Clem Pryke's Logbook

31 Mar 2003 - SZA Simulations Details

Introduction

I have been doing some simulations of SZA mosaic observations at 30 GHz using simulated y maps as input. Here are some of the assumptions I make:

Tracking field with Dec equal to OVRO latitude (37 N) (i.e. field goes directly overhead).
Cut tracks at 45 deg elevation (and for shadowing although this does not occur for array configs. I have used so far given the elevation cut). This implies 7.6 hour tracks. i.e. we would observe in three fields simultaneously spaced 8 hours in RA.
Eight 1 GHz wide bands from 27 to 35 GHz.
As the simulated maps are (mostly) 1 deg^2 I use a seven by seven grid of pointing centers in each field spaced 0.1333 deg. This results in a mosaic image with noise uniform to 20% across the central 0.76 deg^2 of each field (see below). Assuming a single track per pointing gives a survey rate of 21.5 days of running per deg^2. In reality we would probably extend the mosaics to larger contiguous areas.
Aperture field distribution tapered by 14 dB in power at the edge of 3.5m diameter dish.
tau=0.035 at the bottom of the band scaling as nu^2, and atmospheric temperature of 300K.
Telescope apperture efficiency of 75% and correlator efficiency of 90%.

Array Layout

So far I have run simulations for 2 array layouts - a circle of 7 with 5m radius and one in the center, and a circle of 5 with 5m radius, one in the center and 2 outriggers at 15m in north and east directions. These layouts and the resulting u,v coverage tracks are shown in the figure below:

System Temp

The assumed noise from receiver and atmosphere determine the survey sensitivity for given integration time. I have used the average receiver temperature as measured on DASI receivers using loads (Nov 2001 load cal). This is shown in the left plot below: colored lines are DASI 26-36 GHz data and the heavy black line and points are the mean of these at SZA band centers.

Calculating tau for each timestep (zenith angle) and frequency I then calculate Tsys using:

Tsys=(Trx+Tscope).*exp(tau)+Tatm*(exp(tau)-1)+Tcmbrj;

where Trx is as above, Tscope is an additional load of 4K constant with freq. assumed for the telescope optics. (Since Trx from DASI includes a warm lense presumably I should reduce it a bit since I am including Tscope as well?) Tatm is atmosphereic temp (300K) and Tcmbrj is the RJ temp of CMB. This expression takes account of the fact that we correct the vis for atmospheric attenuation and hence effectively increase the receiver noise. The resulting plot of Tsys versus zenith angle and freq is shown at right below. The right y-axis shows the visibility noise assuming apperture efficiency of 75% and correlator efficiency of 90%.

Beams

The primary and synthesized beams for the two configurations are shown below:

Simulated multi-pointing visibility data

Proceed as follows:

Take each simulated y map in turn and scale to uK at each band center.
Take a realization of CMB for vanilla LCDM model.
Add SZE+CMB and scale to brightness (Jy/Sr).
Take a realization of point sources according to dN/dS quoted by CBI for 5-50 mJy. This is possibly a bit high (see figure 13 of MAP foreground paper). Note that so far I have not correlated the point sources to the clusters.
Add point sources and shift each pointing center to image center for each band.
Taper by primary beam for each band.
Go to visibility plane and sample vis for each u,v point.
Add visibility noise using Tsys as calculated above.
Loop over each point center.

Mosaic Maps

I make mosaic maps according to the (simplest possible?) method as descibed in section 3.3 of the CBI mosaic paper. I am skeptical that any more complex method is preferable - any kind of non-linear deconvolution will destroy the Gaussian noise properties of the resulting image making significance of detection hard to quanitify.

Below is the noise map with color scale truncated at 20% greater than minimum noise. This criterion is met for a contiguous area of 0.76 deg^2.

Taking the ratio of the signal and noise maps gives what I am calling a "significance map". Here they are for the first WHS map for the c5 and c7 arrays - same CMB and noise - no point sources:

Peak finding and vis fitting

I take the position of each peak in the significance map greater than +/- 5 sigma and fit the multi-pointing visibility data to a model of a power law point source for positive peaks and an exponential with variable width parameter for negative peaks. The SZE spectral signature is included in this later, as is the differing primary beam taper for the source position in each pointing. The modelled source visibility is then subtracted from the data and the process iterates to generate a new mosaic map. When no peak remains greater than 5 sigma the process terminates.

Below is a plot of before and after this cleaning procedure for the first WHS map, c7 array, both without (top pair of plots) and with (bottom pair of plots) point sources. Note that point sources are an order of magnitude stronger effect in the data than the SZ clusters with the brightest 100's of sigma. They subtract out nicely though - no surprise really as they are injected and removed as perfect point sources - however, it is a nice check of the code.

Catalog cross matching

The final task is to attempt to associate the catlog entries which come with the simulated images to the peaks found in the mosaic maps. For each image I work down the catalog to decreasing mass looking for a peak found within some radius of the catalog position. Currently this search radius is set to 0.025. There is some slop between the y map peaks and the catalog positions which is perfectly legitimate given the way that the clusters are found in the 3D simulation box. Setting the search radius smaller results in clear missed associations. The following plot shows significance map with catlog entries shown as circle with radius proportional to mass. Peaks found are shown as crosses with size proportional to significance. Green pairs of circle and cross are matches. For the red circles no peak was found. The left over peaks are blue crosses.

With and without point sources

It seems that including point sources does not mess things up all that much - the peak fitter still finds the clusters nearly as well even though they are buried below a mass of point sources. Also - surprisingly I guess - the extent to which this is true doesn't seem to depend much on whether one uses the c5 or c7 array configs. Compare the following two pairs of plots: "nps" = "no point source", and "wps" = "with point source". The left panel of each set is a scatter plot of mass versus significance, the middle shows the mass distribution of all catalog entries, and the subset which were detected, and the right panel the ratio of the detected and all distributions.

Note that this result may change when the point sources are correlated witht the clusters as is the case in reality. In that case it will presumably become more important to have the long baselines to help separate the point sources embedded in the clusters. However, we may want to do a pre-survey with the 10m dishes to find the point sources... would still have to fit for their flux in the SZA data because of variability...

Results for different set of ymaps

See next entry