Simulation of a Distant Cluster of Normal Galaxies

We have simulated the observations of a very distant cluster of galaxies at high redshift. Distant clusters of galaxies probe the evolution of galaxies and the large scale structure of the Universe at early epochs. The studies of clusters of galaxies at large redshifts will be important with the new generation instruments since detailed studies of the morphological composition of clusters and the evolution with look-back time of low surface brightness distant objects will be feasible.

The simulations are made for the HST instruments FOC, WFPC II, and the Advanced Camera, and for an 8-m telescope on the ground equipped with adaptive optics. The characteristics of the cameras and detectors are summarized in Table 1. A comparison of the fields of view of post-COSTAR HST imaging instruments with the Advanced Camera (AC) and the ground-based adaptive optics camera (AO) is shown in Fig. 1 superimposed on the noise-free cluster simulation.

The Advanced Camera is ideally suited to mapping large scale structures due to its 200 arcsec FOV, i.e., 1.5 Mpc on the sky at z 2. HST has the advantages of a space-based large telescope: a dark sky background and high angular resolution. The Airy disk (i.e., the resolution power) of the 2.4-m HST has a radius of 0 058 at 5500 Å. From Table 1, it is seen that the detectors on the wide-field and planetary cameras undersample the PSF by a factor > 3. The pixel size for the proposed wide-field mode of the Advanced Camera is half critically sampled. The FOC detector fully samples the PSF. For the 8-m, the resolution power is 0 017, and we have assumed a detector pixel of 0 005.

Modelling the Cluster

The steps involved in the simulations are the following: (1) definition of the cluster parameters, (2) sampling the image to match the detector pixel size, (3) calculating the count rates (sky background, dark noise, galaxies), (4) PSF modelling and convolution, and (5) adding Poisson noise and read-out noise.

Cluster, Foreground Stars

Using the package ARTDATA in IRAF, we have simulated a rich cluster of 1000 galaxies, adopting a Hubble law for the spatial density function, and a Schecter luminosity function. A uniform surface density of foreground faint stars was added. A scaling factor was applied to match the angular size of normal galaxies between z=2 and 3. A spiral disk of diameter 40 kpc at such a redshift extends over 6 arcsec (H=100 km s Mpc, q=0). The cluster extends over the whole AC field, and has a core radius of 100 kpc, typical of present-day regular clusters (Bahcall 1975). No evolution other than cosmological has been considered in the simulations.

Since we are simulating the same cluster viewed by cameras of different resolution power, the positions of the same objects were calculated for each detector pixel grid, and the task MKOBJECTS was run for each case.

Count Rates

The adopted surface brightness averaged over the central 0 1 0 1 is 24.4 mag arcsec for a normal bright spiral in this distant cluster, and 23.3 mag arcsec for a normal elliptical. Such values are predicted for normal bright galaxies at z=2-3. The Ly galaxy near the damped Ly system toward the QSO PHL957 has V 26 mag arcsec averaged over the whole galaxy, or V=23.6 mag integrated over 3x3 arcsec (Lowenthal et al., 1991). The count rates per pixel for the sky and objects were derived using the relations given in the FOC (V4.0, p. 72, eqns. 4 and 5) and WFPC II (V1.0, p. 47) handbooks and the relation between the specific intensity of an extended source and the V surface brightness:

where sr is the solid angle of one FOC pixel.

Filter F480LP was used for FOC, and F555W for WFPC II. is mag for sky and galaxies from the table of extinction coefficients as a function of spectral type and wavelengths (p. 49, V1.0 WFPC II handbook). The dark counts were added to the sky counts. The count rates for the AC and AO cameras were obtained using the WFPC II count rate formula, adjusted for the DQE, angular resolution, and telescope aperture. Finally these simulated observations represent 5 coadded exposures of 40 minutes each.

PSF

For the HST instruments, the PSFs were modelled using TINYTIM. The PSF for the center of the CCD was used in all cases. The PSF of the AC was assumed to be identical to the WFPC II PSF scaled by the pixel size ratio of the cameras (AC/WFPC II). For the adaptive optics camera, we have assumed an 8-m diffraction-limited core containing 20%of the flux, and a seeing-limited halo containing the rest. This AO PSF is modelled by the sum of two Gaussians: one narrow, high peak for the core, and one wide, low peak for the halo. A (very) good seeing of 0 3 was assumed. This PSF is probably overly optimistic in the wavelength region considered here. The realization of such a diffraction-limited PSF with adaptive optics is currently anticipated only for the infrared domain.

Convolution with the original images was done using DCON, a FFT based fast image convolution task under IRAF provided by Richard Hook (1993).

Noise

Poisson noise was added to the images using the task MKNOISE. The same task also added read noise appropriate for 5 co-added exposures (Table 1).

Comparison of the Simulations

The simulated observations are presented in the figures. Fig. 1 shows the whole field before PSF convolution. Fig. 2 (panels a-d) are the simulations obtained for WFPC II and for the AC, while Fig. 2 (panels e-f) show the simulations for the AO field. Simulations for FOC (not shown) show only noise for this distant cluster.

For the large spiral seen in the field, the signal-to-noise ratio, averaged over 0 1 0 1 around the peak is for the AC image (22 pixels), 0.6 for the AO image (2020 pixels), 2.2 for the WFC II image (1 pixel) and 1.2 for the PC II (22 pixels). However, because of the high resolving power of the AO camera in the PSF core, S/N is effectively much higher near the object center, and an extended low surface brigthness spiral can be recognized in the adaptive optics image, whereas it looks like noise in the PC frame. This work shows the advantage of the AC camera over the other instruments. WFC I would also have detected this high redshift cluster with a lower S/N, but the aberrated PSF makes the morphological identification questionable (Freudling and Caulet 1993).