PERSPECTIVA DIDÁCTICA

The AAVSO International Database holds over 20 million brightness estimates dating back over 100 years. For Antares the data consist of over 1000 magnitude estimates spanning more than 60 years. These data are of lower precision than research quality

photometry but provide unprecedented coverage. These magnitude estimates have been used in a handful of many-star studies of the photometric variations in red supergiants and/or small amplitude semi-regular variables (see for example Stothers & Lueng 1971; Percy et al. 1996; Kiss et al. 2006; Percy & Terziev 2011).

6.1.1.1

The AAVSO Brightness Estimates

There are certain caveats involved with using this data however, especially the visual estimates – which of course cover the greatest observational window. For this thesis we need to remain particularly aware of the limit placed on the observations of Antares. Our spectroscopic requirement, that we prefer bright targets, is a detriment to photometric studies. In fact Antares’ magnitude is detrimental since suitable reference stars are difficult to identify for the brightest objects. To make visual estimates a reference star of slighter low magnitude and another of slightly higher magnitude are required. Fewer of these are available as the study star increases in brightness. In addition, the visual

estimates are recorded only to an accuracy of one tenth of a magnitude; thus the AAVSO suggest that their data are binned in intervals of 7-10 days and give the expected standard deviation within a bin to be 0.2-0.3 mag for red stars.

Following this advice, and to make the results more comparable to those of previous authors, the data were binned in 10-day intervals. The resulting light curve is shown in Figure 34. As expected from previous investigations we see variations on more than one time scale and find a mean magnitude of 1.0. Inspection of our 10-day bins reveals standard deviations that are typically ~0.2 with standard errors in the range of 0.06-0.2. We note here that in this thesis we consider only the visual estimates and not the

photoelectric V magnitudes, since we did not wish to introduce spurious effects related to integration of the two data sets.

Figure 34: AAVSO light curve of Antares A the data are binned in 10-day intervals. Each bin contains between one and around ten individual measures. The standard

deviation of the binned data is 0.21, while the standard deviation in any one bin is typically 0.2, with a typical error in the mean of 0.106.

To analyze the timescales associated with the variations, Fourier amplitude/power spectra were computed using both the WINDOW algorithm provided by D. F. Gray and Period04 (Lenz & Breger 2005). The initial Fourier power spectrum of the data is shown in Figure 35. In this power spectrum three frequency peaks are apparent; the window function has been adjusted to coincide with the first peak.

The first peak, seen in the amplitude and power spectra, constructed from the AAVSO magnitude estimates (Figure 35), occurs at a frequency of (1.40±0.02)x10-4 cycles/day or a period of 7140±10 days and has an amplitude of 0.13±0.01 mag. This coincides with the, approximately, 7000-day period reported by Percy & Terziev (2011). The second highest amplitude peak in Figure 35 occurs at approximately 360 days and coincides with the alias of the primary peak. One must be cautious in assigning a period of

period of the Earth. This 1-year period is likely spurious as suggested by Percy & Terziev (2011) for similar data.

Figure 35: Fourier amplitude spectrum of the 10-day binned AAVSO light curve of Antares A. The data are given in black and window function adjusted to the frequency of the primary peak is shown in red. Dotted line shows the noise level.

The primary amplitude peak occurs at 7140 ± 10 days.

To obtain a better understanding of the actual periodicity/variations demonstrated in the AAVSO photometry the primary period (~7140 days) is subtracted from the data and the amplitude/power spectrum reexamined. This is done by subtracting the corresponding sinusoid from the binned data. The sinusoid used is shown by the dotted-red curve in Figure 36. The equation for this sinusoid is determined from the amplitude and frequency of the peak in the power/amplitude spectra and is y = 0.13 sin(2π 0.00014 + 0.035) + 1.00, the phase is found through phasing the resulting sinusoid with the data and

reducing the residuals. The resulting phase is 0.035±0.003. The whitened power spectrum is shown in Figure 37. With the primary period subtracted, the 360-day peak also disappears, supporting the conclusion that this peak is spurious. Percy & Terziev (2011) found many such ~1-year periods using AAVSO visual magnitude estimates, the prewhitening completed here suggests that such periods are artificial. In Figure 37 we see a remaining power peak with a frequency of 0.000789±0.000003 cycles/day, or a period of 1261±5 days, and an amplitude of 0.09±0.01 mag. The periods found from this data will be discussed further individually once we have reviewed the other data.

Figure 36: AAVSO data (as Figure 34) shown with the sinusoid corresponding to the 7140-day timescale plotted in red. The equation for this sinusoid is y = 0.13

Figure 37: Power spectrum after prewhitening of the 7140-day variation. The 360- day peak has also disappeared leaving only the 1260-day peak. The window

function has been scaled to the position and power of the 1260-day peak.

6.1.1.2

Hipparcos Photometry

Hipparcos (the High Precision Parallax Collecting Satellite) was launched in 1989 and operated until 1993. Although an astrometric mission, to precisely determine the

distances to stellar objects, a byproduct of the mission was high precision photometry of the sources. For the purposes of this study we have constructed 1-day bins of the available data, the 1-day binned light curve is shown in Figure 38 with the AAVSO 10- day binned data for the same epoch. There is good agreement between the two data sets over this portion of the AAVSO data.

Figure 38: Light curve of Antares A. ▲ - Hipparcos & Tycho magnitudes in 1-day bins.

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Quoted measurement errors for Hipparcos are 0.042 mag.

While not shown here we did compute a Fourier power spectrum of the Hipparcos data. We found a primary power peak at 1055 days, a period that is longer than the data window which spans 897 days. This period is in fair agreement with those of Cummings (1998) who reports periods of 1000 days and 1111 days. However, since the period detected is longer than the data window one should be cautious. Inspection of the light curve, shown in Figure 38, shows that one could simply be observing part of a longer trend. Figure 39 shows the light curves of Figure 38 again but with a sinusoid

corresponding to a 1260-day period (from Figure 37). The shape of the Hipparcos light curve can be explained by the period found from the AAVSO data. This timescale will be discussed in comparison with others later in this chapter. Looking at the curves of Figures 38 and 39 one sees that there is a shorter timescale (around 200-days) that is most obvious between JD 48250 and 48500. This fits well with the previous findings of 217

days by Cummings (1998). From the Fourier power spectrum on finds a peak at 170 days.

Figure 39: AAVSO (

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the AAVSO data. The fit is not perfect as the 7140-day variation has not been accounted for.