Multisite campaigns

 

The case for multisite campaigns

Measurements for a week at a single observatory are usually insufficient to determine the multifrequency structure of stars with periods from one to several hours. The reason is that the (regular) observing gaps produce aliasing, such as the well-known one-cycle-per-day aliasing. Let us demonstrate this with a numerical example shown in Fig. 1. We have taken a typical frequency of 7.2 c/d and an amplitude of 0.1. The light curves were assumed to be observed for equal amounts of time at a single observatory as well as three observatories spaced around the globe eight hours apart.

Figure 1: A comparison of the amplitude spectra (Fourier transforms) obtained at a single observatory and three observatories spread around the world. Although the number of data points is identical in both cases, the multisite campaign shows much cleaner spectral windows, permitting the determination of unique values of frequencies. This makes a very strong case in favor of the organization of multisite campaigns.

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In the present example, the correct frequency can still be recognized in the data obtained from one observatory alone. However, once additional pulsation modes and observational noise are added, the highest peaks in the power spectrum may no longer be the correct modes. The difficulty with 1 c/d aliasing is increased in the low-frequency region, where the reflection of the pattern at 0 c/d leads to a complex interaction. If an example with a true mode at 1.3 c/d is chosen, the highest peak may well be at 0.3 or 0.7 c/d (=1-f).

Fig. 1 also demonstrates a less well-known effect: in addition to the well-known 1 c/d aliasing, additional spurious modes and patterns may also be produced (e.g., near 3 and 11 c/d). The spurious peaks represent a severe problem since they appear to be at a safe distance from the main peak in frequency space and may therefore be accepted as real. The solution lies in multisite campaigns, e.g., observe on different continents and avoid regular observing gaps. It was demonstrated before (Breger 1992) with real data that the dramatic improvement by using two observing sites separated by eight hours is often already sufficient to eliminate the worst uncertainties.