V426 Oph

V426 Oph was the second CV that we chose to study; it was listed as a "Doubtful" intermediate polar (magnetic system), while there has been some evidence for spin structure commonly seen in such systems. Along with a well-measured orbital period of 6.8 h [ref], there have been a variety of other periods discussed in the literature, such as 28 min periods in both X-ray and optical [ref], and both ~2 hr and ~4 hr periods in X-ray[ref,ref]. Other studies have found no evidence of significant periodic structure in X-ray observations [ref]. It was our thought that with the network of telescopes at our disposal, we would be able to get more complete coverage of this source - including over a single night - and possibly resolve some of the confusion surrounding it's true nature.

The Observations

In the summer of 2019, we used the iTelescope network of telescopes to observe V426 Oph from two dark-sky locations; New Mexico Skies (T21) and Astrocamp (T7) in Spain. Both of these telescopes are 0.431 m Corrected Dall-Kirkhams. We attempted to get as much contiguous observation time as we could over 6 weeks in June and July. An outline of our observations is given in the table below. With over 40 hours spanning 16 days, these observations represent the most extensive study every done on this source (to our knowledge).

The image on the right shows the field of view of this source for a typical observation, as well as the sequence we used to determine the magnitude of the star. The sequence came from AAVSO, and the photometry was done in AstroImageJ. Further data manipulation was done in Excel (or LibreOffice).

Time Series Analysis

The time series analysis for V426 Oph was done in Peranso, a user-friendly GUI-based program for lightcurve analysis. It has a wide variety of tools to handle time-series data like this, and is specifically designed for the study of variable stars, asteroids, and exoplanets. The first image below shows individual light curves for each contiguous observation, shifted arbitrarily and without including the large gaps between them.

(as a sidenote, this source has been reported to exhibit flaring, on timescales of 17 - 55 days, where it brightens to around magnitude 11.5. We do not think we caught any of this flaring activity, since our magnitudes all varied between 13.3 and 12.5).

From a visual inspection of these lightcurves, it's clear that this source does exhibit short-period variations, but it's not at all clear if those variations are either actually periodic or at all stable. Our first goal was to try and find the orbital period, around 6.8 h, which is well-known for this source. The figure below shows a Periodogram of this source, using the ANOVA[ref] algorithm, as well as the folded lightcurve over a period of 6.8399 +/- 0.0281 h, which nicely matches the previously reported value of 6.8475 =/- 0.0023 h[ref]. The relative strength of the orbital period signal in the ANOVA periodogram is not overly large, being only ~30-50% bigger then the next highest, but it is only the peak at 6.8 h which produces a folded light curve that resembles a periodic signal at all. Also note that the higher frequency peak is at a period of 3.44 h, and almost certainly a higher harmonic of the fundamental 6.84 h period. From this plot, we can see no evidence at all of the suggested modulations at periods of 2 h or 4 h that have been seen in X-ray studies.

Moving on to look for higher-frequency structure in this signal, we scanned the lower range of the data with the ANOVA algorithm. The result is shown below. There does appear to be some significant power in the 0.0400 h range, with possible sidebands. The problem is that the average separation between observations (after you clean out the big gaps) turns out to be around 0.050 h, so we really shouldn't be claiming that we can measure any periodic structure below 0.100 h (the Nyquist period). Of course, the usual argument for that assumes a rigid sampling rate, which we do not have - we simply asked the telescope to take a series of pictures, and the calibrations necessary in between each picture made the time separations irregular. So perhaps the Nyquist argument does not apply here, and these signals are real?

To answer this question, we looked at the distribution of the sampling rate of the telescopes. First choosing one of the observations for which this signal was individually strongest to remove the effect of the big gaps (20190625 on T7), we determined the distribution of the sampling rate (shown above to the right). Although it was not constant, the distribution was really very sharp, with most of the samples being separated 2.72 m - 2.75 m. Therefore, the Nyquist argument can probably be applied here. As a final verification (since an observation of these short periods would be an interesting development indeed), we generated some random data with no signal in it to see if we saw similar behavior - if so, then this signal could have been easily generated by our sampling process.

We generated this dataset by randomizing the sampling rate to be Gaussian, centered at the average from 20190625 (T7) and with the same standard deviation, and randomizing the signal to be centered at zero with the same standard deviation in magnitude as 20190625 (T7). The resulting fake light curve is below, to the left. Running the ANOVA process on this light curve resulted in the Periodogram on the right. There are many fewer points in the light curve, but the peaks just above 0.040 h and at 0.020 h and 0.090 h are striking, and very good evidence that these fast signals are a result of our particular sampling rate. It is interesting to note a lack of a peak in the random data around 0.130 h, which appears to be present in the full light curve above. That's above the Nyquist frequency, and deserves a more careful look, which we will discuss more extensively later.

To finish this up, we should look for the other previously reported period, 28 min. This becomes a little frustrating - it appears to be possible to see this signal if one searches for it using very specific parameters. For example, you can see something close to this if you scan the range (0.1,2) h with a resolution of 1500 (see below to the left, around 0.55 h). However, if you choose other parameters, this feature disappears. As a check, we searched using a second algorithm, FALC[ref]. This algorithm also saw no evidence for this spin period in the full dataset. As a final check, we folded the data on the 28 min period (since that's part of the evidence the original authors used to demonstrate it), and did not see anything that looked like a periodic signal (see the figure on the right).

Quasi-Stable Periods

Although we do not find evidence for any other stable periods besides the orbital one, it's possible that this source exhibits periodic motion which is only occasionally visible. Perhaps this is due to some kind of variability in the physical mechanism behind the luminosity (variable mass transfer, etc), it could also be due to additional structure interfering with the source brightness - increasing column densities in certain regions of the system, for example. Indeed, it is probably best to classify the variability of this source as such a quasi-stable phenomena, since it has been seen (apparently definitively) in some observations but not in others.

To look for quasi-stable periods in our data, we separated the entire data set into individual observation runs and analyzed them separately. Although these is no reason to expect that the variability of the source matched the observation windows, they do represent complete (albeit arbitrary) data sets on their own. The data was scanned using the ANOVA algorithm in the low- (<1 hr) and mid- (1-8 h) frequency range, and periods which appeared in only 1 set were ignored.

In the mid-range scanning, no periods were observed. Some of the observations would not have been sensitive to periods of 3+ h (being only a few hours long), but there was also no evidence of the reported ~2 hr periods. Given these were not present in the complete data set as well, we must conclude that these periods are the result of a mechanism which does not produce optical emission.

In the low-frequency search, we found two prominent periods, at around P1=8.0 min and around P2=33 min. The exact value for these periods was not constant, and P2 was not seen in all of the data. The significance of these periods in the data were all below the orbital one, which can be seen to be about +55 in the first figure. At this stage, we are not willing to confirm that these signals are the result of definite physical periods. Details of each of them follow.

P1=8.0 min

This period is very close to the Nyquist limit (which is around 6 min), so it's inappropriate to confidently attribute it to a definite physical phenomena. However, it was seen in every single observation, and as discussed in a previous section, cannot be reliably attributed to the variable sample rate. In each one of these observations, significant sidebands of this signal was seen, within 0.001 h or 0.002 h of the most prevalent one, which are likely associated to the frequencies of gaps in the observation windows. The power level was subdominant to the orbital one, typically being only ~20-30% of it. It is also not unheard of for CVs to exhibit such short periods; a period of 5.71 min was observed in V893 [ref], and in that case the period was only observed on one out of a few nights. This short period might mean this source should be classified as a magnetic system, and one of the Intermediate Polar classes of CV. However, at this stage this signal is too questionable for that identification to be appropriate. A table detailing the observations of this period is given below.

P2=33 min

This period is tantalizingly close the reported 28 min period. It was seen in a total of 6 of the 11 observation windows, which are outlined below. The power column indicates that significance level relative to the P1 period is much reduced, and it must be said that this period might not even have interested us except 1) It was present in more then 1 observation, and 2) it has been seen in both X-ray and optical observations of this source previously.

Summary

The Merrimack Astronomical Research Group has completed the most extensive optical photometric study of the cataclysmic variable star V426 Oph to date, using a network of sub-0.5 m telescopes. The excellent quality of the data (generally SNR >200) and the extensive coverage allows us to add to the current understanding of this rather mysterious source. We find absolutely no evidence for periods at ~2 hr or at ~4 hr, which have been observed in multiple X-ray band studies. We must conclude that the physical mechanism responsible for that behavior does not result in optical emission from the system. We find very weak evidence for the reported 28 min period, which has been seen in previous optical studies. If there is a real physical mechanism behind this signal, it is likely that it's true identity will not be revealed by future optical observations. Only through a more complete physical model, with a definite assignment of the origin of the modulation, is it's identity likely to be definitely determined. Finally, we also detected a very short period but relatively stable period around 8.0 min, which was more experimentally significant then the 28 min period, although very close to the frequency limit of our experiment. While we cannot say conclusively if this period is the result of a real physical phenomena, we have been able to eliminate it as being the result of several unique aspects of our data collection process. The identification of this period as being the result of the spin of the white dwarf would allow us to characterize the magnetic character of this system and classify it as a so-called "Intermediate Polar". However, given the extensive nature of our observations, and the fact that we were not able to fully reject the hypothesis that the signal was a result of our data collection process, we are doubtful that it will ever be possible to absolutely confirm the nature of this source.