Accurate skydip reduction

In principle, the skydip method should be able to derive accurate Tau values. However, the overhead involved means it is only practical to perform a skydip every 1.5-2 hours, and quite often the frequency is even less. Furthermore, in mediocre-poor weather, the skydip model has always had trouble fitting to the 450-µm data, usually over-estimating the Tau, and hence over-estimating the source flux.

There are three realistic causes for the poor fits. The first is the saturation of the atmosphere at high airmass. The second is the atmosphere losing its plane-parallel nature; when this happens the atmospheric model we use is strictly no longer valid (this can also occur when the atmosphere occasionally becomes `layered', i.e. a very distinctive `step' is seen which again compromises our relatively simple model). The third is the suspicion that the load temperatures (T_HOT and T_COLD) used by the model are incorrect. Accurately measuring these temperatures is a non-trivial task, and depends, for example, on an accurate knowledge of the reflectivity and emissivity of the cryostat window (see below).

Figure 2: Secant plot for the night of October 17, 1999 for the wideband 450-µm filter.

We now have a near-perfect dataset for investigating the true value of Tau, which can be used as a cross-check for the values of T_HOT and T_COLD. Mark Amure (University of Cardiff) carried out a series of photometry and skydip measurements on October 17, 1999 in exceptionally stable weather conditions with both the narrowband and wideband filter systems. The secant plots for that night display minimal scatter, indicating a uniform value of Tau across the night, and providing a measure of Tau independent to the skydips. For example, the secant plot for the wideband 450-µm filter (Figure 2) suggests a zenith sky opacity significantly (30-40%) lower than the value derived by the skydip model and the default values of T_HOT and T_COLD.

We have investigated the location of the hot-load temperature sensor and have re-analysed the engineering data taken in October 1999. Accounting for the emissivity and reflectivity of the cryostat window, and the `mis-location' of the hot load temperature sensor, new values for T_HOT and T_COLD have been derived. These values are displayed in Table 1. In order to estimate Tau, the skydip fitting routine also requires $\eta _{\rm tel}$ (the transmission of the telescope). We have re-examined the values of $\eta _{\rm tel}$, and as a result have updated the value at 850µm, although this change does not significantly affect the value of Tau estimated by the skydip routine. The recommended values of $\eta _{\rm tel}$ are also included in Table 1.

Table 1: Updated values of T_HOT and T_COLD for the narrowband and wideband 450:850 filter systems. Note, the new value of T_HOT is expressed as the temperature measured by the telescope (T_measured - this is the value stored in the header of the data file) minus a small correction factor. The value of $\eta _{\rm tel}$ at 850µm has also been revised.

Filter		T_HOT		T_COLD		$\eta _{\rm tel}$
450W		T_measured - 3K		95K		0.75
850W		T_measured - 1K		90K		0.85
450N		T_measured - 3K		102K		0.75
850N		T_measured - 1K		92K		0.85

When the new values of T_HOT, T_COLD and $\eta _{\rm tel}$ are used to analyse the skydips taken on October 17, 1999, the skydips display remarkable agreement with the corresponding secant plots. These new values were applied to skydips in a range of weather conditions, 0.5<Tau₄₅₀<3.5, and with one exception (very noisy data) the skydip model provided excellent fits to all of the data.

At first glance, this indicated that we had found the cause of the typically poor 450-µm skydip fits. A closer analysis of 450µm skydips revealed that in many cases, using the revised values of T_HOT and T_COLD does yield trustworthy fits to the data. However, we have also discovered an instability in the fitting algorithm, which although it does not affect all of the 450µm skydips, does corrupt a large number of them. Thus, we do not recommend that individual 450-µm skydips be blindly trusted. As mentioned in Section 5, in constructing our CSO Tau relations we have been careful to exclude skydips obviously affected by the instability.

On March 13, 2000, the online software was updated to support the new value of T_COLD. On April 25, 2000, it was updated to support the new value of $\eta _{\rm tel}$. Data taken after these dates will have the correct values of T_COLD and $\eta _{\rm tel}$ stored in the file header. Updating the software to support the new values of T_HOT is less trivial. A single value of T_HOT is stored in the data headers. Both the online system and SURF need to be modified to adjust the temperature in a wavelength-dependent manner. The change to the on-line fitting routine is unlikely to happen in the near future.

For observers at the telescope, the on-line 850-µm skydip fits, used in conjunction with the revised CSO Tau relations given in Section 5, will be more than adequate for planning observations. For off-line data reduction, version 1.6 of SURF uses the correct values of T_HOT, T_COLD, and $\eta _{\rm tel}$ for all skydips.