Subject:
From: Tony Tyson
Submitted: Thu, 26 Dec 2002 17:14:52 -0500 (EST)
Message number: 46
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Subject: Simulation of LSST WL performance vs site seeing
An important issue is the marginal advantage in WL science to improved
site seeing. Each of the LSST WL science drivers are affected by site
seeing. Here "site seeing" is taken to be only the round component of
site seeing, described by a FWHM, appropriate to a stack of hundreds of
exposures. Such a stack of exposures, each of which would be corrected
for PSF ellipticity (and thus shear bias), would average over the
remaining uncorrected PSF shear.
There are two effects of seeing on shear: shear dilution and shear
bias. Generally, shear bias must be corrected on each exposure because
there is a component that is different on each exposure. Some of that
different component is due to the atmosphere. I do not consider that
here. Instead I address the more limited question of shear measurement
in a stack of many images. A full exploration of such effects would
simulate the impact on 3-D tomography (by separating sources into z
bins) and the PSF ellipticity systematics in individual exposures. The
component of such systematics due to the atmosphere is worse in poor
seeing. However, as outlined in the last WL memo there are lots of
data on current problems and solutions to PSF shear in single
exposures, and we separately must come up with specifications for shear
bias vs spatial scale for LSST WL science. Moreover, to undertake
realistic simulations of PSF shear in a single exposure we must model
the system as well as the atmosphere -- and that will have to wait for
a better defined telescope-camera system model.
To address the more "focused" question of the effect of delivered FWHM
on WL science, the biggest issues are the effects of poor angular
resolution on ellipticity measurement of small faint source galaxies,
and the resulting limits on source density. There are at least three
effects: (1) faint sources have larger ellipticity measurement error,
(2) at faint limits the high source density and thus source confusion
can more often give large systematic shear error per source, if not
detected and rejected, and (3) FWHM larger than the scale of light in
the source tends to round the image, giving rise to a seeing correction
(this multiplies effect #1 and the intrinsic ellipticity error of
significant contributor to shear systematics in the sense that it can
introduce residual shear bias on small angular scales in a stack of 20
images. Smaller delivered FWHM permits better detection of overlapping
sources, as well as a higher source density. Better FWHM also results
in a smaller shear dilution correction.
How much better can we do WL shear in improved FWHM? The data we have
in 0.7 arcsec seeing is quantitatively better than the data on the same
fields we have in 1.2 arcsec seeing, in the sense that the mass maps
have less noise and are more reproducible at low shear. To simulate
this for LSST over a range of even better FWHM, we need realistic high
angular resolution source images. Rather than use our traditional
approach of simulating the source galaxy images, I take instead the HST
HDF imaging as the source population. Since the question is the effect
of delivered FWHM on shear S/N, we can take the galaxies in the HDF
within a magnitude range to be at some single redshift shell. This
image is then sheared by a modest cluster off the edge of the image and
then convolved with seeing, telescope PDF, and noise added.
We require very low noise images with better than 0.1 arcsec
resolution, which go to the surface brightness levels which can be
achieved by LSST in a stack of 200 images, covering an area equal to
the area around a foreground lens spanning the radial range which will
be used for optimal filter detection of clusters. To get the now noise
image to low surface brightness I coadded the dithered HDFN F450 +
F606 + F814, with a scale of 0.04" per pixel. I constructed a large
area in the following way. First, extract two rectangular areas 2.5 x
1.25 arcmin, one vertical and one horizontal, from the HDF coadded
image. Rotate the "vertical" image by 90 deg, yielding two horizontal
rectangular images. Make all possible XY flips, trim noisy edges,
yielding 8 rectangular horizontal images of dimension 3750 by 1881
pixels. For purposes of galaxy image shear statistics the galaxies on
these 8 images are independent, except for the galaxies in the overlap
of the two rectangular areas in the original HDFN.
To simulate the effect of a foreground lens, over the range of lowest
shear (out to the mass cutoff radius), put a lens off to the left of
each of these eight 2.5 by 1.25 arcmin images. In order to get the
photometric zero points, I ran FOCAS on one of the eight images,
creating a catalog which I calibrated in the R band by matching ten
unsaturated stars to the HDFN F606 photometry. I then put the same
sigma_v=700 km/s "foreground" lens 1000 pixels off left edge of each
image. This lens deflection moved the left edge of the lensed
rectangular field to the right about 200 pixels. So the center of the
lens is 1200 pixels, or 0.8 arcmin, off the middle of the left edge of
each lensed HDFN field.
I used a lens mass with a soft core isothermal with an outer mass
cutoff: Soft core = 10", outer cutoff 200". This is indistinguishable
from a soft core NFW profile, and is similar to the profiles we find in
two high resolution mass maps of clusters obtained by strong lens
inversion. Distort each HDFN extract image with this lens at z=0.3 and
with galaxies in image at z=1.5, using a (0.3,0.7) LCDM cosmology.
Only a range of magnitudes were used (24-27 R mag) corresponding
roughly to this redshift, based on sample spectroscopy in HDFN. This
yields 8 sheared images, effectively covering radial range of 0.8 to
3.3 arcmin from lens center (240 - 1000 kpc in lens plane).
Next, simulate LSST ground based PSF and sky background in simulated
coadded image stack: convolve images with LSST psf (use a 0.2 arcsec
FW80% gaussian for now); convolve these images with various site psfs
(0.5, 0.7, 0.9 arcsec FWHM); then block average (5x5) down to LSST
pixel size of 0.2 arcsec. Finally, add sky background noise
corresponding to 200 LSST 10 sec r band exposures coadded. This
produced three sets (3 FWHM values) of 8 lensed images.
Simulate LSST photo pipeline, catalog filtering, and shear
measurement: Make photometric catalogs with Focas, detecting all
objects to 28th mag, demanding 5 sigma detection with at least 6 simply
connected pixels (an isophotal circle of minimum 0.27" radius.
Calibrate using HDFN F606 mags. Filter the catalogs for the R
magnitude range 24-27 mag, yielding a mean of 26.8 R mag for the 320
galaxies in each of the eight 2.5 x 1.25 arcmin rectangular images.
Demand ellipto error code = 0 (exclude blended galaxies and other
problems), yielding 280 galaxies per image. Finally, exclude galaxies
with ellipticity > 0.6, yielding 240 per image, or 77 source galaxies
per square arcmin. These numbers varied only slightly with seeing over
the range 0.3 - 0.7 arcsec FWHM. In all cases the number counts were
rising somewhat at the faint cutoff.
Imagine these eight rectangular fields arrayed radially around the
center of the lens. Their inner edges are 0.8 arcmin radius, and their
outer edges are 3.3 arcmin radius from the lens center. The annular
area between 0.8 and 3.3 arcmin radius is not fully sampled for source
galaxies, since this area (32 sq. arcmin)is 78% of the total area in
the eight rectangular fields. Moreover, at the outer edge the source
density is only 50% of that potentially available on the sky. The
shear statistical error in this simulation will thus be biased high 13%
overall and up to 40% at 3.3 arcmin radius. However, the effects of
seeing are clear. A plot of shear vs radius in four radial bins is
available at http://lsst.org/sims/hdfn700.gif and a table is appended.
In the plot a line showing the equivalent isothermal profile is shown;
the points at the inner and outer radii fall below this because of the
soft core and outer mass cutoff used in the lens distortion. Shear
error was calculated in two ways: (1) sources were rotated 45 deg and
the shear variance measured, and (2) via bootstrap resampling. [Note
that due to symmetry of 8 flipped images the mean 45 deg values sum to
zero.]
Conclusion:
Shear S/N improves with seeing but in this magnitude range the
improvement for FWHM less than 0.5 arcmin is small. This magnitude
range corresponds to the all-available-sky survey mode of the 8.4m
LSST. It is possible to go deeper over a smaller area, but as Nick
pointed out, survey area wins over depth. Another conclusion is that
LSST should be able to go well below 700 km/s in a mass cluster
survey in which an optimal filter is fit to the shear vs radius.
This can be quantified, but such simulations must wait for a model
of the shear bias at ten times lower shear in typical LSST operations.
I have put the before and after lensing versions of these 8 fits images
in http://lsst.org/sims/HDFN/X1.fits.gz ... X8.fits.gz and dX1.fits.gz
... if you want to play similar games. I will try a tomography
simulation by extracting images in color-z shells.
=======================================================================
HDFN 24-27 R mag @ mean z=1.5 sheared by 700 km/s cluster at z=0.3
=======================================================================
FWHM = 0.3"
R (pix) R (") gamma_T sigma_g_T gamma_45 sigma_g_45
896 180 0.018 0.0063 0.0004 0.004
709 142 0.034 0.0043 0.0026 0.008
521 104 0.045 0.0075 0.0007 0.008
334 67 0.066 0.0076 -0.0009 0.007
FWHM = 0.5"
896 180 0.019 0.005 0.0005 0.003
709 142 0.037 0.007 0.0003 0.006
521 104 0.042 0.008 -0.0006 0.008
334 67 0.057 0.007 0.0005 0.009
FWHM = 0.7"
896 180 0.013 0.005 0.0010 0.005
709 142 0.028 0.008 -0.0003 0.007
521 104 0.039 0.006 -0.0012 0.007
334 67 0.048 0.006 -0.0031 0.009
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