UNFILTERED OBSERVATIONS OF JUNE 7
Question: Does "W Com" vary on minute and hourly time scales, typically? In this section I'll show that during a 1.7-hour observing run the blazar did not vary on a 5-minute time scale by more than about 0.003 magnitudes.
Since this project was started in early June, when "W Com" has already crossed the meridian shortly after sunset, it is difficult to obtain long observing runs in one evening. Another caveat: my color filter wheel is out for repair, so the observatsions reported in this section are unfiltered (the next section shows what changes when a V-filter is used). Unfiltered observations may have a higher signal-to-noise (S/N), but they are subject to the shortcoming that as air mass increases, changing system spectral response, the ratio of the blazar to a reference star will change if the reference star has a different color than the blazar. Therefore, we must deal with the possible existence of apparent brightness trends with air mass (i.e., time).
Unfiltered Short Time Scale Variability Demonstration
The following graph shows the magnitude of the blazar, in relation to 3 photometric reference stars, during a 1.7-hour observing period.
Figure 3. Blazar "W Com" unfiltered magnitude versus time for a 1.7-hour observing period. Each datum is from a 5-minute exposure. The V-magnitudes for the reference stars 121, 131 and 148 were used to establish a magnitude scale for the blazar, and since these observations are unfiltered the blazar magnitudes plotted here are subject to an offset uncertainty of probably 0.25 magnitude.
The trend of blazar magnitude with time during this 1.7 hour period can be discounted since it is most likely due to changes in air mass (from 1.08 to 1.41) and the use of reference stars having a different color from the blazar. Nevertheless, departures of measurments from the fitted straight line can be used to estimate how precisely very short time scale changes can be monitored. Each datum comes from a 5-minute exposure, and the population SE difference from the straight line fit is ~0.0068 magnitude units, corresponding to 0.63%.
As a check of what I allege in the previous paragraph, the following figure adopts one of the reference stars as the "object" and it's magnitudes are estimated using 3 reference stars and the same techniques as used for the blazar in the previous figure.
Figure 4. Reference star "148" used as an "object" for variability monitoring. Reference stars 121, 131 and 135 were used as standards.
This known non-variable reference star also exhibits a brightness trend versus time (i.e., air mass), implying that it's color differs from the 3 reference stars and my system spectral response is matched differently to the 4 stars involved. This iluustrates the importance of using filters for photometric work. The population SE with respect to the fitted straight line is 0.0051 magnitudes, or 0.47%. Population SE for a given observing and analysis procedure should vary with the object star's brightness (assuming the same reference stars are used, or that the reference stars are brighter than the object star in both cases, or that many reference stars are used in both cases). The reference star "148" appears to be 1.5 times brighter than the blazar, on average, for these observations. The reference star's population SE can be adjusted (by square-root of 1.5) to predict a blazar population SE of 0.0062 magnitudes. The measured blazar population SE of 0.0068 magnitudes is only slightly larger, implying that if it was varying during this 1.7-hour observing interval that variation must have been small (~0.0028 magnitudes). I conclude that there is no evidence for blazar variability (at the level of ~0.003 magnitudes) during the 1.7-hour observing run for a data sampling time scale of 5 minutes. Data averaging can be used to make statements about the blazar's variability on time scales of 10-minutes, 15-minutes, etc, but this effort of analysis is hardly worth it for such a short data set.
With more data it will be possible to perform "structure function" analyses
to quantify variability versus time offset.
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This site opened: June 7, 2003. Last Update: June 9, 2003