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\subsection{Gravitational field and galactic mass distribution} %Please give

{\bf{
{Dr. \ P.M.W.\, Kalberla and Dr. \ J. Kerp}\\
{Radioastronomisches Institut der}\\
{Universit\"at Bonn}\\
{Auf den H\"ugel 71}\\
{D-53121 BONN}\\
{Telefon: 0228/735769/ 733667}\\
{Fax: 0228/731775}\\
{Email: \ pkalberla@,astro.uni-bonn.de \ jkerp@astro.uni-bonn.de}\\}}

\subsubsection{Abstract}
Current dark matter models, favoring cold dark matter (CDM), 
successfully describe the mass distribution on scales of 
clusters of galaxies and on larger scales. 
All models, however, fail on galactic scales. We intend 
to focus our attention to galactic scales and 
investigate the mass distribution within galaxies 
(radius R$<$ 50 kpc) and their halos (R$<$ 500 kpc).

Our approach is based on model calculations which already 
successfully describe 
the mass distribution of the Milky Way and similar spiral galaxies 
as a composition of isothermal disks 
(DM, stars, molecular-, neutral- and ionized gas) 
and an isothermal sphere representing 
the a more extended dark matter component. Our model, 
based on a self-consistent 3-D determination of mass and potential, is 
able to satisfy all known observational constraints in our Galaxy.  

We aim to generalize our model and match also mass distributions of low 
surface brightness and dwarfs galaxies to the observational 
constraints. The major burden is the computational effort 
which is needed to determine the mass distribution, 
appropriate to the observations,  for such systems in a 
self-consistent way. 

\subsubsection{Current status of research}

CDM may be considered as the leading cosmological model which has 
its merits on large scales. Here we intend to focus on 
smaller galactic scales. 

The current dark matter hypothesis fails to explain the dark matter 
distribution in galaxies. The severity of 
the mass discrepancy in spiral galaxies is strongly correlated 
with the central surface brightness of their disks. The lower the 
surface brightness, the larger the discrepancy (McGaugh \& Blok 1998). 

Mass models for the Milky Way (Dehnen \& Binney 1998) encounter a 
similar problem. Minor modifications of the mass model in the 
center of the Galaxy cause significant changes of the dark 
matter distribution on large scales. Apparently the tail is wagging the dog. 

In our local vicinity we find inconsistencies due to 
the standard halo model which has been used.  
If we consider $K_z$, the gravitational acceleration perpendicular 
to the disk, we have the problem that the general accepted 
$K_z$ relation (Kuijken \& Gilmore 1989) implies continously rising 
gravitational forces with increasing distance $|z|$ from the disk, 
a rather unphysical assumption.

Even in the Milky Way halo and the local group on scales up to 
1000 kpc, we encounter 
significant discrepancies between predictions based on CDM models and 
observations. The number of observed satellite galaxies in the 
local group is by far too low in 
comparison with model predictions (Moore et al. 2000). High velocity 
clouds (HVCs) have been proposed to carry the necessary amount of dark 
matter as members of the local group.

\subsubsection{Own experience}

Within the last years we have made considerable efforts to observe and 
model the gaseous Galactic halo (e.g. Pietz et al. 1998, Kalberla et al. 1998). 
We describe the halo gas as a multi phase medium which is in equilibrium 
with magnetic fields and cosmic rays (Kalberla \& Kerp 1998). Common to all 
these investigations is the determination of the scale height of the 
gaseous halo. For the solar vicinity we derive an exponential scale height 
of 4.4 kpc, common for HI gas, hot plasma ($ T = 10^{6.2}$ K) and highly 
ionized gaseous phase ($ T \sim 10^5$ K).

These investigations provide an important constraint for the dark matter 
distribution in the Milky Way which was not considered previously. 
The gaseous halo may be used as a tracer 
for the gravitational potential perpendicular to the Galactic disk. 
The observed HI gas allows to determine the rotation curve at high 
z-distances. Most important, however, is the hottest ($ T = 10^{6.2}$ K) 
phase. Its distribution unambiguously reflects the potential outside the disk. 

Based on our hydrostatic halo model (Kalberla \& Kerp 1998) 
we developed a procedure 
to determine the mass distribution in the Milky Way which explicitely 
fits the observed vertical mass distribution in the Milky Way. We use 
isothermal disks to represent the density distribution of 
dark matter and the observed mass components and 
use an iterative scheme to solve 
the Poisson equation in 3-D. Observed mass components as well as 
DM distribution are constraint by observational facts 
such as rotation curve in $R$ and $|z|$, 
radial scale lengths for stars and gas, their surface densities, 
local gravitational acceleration $K_z$, observed and 
dynamical mass density (Oort limit) as well as scale heights 
of the stellar and gaseous mass components and their flaring  
with galactocentric radius R. 

Our calculations result in two distinct different 
dark matter components. The gaseous disk is associated with an 
isothermal dark matter disk which has a scale height of 4 kpc. 
This mass component dominates the rotation curve on scales 
$R < 50$ kpc. In addition we find evidence for a more extended halo 
component which dominates the mass distribution on scales 
($ 50 < R < 350$ kpc) and can be fitted best by an isothermal sphere.

\subsubsection{Goals of the project}

The isothermal mass model derived by us fits the observations on 
galactic scales much better than previous models which were based 
on isothermal DM spheres only. A flattened dark matter disk implies 
a significant baryonic dark matter component in the Milky Way which is 
linked to the visible matter. Assuming that the extended (spherical) 
dark matter halo is non-baryonic we derive that 13\% of the Galactic 
mass within $R < 350$ kpc is in baryonic form. We find in addition
that the baryons carry 12\% of the total angular momentum in the Milky Way. 
The baryon fraction is in good agreement with current cosmological 
models. The rotation characteristics of baryonic and non-baryonic matter 
implies that during the formation of the Galactic disk 
most of the angular momentum was conserved.

Our analysis implies that baryonic and non-baryonic dark matter have 
distinct different spatial distributions. A significant fraction of the 
dark matter couples directly with the visible mass in stars and gas. 
Our self-consistent calculations indicate that such coupling of 
(presumably baryonic) dark matter with the stellar distribution is 
strongest close to the Galactic center. This is exactly the behavior 
of the dark matter which is needed to solve the discrepancies between 
the current dark matter hypothesis and the observations as discussed 
in Sect. 1.2. Our self-consistent solution is stable against 
changes in the stellar distribution, the tail is no longer wagging the 
dog. Also the gravitational forces are no longer rising to infinity. 
Our model predicts that HVCs are born within the baryonic 
Galactic halo. The spatial distribution is entirely consistent with 
recent observational distance constraints from optical emission 
lines as reported by Weiner et al. (2000). 

Based on the successfull application of our method to the Milky Way,  
we propose to extend our investigations to extragalactic systems. 
In particular we would like to apply the model calculations 
also to LSB and dwarf galaxies. 
Sources of interest should have well defined observational constraints 
which allow to model the mass distribution. Of special interest are 
those objects which cannot be fitted with current models 
(for discussion see e.g. McGaugh \& Blok 1998). \\
\\

\noindent{\bf References:}\\
Dehnen W., \& Biney J., 1998, MNRAS 294, 429\\
Kalberla P.M.W., Kerp J., 1998, A\&A 339, 745\\
Kalberla P.M.W., Westphalen G., Mebold U., Hartmann Dap., Burton W.B., 1998, A\&A 332, L61\\
Kuijken K., Gilmore G., 1989, MNRAS 239, 651\\
McGaugh S.S., \& de Blok, W.J.G., 1998, ApJ 499, 41\\
Moore B., Gelato S., Jenkins A. et al., 2000, ApJ 535, L21\\
Pietz J., Kerp J., Kalberla P.M.W., et al., 1998, A\&A 332, 55\\
Weiner B.J., Vogel  N., Williams T.B., 2000, astro-ph/0008263

\subsubsection{Estimate of resources expected from DFG}

The main burden of our proposal is that extremely CPU expensive 
calculations are needed. At present the calculations need 1-2 CPU weeks on 
a DEC433au workstation for a single parameter set.  
This is due to the iterative method 
which is needed to determine from an observed surface density 
distribution the self-consistent 3-D distributions in mass and gravitational 
potential which solve the Poisson equation. A fast workstation is 
needed for program development, testing. 

Despite programming and model fitting, it is necessary to obtain useful 
observational constraints. Here we assume that most of the necessary 
data are available in literature or can be obtained in 
collaboration with other projects of the current SFB proposal. 

We apply for a fast 667 MHz XP1000 workstation (20.000.- DM) and for 
a post doc position (alternatively, this work can be 
done by 2 Ph.D. students).

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

Dr. \ P.M.W.\, Kalberla and Dr. \ J. Kerp, 
Radioastronomisches Institut der Universit\"at Bonn\\


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

Our proposal is closely related to the proposal ``structure of dark matter 
halos in galaxies'' which emphasizes on observational aspects.  


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