2 THE OBSERVING PROCESS

In order to obtain the best absolute calibration scale possible, first measures have to be taken during (or even before) the actual observing process.

1 Atmospheric conditions

The atmospheric transmission of the astronomical signal is a strong function of frequency. The most important limiting factor in the sub-mm range is absorption lines of water. The amount of gaseous water in the atmosphere above a certain location is known as precipitable water vapor ($pwv$), measured in mm. Fig. 1 illustrates this dependency.

With its facility receivers, APEX covers a frequency range between 200GHz and almost 1.4THz. It is therefore almost always possible to select the science project to be observed (and hence the receiver to be used) according to the current atmospheric conditions. The main selection is made based on the current value for the precipitable water vapor. Table 1 summarizes the selection criteria used by the APEX staff.

Figure: Atmospheric transmission as function of observing frequency at the APEX site on Chajnantor for 0.4mm (red, upper curve) and 2.0mm (green, lower curve) of precipitable water vapor.

Until $pwv=5{\rm mm}$, the atmospheric transmission at e.g. 230GHz is still 80%, which justifies observations with the APEX-1 receiver. If the water vapor rises to even higher values, there are usually other factors which prevent observations as well, like very strong winds or snowfall, thus at APEX we do not perform science observations if $pwv>5{\rm mm}$.

Besides the absolute value of the water vapor, a number which is more important in terms of calibration is the variation in the water vapor. Some results are presented in Section 4.3.

Table: Facility receiver usage as function of the precipitable water vapor. Further information about the receivers is available on the APEX website [7].

Receiver	APEX-1	APEX-2	APEX-3	APEX-T2	LABOCA	SABOCA
Frequency [GHz]	211-275	275-370	385-500	1250-1390	345	850
Recommended water vapor [mm]	1.5-5.0	0.8-2.5	0.2-1.0	$< 0.2$	0.5-2.0	$<0.6$

2 Positional accuracy and pointing models

An exact positioning of the telescope is vital for observations of point sources and sources with spatially changing physical properties.

The absolute position of the telescope is measured by a set of optical encoders in Azimuth and Elevation with an angular resolution of $0''\!\!.02$. The astronomical position where a certain receiver is looking at differs from this because of several influences: telescope tilts, deformations of the dish, feed legs, and backup structure, alignment accuracy of the various mirrors in the optical path, receiver offset from the optical axis, etc. These differences are described by a pointing model which is automatically loaded into the system to correct for these differences.

A basic pointing model is regularly obtained on stars with an optical telescope mounted off-axis behind the primary mirror. The use of stars (compared to radio sources) has the advantage that several hundred sources can be observed within a few hours of observing time to obtain a good estimate of the second and third order terms in the pointing model.

APEX uses a model with a total of 28 free parameters. Many of them are telescope "constants", thus they are fitted using data collected through several pointing sessions. Only a few parameters are expected to vary from one pointing run to the next, or from one receiver to another. They can be obtained on a dedicated pointing session with a given receiver. The procedure to obtain a pointing model is described in somewhat more detail elsewhere in this volume[8].

The uncertainties of this pointing model represent the main error in the telescope positioning. The residual positioning error of the pointing model, dependent on various factors (availability of pointing sources, atmospheric conditions) varies around $2'' - 3''$, independent of the actual receiver. Since the pointing accuracy is also constantly verified on strong point sources during an observing run, the actual average positioning error is estimated to be about $1''\!\!.5$.

In Table 2, we have summarized the expected intensity losses (calculated from the beam size) when observing a point source with a telescope positioning error between $1''$ and $3''$. Obviously, the intensity loss is more severe for higher frequencies and the corresponding smaller beam sizes. Another limiting factor for the pointing accuracy at high frequency is the fact that the number of strong point sources to allow a pointing check does decrease with frequency.

The facility bolometers (LABOCA, SABOCA) are not as much affected, since the default observing mode is mapping. Thus a pointing error may result in a position error in the final map, but not in an intensity loss. This is not true for the recently commissioned photometric mode for the APEX bolometers.

Table: Point source intensity loss for various positioning errors.

Frequency [GHz]	230	345	460	850	1300
Receiver	APEX-1	APEX-2, LABOCA	APEX-3	SABOCA	APEX-T2
$HPBW$	$27''$	$18''$	$13''\!\!.5$	$7''\!\!.3$	$4''\!\!.8$
Intensity loss for a positioning error of
$1''\!\!.0$	0.4%	0.9%	1.5%	5.1%	11%
$1''\!\!.5$	0.9%	1.9%	3.4%	11%	24%
$2''\!\!.0$	1.5%	3.4%	5.9%	19%	38%
$3''\!\!.0$	3.4%	7.4%	13%	37%	66%

3 Focusing of the telescope

Besides the positional accuracy, also the proper focusing of the telescope has a significant effect on the absolute calibration.

The focus is adjusted by moving the secondar mirror (subreflector), which is mounted on a hexapod that gives the necessary degrees of freedom for these movements. The subreflector can be moved along three axes ($x$, $y$, and $z$, which correspond to azimuth, elevation, and along the optical axis, respectively) and tilted around two axes ($x$, $y$). A tilt around the $z$ axis would not make sense since it translates into a pure rotation of the subreflector, which does not change anything because of the subreflector's symmetry.

In praxis the tilts have been determined during the commissioning of the telescope and have been constant since. The translations along the axes are measured and corrected, if necessary, on a strong pointing source at the beginning of each observing session and whenever the focus is expected to change, mainly because of temperature changes (i.e. after sunrise or sunset, or when changing the illumination (by sunlight) of the telescope structure). Thus the absolute focusing error is usually kept $< 0.2\,{\rm mm}$, which translates to intensity losses of $< 1\,\%$ to a few percent, depending on frequency.

4 Additional factors

Overall it should be mentioned that the factors described here are not only valid for APEX. All radio telescopes encounter similar challenges. In comparison with other telescopes, and given the excellent pointing and focus accuracy, we conclude that these factor do not affect the absolute calibration. This is not true when comparing data at different fequencies. Because of the factors described in this section and their semi-statistical nature, we would expect a systematic underestimate of line intensities at high frequencies, with negligible effects below 500GHz, but rather considerable effects above 1THz. These effects are not taken into account for the delivered science data product. It remains the PI's task during post-processing.