%\documentclass[a4paper,12pt]{article}
%\usepackage{epsfig,color}
%\begin{document}

\subsection{Constraining the luminous and dark mass in the Local Group 
through high-precision proper-motion measurements of nearby galaxies
with VLBI.}


{\bf{
{Dr. Heino Falcke}\\
{Max-Planck-Institut f\"ur Radioastronomie}\\
{Auf dem H\"ugel 69}\\
{D-53121 BONN}\\
{Telefon: 0228/525217}\\
{Fax: 0228/525229}\\
{Email: hfalcke@mpifr-bonn.mpg.de}\\}}


\subsubsection{Abstract}
A key and still largely missing parameter for measuring the mass
content and distribution of the Local Group is the proper motion
vectors of its member galaxies. So far only the radial component of
these vectors are known. Already the inclusion of a few galaxies with
the full three-dimensional velocity information would start to break
the ambiguity and degeneracy of current mass models for the Local
Group and its galaxies. The expected proper motion of galaxies on the
sky is typically expected to be between a few milli-arceconds down to
some 50 micro-arcseconds per year. Such motions are well measurable by
radiointerferometry techniques with very long baselines (VLBI).  Ideal
radio targets for such a research are stellar masers in star forming
regions of galaxies such as the bright masers in M33 and IC10.
Multi-epoch observations of these masers can be used to determine a
geometric distance to the galaxies and their proper motion out to one
Megaparsec. This will provide unique data not available through other
means. The proposed project will consist of a) bi-annual monitoring of
the masers in M33, IC10 b) of a systematic search for additional
masers in other galaxies that can and will be included in the VLBI
studies, and c) modelling of the Local Group mass distribution based
on the new data. These observations will then seriously constrain
dynamical models for the Local Group and the mass and dark matter halo
of Andromeda and the Milky Way.

\subsubsection{Current status of research}
An important astrophysical question is the nature and existence of
dark matter in the universe, which had been inferred originally from
the flat rotation curves of galaxies (e.g. Fich \& Tremaine 1991). The
closest place to look for dark matter halos is the Milky Way and
Andromeda in the Local Group. Various attempts have been made to weigh
the galaxies in the Local Group and determine size and mass of the
Milky Way and its not very prominent dark matter halo (Kulessa \&
Lynden Bell 1992; Kochanek 1996). Other attempts use Local Group
dynamics in combination with MACHO data to constrain the universal
baryonic fraction (Steigman \& Tkachev 1999).

The problem when tyring to derive the gravitational potential of the
Local Group is that usually only radial velocities are known and hence
statistical approaches have to be used. Kulessa \& Lynden-Bell (1992)
introduced a maximum likelihood method which requires only the
line-of-sight velocities (Hartwick \& Sargent 1978), but it is
also based on some assumptions (excentricities, equipartition).

Clearly, the most reliable way of deriving masses is using orbits,
which requires the knowledge of three-dimensional velocity vectors
obtained from measurements of proper motions. The usefulness of proper
motions was impressively demonstrated for the Galactic Center where
the presence of a dark mass concentration has been umambiguously
demonstrated by stellar proper motion measurements (Eckart \& Genzel
1996).

However, measuring proper motions of members of the Local Group to
determine its mass is difficult. For the LMC Jones et al. (1994) claim
a proper motion of $1.2\pm0.28$ mas/yr obtained from comparing
photographic plates over a timespan of 14 years.  Schweitzer et
al. (1995) claim $0.56\pm0.25$ mas/yr for the Sculptor dwarf
spheroidal galaxy from plates spanning 50 years in time. Kochanek
(1996) shows that inclusion of these marginal proper motions can
already significantly improve the estimate for the mass of the Milky
Way, since it reduces the strong ambiguity caused by Leo I, which can
be treated as either bound or unbound to the Milky Way. The same work
also concludes that if the claimed optical proper motions are true,
the models also predict a relatively large tangential velocity of the
other statellites of the Galaxy.

The dynamics of nearby galaxies are also important to determine the
solar motion with respect to the Local Group to help define a standard
inertial reference frame (Courteu \& van den Berg 1999). And again, as
Courteu and van den Berg point out ``interpretation errors for the
solar motion may linger until we obtain a better understanding of the
true orbital motion of Local Group members''.

Despite the promising start, the disadvantage of the available optical
work is obvious: a further improvement and confirmation of these
measurements requires an additional large time span of many decades
and will still be limited to only the closest companions of the Milky
Way.

\paragraph{Proper Motions with VLBI}

On the other hand, the expected proper motions for galaxies within the
Local Group, ranging from 1 mas/yr to 20 $\mu$as/yr, are relatively
easy to see with VLBI using the phase-referencing technique. A good
reference point is the motion of Sgr A* - the black hole in the
Galactic Center - across the sky at a speed of 6 mas/yr reflecting the
Sun's rotation around the Galactic Center at a speed of about 220
km/sec. This motion is well detected between epochs separated by only
one month with the VLBA (Reid et al. 1999).

\paragraph*{Useful Local Group galaxies}
The most suitable candidates for such a VLBI phase-referencing
experiment are the strong H$_2$O masers in IC 10 ($\sim$ 10 Jy peak
flux in 0.5 km/sec line, the brightest known extragalactic maser;
Becker et al. 1993) and IC 133 in M33 ($\sim2$ Jy, the first
extragalactic maser discovered). Both masers have been observed
successfully with VLBI~(e.g. Argon et al. 1994, Greenhill et
al.~1993). Additional fainter masers also exist in both galaxies that
can be used to determine accurately the galactic rotation.
The two galaxies belong to the brightest members of the Local Group
and are thought to be associated with M31. 

%Their line-of-sight
%velocities are -344 km/sec and -180 km/sec respectively and are
%located at a distance of about 800 kpc.
%
%The proper motion vectors of the observed masers will consist of
%various contributions, which we list in the following (with numbers for
%M33 roughly valid also for IC 10):
%
%\begin{itemize}
%\item[a)] solar motion around the Galactic Center: 220 km/sec ($\sim$60 $\mu$as/yr at a distance of 800 kpc times the sine
%of the angle between the solar motion vector and the line-of-sight to
%the galaxy);
%\item[b)] motion of M31 with respect to the Milky Way: predicted
%to be $\sim$60 km/sec (16 $\mu$as/yr);
%\item[c)] orbital motion of M33 (or IC 10) around M31: 100-200
%km/sec (25-50 $\mu$as/yr);
%\item[d)] internal galactic rotation: 210 km/sec (55 $\mu$as/yr);
%\item[e)] velocity of individual components: $\sim$20-50 km/sec ($\sim$5-13
%$\mu$as/yr).
%\end{itemize}
%
%The proper motion vectors (a-c) basically depend on the mass of M31
%and the Milky Way and the distance to the galaxies, hence parameters
%we want to constrain with our observations.  The galactic rotation (d)
%is very well determined from HI observations. For the intrinsic
%velocity of maser components (e) we note that through individual maser
%components can have velocities of several tens of km/sec, the average
%velocity (79 components in IC 133) is just a few km/sec and hence
%negligible.

%Depending on how the vectors add up, we can conservatively expect a
%measurable motion of 50-100$\mu$as/yr. With an expected astrometric
%precision of 30-50$\mu$as a 1$\sigma$ proper motion result should be
%achieved within a year.  Roughly half of this detectable motion is due
%to the astrophyscially interesting vectors (a-c). Vector (a), for
%example, simply contains a secular parallax which is, however, not
%independent of the mass of Andromeda and the Milky Way (vectors b \&
%c). 

For a simple model of the Local Group with two dominant galaxies
and a fixed mass ratio between Milky Way and Andromeda (usually
assumed to be 1:1.5) our two proper motion measurements would already
significantly constrain any mass model for the Local Group. In a more
ellaborate approach, which takes the full data set of radial and
proper motions in the Local Group into account (see Kochanek 1996),
the constraints would be even stronger leading to significantly
improved mass estimates and distances.

Additional information can be gained from the measurements of
individual maser components. Since one knows the distance-independent
radial velocity dispersion from the radio spectrum and the
distance-dependent proper-motion dispersion from the VLBI-monitoring,
one can simply determine the distance by matching the two. This has
been demonstrated in a preliminary way already by Argon et
al.~(1998). A similar determination can be made from comparing the
velocities of different maser regions that are found in different
locations in the galaxy but are at a similar radius (as for example is
the case in M33).

Besides those two galaxies there are a number of other galaxies with
tentative detections of stellar maser from old surveys (Huchtmeier et
al.~1978, 1980, 1988) that have not been revisited with current
sensitive receivers, moreover there is no systematic survey of water
masers in Local Group galaxies. Especially there are no masers found
so far in the Milky Way's sister galaxy M31 - in part because it
covers a large area on the sky. The 100m telescope in Effelsberg, now
equipped with new sensitive HEMT receivers, is an ideal instrument to
undertake a succesful survey of starforming region, e.g. those
identified in CO surveys (Neininger et al. 1998), of Local Group
galaxies. Masers found in companions of the Milky Way should exhibit
very large proper motions of the order milliarseconds per year which
could be easily measured within one year at 22 GHz with VLBI.


\paragraph{References}\parindent0cm
{\footnotesize 

Argon et al. 1994, ApJ 422, 585

Argon, A. L., Greenhill, L. J., Moran, J. M., Reid, M. J. \& Menten,
K. M. 1998, ASP Conf. Ser. 144, ``IAU Colloq. 164: Radio Emission from
Galactic and Extragalactic Compact Sources'', p. 235  

Becker et al. 1993, A\&A 268, 483

Crane, Patrick C., Cowan, John J., Dickel, John R. \& Roberts, Douglas
A. 1993, ApJ, 417, L61 

 Eckart A., Genzel R. 1996, Nat 383, 415
Fich, M., Tremaine, S. 1991, ARA\&A, 29, 409

 Greenhill, L. J.,
Moran, J. M., Reid, M. J., Menten, K. M. \& Hirabayashi, H. 1993, ApJ,
406, 482 

 Hartwick, F.D.A., \& Sargent, W.L.W, 1978, ApJ 221, 512

Huchtmeier, W.K., Witzel, A., K{\"u}hr, H., Pauliny-Toth, I.I., Roland, J.,
          1978, A\&A 64, L21 
Huchtmeier, W.K., Richter, O.-G., Witzel, A., Pauliny-Toth, I.I., 1980,
          A\&A 91, 259 
Huchtmeier, W.K., Eckart, A., Zensus, A.J., 1988, A\&A 200, 26 

Kochanek, C.S. 1996, ApJ 457, 228
 Kulessa, A.S., Lynden-Bell,
D. 1992, MNRAS 255, 105

Neininger, N., Gu{\'e}lin, M., Ungerechts, H., Lucas, R., Wielebinski, R., 1998, Nature 395, 871

 Reid, M.J., Readhead, A.C.S, Vermeulen,
R.C., Treuhaft, R.N. 1999, ApJ, in press

 Schweitzer, A. E.,
Cudworth, K. M., Majewski, S.  R. \& Suntzeff, N. B. 1995, AJ, 110,
2747 

 Steigman, G., Tkachev, I. 1999, ApJ 522, 793
}

\subsubsection{Own experience}
This project will be undertaken by a collaboration between the
Max-Planck-Institute and the Center for Astrophysics at Harvard,
consisting of Heino Falcke (MPIfR), Christian Henkel (MPIfR), and Mark
Reid (CfA). Christian Henkel has been involved in the discovery of
most extragalactic masers known to date, many of which were found with
the 100 m telescope in Effelsberg. Similarly, Mark Reid has been in
involved in the development of the VLBI-technique for masers since its
beginning and he is an expert in VLBI astrometry. He has lead many
VLBI-observing campaigns on the masers in M33 and other masers so
far. Heino Falcke is a theorist and an observer who has been involved
in maser search and VLBI observations for the last 4 years. As a
lecturer at the university of Bonn he is currently supervising a PhD
project (Andreas Brunthaler) with the topic of this project.

So far observing proposals for the VLBA and the 100 m telescope in
Effelsberg have been submitted that received an excellent
ranking. First test experiments to find nearby calibrators and test
the astromerty have been performed already which demonstrate the
feasibility of the technique. Effelsberg surveys of some selected
fields in M31, M33, and a few other galaxies are about to commence
this winter.

\subsubsection{Goals of the project}
The goal of the project will be to a) determine the first convincing
proper motions of galaxies like M33 and IC10 with VLBI, b) find new
maser sources in Local Group galaxies that can be used to trace their
proper motion with VLBI, and c) construct mass models for the Local
Group based on these measurements to determine reliably the mass of
the Milky Way, Andromeda and the entire Local group. This will provide
us with a unique estimate of the dark matter content and istribution
in the Local Group.

\subsubsection{Estimate of resources expected from DFG}
The Effelsberg surveys and the VLBI observations require one full-time
position each because of the large data volume expected: one
VLBI-epoch observation of one galaxy will typically have about 10 DAT
tapes of data. The surveys are an ideal starting project for one or
several PhD theses, while the VLBI-observations require more skills
and are suitable for a PostDoc. To get reliable proper motion
measurements one has to continue observing over several years - the
error will decrease with the length of the project. Similarly, the
Effelsberg surveys have to be performed over several years to achieve
completeness. Hence, the minimum requirement for the project are one
PhD student and one PostDoc over the entire duration of the SFB.

In addition we will need the computing and data storage resources for
the data reduction (2 powerful work stations plus periphery and large
harddisks of $\sim$ DM 25.000,- each). We also need travel funds
mainly for collaboration with Harvard, scientific conferences, and the
invitation of external experts of about DM 10.000,- per year.

\subsubsection{Members of research group relevant for the project}
Dr. Heino Falcke, MPIfR Bonn (PI)\\
Dr. Christian Henkel, MPIfR Bonn (Effelsberg)\\
Prof. Mark Reid, MPIfR Bonn (VLBI)\\
Dipl. Phys. Andreas Brunthaler (student)\\

\subsubsection{Connections to other projects of current SFB proposal}
This project will determine the presence and amount of dark matter on
scales between the Galaxy and large galaxy clusters. Naturally, proper
motion studies can only be done for small distances, hence the Local
Group is an ideal target. At larger distances such small groups are
difficult to treat observationally since techniques like X-ray
observations and gravitational lensing only sufficiently work for
large clusters of galaxies. On the other hand conventional stellar
astrometry with optical interferometers will only works on scales of
our Galaxy. Hence, in order to obtain information on the dark matter
content on all scales, VLBI is the most promising technique to probe
the Local Group scale.
%\end{document}

