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\subsection{The mass profiles of galaxies and clusters} %Please give
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{\bf{
{Prof. Peter Schneider}\\
{Institut f. Astrophysik u. Extraterrestrische Forschung}\\
{Universit\"at Bonn}\\
{Auf dem H\"ugel 71}\\
{D-53121 BONN}\\
{Telefon: 0228/733671}\\
{Fax: 0228/734022}\\
{Email: peter@astro.uni-bonn.de}\\}}


\subsubsection{Abstract}
The nature and spatial distribution of dark matter in the Universe is
the central issue of modern cosmology. Weak gravitational
lensing, the distortion of distant faint galaxy images by the tidal
gravitational effect of intervening matter, provides an ideal tool to
study the dark matter distribution, as the light deflection depends on
the total (dark + luminous) mass distribution. Measuring the
distortion field from the image ellipticities of background galaxies,
the tidal gravitational field of the deflector, and thus its
(projected) mass distribution can be derived. One can therefore derive
the density distribution of these deflectors, either individually
(which is possible for clusters of galaxies) or as an ensemble. The
current project aims at exploiting these possibilities to test
fundamental properties of the dark matter distribution in virialized
halos. 


\subsubsection{Current status of research}
Weak gravitational lensing (see Mellier 1999; Bartelmann \& Schneider
2001 for recent reviews) employs the fact that light bundles are
distorted when passing a matter inhomogeneity; the corresponding tidal
gravitational field changes the observable image ellipticity of
background sources in a predictable way. Since the extragalactic sky
is densely filled with faint galaxies, the statistical investigation
of their image shapes directly yields information about the matter
distribution of the deflectors.

As was first shown by Kaiser \& Squires (1993), from the observable
tidal field (or gravitational shear) the projected mass distribution
of clusters of galaxies can be reconstructed in a parameter-free
way. Several modifications have improved the original method and
made it more versatile (Schneider 1995; Kaiser 1995; Schneider \&
Seitz 1995; Seitz \& Schneider 1995, 1996, 1997, 1998; Bartelmann et
al.\ 1996; Seitz et al.\ 1998; Lombardi \& Bertin 1998a,b, 1999a,b).
These methods have been applied to quite a number of clusters hitherto
(e.g., Fahlman et al.\ 1994; Smail et al.\ 1995; Squires et al.\
1996a,b; Seitz et al.\ 1996; Kaiser et al.\ 1998; Hoekstra et al.\
1998, 1999; Fischer et al.\ 1999; Clowe et al.\ 1998, 2000, Athreya et
al.\ 2000; Lombardi et al.\ 2000). The results of these studies show a
variety of mass-to-light ratios, amounts of substructure, and radial
mass profiles; in many cases, cluster galaxies follow the dark matter
distribution, whereas in others this is not the case.

The mass properties of individual galaxies cannot be probed with weak
lensing as they are not massive enough. However, the lensing
properties of galaxies can be statistically superposed, a technique
called galaxy-galaxy lensing. It has been successfully applied to a
few sets of data (Brainerd et al.\ 1996; Griffiths et al.\ 1996;
Hudson et al.\ 1998; Fischer et al.\ 2000); the main result from these
studies is that the dark matter halo of galaxies is very extended, and
only lower limit to the tidal cut-off radius have been derived.


\subsubsection{Own experience}
The proposer has been leading a group on gravitational lensing
research for about 10 years in which more than 100 refereed
publications were written. He first-authored the monograph on the
topic (Schneider, Ehlers \& Falco 1992). The group played a leading
role in the development of weak gravitational lensing, both in theory
(see Bartelmann \& Schneider 2001 and references therein) and from an
observational point-of-view (e.g., Seitz et al. 1996; Erben et
al. 2000; Clowe et al. 2000). In particular, our group has been at the
forefront of cluster mass reconstruction techniques (Schneider 1995;
Kaiser 1995; Schneider \& Seitz 1995; Seitz \& Schneider 1995, 1996,
1997, 1998; Bartelmann et al.\ 1996; Seitz et al.\ 1998), and
developed the state-of-the-art technique for the analysis of
galaxy-galaxy lensing (Schneider \& Rix 1997).


\subsubsection{Goals of the project}
\begin{itemize}
\item
The selection of clusters for which mass distributions have been
reconstruted up to now was mainly done on the basis of cluster
peculiarities: eiher the most massive clusters, the highest redshift
clusters, or those which show strong lensing effects in the form of
giant arcs. It is therefore unclear how characteristic the results
derived from these individual clusters are. The goal of this project
is to study the mass distributions of a well-defined cluster sample
(e.g., selected by their X-ray flux), and to obtain statistically
significant results on their radial mass profile, their elongations,
their amount of substructure, and their mass-to-light ratio. In
particular, appplying a newly developed method for determining mass
profiles (Schneider et al.\ 2000; King \& Schneider 2000), the
applicability of the `universal' dark matter halo mass profile
(Navarro et al.\ 1996, 1997) shall be tested. Several data sets have
already been obtained and can be used for this purpose. Furthermore,
most of the cluster investigations up to now have been restricted to
the inner $\sim 500$\ kpc, whereas it would be of utmost interest to
follow the profile up to the tidal radius, about a factor of 3 further
out in radius; the new wide-field imaging cameras allow us to do so,
and one very high quality data set has already been obtained -- the
shear can be followed right up to the tidal radius in this cluster. It
should be stressed that the mass profile in the inner part of the
cluster provides a sensitive test for the hypothesis that dark matter
particles are weakly dissipative, as that will affect the central
density profile; hence, the results of this study has direct
implications for the nature of the dark matter particles. 

Given the expertise of some Bonn astronomers in X-ray astronomy, these
lensing studies shall be complemented with X-ray studies of clusters,
making use of the new European X-ray satellite XMM-Newton. Already the
first results from this observatory show its great capabilities in
studying the mass distribution in clusters. A further constraint on
the (baryonic) mass distribution comes from observations of the
Sunyaev-Zeldovich effect in clusters, the Compton upscattering of CMB
photons. Current instrumental developments at the MPIfR bear the
promise that these studies can soon been carried out in Bonn, in which
case all three observational techniques shall be combined into a
coherent study of cluster mass profiles. 

\item
The results from galaxy-galaxy have been rather sparse up to now,
mainly because the data sets used for the analyses have been
moderate. The currently available wide-field imaging cameras allow us
to use a much larger data set of galaxies, which when supported by
photometric redshift estimates can greatly improve the parameter
estimates for the dark matter halos of galaxies. The techniques for
this are available, e.g., to obtain a much more sensitive probe for
the spatial extent of the halo (Schneider \& Rix 1997; see also Geiger
\& Schneider 1999), or to study the
flattening of dark matter halos (Natarajan \& Refregier 2000). Whereas
the previous studies obtained the dark halo properties of the average
galaxy population, multi-color photometry can split the lens galaxy
sample into various subclasses and investigate the dependence of the
halo mass on the classification (early vs. late-type galaxies; high
vs. low-redshift galaxies; galaxies in clusters vs. field galaxies).
In particular, if cluster galaxies are found to have a different halo
size than field galaxies, this would yield invaluable constraints on
the formation of clusters and the evolution of their substructure,
including the question of how the metal-enriched X-ray gas in clusters
was formed. In addition, the detection of a flattening of galaxy halos
would yield insight into the formation of galaxies and the relation
between the dark and baryonic matter in them. The goal of this project
is therefore to exploit the potential of galaxy-galaxy lensing, by
applying state-of-the-art analysis methods with high-quality
wide-field imaging data that our group has access to.

\item
Although still quite some time in the future, the Next Generation
Space Telescope will provide astronomers with unprecedented
observational opportunities. These will revolutionarize the field of
dark matter investigations with weak lensing. The proposer has been
involved in devising the weak-lensing proposal within the Design
Reference Mission for NGST (see also Schneider \& Kneib 1998). The
experience gained by a young generation of astronomers
from the currently proposed project will be of great
value when the opportunity arises to use NGST. In addition, owing to
the unprecedented depth and angular resolution of NGST, analysis
techniques need to be modified substantially; for example, the
characteristic redshift of a galaxy observed with NGST is so high that
the assmption of having only a single deflector along a line-of-sight
certainly breaks down, and new methods for `redshift tomography' in
gravitational lensing need to be developed. This preparation for NGST
shall be done to some degree within this project in order `to be
ready', and thus to profit maximally once it flies.
\end{itemize}


\subsubsection{Estimate of resources expected from DFG}



\subsubsection{Members of research group relevant for the project}
Prof. Peter Schneider, Dr. Douglas Clowe, Dr. Lindsay King, Dr. Marco
Lombardi, Dipl. Phys. Thomas Erben, Dipl. Phys. Hannelore H\"ammerle,
Dipl. Phys. Martina Kleinheinrich, Dipl. Phys. Michael Schirmer

\subsubsection{Connections to other projects of current SFB proposal}
Schau mer mal

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