Chapter 4 described the procedure for separating a Ceduna flux density time series into two complementary zero-mean components. The xzeroData data set contains flux density fluctuations on time scales longer than about a day, after correction for the minor fluctuations observed in calibrator data on these time scales, which are interpreted as synoptic weather effects; and is the basis for the analysis of the PKS B1622-253 and PKS B1519-273 data considered by this thesis.
The xFastzero data contain flux density fluctuations on time scales of less than a day. The key assertion is that, for PKS B1622-253 and PKS B1519-273, this variability is a combination of systematic fluctuations and random observation errors, and can be ignored in a variability analysis of these two blazars. Three lines of evidence support this assertion.
1) Fluctuation correlations
Figure 5.12 shows three days of xzeroFast flux density data, and running means through the data, for PKS B1622-253 and PKS B1519-273, both northern observing group sources. Figure 5.13 presents all the xzeroFast data for these two blazars, for the second half of 2003.
Figure 5.12 Three days of PKS B1622-253 (blue) and PKS B1519-273 (red) data,
with 3-point running means highlighting correlation of the variations.
The 3C227 calibrator data are not shown in Figures 5.12 and 5.13, since there is almost no overlap between its daily observation times and the observation times of the two blazars.
The flux density fluctuations of the two xzeroFast data sets are clearly well correlated, which is strong evidence that the fluctuations are systematic in nature and do not represent genuine variability. However, Dr Jim Lovell pointed out that there are rare occasions in Figure 5.13 when the fluctuations are notwell correlated, such as the data for day 151. This is believed to be due to interstellar scintillation in PKS B1519-273 occurring on time scales of just over a day during the speed-up time of year. For observing periods near the speed-up time of year, PKS B1519-273 variability must thus be analysed using allthe flux density data, not just the xzeroData data set.
2) Blazar RMS values vs calibrator RMS values
Figure 5.14 shows the data processing procedure, as described in Chapter 4, applied to flux density data for PKS B1622-253 observing period 9.
Figure 5.14 Data processing applied to PKS B1622-253 observing period 9.
The RMS values of the slow and fast flux density components, xsmoothData and Fast zero
x are related in quadrature to the RMS value of the data, xData, as follows:
Table 5.4 gives the RMS values associated with the data shown in Figure 5.14.
Component Plot RMS
Data, xData Top plot 213 mJy
Slow component, xsmoothData Top plot 195 mJy
Zero-mean slow component, xDatazero Third plot 170 mJy Zero-mean fast component, xFastzero Bottom plot 83 mJy
Table 5.4 RMS values (mJy) for the data components shown in Figure 5.14
The relationship between the RMS values is thus confirmed:
(195)2 + (83)2 (213)2 All values in mJy
The RMS value of xsmoothData is lower that of Data zero
x because xsmoothData includes corrections for the linear flux density trend across the observing period, and corrections (based on the calibrator data) for minor weather-related fluctuations on time scales of days. If genuine variability in PKS B1622-253 and PKS B1519-273 is all contained in the xzeroData flux density components, then the xzeroFast components should be comparable to the calibrator data. Figure 5.15 shows this comparison.
Figure 5.15 Comparison of the xzeroFast data components of PKS B1622-253 and
PKS B1519-273 with calibrator data. RM = running mean.
Figure 5.15 omits PKS B1934-638 data points for southern source observing periods 12, because Ceduna was then recording with only one polarisation channel, and for observing periods 15, 16, & 17 which were characterised by bad weather and poor data. It also omits data points for northern source (3C227 and the blazars) observing periods 13 &14, and observing periods 19 & 20, for the same reasons. These data are given in Chapter 6.
---RMS values--- Data Fast RM PKS B1934-638 N/a o 3C227 N/a o PKS B1519-273 PKS B1622-253 + Observing period 9
In Figure 5.15, the calibrator data RMS values are separated into the RMS of the data (*), and the RMS of a 5-point running mean (RM) through the data (o), which is a measure of the systematic fluctuations. The flux densities of 3C227 and PKS B1934-638 at 6.7 GHz are 1.9 Jy and 3.92 Jy respectively, and have not been corrected for seasonal effects (which would affect the RMS values by less than 1 mJy). The solid black line shows the RMS prediction curve (see Section 5.3), which of course fits the calibrator total RMS data from which it was derived.
For PKS B1519-273 and PKS B1622-253, Figure 5.15 shows the RMS values of:
a) the overall data, xData (and );
b) the xzeroFast data (x and +); and
c) a 5-point running mean through the xFastzero data (and ).
PKS B1519-273. The RMS values of the running means through the PKS B1519-273 xzeroFast data () and the 3C227 data (o) are clearly in excellent agreement, strong evidence that the PKS B1519-273 xFastzero data component contains only variability associated with the
systematic fluctuations and random observation errors.
PKS B1622-253. The RMS values of the running means through the PKS B1622-253 xzeroFast data () are slightly elevated compared to the RMS values of the running means through the calibrator data (o). This is believed notto be due to the presence of genuine variability, but rather is attributed to quite pronounced variability in the overall data (), such that the data filtering procedure is harder pressed to properly smooth through the data and isolate the
Fast zero
x data component.
Consider, for example, the PKS B1622-253 xzeroFast data from observing period 9 shown in the last sub-plot of Figure 5.14. These data are flagged in Figure 5.15, which shows that the total xFastzero RMS is 83 mJy (+), and the RMS value of the running means is 65 mJy ().
However, Figure 5.16 shows the running means through the data. The running means have means of {-13 +34 -15 +22 +21 -5 +6} mJy, and the genuine variability signal is not entirely contained in the xzeroData component of the data. However, the genuine variability is pronounced, so this does not pose a problem for its analysis.
Figure 5.16 Running means through PKS B1622-253 xzeroFast data. Observing period 9.
3) Blazar Power Spectral Densities (PSDs) vs calibrator PSDs
Figure 5.17 shows cumulative PSDs for the fast signal components of PKS B1622-253 and PKS B1519-273. As before, each cumulative PSD is calculated by summing the individual PSDs of the xzeroFast data sets, considered separately, for each observing period in 2003.
Figure 5.17 Cumulative PSDs for the fast components of PKS B1622-253 and
PKS B1519-273 2003 data.
The PSDs in Figure 5.17 are similar to the cumulative PSDs of the two calibrators, shown in Figure 5.10. The dominant peaks in the vicinity of 1 day-1are further evidence that the xFastzero data components of PKS B1622-253 and PKS B1519-273 contain diurnal fluctuations which are of a systematic nature, and contain little, if any, genuine variability. The dominant peak for PKS B1519-273 is at slightly less than 1 day-1because this source exhibits some genuine variability on timescales of just over a day during the speed-up time of year, as noted above.