our typical data spacings do not resolve the ∼19 hr oscillations (that is, the normal DN-like OBs), statistical analysis of data with ∼0.5 days spacing shows that the declines are slower than the rises. A similar result is found using ∼4 hr sparse sequences with typical exposure separations of 17 minute.
• 4.  
  Further analysis of the sparse sequences showed that for those runs with mean V brighter than 14.55 the light curves were all flat or nearly flat. This is in contrast to those runs with mean V fainter than 14.55 in which typical rampings of ± 0.1 mag hr^-1 are always apparent, consistent the findings of earlier investigations.
• 5.  
  There are occasional changes in the character of the light curve on time scales of years. These include (a) alternations in the amplitude of the DN OBs between the ranges V = 14.5–16 and V = 14.5–17, (b) intervals during which CR Boo stays near V = 17 for weeks, with occasional excursions to brighter magnitudes, and (c) intervals during which the alternations of SOBs and normal OBs are quite apparent, along with years in which the system varies erratically and rapidly V = 14–16 with no apparent OBs of either type.

These properties suggest that deterministic chaos is at work in shaping the long-term light curve of CR Boo, and it is argued that the necessary physical instabilities and feedback needed for chaotic behavior are likely to be present in CR Boo.

A full understanding of the CR Boo light curve must come to grips with the nature of the bright data points that are not obviously part of a SOB. Using archival data from 1952 to 1957 Wood et al. (1987) reported that for ∼74% of the time CR Boo was brighter than m_ptg ∼ 14.0. Wood et al. measured the mean B - V color as -0.07; therefore for our purposes we can assume V ∼ B. The histograms in Figure 2 show that only ∼4% of our points have V brighter than 14, a significant change from 1952–1957 to 1990–2012. The Wood et al. measures are estimates from photographic meteor films, but they are unlikely to be uncertain enough to account for the fainter appearance of the CR Boo at this later epoch, for which we find ∼65% of our measures are brighter than magnitude 15. Although the peak of the magnitude distribution seems to have shifted faintward by about 1 mag over 50 years, the fact that most of the brightness measures remain concentrated in the brightest 1 mag of the distribution remains a persistent feature.

The distribution of SOBs magnitudes has a maximum near ∼14.3, which is also the peak of the overall distribution of CR Boo magnitudes (see Fig. 2). There are ∼1450 data point making up the 1-mag-wide bright peak in Figure 2, but there are only 361 points in the groupings we identified as likely SOBs in Table 4. We argued in § 4.3 that the peaks of normal OBs do not contribute significantly to this bright peak. The fact that the bright peaks in Figure 2 fall at the brightnesses of the SOBs in CR Boo suggests to us that the SOB phenomenon is at work in populating the histogram peak in Figure 2 with "failed" SOBs. In such a scenario the 3∶1 tidal resonance would be responsible for the bright points, but the thermal instability, interacting chaotically with the irradiation feedback mechanism and the tidal instability, would often be able to quickly take the disk back to a low state, terminating the brief SOB but populating the histogram peak with many points near magnitude 14. There is evidence (admittedly weak) for this scenario in the presence of two different SOB durations in CR Boo, suggesting that even shorter SOBs might be present.

Kato et al. (2004) explored somewhat similar erratic behavior in the long-term light curve of another AM CVn star, V803 Cen. This system appears to alternate at intervals of 1–2 years between having SU-UMa cycles of outbursts and a standstill-like state. There is good evidence for long-term variations in hydrogen-rich SU UMa systems (such as in SU UMa itself; see Rosenzweig et al. [2000]) and other systems listed in Kato et al. (2004). However, the long-term changes in helium disks seem to be more continuous and more erratic. Kato et al. (2004) suggested that this extreme changeability may be due to difficulty in maintaining the hot state in a helium disk, perhaps due to a reduction of the tidal torque responsible for SOBs, resulting from the extreme mass ratio.

We were not able to study very well the quasi-periodicity of the normal OBs in CR Boo (probably because our cadence is ill-suited for the task), but there is evidence that the character of these DN OBs change erratically over years. First, changes in DN amplitude are easily seen in Figure 1. Secondly, Wood et al. (1987) reported quasiperiodic variation over the range B = 13.6–17.2 with quasi-periods of 4–5 days for the years 1983–1985. Third, Patterson et al. (1997) showed strong evidence for nearly sinusoidal DN events in the range 15–22 hr using data mostly acquired in 1996. Provencal's (1993) data displayed in Warner (1995c) showed flare-like outbursts from a quiescent level. We see what are probably similar kinds of relatively isolated OBs in 1991–1992 (Fig. 3) and in 1993–1994 (Fig. 4). Interesting, all studies (including ours) agree that the DN events have faster rise times than decay times, but there is little or no agreement in the characteristic period, nor on whether the duty cycle is sinusoidal or more like isolated DN OBs. It appears that the character of the DN OBs in CR Boo are also unstable, much as we have concluded for the SOBs.