FILTERED OBSERVATIONS OF JUNE 8
This section describes observations of W Com during a 2.3-hour interval on the night of June 7 (June 8, UT) using a V-filter.
Extinction Plots
The 19 images on June 8 span a large air mass range, so it will be instructive to see the effect of atmospheric absorption and assess this potential error source on the goal of monitoring small brgihtness variations of an object of interest.
MaxIm DL can be used to measure "intensity" for a user's choice of aperture, dead annulus and reference annulus. I adopted 5, 3 and 6 pixels for these three parameters. Intensity for each of 7 stars was measured by moving the annulus pattern to achieve maximum intensity. Each image was time tagged, so an air mass could be calculated for each image (using TheSky). The matrix of 7 star intensities for each of 19 iamges is plotted in the next figure.
Figure 5. Log10 of intensity versus air mass for 7 stars. The straight lines are LS fits to each star's data.
Each star becomes fainter with increasing air mass at approximately the same rate. This rate can be expressed in several ways. I prefer to use an extinction rate K having units of "Nepers per air mass" because intensity can be simply related to air mass using the following expression:
Im = Io * e -Km
where Im is the intensity at air mass
m,
Io is the intensity at zero air mass (outside
the atmosphere), m is air mass and K
is the extinction [Nepers/air mass] for the date in question.
Using this definition yields K = 0.274 +/- 0.009 [Nepers/air mass] for the data under discussion. As an alternative, it can be stated that extinction = 0.298 +/- 0.010 [magnitudes/air mass]. Or, extinction = 0.119 +/- 0.004 [Log10 units/air mass]. Or, extinction = 24.0 +/- 0.9 % per air mass.
Notice in Fig. 5 that all stars depart from a straight line fit with the same approximate departure pattern. The following plot for just one star (Mv = 13.1) shows this better.
Figure 6. Log10 of the intensity for one star versus air mass.
The departures of the data from the fitted line in this figure repeat for the other stars. Thus, it appears that the atmospheric extinction varied slightly during the observing period. Either that, or my CCD's response varied (the TEC cooler maintained a temperature of -10 C the entire evening).
Figure 7. Departure of each star's brightness (Log of intensity) during hte 140-minute observing session.
It's possible a "sub-visible cirrus cloud" passed overhead on a couple occasions during the observations. The loss of intensity at 65 minutes is ~0.027 Log units, or 6%.
A proper procedure for measureing extinction should involve observations of both rising and setting stars during the same observing run. When this set of measurements is available it is possible to simultaneously solve for the temporal as well as air mass terms. (I will deal with this matter at greater length on another web page).
The implications of this amount of extinction, and its possible variation, will be dealt with in a later section.
Photometry Analysis
MaxIm DL was used to perform an aperture photometric analysis of 9 stars in each of the 19 images using 7 aperture/annulus size choices (that were compatible with the "point spread function" for the image having the worst resolution). Six of the stars were designated as "reference" stars and are the brightest of the 7 AAVSO reference stars (shown in Fig. 1). Three stars were designated "object" stars; one of these was the blazar and two others are to be used as "check" stars (for stability, not magnitude).
Whenever there are more than one reference star used in setting the magnitude scale for an object, it is prudent to check the measured and predicted magnitudes for the reference stars. If an error had been made entering a reference star's magnitude, for example, or if the wrong star was used for an intended reference star, the scatter plot of measured and predicted magnitudes would show a discrepancy. This also checks for linearity of the CCD system, and for the presence of saturation of any of the reference stars.
Figure 8. Measured versus "true" V-magnitudes for 7 reference stars used in this analysis.
The agreement is satisfactory, considering that the reference star magnitudes were rounded-off to 0.1.
The following graph shows the blazar V-magnitude versus time.
Figure 9. Blazar's V-magnitude versus time. The population S.E. with respect to the trend line is 0.019 magnitudes. Each epoch's set of points correspond to the 8 aperture/annulus size choices.
According to this figure the W Com blazar was brightening at a rate of 34 millimags/hour. There seems to be a coherence of brightness values within each image, and changes from image to image. Note that since each measurement is based on the relative intensity of the blazar with respect to the set of 6 reference stars we can't (automatically) ascribe changes in the blazar magnitude on atmospheric transparency changes.
Before the blazar brightness trend and short term changes in Fig. 9 can be taken seriously we must consider the same analysis performed on the other two check stars.
Figure 10. Check star V-magnitude versus time. The population S.E. with respect to the fitted trend line is 0.009 magnitudes. The star used is the northern-most (same RA as 121) in Fig. 1.
The check star has half the population S.E. as the blazar, and there appears to be no evidence for image-to-image changes. Note that the check star is one magnitude brighter than the blazar. Stochastic variations of magnitude should therefore be square-root of 2.512 smaller.
Let's inspect the other check star's behavior.
Figure 11. Check star #2 V-magnitude versus time. This star is near a corner of the original image (beyond the cropped version in Fig. 1).
It is apparent that Check Star #2 suffers from an inaccurate flat frame calibration. The first group of magnitudes come from a sequence of images made with a slightly different pointing position. I've noticed that with the AO-7 in the optical path the flat field calibration is more difficult to achieve. Reflections of the nearby moon may be present, for example, and such a feature cannot be removed using flat fields. Nevertheless, with a good flat field calibration the effects seen in Fig. 11 should not be present. The additional scatter in this check star magnitudes may also be related to flat field problems.
Check star #3 is close to check star #2, and it shows the same "misbehavior," consistent with the flat field explanation. The lesson here is that if you can't perform good flat fields, then at least keep the pointing the same for all observations. This strategy will not allow accurate absolute measurments to be obtained, of course; it is only permissible when searching for changes in an object during a night's series of observations.
For some purposes it is permissible to use a "reference" star to check for behaviors found in an "object." For example, the blazar "object" exhibits a trend of increasing brightness during the observing session whereas Check Star #1 does not. Either the blazar is actually brightening, or the blazar is redder than the check star that as the air mass increases it suffers less absorption than the check star. This can happen even with a V-filter. The filter is not narrow enough to prevent such effects, it just reduces their magnitude from the case of being unfiltered. Recall that atmospheric absorption varies with wavelength, and it increases dramatically in going toward the blue throughout the V-filter region, as illustrated by the next figure.
Figure 12. Spectrum of atmospheric absorption, formed by resonant absorption by molecules (oxygen and water vapor) and Raleigh non-resonant scatter and absorption (increasing toward the blue). The 4 thick black horizontal lines are an approximate absorption at zenith for filters B, V R and I. Clouds, of course, will produce large additional absorptions. Normal weather changes will produce small variations of this absorption spectrum.
The following figures are meant to show a typical range of "trends" of brightness versus time (including the air mass effect) using reference stars. Since a reference star has been used in my analysis procedure to establish a magnitude scale, we can expect to see smaller variations of reference star magnitude than for the "object" stars. Also, all magnitude trend figures in this web page have the same magnitude and time scale ranges (to facilitate comparisons).
Figure 13. Reference star "121" magnitude versus time.
Figure 14. Reference star "131" magnitude versus time.
Figure 15. Reference star "148" magnitude versus time.
Figure 16. Reference star "135" magnitude versus time.
Figure 17. Reference star "101" magnitude versus time.
The message from Fig's 13 to 17 is that it is unwise to try to use reference stars if they're near the edge of the CCD's FOV. Flat field uncertainties are greatest there. The empirical evidence I've just presented shows that reference stars, even the bright ones (like the 10.1 magnitude one in the last figure) cannot be relied upon to monitor system response near the center of the CCD's FOV. In this specific case, it would be better to use just one reference star for the blazar, the 12.1 magnitude star less than 1'arc away. It should share the same variations of flat field correlation,.which are likely to be small since both objects are close the the center of the chip's FOV.
The following figure shows what happens when only the nearby reference star is used (Ref 121).
Figure 18. Blazar magnitude versus time using only one reference star, the nearby "121". Four aperture and annulus choices were used.
I don't understand what could be causing the variations in Fig. 18 (unless
it's the blazar, which I doubt). More analyses and observations are
planned.
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This site opened: June 7, 2003. Last Update: June 9, 2003