Temporal Drift and Spatial Drift

Figure 1 shows the temporal drift (the average difference of all the standards observed on a given night as the function of time) and Figure 2 shows the spatial drift (the average difference for the same fiducial standard over the length of the survey as the function of coordinate). The error bars on the spatial drift plot show the standard deviation of the average, not the errors from the global solution. We expect these $1/\sqrt{N}$statistical errors to decrease as the survey progresses.

The temporal drift can be fit by a sinusoidal function

$$\Delta (t) = A + B \sin \left(\frac{2 \pi}{T} t + \phi \right).$$ (2)

The numerical values of the fitting parameters (period and amplitude) of the sinusoid are listed below in Table 2 (Model a).

Figure 3 shows the K-band sensitivity (photometric zero points a_n) as the function of time. The linear fit gives the slope of the relation of $(-2.10\pm 0.71)\times 10^{-4}$ mag/day, which is probably an artifact due to lower sensitivity at the beginning of the survey.

Because of the natural one-year period in sky coverage (cf. Figure 4) temporal and spatial drifts are coupled, i.e. one probably induces the other. From equation (1), there could be several possible reasons for variations in the difference:

1.

Real instrumental seasonal effect (either temporal or spatial);

2.

Inaccurate magnitudes of the fiducial standards;

3.

Varying atmospheric extinction.

The latter possibility seems the most reasonable, as the evidence of seasonal variations in the atmospheric extinction was indeed found (e.g. Frogel 1998). The variations are due to seasonal changes in the H₂0 content of the atmosphere. To test whether the temporal drift is caused by the changing atmospheric extinction, we note that the extinction parameter should affect low airmass and high airmass observations differently. Indeed, if we split the northern data into two subsets of low (X < 1.3) and high (X > 1.3) airmass and find the photometric solution for each subset, we would expect to see greater oscillations for high-X residuals than for low-X residuals. Figure 5 shows the mean differences for both low-X and high-X solutions along with the corresponding sinusoidal fits. The fitting parameters are listed in Table 2, both for low-X (Model b) and high-X (Model c) solutions.

 

Table 2: Amplitudes and periods of the fitting sinusoids. Models: a - single solution for high and low airmass scans; b - separate solution for low-airmass scans; c - separate solution for high-airmass scans.

Model	Amplitude (mag)	Period (days)
a	$0.015\pm0.002$	$400.57\pm39.37$
b	$0.014\pm0.002$	$396.99\pm35.67$
c	$0.025\pm0.002$	$390.08\pm15.76$

The amplitude of the variations in the high airmass data is almost two times greater than in the low airmass data, suggesting that at least one of the reasons for the oscillations is varying extinction parameter. Moreover, the amplitude of the variations, viz. 0.015 mag/airmass is of the same order (a few hundredths of a magnitude) found by Frogel 1998 based on CTIO data.