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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.
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.
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.
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.
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).
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).
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 (2
2 pixels),
0.6 for the AO image (20
20 pixels),
2.2 for the WFC II image (1 pixel) and 1.2 for the PC II (2
2 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).