Version 2 - 30 Aug 2006: clarifies wording on case "Mapping small areas"

LABOCA Observing Time Estimate

LABOCA (Large APEX BOlometer CAmera) is a bolometer array camera operating in the 870 micron (345 GHz) atmospheric window. It has 295 channels arranged in a hexagonal layout consisting of a center channel and 9 concentric hexagons. The APEX beam size at this wavelength is 18 arcsec and the total field of view for LABOCA is 11.4 arcmin. The array is undersampled on the sky; the separation between channels is twice the beam size (36 arcsec).

To obtain fully sampled maps it is necessary to move the array on the sky during observations. This is usually done by scanning in one direction and then stepping in the other, or by moving in a circular or spiral pattern in the telescope or astronomical coordinate system.

The first LABOCA observations will most likely be done by scanning in Az (or RA) and stepping in El (Dec). We will try to implement a spiral pattern as well. The chopping secondary will not be available. In order to reduce the residual effects of skynoise, the scanning speed should be as large as possible, however small enough to sample the source well and place most of the source spatial frequency spectrum below the instrumental high-frequency sensitivity cutoff (30 Hz). For example, with a maximum effective sampling frequency of 30 Hz and a minimum 3-point sampling per beam FWHM, the maximum speed is 18 arcsec x30/3 Hz = 180 arcsec / sec = 3 arcmin / sec. The telescope drive control will provide good tracking up to about 5 arcmin/sec. Thus the recommended scan speeds will be of order several arcmin/sec, depending also on the overheads invoked by turning around at the end of an azimuth subscan, which may take up to several seconds. Although a continuous data taking mode is implemented, it is beyond control where the telescope moves during turnaround and thus whether that data is useful.

Per channel sensitivity

In the following time estimates will will assume that each channel on the array has a sensitiviy (noise equivalent flux density)

• NEFD = 125 mJy s^1/2.

This is not an actually measured value but an extrapolation of sensitivities we obtained for MAMBO on the IRAM 30m to LABOCA at APEX, as shown in this document: nefd_laboca.pdf

The actual sensitivity may be better or worse and will be determined during commissioning. This NEFD assumes that the correlated skynoise was effectively subtracted and that observations are done at 45 deg elevation with a line-of-sight sky opacity of 0.2. When observing at lower elevation one should use a correspondingly higher NEFD.

Although LABOCA has 295 channels, for the September 2006 observations we assume that for various reasons only N_bolo=240 channels will be available.

Mapping large areas

A large area is one much larger than the LABOCA FoV of 11 arcmin. The recommended observing mode is on-the-fly mapping by scanning in Az or RA and stepping in El or Dec, respectively. A map scanned over an area Az x El will have a uniform noise level over an area (Az-FoV) x (El-FoV) and a gradual increase of the rms noise in a ring with width FoV around this rectangular region. If one requires a uniform noise level in a given area, then the scan dimensions must add the FoV to that field's dimension. If one can live with a gradual increase of noise toward the edge, one can save observing time by making the scanned area more compact.

The rms in the center of the resulting map can be understood and computed as follows:

Each channel scans a map of Az x El that contains N_beams= Az El/1.13FWHM² beam areas. If the time of the observation within this area is t, then per beam area the time of observation is t_c = t/N_beams and the rms noise level of the single channel map is NEFD / t_c^1/2. If N_bolo bolometer channels all cover a region under consideration (that is only the case for the central uniform rms part of the final map) then the rms noise level there (i.e. in a fully sampled map with resolution 18") is NEFD /(N_bolo t_c)^1/2. To summarize:

• rms = NEFD ( Az El / 1.13 t FWHM² N_bolo)^1/2 = 3.3 mJy ( Az[arcmin] El[arcmin] / t[min] )^1/2 (eq.1)

or conversely

• t[min] = (3.3mJy/rms)² Az[arcmin] El[arcmin] (eq.2)

Mapping small areas

If the target diameter, D, is smaller than the LABOCA FoV of 11 arcmin (which also applies for a single point source), the Az (RA) scan length should be chosen such that the array is always on the source. For an Az-El scan pattern, e.g., one should then choose a scan length with a minimum of 3FWHMx3FWHM and a maximum of 0.7(FoV-D) - latter assures that the sources is always on the array. Equation (2) for the required observing time should take as source dimension the array size, i.e. Az=El=11', so that

• t = 120 (3.3mJy/rms)² minutes (eq.3)

Note that the observing time does not scale with the area of the target when the source is smaller than the array, because not all bolometer channels will cover the source, which is in effect like observing with a smaller array. The best observing technique for such observations will be determined by the LABOCA staff during commissioning - it may be an Az scanning pattern or a spiral. In any case, the final map should have a uniform rms over an area slightly smaller than the array footprint and cover a total area slightly larger than the FoV.

Because the wobbler is not available in September, point sources will need to be observed in this mapping mode. This is at least a factor 2 less efficient in time compared with on-off observations with a wobbling secondary.

Overheads

Proposals for observing time shall add a 50% overhead to the observing time estimate of eq.(2) or (3). This accounts for possible overheads in on-the-fly maps at turn-aroud as well as for pointing, focus, and calibration observations.