**2. The Science of the Dark Energy Survey**

**2.1 Background: Dark Energy**

In 1998, two competing research groups studying distant Type Ia
supernovae independently announced the direct evidence that the
expansion of the Universe is accelerating. This is arguably the most
important discovery in cosmology since the serendipitous detection of
the cosmic microwave background (CMB) radiation by Penzias & Wilson in
1965. According to General Relativity, if the Universe is filled with
ordinary matter, the expansion should be slowing down due to gravity.
Since the expansion is speeding up, we are faced with two logical
possibilities either of which would have profound implications for our
understanding of the fundamental laws of physics: (i) the Universe is
filled with a completely new kind of stress-energy with bizarre
properties (in particular, negative effective pressure), or (ii) General
Relativity breaks down on cosmological scales and must be replaced with
a new theory. For simplicity, we will subsume both of these
possibilities under the general rubric of 'Dark Energy', since in both
cases the effects on the expansion of the Universe can generally be
approximated by that of an effective fluid with equation of state
parameter *w* = *p/p* \< -1/3. For example, the Dark Energy could be the
energy of the quantum vacuum, or it could signal the existence of a new
ultra-light particle with mass of order 10^-33^ GeV or less; in either
case, particle physics currently provides no understanding of why the
Dark Energy density should have the value (about 70% of the total energy
density of the Universe) that would explain the acceleration of the
Universe.

Since 1998, independent but indirect evidence for Dark Energy has come
from several sources, most notably the combination of the CMB
temperature anisotropy pattern---which points to a spatially flat
Universe---and the evidence from large-scale structure that the density
of ordinary matter (mostly dark matter) is about one-third that of a
flat Universe. These studies have indicated that the Dark Energy
comprises about 70% of the energy density of the Universe and that its
equation of state parameter *w* \< -0.75 (the exact upper bound depends
on priors assumed on other cosmological parameters). In order to pin
down the nature of the Dark Energy and decide between the theoretical
alternatives, we need to measure *w* with greater precision and
determine whether and how it evolves with cosmic time.

2.  **The State of Dark Matter and Dark Energy Observations**

> ![](media/image1.png){width="3.5in" height="3.422222222222222in"}

Constraints from joint analysis of WMAP, SDSS and supernovae surveys.

The cosmic microwave background measurements, the large scale structure
measurements, and the supernova measurements provide a consistent view
of dark matter and dark energy. This will be a recurrent theme: the
combination of the CMB with other techniques provides the basis for
precision cosmology. The SDSS large scale structure results paper
(Tegmark et al 2003) shows this clearly. There are 15 parameters that
must be constrained in the concordance model of cosmology. The
constraints provided by WMAP and the SDSS are roughly 10%.

The reason for this complementarity is that the CMB is a measurement of
the temperature distribution of the blackbody radiation at z=1000, which
constrains the matter distribution at that epoch. The SDSS galaxy power
spectrum is a measurement of the distribution of galaxies at z\~0.1,
which is an indirect measure the matter distribution in the local
universe. **The dark energy affects the growth of structure, and
comparison of the matter distribution at different epochs provides
direct constraints on its density and nature.** Supernovae provide
relative distances in the redshift range 0.1 \<=z \< 2, where the
effects of dark energy on the evolution of the universe became
especially important.

Our experiment, the Dark Energy Survey (DES) will probe the universe out
to beyond redshift z=1. We are proposing a 5000 sq-degree survey of the
South Galactic cap to i=24 aimed at finding and measuring the clusters
of galaxies out to z\~1, studying the galaxy clustering and its
evolution, and constraining the local dark matter distribution using its
weak lensing effects on distant galaxies. Figure Huan is the redshift
distribution of the roughly 300 million galaxies we will find in our
survey. In addition to the primary survey, we will revisit 40 deg^2^ of
sky every third night, enabling a time domain component that will
deliver \~2000 Type Ia SNe in the redshift range 0.3\<z\<0.8. This
survey will enable an analysis of the properties of the dark energy from
four independent directions, making it the most sensitive dark energy
experiment of its time.

The timing and scientific leverage of the DES make it complementary to
two forefront CMB mapping experiments that will begin in 2007. Plank,
the next generation CMB mapping satellite to be launched in 2007, will
provide constraints at the roughly 1% level on a wide range of
cosmological parameters. The South Pole Telescope, a ground based high
angular resolution CMB mapping experiment will begin surveying in 2007.
It is the combination of DES with these CMB experiments---especially
SPT---that will provide the most information about the dark energy. Note
also, that DES is an important precursor experiment for Supernova
Cosmology Probe (SNAP)---developing science expertise in both SNe and
cosmic shear studies, and DES is also a precursor for the nearer term
Large Synoptic Survey Telescope (LSST). For LSST, DES serves not only as
a science precursor---through studies of clusters, cosmic shear, the
galaxy angular power spectrum and SNe---but also as a precursor
experiment for the data acquisition and the data management (led by
University of Illinois scientists in both cases).

3.  **New Probes of Dark Energy**

The Dark Energy affects the history of the cosmic expansion rate, *H*
(*z*), over the last 10 billion years; this history determines the
observables upon which all Dark Energy probes are based. Type Ia
supernovae are nearly standard candles, and the observable is the peak
apparent brightness (or luminosity distance) as a function of redshift.
In the last three years, several other techniques for probing the Dark
Energy, which complement the supernova method, have been undergoing
rapid development. The Dark Energy Survey is designed to exploit several
of the most promising of them.

First is counting the number density of massive clusters of galaxies as
a function of their mass and redshift. Galaxy clusters are the largest
gravitationally bound systems in the Universe, containing up to hundreds
or thousands of individual galaxies. Since the expansion rate of the
Universe determines the cosmic volume as a function of redshift as well
as the growth rate of density perturbations, the abundance of clusters
and its cosmic evolution provides a sensitive new probe of the Dark
Energy equation of state. Realizing this technique is the primary
science driver for the Dark Energy Survey.

A major project aimed at realizing the cluster counting technique is now
being planned for the South Pole. The South Pole Telescope (SPT, John
Carlstrom, U. Chicago, PI), funded by the National Science Foundation,
is an \$18 million project that will start operations in 2007. This
project will use the Sunyaev-Zel'dovich effect (SZE) to detect galaxy
clusters out to large distances. The SZE is inverse Compton scattering
of CMB photons and the hot gas (free electrons) that permeates clusters.
By precisely mapping the background radiation, the SPT will detect and
provide a census of tens of thousands of clusters over about 4000 square
degrees. Because the SZE signal from a cluster is a measure of the
thermal energy in the electron population, it is expected to be a very
robust indicator of cluster mass.

One advantage of the SZ effect is that it is independent of the distance
to the cluster---one can use it to detect clusters at all redshifts.
However, one needs another method to determine the redshifts of these
clusters, since they are required in order to measure the cluster
abundance and use it as a Dark Energy probe. The most efficient way to
obtain the redshifts of clusters to the desired accuracy is by measuring
the magnitudes and colors of the galaxies they contain: all clusters
contain a population of luminous red galaxies, and the farther the
cluster the redder the galaxies appear. Thus, the SPT survey must be
complemented by an optical survey in several filters (to determine
colors) over the same are of sky. Currently, no telescope in the
Southern Hemisphere (which can survey the same region of sky seen from
the South Pole has an instrument capable of carrying out such a
photometric redshift survey on a reasonable timescale (a few years).

In addition to providing distance estimates for the SPT clusters, the
Dark Energy Survey will provide an independent cluster counting probe of
the Dark Energy. The cluster counting method depends on having a good
estimate of the mass of each cluster. The Sunyaev-Zel'dovich technique
provides one estimate of cluster mass. However, optical observations of
clusters provide other estimates of their mass: the more massive a
cluster, the more luminous galaxies it contains and the stronger its
gravitational lensing effects on background galaxy images. Current
observations indicate that gas-based probes of clusters (i.e. SZE or
X-ray signatures) provide much more accurate estimates of cluster masses
than optical techniques alone. Thus, by coordinating the DES with the
SPT survey, we expect to gain significant additional leverage on the
properties of the dark energy.

Second, a new technique for probing the Dark Energy involves weak
gravitational lensing 'cosmic shear': by precisely measuring the shapes
of distant galaxies, we can infer how those shapes have been distorted
due to their light bending around foreground mass concentrations. The
statistical pattern of these distortions---for example, its angular
power spectrum---is sensitive to the cosmic expansion history and thus
to the Dark Energy. Weak lensing studies of Dark Energy require surveys
that cover a large are of sky, they cannot tolerate sites where
atmospheric turbulence causes blurring of the images. The site at CTIO
is known to have excellent image quality.

Third, there is great precision available in the power spectra of the
spatial distribution of galaxies. The matter power spectrum shows
several features: there is a broad peak, and there are the baryon
wiggles, comparable to the Doppler peaks in the CMB power spectrum. Our
photometric redshifts will not support a project to measure the
information in the radial direction; we cannot measure H(z) directly. We
will be able to explore the projection of the power spectrum on the sky,
the angular power spectrum, in different redshift shells out to z=1.1.
This approach will provide cosmological information from the shape of
the transfer function and provide physically calibrated distance
measurements to each redshift shell (Cooray et al 2001, Hu & Haiman
2003).

Recent studies indicate that these new methods have the potential to be
even more powerful than supernovae distances in probing the Dark Energy.
Because we do not yet know the fundamental limitations of these
different techniques, and because the problems raised by Dark Energy are
so profound, the most promising ones must each be pursued. Note that
these new techniques rely on an underlying paradigm for the formation of
large-scale structure, based on gravitational instability in a cold dark
matter Universe with nearly scale-invariant initial density
fluctuations. Despite the challenge of modeling all the details of
galaxy formation, recent CMB and large-scale structure data have
repeatedly shown that this paradigm is robust, allowing us to probe the
cosmological parameters in these new ways.

The fourth approach will be to revisit 40 deg^2^ of the sky every third
night, enabling the discovery and followup of a sample of 2000 SNe at
0.3\<z\<0.8. These SNe will provide relative distance estimates that can
be used to constrain the properties of the dark energy---especially when
combined with the other three approaches.

We propose a survey to pursue the promise of these dark energy probes.
Our survey will cover 5000 sq-degrees of the South Galactic Cap to
i=24.0, with the 4 bandpasses necessary to obtain precise photometric
redshifts of ½ L\* galaxies to z=1, and obtaining observations with
enough resolution and depth to reach 10 useful galaxies per sq-arcminute
for weak lensing measurements of clusters and large scale structure. We
call this project the Dark Energy Survey.

4.  **Galaxy Cluster Studies of the Dark Energy**

We plan to use the Dark Energy Camera (DEC) to carry out a \~4000deg^2^,
multi-band optical survey. This survey, together with a multi-band
mm-wave survey of the same region using the South Pole Telescope (SPT;
PI: Carlstrom), will enable the most sensitive, large solid angle
cluster survey every undertaken. The analysis of this survey will
produce precise constraints on the nature of the dark energy, and in
combination with the other dark energy probes enabled by the Dark Energy
Camera, these constraints will lead to the most precise knowledge yet of
the properties of the dark energy and a host of other interesting
cosmological questions. Below I provide a brief review of the cluster
survey technique and then provide detailed forecasts of constraints on
the dark energy.

Galaxy cluster studies have long been relevant to cosmology.
Measurements of the galaxy cluster baryon fraction together with
primordial nucleosynthesis constraints on the universal baryon density
(i.e. Burles & Tytler 1998) lead to constraints on the matter density
parameter Ω~m~ (White et al 1993b, David et al 1995, Mohr et al 1999,
Lin et al 2003a). Measurements of the local cluster abundance or number
density constrain a combination of the matter density parameter Ω~m~ and
the amplitude of density fluctuations on cluster scales in the local
universe, which we will refer to as σ~8~ (White et al 1993a, Viana &
Liddle 1999). Extending cluster abundance measurements to higher
redshift breaks the degeneracy between the matter density and the
amplitude of density fluctuations (Bahcall & Cen 1997, Eke et al 1998).
Over the last decade, a wide range of cluster observations, including
baryon fractions, mass to light ratios, local abundance and its
evolution, provide clear evidence that the matter density in the
universe is well below the critical value. This is in good agreement
with the current best matter density constraints from cosmic microwave
background anisotropy measurements (Bennett et al 2003, Spergel et al
2003).

Not long after the discovery of dark energy using observations of
distant supernovae (Schmidt et al 1998, Perlmutter et al 1999), the
first paper appeared suggesting studies of the cluster abundance and its
evolution as a way of constraining the properties of the dark energy
(Wang & Steinhardt 1999). In principle, very large cluster surveys
extending to redshifts z\~1 or beyond can deliver precise constraints on
the amount and nature of the dark energy (Haiman et al 2001). In fact,
large cluster surveys place direct constraints on the expansion history
of the universe (i.e. the way the Hubble parameter has changed with
cosmic time), and this behavior constrains and density and nature of the
various components of the universal energy density. A cluster survey
carried out over large solid angle provides another independent
constraint on cosmology through the clustering of the galaxy clusters in
space. The correlated positions of galaxy clusters (i.e. the cluster
power spectrum *P~cl~(k,z)*) reflects the underlying correlations in the
dark matter field, and these correlations contain a wealth of
cosmological information, much like the information contained in the
cosmic microwave background anisotropy power spectrum. We plan to use
the cluster redshift distribution and the cluster power spectrum as
powerful cosmological probes to study the density and nature of the dark
energy.

The sensitivity of the redshift distribution to the dark energy is
straightforward. The observed cluster redshift distribution in a survey
is the comoving volume per unit redshift and solid angle *d^2^V/dzdΩ*
times the comoving density or abundance of detected clusters *n~com~*,
written as

> $\frac{d^{2}N}{\text{dzd}\Omega}(z) = \frac{d^{2}V}{\text{dzd}\Omega}(z)n_{\text{com}}(z) = \frac{c}{H(z)}d_{A}^{2}(1 + z)^{2}\int_{0}^{¥}{\text{dM}f(M,z)\frac{\text{dn}}{\text{dM}}(z)}$
> (1)

where *dn/dM* is the cluster mass function, *H(z)* is the Hubble
parameter as a function of redshift, *d~A~* is the angular diameter
distance, and *f(M,z)* is the redshift dependent mass selection function
of the survey. Figure 1 contains a characteristic redshift distribution
for the SPT+DEC cluster survey. The cosmological sensitivity comes from
the three basic elements:

-   **Volume**: the volume per unit solid angle and redshift depends
    sensitively on cosmological parameters and has much in common with a
    simple distance measurement (like that delivered using a standard
    candle).

-   **Abundance Evolution**: the evolution of the number density of
    clusters at a given redshift depends sensitively on the growth rate
    of density perturbations. This growth rate is highly sensitive to
    cosmological parameters. For example, the faster growth in the
    presence of higher matter density would lead clusters to disappear
    more quickly as we probe to higher redshift.

-   **Mass selection function**: surveyed clusters are selected using
    some observable like the integrated SZE flux (a measure of the
    thermal energy in the intracluster medium), galaxy number or light,
    or perhaps the weak lensing shear. In general, all these observables
    are correlated with cluster virial mass. A flux limited survey will
    therefore pick out all clusters, which are massive or luminous
    enough to lie just above the flux limit. Thus, the cluster selection
    function depends on the luminosity distance to that redshift, which
    is clearly cosmologically sensitive. For example, in a flux limited
    survey a redshift z=1 cluster would have to be more luminous in a
    flat, lambda dominated universe to be detected than a z=1 cluster in
    a matter dominated universe. The form of the selection function
    encodes the scatter about the characteristic mass---observable
    relation, and at any redshift will transition from 0 for very low
    mass, undetectable clusters to 1 for very high mass, easily detected
    systems.

> ![](media/image3.png){width="2.9659722222222222in"
> height="2.7930555555555556in"}

Figure 1: The redshift distribution (blue) for the SPT+DEC cluster
survey for the fiducial model. A particular realization of the model
appears with red points and error bars. The green model is an example
model that can be excluded with 3σ confidence using a likelihood
analysis. The lower panel shows the deviations between the 3σ model and
the fiducial model as a function of redshift in units of ν=∆/σ.

The cosmological sensitivity of the cluster power spectrum arises
primarily because there are features---include a break---in this power
spectrum that depend on the matter density and baryon density. These
features provide a standard rod. By measuring the cluster angular power
spectrum (the clustering of the clusters on the sky) in a redshift bin,
one measures the angular scale of these features. Comparing the angular
and physics scale of these features provides direct angular diameter
distance information to that redshift (Cooray et al 2002). The
cosmological constraints from the cluster power spectrum are independent
from the constraints from the cluster redshift distribution. By bringing
these two reservoirs of cosmological information together, it is
possible to study cosmology in a very robust manner (Majumdar & Mohr
2003b).

There are several crucial components that---if brought together---make
precision studies of dark energy using galaxy cluster surveys possible.
First, the formation and evolution of dark matter halos in the universe
is well understood theoretically (Press & Schechter 1974, Sheth & Tormen
2001) and well tested using N-body simulations of structure formation
(Jenkins et al 2001, Kravtsov & Hu 2002, Linder & Jenkins 2003). Second,
special purpose surveys must be designed to cleanly select clusters over
a large range of mass and redshift and over a large solid angle. It is
important that the survey completeness and contamination be well
understood when analyzing the cluster redshift distribution. Third,
crude redshift estimates for large numbers of clusters must be available
through photometric techniques. This drives the synergy between the SPT
mm-wave and DEC optical surveys. Finally, a mass---observable relation
must exist that can tie observable cluster properties (like the SZE
flux) to the underlying halo mass. The combination of the DEC optical
survey and SPT mm-wave survey bring these four ingredients together as
never before, making it possible to deliver high precision and robust
constraints on the dark energy from a sample of \~20,000 clusters.

![](media/image4.png){width="2.9659722222222222in"
height="2.7930555555555556in"}![](media/image5.png){width="2.9659722222222222in"
height="2.7930555555555556in"}

Figure 2. Forecasts of the joint constraints on the dark energy equation
of state parameter *w*, the dark energy density parameter Ω~E~ and the
matter density parameter Ω~m~ for the SPT+DEC galaxy cluster survey
(blue). For comparison, forecasts for SNAP distances (green; Perlmutter
& Schmidt 2000), current constraints from WMAPext (black; Spergel et al
2003) and forecasts from Planck polarization (red) are shown. The
cluster constraints (left) either assume a flat universe (solid blue) or
solve for geometry and *w* simultaneously (dashed blue). These
constraints include survey self-calibration---that is, the survey data
are used to solve for the mass---observable relation and its evolution
directly. The constraints arise from the cluster power spectrum, the
cluster redshift distribution and 100 cluster mass measurements each
accurate at the 30% level (1σ). Note that the parameter degeneracies
from the clusters are quite complementary to those from pure distance
measurements or from the CMB. In both figures the fiducial cosmological
model comes from the WMAP analysis (Spergel et al 2003).

Figure 2 contains forecasts for the dark energy constraints from the
cluster survey that is possible by coordinating the SPT mm-wave and DEC
optical surveys. For comparison, SNAP forecasts (green) and the existing
CMB-only (black & red) constraints on dark energy are shown. It's clear
from this plot that the cluster constraints are competitive with those
possible through the SNAP mission. The different parameter degeneracies
underscore the gains one can achieve by carrying out both cluster
surveys and distance measurements, as we plan to do in the Dark Energy
Survey. The cluster constraints use the cluster redshift distribution,
the cluster power spectrum and assume 100 mass measurements (accurate at
the 30% level 1σ) are available within the survey region, distributed
uniformly out to redshift z=1. These mass measurements will come from a
combination of weak lensing constraints directly from the Dark Energy
Survey, deep pointed X-ray observations with Chandra or XMM-Newton, and
perhaps through cluster dynamical estimates arising from spectroscopic
studies of a subset of the clusters. We emphasize that these forecasts
include survey self-calibration. That is, the mass---observable relation
and its evolution are extracted from the survey directly (Majumdar &
Mohr 2003, 2004; Hu 2003, Lima & Hu 2004). The precision of cosmological
constraints suffers when one requires self---calibration of this nature,
but the accuracy is improved by eliminating biases introduced by
theoretically driven assumptions about the expected form and evolution
of the mass---observable relations.

In calculating the forecasts shown above we have reserved considerable
cosmological information for cross checking our analysis. As shown in
Equation 1, the redshift distribution involves an integral over the mass
function. Using the shape of the mass function directly would improve
the cosmological constraints (Hu 2003), but with the approach outlined
here we can---at the end of the analysis of the redshift distribution
and cluster power spectrum---predict the cluster mass function as a
function of redshift. A direct comparison of the theoretical mass
functions for the best fit cosmology and the observed mass functions in
the survey (in essense, the observed luminosity functions, which can be
converted to a mass function using the parameters of the
mass---observable relation) will give a direct indication of the level
of agreement---and effectively the level of accuracy---in our best fit
model. These multiple, independent sources of information from a cluster
survey provide a level of robustness simply not available in some other
dark energy probes.

1.  **Optical Cluster Finding**

    1.  **Cluster finding using red sequence**

    2.  **Photo-z**

    3.  **Mass scaling relations and weak lensing**

    4.  **Working to z=1**

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2.  **Weak Lensing**

3.  **Studies of the Dark Energy Using the Galaxy Angular Power
    Spectrum**

The \~4000deg^2^ Dark Energy Survey (DES) will deliver a sample of
approximately 400 million galaxies extending well beyond a redshift z=1.
The clustering of these galaxies and its evolution with redshift
reflects the underlying clustering and evolution in the dark matter
distribution. On large physical scales (\>10Mpc comoving), the
relationship between the galaxy clustering and the underlying dark
matter clustering can be described by a scale independent bias factor,
whose value depends on the mass distribution of the galaxies detected in
our survey. In general, this distribution changes with redshift, and so
the bias factor is a function of redshift *b(z)*. We can write the power
spectrum of galaxy clusters as

$P_{\text{gal}}(k) = d_{H}^{2}k^{n}T^{2}(k)g^{2}(z)b^{2}(z)$, (1)

where the initial dark matter power spectrum is $d_{H}^{2}k^{n}$, $T(k)$
is the scale dependent transfer function for dark matter perturbations,
and $g(z)$ is the scale independent growth function. Thus, we will use
the DES galaxy sample as a tool to study the dark energy and its effect
on the characteristics and evolution of the dark matter distribution.
This approach is complementary to and independent of the other DES dark
energy analyses.

We will use the angular power spectrum within redshift shells, because
photometric redshifts will not have the required accuracy to analysis
the three dimensional clustering of the galaxies. Those galaxies that
lie within a redshift z\~1.1 will have photometric redshift estimates
accurate to about δz\~0.06 (see Photo-Z section). These redshift
uncertainties correspond to comoving distance uncertainties of 200Mpc at
z=0.5 and 135Mpc at z=1.1, effectively erasing the clustering
information along the line of sight. However, we will use the
photometric redshifts to divide the sample into redshift shells, and
analyze the angular clustering as a function of redshift. The angular
power spectrum within a redshift shell can be written as

$C_{\text{gal}}^{i}(l) = \int_{}^{}{k^{2}\text{dk}}\frac{2}{p}f_{i}^{2}(l,k)P_{\text{gal}}(k)$,
(2)

where $f_{i}(l,k)$ is the Bessel transform of the radial selection
function for redshift shell *i* (Tegmark 2002, Dodelson 2002). Figure 1
contains a plot of the angular power spectrum with error bars that we
expect to measure in the DES.

The cosmological information content in this measurement can be crudely
understood as coming largely from the transfer function. (The varying
bias as a function of redshift significantly reduces information coming
from the growth of structure) The transfer function has a characteristic
break on a physical scale corresponding to the horizon size at
matter-radiation equality (i.e. Peacock 1999). This physical scale
depends on the matter and radiation densities in the local universe. In
addition, there are other low contrast features associated with the
effects of baryon oscillations on the dark matter distribution. Within
each redshift shell, the angular power spectrum will reflect this
characteristic break at some characteristic angle. Thus, the angular
power spectrum constrains a redshift dependent combination of the matter
density and the angular diameter distance (i.e. Cooray et al 2001). With
the large sample of galaxies extending over a broad range in redshift,
it is possible to solve for the bias within each redshift bin while
simultaneously constraining a range of interesting cosmological
parameters, including the density and nature of the dark energy.

In Figure 2 we plot the constraints on the matter density parameter and
the equation of state of the dark energy. We also show the constraints
on the neutrino mass, which should be quite competitive (Jon Thaler, DJ
Box and I are still working on these calculations... don't have figures
we can show at this time).

4.  **Dark Energy with Supernovae**

Using the information contained in supernova (SN) light curves to
measure the expansion history of the universe has rapidly become a
foundational standard of cosmological studies. Studies of nearby SNe
(*e.g.*, Hamuy et al 199x) provided the basis for development of methods
of using Type Ia SNe as precision distance indicators (*e.g.,* Phillips
199x), and the application of these methods to studies of high redshift
SNe provided the first direct evidence of the accelerating expansion of
the Universe (Riess et al, Perlmutter et al). While most of the success
of these studies in constraining the cosmological expansion has been due
to the precision to which the light curves can be measured and compared
against local templates, much of the power in determination of other
cosmological parameters relies upon the complementary nature of the
confidence contours derived from SN studies with those derived from
studies of galaxies and large scale structure (figure X showing the
current situation). The combination of the results from these very
different methods, basically restricting the allowable parameter space
to the minor axes of the confidence contours of each method, results in
extremely strong constraints on cosmological parameters such as Ω~m~,
Ω~Λ~, and *w*.

Just as the studies described above represent a major advance in
cosmological studies using clusters and large scale structure, the
methods used to extract information from SN light curves are now
undergoing the sort of rapid refinement and improvement that the CMB
experienced over the previous few decades. The sources of systematic
uncertainty are being addressed one by one and either minimized or
eliminated by new measurement capabilities and larger samples. As this
understanding of controlling the systematic uncertainties improves, new
supernova surveys successively take advantage of this knowledge by
performing more detailed and controlled measurements on both the
supernovae and the supernova samples, lowering the statistical
uncertainty to the improved systematic limit.

With the DEC we have the opportunity to make the next step forward in
this progression. Compared to the current generation of supernova
surveys (ESSENCE and CFHT SN Legacy Survey), we will have new
measurement capabilities and a wider field to collect larger numbers of
supernovae over a wide range of redshifts. The proposed design will
allow much better control over the wavelength response of the entire
photometric system, and the proposed sensors will allow much better
throughput in the redder wavelengths that are crucial both to cover the
range in redshift and to control and quantify at lower redshifts the
systematics related to dust and intrinsic SN dispersion.

Based on these new capabilities, we have designed a baseline
experimental design which uses approximately 12% of the time dedicated
to the DEC survey operations, assumed to be 30% of the telescope time
over a five year period. The requirements of this design include the
production of a large number of well-sampled SN light curves in three
bands in an observing strategy which fits within the 4000 deg2 DES
survey area and execution strategy. Based on previous modeling,
balancing desired spatial coverage with desired depth to cover a wide
range of redshifts (0.25 \< z \< 0.75 ), we've selected exposure times
of 200s in r', 400s in i', and 400s in z. These exposure times should
give is reasonable signal to noise SN light curves in these bands out to
z\~0.75. We would use roughly one hour per night over four months each
year for five years. Each night we would cover roughly one third of our
total survey area, returning to the same fields every third night. Each
observation of a given field would be taken in r' and alternately in i'
and z, as follows:

Night 1: set A, r+i

Night 2: set B, r+i

Night 3: set C, r+i

Night 4: set A, r+z

Night 5: set B, r+z

Night 6: set C, r+z

Night 7: same as Night 1

With this cadence, we would obtain r band SN light curves sampled every
third night, with i and z band light curves sampled every sixth night.
In total we would cover 16 DEC fields or roughly 40 square degrees of
sky, a much larger area than that covered by any current intermediate to
high redshift SN surveys.

With this baseline design, we've run models assuming that the DEC has
roughly similar r and i response to that of the current CTIO Mosaic
camera (a conservative assumption) and the z response assumed in
sections above. CHANGE THIS? GET MORE "REAL" DEC NUMBERS? Folding these
sensitivities in with the historical weather, seeing, and other
observational factors, we estimate that we will identify more than 1900
Type Ia SNe (along with many SNe of other types) over the course of the
five year program.

Using this large sample of well characterized SNe, we can turn our
attention not just toward remeasuring the accelerating expansion of the
Universe, but more importantly toward constraining cosmological
parameters such as *w*. Figure X shows the results of propagating the
simulated light curves through a sample analysis to determine the
resulting cosmological parameters. The upper panel shows the results
combined with the existing constraints coming from the large scale
structure results of the 2dF survey. The lower panel shows the results
of the combination of our SN results with the determination of
cosmological parameters from the observations described in previous
sections (the South Pole Telescope and associated DEC observations),
putting a constraint of roughly +/-0.02 on the value of *w*. These
constraints on *w* are almost order of magnitude smaller than those
*hoped* for from the set of SN surveys currently underway.

It is important to note that the DEC would be one of the primary
instruments in the world for such supernova survey work during its years
of operation. We expect that the previous generation of surveys will
yield suggestive results and puzzles that will be addressed by the DEC
supernova work, so the baseline plan is very likely to be updated with a
significantly more sophisticated plan that builds on what we know at
that time.

HAVENT MENTIONED SPEC YET... STILL NEED TO DISCUSS... above plot assumes
good knowledge of SNe types, etc.

![](media/image6.png){width="4.608333333333333in"
height="3.392361111111111in"}

![](media/image7.png){width="4.61875in" height="3.4in"}

Figure X2. Constraints on Omega_matter and w after full 5 year DECcam SN
survey. A flat (Omega=1) cosmology has been assumed. Contours in red are
from the SN survey alone; countours in blue show joint constraints from
SNe + 2dF (Omega_matter = 0.278 +/- 0.042) (top) and joint constraints
from SNe and SPT (cluster number counts\...?) (bottom). Contours
represent 1,2 and 3 sigma confidence intervals. The curves at right
represent the constraints on w after marginalization over Omega_matter.

## 2.7 Photometric Redshifts

In the absence of spectroscopic data, the redshifts of galaxies and
other extragalactic objects may be estimated using solely multi-band
photometry, which may be thought of as very low resolution spectroscopy.
Though such "photometric redshifts" (or photo-z's) are necessarily less
accurate than true spectroscopic redshifts, they nonetheless can provide
reliable redshift estimates that are sufficient for a large variety of
science applications, with the advantage that photometric redshifts may
be obtained more inexpensively and for much larger samples than is
possible with true spectroscopy. In particular, in order to achieve its
scientific goals, the Dark Energy Survey will need to obtain accurate
measurements of photometric redshifts for a large sample of cluster and
field galaxies.

There are two basic approaches to measuring galaxy photometric
redshifts. The first relies on fitting model galaxy spectral energy
distributions (SEDs) to the photometric data, where the models span some
range of expected galaxy redshifts and spectral types (e.g., Sawicki et
al. 1997). The second approach depends on using an existing
spectroscopic redshift sample as a training set to derive an empirical
photometric redshift fitting relation (Connolly et al. 1995). There are
advantages and disadvantages in either approach, as well as a number of
variants and hybrids of these basic techniques (e.g., Csabai 2003).
However, photometric redshift methods ultimately rely on measuring the
signal in the photometric data arising from prominent "break" features
present in galaxy spectra, e.g., the 4000Å break in red, early-type
galaxies, or the Lyman break at 912Å in blue, star-forming galaxies. The
key is to have photometric bands which cover such break features
throughout the redshift range of interest, so that the primary redshift
signal may be readily detected. Additional refinements in the
photometric redshift measurement then come from the strength of the
break features and the gross shape of the galaxy SED, as determined by
the photometric data on either side of the spectral break.

2.7.1 Photo-z Simulations for Cluster Galaxies

The measurement of accurate photometric redshifts for galaxy clusters
out to *z*=1 is a necessary component in carrying out our central
science goal of constraining dark energy using cluster abundances. Such
cluster photometric redshift measurements are greatly facilitated by the
strength of the 4000Å break feature prominently seen in the spectra of
red cluster galaxies. This is illustrated in Figure 0, which shows a
red, elliptical galaxy spectrum at redshifts *z*=0, 0.5, and 1,
superimposed on the *griz* filter bandpasses. We see how the 4000Å break
moves to longer wavelengths and through the different filters in turn as
the galaxy redshift increases. We also see that measurements of the
relative galaxy fluxes through the different filters should provide us
with an estimate of the observed wavelength of the 4000Å break and hence
an estimate of the galaxy redshift. This is demonstrated in practice in
Figure 1, where we compare photometric and spectroscopic redshifts for a
sample of SDSS red galaxies, for which we are able to obtain photometric
redshifts with a scatter σ~z~=0.03, out to redshifts z≈0.6. However, at
higher redshifts we do not have such large samples of real red galaxies
available, and so we will need to rely instead on Monte Carlo
simulations to fully assess the quality of cluster galaxy photometric
redshifts for the Dark Energy Survey.

![](media/image8.png){width="5.979166666666667in"
height="5.979166666666667in"}

Figure 0: The spectrum of a red, elliptical galaxy is shown at redshifts
*z*=0, 0.5, and 1, with the location of the prominent 4000Å break
feature marked. The spectra have been vertically offset for clarity.
Also shown are the *griz* filter bandpasses, arbitrarily normalized to
the same peak value. Photometric redshift information for red galaxies
comes primarily from changes in the relative galaxy fluxes in the
different filters as the 4000Å break moves to longer observed
wavelengths at higher redshifts.

In our Monte Carlo simulations, we adopt two different galaxy spectral
energy distribution (SED) models to simulate the colors of a red cluster
galaxy as a function of redshift: (1) an empirical non-evolving
elliptical galaxy SED taken from the sample of Coleman, Wu, & Weedman
(CWW; Coleman et al. 1980); and (2) a passively evolving elliptical
galaxy model taken from the Pegase-2 SED library (Fioc &
Rocca-Volmerange 1997). The Pegase-2 model is designed to match the
colors of SDSS red galaxies at low redshifts, while the CWW model will
provide an alternative SED for comparison purposes. Separate sets of
Monte Carlo simulations are generated with galaxy absolute luminosities
fixed at 0.5L\*, L\*, 2L\*, or 5L\*, and with 5000 galaxies generated
per simulaton, distributed uniformly over redshifts 0\<*z*\<1. A flat
cosmology, with and , is used to calculate galaxy apparent magnitudes as
a function of redshift, and the models are normalized so that a 0.5L\*
galaxy at redshift one has a *z*-band magnitude of 23. The 10σ galaxy
magnitude limits for the Dark Energy Survey are *griz* = 24.6, 24.1,
24.0, 23.6. Expected galaxy photometric errors are calculated by
appropriately scaling the *S*/*N* relative to the 10σ magnitude limit,
and by adding in quadrature a 2% error floor due to photometric
calibration uncertainty. The photometric errors for each simulated
galaxy are then drawn from Gaussian distributions. Finally, photometric
redshifts are determined using a polynomial-fitting technique (Connolly
et al. 1995), where we adopt a photometric redshift relation of the form
redshift = *f(g,r,i,z,g^2^,gr,r^2^,...)*, where *f* is a polynomial
containing terms up to quadratic order in the *griz* magnitudes.

Representative simulation results, for 0.5L\* and 2L\* galaxies, are
shown in Figure 2, which plots the difference between photometric
redshift and true input redshift, as a function of the true redshift. We
find good photometric redshift results for 0\<*z*\<1, with a 1σ
photometric-redshift scatter σ~z~\<0.03 per galaxy, and only small
systematic biases of size \<0.01 in redshift. Note that we can do even
better for a whole galaxy cluster, since we can average the photometric
redshifts for, say, *N* individual cluster members and improve the
photo-z estimate by the expected factor of .

One can see from Figure 2 that there are small differences in the
results for the CWW vs. Pegase-2 models, a consequence of the detailed
differences in the color vs. redshift relations for the two galaxy
models. In practice, for the Dark Energy Survey we will need to acquire
a spectroscopic redshift training set in order to empirically measure
the correct cluster galaxy SED to use for our final photo-z calibration,
especially at redshifts *z\>*0.7 where existing galaxy cluster data are
very sparse.

### 2.7.2 Photo-z for the General Galaxy Population

We would also like to obtain photometric redshifts for the general
galaxy population, beyond red cluster galaxies, in particular to
facilitate dark energy constraints using weak lensing, galaxy
clustering, and supernova measurements. Such photo-z's are necessarily
somewhat less accurate than those possible for cluster galaxies, as we
must consider a much broader distribution of galaxy SEDs. Nonetheless,
good photometric redshift measurements out to *z*=1 are still readily
achieved for the general galaxy population.

We demonstrate this using the publicly available ground-based *VRIz*
photometric data obtained by Capak et al. (2004) in the GOODS/HDF-N
area, combined with a training set of 1800 spectroscopic redshifts from
the compilations of Wirth et al. (2004) and Cowie et al. (2004). The
*VRIz* photometry serves as a best-effort approximation to *griz*, as we
are not aware of a sample with *griz* photometry of sufficient depth for
this purpose. We add noise to the original *VRIz* photometry in order to
match the Dark Energy Survey depths. We again derive photo-z's using
polynomial fitting, including terms up to quadratic order in the *VRIz*
magnitudes, and the results are shown in Figure 3r. We find a
photometric redshift scatter σ~z~≈0.05 at *I~AB~*=22, increasing to
σ~z~≈0.1 at *I~AB~*=24, the approximate 10σ galaxy limit for the Dark
Energy Survey. The photo-z scatter increases at fainter magnitudes, as
expected, and also increases with bluer galaxy color, a consequence of
the weaker break features seen in the spectra of blue star-forming
galaxies. Note that the photo-z trends vs. spectroscopic redshift are in
general well behaved, except at the lowest redshifts *z\<*0.3, where
there is a tail such that the photometric redshift is scattered
systematically high. This is likely a consequence of the lack of a
constraining filter blueward of the 4000Å break at these low redshifts.
In general, it will be important to understand any such biases by
carefully measuring the photo-z error distribution using a large
spectroscopic redshift training set. Two such large redshift surveys,
the VIMOS VLT Deep Survey (VVDS; Le Fevre et al. 2003) and the Keck
DEEP2 Survey (Davis et al. 2002), are both currently in progress. These
surveys should provide spectroscopic redshifts sufficient to calibrate
general galaxy population photo-z's down to the Dark Energy Survey limit
of *I~AB~*=24. In particular, the VVDS will obtain about 100,000
redshifts, and it is also being carried out from Chile. Thus all the
VVDS fields will be accessible to *griz* imaging using the Dark Energy
Camera, thereby allowing us to derive detailed photometric redshift
calibrations for the Dark Energy Survey.

> ![](media/image10.png){width="5.979166666666667in"
> height="5.979166666666667in"}

Figure 1: Photometric and spectroscopic redshifts are shown for a sample
of SDSS red galaxies, for which a photometric redshift scatter σ~z~=0.03
is obtained.

> ![](media/image11.png){width="5.979166666666667in"
> height="5.979166666666667in"}
>
> Figure 2: Photometric redshift results are shown for the 0.5L\* and
> 2L\* cluster galaxy Monte Carlo simulations described in the text. The
> red lines show the median difference between photometric and input
> redshift, the blue lines show the 1σ scatter (68% limits), and the
> green dashed lines are set at ∆*z*=±0.03.
>
> ![](media/image12.png){width="5.979166666666667in"
> height="5.979166666666667in"}
>
> Figure 3: Photometric vs. spectroscopic redshifts for the general
> galaxy population in the GOODS/HDF-N field. Noise has been added to
> the original *VRIz* magnitudes in order to match the depths that will
> be reached by the Dark Energy Survey.

5.  **Dark Energy Survey Science Requirements**

```{=html}
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```
1.  
2.  
3.  

The dark energy probes we outline above require an imaging survey of a
large area of the sky. Levine et al (2002), among other papers, suggest
that the optimal area to for cluster surveys is a few thousand
sq-degrees. We choose:

1.  5000 sq-degrees in the South Galactic cap

    a.  4000 sq-degrees to overlap SPT survey at Dec \< -30

    b.  270 sq-degrees to overlap redshift surveys for photo-z training
        samples

    c.  700 sq-degrees optimal for CTIO and Atacama telescopes

The science programs rest heavily on our ability to locate clusters out
to redshift 1, and on our ability to assign precise and accurate
photometric redshifts to these galaxies. We choose:

2.  Photometric redshifts to z=1 and ½ L\* at delta-z \<= 0.05.

    a.  SDSS g,r,i,z are sufficient, if z is made x5 more sensitive

    b.  g=23.1 r= 23.7, i=24.0 z=23.6

    c.  photometric calibration to 2%

The dark energy probes all require good seeing. Weak lensing is the most
sensitive to the effects of seeing, but in fact the signal to noise on
faint galaxies is also quite sensitive to seeing. For all of our
calculations we have assumed 0.9".

3.  PSF and galaxy density sufficient for weak lensing

    a.  Seeing \<= 0.9"

    b.  Pixel size to fully resolve PSF

    c.  Focus and guiding sufficient to obtain 0.9"

We now turn to the arguments and calculations supporting these
requirements, and calculate the area of the imaging instrument we will
need to pursue the program.

1.  **Science Requirements** **to Technical Specifications**

    1.  Survey Footprint

![](media/image14.png){width="4.864583333333333in"
height="4.864583333333333in"}

We aim at 5000 sq-degrees in the south galactic cap. The primary
decision that shapes the footprint is overlap with the South Pole
Telescope survey area. The SPT can observe down to 70 degrees zenith
angle, corresponding to south of declination --30, over a right
ascension region that is limited by South Pole winter and the galactic
plane. The south equatorial pole, overhead of the south pole, is an area
of high dust extinction and can usefully be excised from the survey.
This leaves us a 150 degree wide swath of survey from --30 declination
to --75 declination, extending from 20h to 6hr, and covering the bulk of
the low extinction area available. The noticeable exception to the low
extinction is the Large Magellenic Cloud in the corner of the survey, We
extend the 4000 degree area by surveying a 700 sq-degree area overhead
of CTIO and the telescopes on the Atacama Plateau, with the intent of
providing targets and optical follow up for those powerful machines.
Last, we image a 200 sq-degree region on the equator to pick up the
redshifts of the SDSS Southern Survey and the Virmos Redshift Fields,
redshifts we need to calibrate photometric redshifts. We will need on
order of 1000 redshifts per 0.1 in z to calibrate the photometric
redshifts, so we must image areas already under study in redshift
surveys. The equator between 21h and 6 hr contains the SDSS Southern
Survey, a collection of programs that collectively have 5 times the
surface density of targets that the main SDSS contains, and which probe
higher redshifts, fainter magnitudes, and smaller objects than the main
survey. This area also contains the 8 sq-degrees of the Virmos-VLT Deep
Survey Wide (to I_AB = 22.5) and 2 sq-degrees of the Virmos-VLT Deep
Survey Deep (to I_AB = 24.0).

2.  Wavelength Coverage

The filters must provide a bracketing of the 4000A break signal in the
elliptical galaxy spectrum typical of cluster galaxies. At z=0, the blue
side limit is 400 nm. At z=1, the 4000A break is at 8000A, and we need a
filter redward of this. The SDSS filter set provides a filter set with
the required characteristics: we need g, r, i, z

We need four bandpasses to achieve delta-z \<= 0.05. The SDSS filter set
works well for this, with the exception that we will need a higher
system response in the z band than the 10% that the SDSS enjoyed.

**As noted elsewhere, our z band red cutoff differs slightly from the
SDSS z band. While both are effectively defined by the red cutoff of the
silicon, the thick, high resistivity silicon CCDs that we plan to use
have a much higher QE in the z band than the SDSS chips. These filter
characteristics were selected to bracket the Calcium H and K break at
394 nm in the spectrum of red galaxies, which is typical of galaxies in
clusters. At zero redshift the H and K break is at 410 nm, just
blue-ward of blue cutoff (50%) of the g band filter.. At a redshift of
1.2 the break is at 830nm, just red-ward of the red edge (50%) of the i
filter.**

3.  Limiting Magnitudes

The aim is to achieve good photometric redshifts on massive clusters of
galaxies out to *z*≈1. Since most of the galaxies in clusters have E/S0
spectra, the problem becomes predicting the magnitudes of ellipticals at
*z*≈1.

One can obtain quite complete and reasonably pure cluster catalogs using
optical selection techniques if one is able to obtain if one has ≥10σ
observations of the colors of elliptical galaxies of . Clusters at the
limit of the SPT have masses of (neglecting the scatter of the SZ mass
estimator). The mean = 20 galaxies for , with 1σ scatter of σ≈35%≈6. To
reach 95% completeness limit, we will need to reach down to .

At this lower limit, each cluster has ≈10 red galaxies. If the inherent
photo-z uncertainity per galaxy is 0.05, then we can expect cluster
photo-z's of less than this, ∆*z*=0.016. This level of precision of
cluster photo-z has been demonstrated in the SDSS.

We need precision colors to pursue photo-z's, and we need them at the
limit of the photometry. We will aim to track an galaxy out to *z*=1.
Blanton et al (2003) have (z=0, evolution corrected). An galaxy is then
.

We need precision colors, which correspond to a S/N of 8σ in the blue
color, 13σ in the red color and 13σ in magnitudes. We therefore require
g,r,i S/N of 10σ. For the z filter we must be a little more careful: 13σ
is uncomfortably close to where the number counts in real data turn
over, an indication that it is close to the completeness limit. We will
want to go somewhat deeper, say 0.3 magnitudes, in order to safely
construct a flux-limited sample of galaxies. We therefore require a 13σ
z observation, converted to a 10σ measurement by adding 0.3 to the
apparent magnitude, and asking for a 0.3 magnitudes deeper to obtain a
clean flux limited sample.

  -------------- -------------- -------------- -------------- --------------
  Required                                                    
  Magnitudes                                                  

  Filter         g              r              i              z

  mag (10σ)      22.8           23.4           24.0           23.6
  -------------- -------------- -------------- -------------- --------------

  -----------------------------------------------------------------------

  -----------------------------------------------------------------------

4.  Exposure Times

A calculation of the exposure time to reach a given magnitude at a given
S/N depends on the mirror area, the throughput of the system, the read
noise of the instrument, the pixel size, the sky background, and the
area over which the object is spread.

First, we assume that the system throughput in z is 4 times higher than
it is in the SDSS. The table below shows the assumed system
characteristics, where QE is the CCD quantum efficency at the filter
central wavelength, T is the transmission of the atmosphere (1.2
airmasses), primary mirror, optics, and filter at the filter central
wavelength, dl/l is the filter FWHM divided by the filter central
wavelength. All the numbers here are for the SDSS system, with the
exception of the modified z filter.

  ----------------- ----------------- ----------------- -----------------
  Filter            QE                T dl / l          QE T dl / l

  G                 0.65              0.18              0.118

  R                 0.85              0.14              0.117

  I                 0.65              0.13              0.087

  Z                 0.5               0.18              0.09
  ----------------- ----------------- ----------------- -----------------

We assume the camera has a readnoise of , and that the pixel size is
0.25"/pixel.

The Blanco 4m telescope has a light collecting area of 10.0 sq-meter..
As our reference design has two more optical elements then the SDSS
design, an overall factor of 0.9 has been multiplied into the above T
dl/l, modeling the losses in transmission.

The sky background is that from APO, the 25% quartile (bright) of all
the frames of all the runs taken in the SDSS:

  --------------- -------------- -------------- -------------- --------------
  Sky brightness                                               

  Filter          g              r              i              z

  mag/sq-arcsec   21.7           20.7           20.0           18.7

  moony ∆mag      -2.0           -1.0           -0.75          -0.2
  --------------- -------------- -------------- -------------- --------------

The last line is the increased sky brightness measured at 45 degrees
from a half to full moon, as measured using observations from the SDSS
PT. This suggests we can work in all moon conditions using z, and most
using i.

There is also a half magnitude increase in the sky brightness results in
a quarter magnitude decrease in the limiting magnitude. The solar cycle
causes sky brightness variations on order of 0.5 magnitude. The next
solar max is roughly 2012. The sky brightness above are from the SDSS
data, taken in the years right across the last solar maximum.

The area over which an object is spread is more tricky. A star is best
case, and a very spread out object is worst case. Further, the Megaprime
calculator assumes, for galaxies, that the intent is to measure 95% of
the objects flux which takes a large aperture. For colors, one wishes a
more compact apodized aperture; PHOTO uses a (seeing-convolved)
deVaucouleurs profile to measure the color of faint ellipticals. This is
effectively a factor of 1.67 larger than a PSF[^1] . We assume the 4m
seeing is 1.0", and use a conservative aperture of 1.7" diameter to
measure the flux.

  ----------------- ----------------- ----------------- -----------------
  Aperture Sizes                                        
  for Galaxy Colors                                     

  DIET version      Target            x seeing          comment

  CFH12K            point source      1.45              

  CFH12K            Galaxy            1.67              more appropriate
                                                        for colors

  Megaprime         Galaxy            2.8               aimed at total
                                                        magnitude
  ----------------- ----------------- ----------------- -----------------

  ------------------ --------- -------------- -------------- --------------
  Exposure Times                                             

  Filter             g         r              i              z

  mag (10σ)          22.8      23.4           24.0           23.6

  Exposure (sec)     27        130            900            1600
  ------------------ --------- -------------- -------------- --------------

  -----------------------------------------------------------------------

  -----------------------------------------------------------------------

We will see in the Survey Strategy section that we need  5 exposures to
do precise photometric calibration. The shortest exposures that make
sense given the 35 second slew times fort the 4m over 2 degree scale
slews is 100 seconds. Let us assume we observe 500 seconds in g and r.

  -------------- -------------- -------------- -------------- --------------
  Magnitude and                                               
  Exposure Times                                              

  Filter         g              r              i              z

  Exposure       500            500            900            1600

  mag (10σ)      24.6           24.1           24.0           23.6
  -------------- -------------- -------------- -------------- --------------

5.  Overhead per field

We define field to be all observations taken through all bandpasses on a
given location on the sky. For the purposes of the following
calculation, it is convenient to think of the data making up a field as
being taken at one time. We will see in Survey Strategy that the optimal
strategy will be quite different. Taking the results of that section, we
break the total exposure time needed into 100 second exposures, and we
assume we move after every exposure. Then the total exposure time is
3500 seconds per field. Next we turn to the calculation of overhead. 35
slews each taking 35 seconds (the slew times of the Blanco Telescope is
known to be 35 seconds or less for slews less than 4 degrees) gives 1200
seconds of overhead per field, where we are assuming readout time is
less than the slew time. We'll assume we can do 8 fields a night. We
take nightly setup time as 0.5 per hour, and we assume 4 observations of
standard stars per night that take a total of 0.5 hours. We then assume
that equipment failure over the life of the survey averages to 0.5 hour
per night, Taking this overhead per night of 1.5 hours, dividing by 8
fields/night, we find another 700 seconds of overhead to add to the slew
times. The total overhead is 1900 seconds. The grand total time spent
per field is then 5400 seconds. These numbers are summarized below.

  ----------------------------------- -----------------------------------
  Filter:                             g, r, i, z

  unit exposure time:                 100

  Total exposure time:                500, 500, 900, 1600

  Total exposure :                    3500 seconds per field.

  pointing overhead:                  35 seconds slew, 35 images: 1200
                                      seconds.

  Other overhead:                     700 seconds/field

  Total:                              5400 seconds/field
  ----------------------------------- -----------------------------------

6.  Available Time

NOAO has guided us to assume 30% of the available time over 5 years.

7.  Cerro Tololo Weather

To be replaced by William's write up.

In \"Useful Observing at CTIO\", we have calculated the amount of dark
time available during the years 2008-2013 for the montsh of September
through February. We find 1910±10% hours of dark time. There is probably
80% of that amount available in gray time.

This amount of time needs to be modified to take into account the
fraction of that time that the survey area is available abouve 1.5
airmasses. We take as an initial estimate 85%, leading us to 1600 hours
of dark time and 1300 hours of gray time.

This is 2900 hours over the survey, and 580 hour per year.

We note that both the site seeing and the weather statistics drive us to
observe as late in the year as possible. We show the seeing statistics
below[^2] . It is also worth noting that seeing goes as

\(1\)

where *z* is the zenith angle. This takes 0.9" seeing at r to 0.8" at z
for observations at the zenith.

  ---------- ---------- ---------- ---------- ---------- ---------- ----------
  Seeing                                                            

  Month      Aug        Sept       Oct        Nov        Dec        Jan

  median     0.9\"      0.9\"      0.85\"     0.65\"     0.65\"     0.60\"
  seeing                                                            
  ---------- ---------- ---------- ---------- ---------- ---------- ----------

8.  Camera Size

The camera size then falls out.

To do a 5000 sq-degree survey in 2900 hours implies 1.7 sq-degrees/hr.
The exposures take 5400 seconds (1.5 hrs) per field. Then

FOV = 1.7 sq-degree/hr \* 1.5 hrs/field = 2.6 sq-degrees/field

Note that a corrector with a 2.1 degree diameter field of view has 3.5
sq-degrees available in the circular area. But the largest useful
pattern in that circular area is a hexagon, which if inscribed in that
circle has an area of 2.9 sq-degrees. Further, the dead area between
CCDs tends to be about \$10\\%\$, leading to an active area of 2.6
sq-degrees.

**References**

> \[12004Capak et al.\] Capak, P., et al. 2004, AJ, 127, 180
>
> \[21980Coleman et al.\] Coleman, G.D., Wu, C.-C., & Weedman, D.W.
> 1980,43, 393 (CWW)
>
> \[31995Connolly et al.\] Connolly, A.J., et al. 1995, AJ, 110, 2655
>
> \[42004Cowie et al.\] Cowie, L.L., et al. 2004, AJ, submitted,
> astro-ph/0401354
>
> \[52003Csabai et al.\] Csabai, I., et al. 2003, AJ, 125, 580
>
> \[62003Davis et al.\] Davis, M., et al. 2002, SPIE, astro-ph/0209419
>
> \[71997Fioc & Rocca-Volmerange\] Fioc, M., & Rocca-Volmerange, B.
> 1997, A&A, 326, 950
>
> \[82003Le Fevre et al.\] Le Fevre, O., et al. 2003, astro-ph/0311475
>
> \[91997Sawicki et al.\] Sawicki, M.J., Lin, H., & Yee, H.K.C 1997, AJ,
> 113, 1

\[102004Wirth et al.\] Wirth, G.D., et al. 2004, AJ, submitted,
astro-ph/0401353

[^1]: Taken from the CFH12K version of the DIET exposure time calculator
    (see the tables at
    http://www.cfht.hawaii.edu/Instruments/Imaging/CFH12K/DIET/CFH12K-DIET.html#P3
    in particular the one labeled \"Galaxies in dark time\"), which
    differs from the MegaCam version of DIET in that it uses a smaller
    aperture for galaxies.

[^2]: These are site statistics. The experience on the 4m is that
    delivers 0.9" in January.