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\subsection{(Dark) matter distribution in galaxies} %Please give
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{\bf{
Dr. Alok Patnaik\\
Max-Planck-Institut f. Radioastronomie\\
Auf dem H\"ugel 69\\
{D-53121 BONN}\\
{Telefon: 0228/525231}\\
{Fax: 0228/525229}\\
{Email: apatnaik@mpifr-bonn.mpg.de}\\}}


\subsubsection{Abstract}
High-redshift sources, gravitationally lensed and multiply imaged by
foreground galaxies, provide one of the most precise measurements of
the mass distribution in galaxies; in some cases, mass estimates with
accuracies of a few percent have been obtained. In addition to these
mass estimates, such multiple image systems allows the study of
substructure in the (dark) mass distribution of lensing galaxies. Based on
very high precision measurements of such strong lensing systems, we
intend to explore the properties of galaxy mass distributions, and in
particular their small-scale structure.


\subsubsection{Current status of research}

The bending of light by a gravitational field can be used to measure
the distribution of matter causing this gravitational field. The image
of the background object, e.g. a distant quasar, can be split into two
or more images when the light passes close to a massive object such as
a galaxy. One can estimate the total mass of the galaxy as well as its
spatial distribution by studying the properties of these
gravitationally lensed images of the quasar.

One can also determine the Hubble constant from the study of
gravitational lens systems. The light paths of the multiple images are
not equal. If the background quasar is variable, the signature of this
variability will reach the observer at different epochs from different
images. By measuring the `time-delay' between the images, one can
estimate the Hubble constant, provided the mass distribution of the
lens is sufficiently well known.

Currently, there are six gravitational lens systems for which this
time delay has been measured. The uncertainty in the measurement is
less than 10\%, and in one case it is 1\%. However, it is difficult to
get a unique mass model for the lens which dilutes the significance of
the Hubble constant determinations. Therefore, it is very important to
determine the mass distribution of the lens to much better accuracy
than has yet been possible.

For most of the known lens systems, the image positions can be well
fit with relatively simple mass models. However, in some cases the
flux ratios are extremely difficult to understand, the best example
being the quadruple QSO 1422+231; here, no smooth mass distribution
has been found which can account for the image positions and flux
ratios. Mao \& Schneider (1998) have argued that this deficit of the
lens models can be remedied with just a small amount of substructure
in the lens. Such small amounts of substructure affects the flux
ratios, but leaves the time delays basically untouched.

There are now several lens systems for which the presence of
substructure provides a natural explanations for their flux ratios
which cannot be reproduced with smooth mass profiles. In addition, the
accuracy of image position measurements is becoming so impressively
good (e.g., Patnaik, Kemball, Porcas \& Garrett 1999) that even image
position are not easily fitted with simple smooth mass models. These
new observations thus open up a new sensitive probe for the
substructure in (and around) lensing galaxies.

In fact, the existence of this substructure is expected from
theoretical studies of the formation of galaxies. N-body simulations
of the large-scale structure in the Universe predict that every
massive galaxy shall be surrounded by several hundred of much less
massive satellite `galaxies'. Whereas the Milky Way has a number of
satellites, most prominently the Magellanic Clouds, their number is
far less than theoretically expected. The low-mass satellites may have
had a completely different history of star formation, perhaps blowing
out their gas shortly after a first brief period of star-bursting, and
since then remain basically dark. These dark satellites would be
difficult to detect with any other means than gravitational
lensing. Demonstrating their existence, or otherwise, provides one of
the most important tests of cold dark matter-dominated structure
formation in the Universe.

In addition to the above aspects, we can study the source of background
light as a probe of the interstellar medium of the lensing galaxy. The
molecules in the ISM can absorb the background light, and one can
determine the abundances of various species of molecules and compare
them to those in our Galaxy, thereby studying the physical condition
and the composition of the ISM of a distant galaxy. As an important
spin-off of these absorption line measurements, one can also determine
the cosmic microwave temperature at the redshift of the lensing
galaxy, thus probing directly the $T\propto (1+z)$-dependence.

\subsubsection{Own experience}

Our team has extensive experience in the observations of gravitational
lens systems, in particular in radio observations with interferometers
and with Very Long Baseline Interferometry (VLBI). The PI has been the
discoverer of some of the best studied lens systems (Patnaik et
al. 1992, 1993, Winn et al. 2000a, b), and has carried out extensive
follow-up studies of many of the known radio lenses (e.g., Patnaik et
al. 1995, 1996, 1999, Patnaik \& Porcas 1996, Porcas \& Patnaik 1996),
including the very high precision measurements of image positions with
VLBI measurements (Patnaik et al. 1999). Our team was strongly
involved in the study of lens systems in the JVAS survey, the first
complete lens survey (e.g., King et al. 1998a, b, 1999) and its
statistical analysis (King \& Browne 1996). Furthermore, our team is
experienced in detailed modelling of lens systems (e.g., Kormann,
Schneider \& Bartelmann 1994a, b), and initiated the research for
substructure in lens systems (Mao \& Schneider 1998). Schneider (1998)
has shown that the lensing effects of the large-scale matter
distribution in the Universe on the lensing property of a galaxy can
be described by a simple shear term, so that this does not provide an
increased level of difficulty. We also have wide experience with
molecular spectroscopy of lens systems, that led to the discovery of
rather complex molecules at very high redshifts (Menten \& Reid 1996,
Gerin et al. 1997, Menten, Carilli \& Reid 1999).


\subsubsection{Goals of the project}


As mentioned above, we aim to study the distribution of matter in
distant galaxies through gravitational lensing. We will continue in
obtaining very high angular resolution radio observations using VLBI
to measure the image positions, brightness distributions and
polarisation distributions of lens systems, thereby providing very
stringent constraints to lens models. In order to make the best use of
the imaging data, a new mapping algorithm shall be developed which
accounts simultaneously for the visibility data and the relative image
transformation matrices of the individual lensed images. In this way,
the most stringent relative magnification constraints will be
derived, using both total flux and polarized flux measurements
which complement each other.

On the theoretical side, these new constraints will be used
to construct mass models for the lenses. As a first step, the
best-fitting smooth mass model will be obtained, and checked whether
the modeled image positions and flux ratios are compatible with the
observed ones. Secondly, we shall allow for the presence of
substructure and determine the minimum amount of substructure with
which an acceptable fit to the data can be obtained. In principle, we
can determine structures in the lens at mass scales of 10$^6$ to
10$^7$ solar masses.  Currently, there are about 6 lens systems which
can be used to obtain such stringent constraints on the amount of
substructure; with the upcoming Sloan Digital Sky Survey, several
hundred new lens systems will be detected, of which a fraction of
$\sim 10\%$ can be used for detailed radio follow-up studies including
VLBI. Hence, over the course of the next $\sim 5$ years there will be
more than 20 galaxies for which we can test for the presence of
substructure, and therefore the presence of satellite galaxies which
are predicted from cosmological CDM models. The influence of the
substructure on time delays, and thus on the determination of the
Hubble constant will be derived. 

Molecular spectroscopy of the lenses will be carried out to study
their interstellar medium, thereby obtaining the chemical evolution
and its relation to the star-formation efficiency. Combined with
optical studies of these lens systems, the relation between molecular
contents and dust obscuration can be derived (note: since a lens
allows the observation of the {\it same} sources through different
sightlines through a galaxy, the reddening of images can be obtained
directly without any assumptions on the unreddened source
spectrum). The current uncertainties of the amount of obscuration, in
particular in star-forming systems, provides the major obstacle in
understanding the global star formation history in the Universe.

Bonn is an ideal place for carrying out this research, combining the
expertise in observations and modelling of lens systems with the
presence of hardware, like the Effelsberg 100m radio-telescope, one
of the cornerstones for high-sensitivity VLBI experiments, the VLBI
correlator, one of only a few in the world and our group has a strong 
presence at the telescopes such as 30m at Pico Valeta, the 10m HHT at
Arizona for molecular spectroscopy research as well as a contributor
to the ALMA project. 

\subsubsection{Estimate of resources expected from DFG}

The research project outlined above requires the participation of
three PhD students. One of them shall be involved in the VLBI
observation of radio lens systems, but the main task will be to
develop an efficient procedure for the reconstructions of the multiple
radio source images using the fact that they are basically linear
mappings of each other. This will reduce significantly the noise of
the resulting images, and at the same time yield the best estimates
for the relative magnification matrices, i.e., that quantity that will
be used in the detailed lens modelling. A second PhD student will work
on the theoretical aspects of this project, developing modelling tools
which yield the constraints on the presence, amounts, and
characteristic scales of substructure present in lenses. The
substructure studies currently available have been very rudimentary,
which is good enough for individual lens systems, but falls short of a
systematic study of a sample of well-studied lenses. The third PhD
student shall combine molecular spectroscopy data of lens systems with
optical observations from the HST, which are publicly available from
the CASTLE survey, and study the relation between molecular contents,
reddening and obscuration. This project will be a healthy mixture
of observational research and theoretical modelling for which Bonn
provides a unique location.

\subsubsection{Members of research group relevant for the project}

Dr. Alok Patnaik (MPIfR), Dr. Karl Menten (MPIfR), Dr. Richard Porcas
(MPIfR), Prof. Peter Schneider (Uni Bonn), Dr. Lindsay King (Uni Bonn).

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

To be filled in later ...

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