Revised CSO Tau relations

We have generated revised Tau relations by comparing the smoothed CSO Tau data to skydips analysed with the correct values of T_HOT, T_COLD and $\eta _{\rm tel}$.

Table 2: Revised Tau relations. The relations have been constructed using smoothed CSO Tau data and skydips reduced with the revised values of T_HOT, T_COLD, and $\eta _{\rm tel}$.

Filter System	Time Period	TauY=a(TauX-b)
		TauY	TauX	a	b
450N:850N	Feb. 04, 1998-Oct. 10, 1999 (pre-upgrade)	Tau850	TauCSO	3.99±0.02	0.004±0.001
		Tau450	TauCSO	23.5±0.2	0.012±0.001
		Tau450	Tau850	5.92±0.04	0.032±0.002
450W:850W	Dec. 05, 1999-Sept. 30, 2000 (post-upgrade)	Tau850	TauCSO	4.02±0.03	0.001±0.001
		Tau450	TauCSO	26.2±0.3	0.014±0.001
		Tau450	Tau850	6.52±0.08	0.049±0.004

Figure 4: Revised Tau relations for the pre-upgrade narrowband 450N:850N filter system. The relations have been constructed using smoothed CSO Tau data and skydips reduced with the revised values of T_HOT, T_COLD, and $\eta _{\rm tel}$. The left plot depicts the relationship between the skydips and CSO Tau. The blue points are the Tau₄₅₀-Tau_CSO correlation, the red points are the Tau₈₅₀-Tau_CSO correlation. The right plot depicts the Tau₄₅₀-Tau₈₅₀ correlation (turquoise data) derived from comparing 450-µm and 850-µm skydips. Models of the form Tau_Y=a(Tau_X-b) have been fit to the data in every case.

Figure 5: Revised Tau relations for the wideband 450W:850W filter system. The relations have been constructed using smoothed CSO Tau data and skydips reduced with the revised values of T_HOT, T_COLD, and $\eta _{\rm tel}$. The left plot depicts the relationship between the skydips and CSO Tau. The blue points are the Tau₄₅₀-Tau_CSO correlation, the red points are the Tau₈₅₀-Tau_CSO correlation. The right plot depicts the Tau₄₅₀-Tau₈₅₀ correlation (turquoise data) derived from comparing 450-µm and 850-µm skydips. Models of the form Tau_Y=a(Tau_X-b) have been fit to the data in every case.

The method used to construct these relations is as follows:

1.

We threw out skydips for which the model failed to fit the data or for which the fitting algorithm became unstable returning unbelievable values for the parameters. This involved discarding ~20% of the data at 850µm and ~50% of the data at 450µm.

2.

We ignored data taken when the CSO Tau monitor was broken.

3.

If either the CSO Tau monitor or the skydip indicated a non-physical value of Tau, i.e. negative or zero, we ignored the observation.

4.

We restricted the datasets to Tau_CSO<0.2 (SCUBA is not used in weather conditions worse than this).

5.

A model of the form Tau_Y=a(Tau_X-b) was fit to the data to derive the Tau relations.

6.

At 450µm, the model was only fit to data taken in Grade 3 weather conditions or better, i.e. Tau_CSO<0.12. The reasons for this were twofold: (i) 450µm observations are not recommended in worse weather conditions and (ii) we do not have much data for Tau_CSO>0.12. However, fitting to the entire dataset yields an identical relation, suggesting our relation holds in Grade 4 weather.

The relations have been calculated for the narrowband pre-upgrade and the wideband filter systems at both 850µm and 450µm. They are displayed in Table 2, Figure 4, and Figure 5. Note, there is a lack of post-upgrade narrowband data owing to the CSO Tau monitor being broken for about 3 weeks in November 1999, and the SCUBA filter drum problem, which has necessitated operation in the wideband filter position only since December 1999 (further details on the filter drum problem can be found here ). The small number of data points means we are not yet able to construct robust relations for the post-upgrade narrowband filters. However, we do not expect these relations to differ from those estimated for the pre-upgrade narrowband system. In Figure 6, we overlay the pre-upgrade relations on the post-upgrade data, demonstrating that the pre-upgrade relations are a good approximation.

Figure 6: Post-upgrade narrowband data with the pre-upgrade relations depicted in Figure 4 overlayed.

Given the lack of post-upgrade narrowband data, we will restrict the following discussion to the wideband filters and the pre-upgrade narrowband system.

Looking carefully at the revised relations, there are several points worth mentioning:

1.

For each filter system, we have derived two sets of relations: the first compares the skydips at 450µm and 850µm with the CSO Tau data, the second compares the 450µm and 850µm skydip data directly. For both the wideband and the pre-upgrade narrowband filters, the 450-850 skydip relation agrees remarkably well with what one would expect given the CSO Tau relations.

2.

Comparing the wideband and pre-upgrade narrowband filters to each other, the wideband CSO Tau relations are steeper at 450µm but are almost identical at 850µm. The difference at 450µm is to be expected given the lower central wavelength of the wideband filter (at 850µm, the narrow and wideband filters have almost identical central wavelengths).

3.

There is a small difference between the re-analysed narrow pre-upgrade relations presented here and the original relations calculated by Ed Chapin. This will affect data reduced using the old values of T_HOT and T_COLD and the original relations. The extent to which the data reduction will have been affected is discussed in Section 7.

4.

The new relations display relatively little scatter, even in the poorest weather conditions, providing hope for meaningful 450-µm calibration in Grade 3 weather. Figure 7 gives an example of how much the scatter has been reduced by the new analyses presented here.

Figure 7: The pre-upgrade narrowband Tau₈₅₀-Tau_CSO relation before and after the analyses presented here were applied to the datasets. The left plot displays the relation with Tau_CSO taken from the data headers, skydips reduced with the wrong values of T_HOT, T_COLD and $\eta _{\rm tel}$, and including all of the skydips. The right plot shows the relation with Tau_CSO calculated using the polynomial fits, the skydips reduced with the correct parameters, and with the untrustworthy skydips having been thrown away.

5.

If the submillimetre opacity is due solely to water vapour, the Tau relations for the different filters are expected to intercept the origin: if there is no water vapour in the atmosphere, Tau_CSO, Tau₈₅₀ and Tau₄₅₀ will all equal zero. However, we have found evidence for non-zero intercepts. Assuming the straight-line model can be extrapolated to the intercept, these intercepts could be explained by ozone contributing to the opacity at 225GHz, with a small contribution at 850µm and little/no contribution at 450µm. The ozone contribution is relatively invariant for long periods of time, and these offsets should be constant.

6.

We have taken care only to include 450-µm skydips for which the fit and output parameters are believable. Thus, in spite of the instability in the 450-µm fitting algorithm, we believe the relations presented here to be trustworthy.

Version 1.1 of ORAC-DR supports these new relations.