------------------------------------------------------------------------
From: "Andrew S. Wilson"  wilson@astro.umd.edu 
To: hfalcke@mpifr-bonn.mpg.de

\documentclass[letterpaper,twocolumn]{esapuba}

\title{Studies of Galactic Nuclei with Darwin} 
 
\author{Andrew S. Wilson}
\affil{Astronomy Department, University of Maryland, College Park, MD
20742,
U.S.A.
\\
and\\
Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD
21218}

%\lefthead{LEFT head}
%\righthead{RIGHT head}
\begin{document}
\maketitle

\begin{abstract}
This paper describes a number of potential observing programs for Darwin
in
the area of galactic nuclei. Observations of our Galactic centre at the
shorter wavelengths (5 $\mu$m) covered by Darwin will detect large
numbers of
stars.
Extrapolation of the existing K band counts to the flux levels expected
to
be reached by Darwin in 1 hour suggests $\sim$ 5,000 detectable stars
(arc sec)$^{-2}$ around the compact radio source Sgr A$^{*}$, which is
commonly believed to be associated with a
black hole of mass 2.6 million M$_{\odot}$.
Over its lifetime,
Darwin will be capable of exquisitely
accurate measurements of stellar proper motions, including the ability
to
follow entire stellar orbits around the hole for stars with orbital
radii
$\sim$ 10$^{-3}$ pc.
It may also be able to observe the general relativistic advance
of the pericenter of stellar orbits somewhat closer to the hole. Stars
behind 
the hole will be gravitationally lensed by it.
It appears that the probability
of observing a lensing event at any given time is of order unity at
Darwin's
resolution and sensitivity, so this 
should be a rich area of research. Darwin will measure the 
infrared spectrum of Sgr A$^{*}$ with a gain of $\sim$ 4 orders of
magnitude
of sensitivity over present upper limits, easily detecting the source if
it 
conforms to
the predictions of current ADAF models.
Stars which approach too close to the black hole will be tidally
disrupted by it, and Darwin's resolution is sufficiently good to
spatially
separate such a tidally disrupted red giant or supergiant from the
black hole itself. However, the event rate is almost certainly too low
for such
a disruption to be seen in the mission lifetime.
Dust shells around
stars in the vicinity of the Galactic centre 
will be promising candidates for study. Darwin will be able to study the
stellar luminosity function and stellar proper motions in the nucleus of
M31. The possibility
of using the stellar proper motions to estimate the mass of the nuclear
black
hole is discussed.

Potential investigations of the distributions of warm dust and gas in
the
nuclei of nearby active galaxies are described. Darwin should be able to
image the dusty accretion disks in Seyfert galaxies, compact starbursts
around
active nuclei and, depending on the available spectral resolution, study 
the
stratification of different ionic species through observations of
fine structure lines. It may be possible to resolve the broad line
region if
the wavelength coverage extends to short enough wavelengths. Darwin's
nulling mode will be valuable for blocking the bright, compact light of
quasars and investigating the kinematics of the surrounding gas. Whether 
stars, gas or dust are observed, galactic
nuclei present
densely-populated, bright fields,
so the primary technical requirement for good
imaging fidelity is very extensive coverage of the uv plane.
\end{abstract}

\section{Introduction}

The expected field of view of Darwin - a few arc sec - and best
resolution -
a few milliarcsec (mas) - will allow
detailed studies of individual galactic nuclei.
Stars, gas and dust will be observable given Darwin's anticipated
wavelength
coverage of 5 to 28 $\mu$m. I shall focus here on studies of stars in
our
own Galactic centre and M31, and studies of gas and dust in active
galactic
nuclei 
and quasars. A more complete discussion of Darwin's capabilities on
active
galaxies can be found in the paper by Ward in these proceedings. 

Estimates of the resolution and sensitivity of these observations
must, inevitably, be tentative given the early state of mission
planning.
However, when such estimates are appropriate, I shall assume a
resolution of
2 mas 
at 5 $\mu$m and an approximate sensitivity of 1 $\mu$Jy for
a S/N of 5 in 1 hour's observation, as given in the Darwin web site.
Most of
the studies described will involve imaging mode observations and will
require
adequate coverage of the uv plane given the complex structures expected
at
mas resolution in galactic nuclei. Nulling mode will also be valuable
for cases, such as quasars, in which a bright, compact source dominates
the
infrared light.

\section{The Galactic Centre}

\subsection{The Dark Mass at the Galactic Centre}

It has long been suspected that a black hole with
mass of order a million solar masses resides at the nucleus of of our
Galaxy
(e.g. Genzel \& Townes 1987). Recently, the evidence has become much
stronger
thanks to the development of shift-and-add speckle imaging plus CLEAN
techniques
in the near infrared
(observations in the optical are precluded by the high obscuration of
A$_{V}$ $\simeq$ 30 mag). The pioneering work of the MPE (Garching) and,
more recently, the UCLA groups has provided images of the stars in the
galactic
centre region at K band with resolutions of 0.15$^{\prime\prime}$
(0.0058 pc)
and 
0.05$^{\prime\prime}$ (0.0019 pc), respectively (Genzel et al. 
1997a; Ghez et 
al. 1998). Of particular interest is the region near Sgr A$^{*}$, the
ultracompact
(e.g. Lo et al. 1998), peculiar radio source which appears to coincide
with the
dynamical centre of the Galaxy. Here one finds a 1$^{\prime\prime}$
(0.038 pc)
diameter 
concentration of faint stars with high proper motions. Observations over
the period 1992 to the present have revealed proper motions of up to
1,400
km s$^{-1}$; the proper motions decline with increasing distance from 
Sgr A$^{*}$. The projected velocity dispersion declines as p$^{-1/2}$,
where $p$ is the projected distance from the Galactic center, between
$p$ $\sim$ 1 pc and $p$ $\sim$ 0.01 pc (Genzel et al. 1997a;
Ghez et al. 1998;
see also Genzel \& Eckart 1999).
The peaks of both the stellar surface density and the velocity
dispersion are
consistent with the position of Sgr A$^{*}$ to within
0.2$^{\prime\prime}$
(Ghez et al. 1998). These stel-

\vskip 6.5cm

\noindent
Fig. 1 (from Genzel et al. 1997a). Mass modelling of the stellar proper
and
radial motions in the Galactic centre, with the addition of two points
from
gas kinematics at R = 1.5 and 4 pc. Shown as filled circles with
1$\sigma$ error bars are various mass estimates.
The thick dashed curve represents the
mass model of the (visible) stellar cluster. The thin continuous curve
is the
sum of this stellar cluster and a point mass of 2.61 $\times$ 10$^{6}$
M$_{\odot}$. The thin dotted curve is the sum of the visible stellar
cluster and
a Plummer model of a dark central cluster. See original paper for
further
details.

lar dynamical data have been analysed to derive
the enclosed mass as function of $p$. Both groups find that at $p$ $>$ 1
pc,
the enclosed mass increases with $p$ and is consistent with the mass
model for
the
visible stellar cluster with a core radius $R_{core}$ = 0.38 pc. Within 
$p$ = 0.1 pc, the enclosed mass flattens out reaching a constant value
of
2.6 $\times$ 10$^{6}$ M$_{\odot}$ (Fig. 1). The data are formally
consistent with a
compact ($<$ 0.01 pc) cluster of dark (M/L $>$ 100) stars with central
density
2.2 $\times$ 10$^{12}$ M$_{\odot}$ pc$^{-3}$, but such a cluster cannot
be stable for more than 10 million years (e.g. Maoz 1995; Genzel \&
Eckart
1999). The general (but not universal) conclusion is that the dark mass
is a
black hole of mass 2.6 $\times$ 10$^{6}$ M$_{\odot}$.

\subsection{Darwin Observations of the Galactic Centre}

We can expect major advances in our knowledge of the stars and the
putative
black hole in the Galactic centre before
Darwin flies. For example, the VLT and Keck interferometers, observing
in the
near
infrared, are expected to make a major impact on many of the topics
discussed
below. I shall, nevertheless, describe
how Darwin will enhance our understanding taking ``present knowledge''
as 
my baseline. Darwin observations of the Galactic centre may be limited
by its
proximity to the ecliptic. Confusion of observations by zodiacal dust
emission
will need to be assessed on a case by case basis and such is not
attempted
here.

\subsubsection {Stellar Luminosity Function}

Recalling that 1 $\mu$Jy corresponds to an apparent magnitude at $M$
band of
m$_{M}$ = 20.65, this sensitivity corresponds to M$_{M}$ = 5.4 if
A$_{M}$ = 0.7 mag (Rieke \& Lebofsky 1985) or M$_{M}$ = 4.4 if A$_{M}$ = 
1.7 mag (Lutz et al. 1996). Such stars, if observed at 2 $\mu$m, would
have 
m$_{K}$ = 22 - 23 mag. This is a major advance on current ground-based
observations, which reach m$_{K}$ $\simeq$ 17 mag. For comparison, 
M$_{M}$($\odot$) = 3.3. Thus, in this relatively short integration,
Darwin will
be capable of imaging stars 1 - 2 magnitudes less luminous
than a solar-type star.
Such an observation will have major ramifications for the stellar
population
and star formation history in the Galactic centre.

To estimate how many stars might be visible to these magnitudes, I have
extrapolated the number counts as a function of m$_{K}$ within the
central
arc second (Genzel et al. 1997a; Ghez et al. 1998) using a continuous
star
formation model kindly provided by Don Figer. The result is 5,500 stars
(arc sec)$^{-2}$ with m$_{K}$ $<$ 23; the average separation of the
stars
on the sky is 13 mas. It should be emphasised that this stellar
surface density
is strongly dependent on the model of star formation adopted. With 
a 2 mas resolution, Darwin would be able to separate the stars
cleanly in this example, provided sufficient fringe visibility
measurements are made.
For an interferometer with N elements, the number of simultaneous
measurements
of visibility is N(N-1)/2, which is 6 if N = 4 or 15 if N = 6. To image
these 5,500 point sources (assuming a field of view of 1 arc sec), at
least
that number of visibility
measurements would have to be made. This example emphasises that
obtaining
adequate uv coverage to image
the Galactic centre will be a challenge for Darwin.

\subsubsection {Stellar Proper Motions}

It will be possible to measure stellar proper motions with Darwin
through multi-epoch imaging,
providing a much stronger check on the
expected Keplerian behaviour of the velocities than
hitherto possible.
Assuming that all the 5,500 stars (arc sec)$^{-2}$ are physically within
0.019 pc (i.e. 0.5 arc sec) of the center, we may expect to find at
least one 
star within 10$^{-3}$ pc of the centre. Such a star would have a
Keplerian
velocity of 3,400 km s$^{-1}$ and an orbital period of 1.8 yrs. Thus
entire orbits could be imaged in Darwin's lifetime. Orbital curvature,
which would prove that the stars are, indeed, bound to the Galactic
centre
and not just ``passing through'' should be measurable at much larger
radii.

The general relativistic advance of peribothron (from the Greek
``bothros'',
meaning pit - Frank \& Rees 1976) may also be measurable.
The angle of precession per revolution due to this effect is

\begin{equation}
\Delta\phi = 6 \pi \xi^{-1} (1+e)^{-1}
\end{equation}

where $\xi$ is the pericentre distance in units of the gravitational
radius of the central object ($\xi$ = $r/r_{g}$, $r_{g} = GM/c^{2}$),
and $e$ 
is the orbital eccentricity. The precessional period may thus be written

\begin{equation}
P_{gr} = 16 M_{6} \xi_{3}^{5/2} \hspace{1mm} {\rm yr}
\end{equation}

where $M_{6}$ = $M_{h}$/10$^{6}$ M$_{\odot}$ and
$\xi_{3}$ = $\xi/10^{3}$.
If we consider a star at $r$ = 6 mas = 2.3 $\times$ 10$^{-4}$ pc from
the
black hole, $\Delta\phi$ $\simeq$ 0.4$^{\circ}$, the period of the orbit
is
about 0.2 yrs and $P_{gr}$ = 180 yr. Thus in a 5 year Darwin mission,
the
angle of precession would be $\sim$ 10$^{\circ}$, which may well be
measurable.
This could be the first unambiguous observation of a general
relativistic
advance of the pericenter in a galactic nucleus. Of course, there could
be a 
contribution to the observed advance from the gravity of the nuclear
``cusp''
stellar 
cluster; the magnitude of this effect
would have to be evaluated through modelling of the stellar
distribution.

\subsubsection {Gravitational Lensing of Stars by the Putative Black
Hole}

The Einstein radius for gravitational lensing by an object of mass
$M_{h}$ of a star a distance $r$ behind
the mass is given by (e.g. Alexander \& Sternberg 1999)

\begin{eqnarray}
R_{E} & = & \left({4GM_{h}Dr\over{c^{2}(D+r)}}\right)^{1/2} \cr
      & = & 2.2 \times 10^{15} (M_{2.6}r_{1})^{1/2} \hspace{1mm} {\rm
cm}
\end{eqnarray}
where $D$ is the distance from the observer to the mass,
$M_{2.6} = M_{h}/2.6 \times 10^{6} M_{\odot}$ and $r_{1} = r/1$ pc.
The angular size of the Einstein radius is

\begin{equation}
\theta_E = 0.018 D_{8}^{-1} \left(M_{2.6} r_{1}\right)^{1/2}
\hspace{1mm} {\rm arc sec}
\end{equation}

where $D_{8}$ = $D$/8 kpc. 
$\theta_E$ represents the characteristic angular scale of gravitational
lensing; a useful criterion for lensing is that the true position of the
source should lie within its Einstein ring (Turner, Ostriker \& Gott
1984). 

Gravitational lensing of stars by the putative Galactic centre black
hole has been discussed by Wardle \& Yusef-Zadeh (1992) and 
Alexander \& Sternberg (1999).
Lensing produces two images of each star that lies behind Sgr A$^{*}$.
One image is always brighter than the source and lies outside the
Einstein
ring, the other is fainter than the first and lies within the ring
(Wardle \& Yusef-Zadeh 1992). Large magnifications require the star to
lie almost directly behind the black hole. Thus the proper motions
induce
changes in the magnification on a timescale (Wardle \& Yusef-Zadeh 1992)

\begin{equation}
\Delta t \sim \left({|X|\over{10}}\right)
\left({\theta_E\over{20 \hspace{1mm}
\mbox{\rm mas}}} \right) 
\left({V_{\perp}\over{100 \hspace{1mm} \mbox{\rm km
s$^{-1}$}}}\right)^{-1}
\hspace{1mm} {\rm yr}
\end{equation}

where $|X|$ is the magnification and $V_{\perp}$ is the transverse
velocity.
The two images should lie on either side of Sgr A$^{*}$ and their
brightnesses
will rise and fall almost together, with a small time delay.

Wardle and Yusef-Zadeh (1992) considered lensing of the large scale
visible
stellar cluster adopting a core radius
r$_{c}$ = 10$^{\prime\prime}$ = 0.38 pc,
within which the stellar number density is assumed 
constant. Equation (4) shows that the
Einstein radius for a star at this distance from the putative black hole
is
11 mas, so the two images of most lensed stars in this cluster will be
spatially separated by Darwin. Alexander \& Sternberg (1999) modelled
the
stellar population using modern data and calculated lensing rates, but
were
mainly concerned with microlensing (events in which the amplified images
are detected but the two images are not spatially separated) 
in view of current
limitations on observational sensitivity and resolution.

Tal Alexander has kindly adapted his work to the sensitivity and
resolution of
Darwin. He considers two alternative models for the stellar
distribution. The first is a flattened isothermal model
with r$_{c}$ = 0.38 pc and $\rho_{0}$ = 4 $\times$ 10$^{6}$ M$_{\odot}$
pc$^{-3}$
(Genzel et al. 1996,
1997a). The second is a ``cusp'' model, approximated as a flattened 
isothermal stellar system with r$_{c}$ = 0.038 pc and
$\rho_{0}$ = 2 $\times$ 10$^{8}$ M$_{\odot}$ pc$^{-3}$.
These models give surface densities of 2,750 and 6,000
stars (arc sec)$^{-2}$, respectively, at Darwin's sensitivity. In the
first
model,
the rate of
spatially unresolved lensing events (i.e. stars
with $r_{1}$ $<$ 0.01, see equation (4)) is $\sim$ 
0.006 yr$^{-1}$ 
with timescale $\sim$ 0.03 yr, while spatially resolved lensing events
($r_{1}$ $>$ 0.01) occur at a rate of $\sim$ 0.22 yr$^{-1}$ with
timescale $\sim$ 3.4 yr.
In the second model, the 
unresolved lensing rate 
is $\sim$ 0.13 yr$^{-1}$ with timescale
$\sim$ 0.03 yr, and the resolved lensing rate 
is $\sim$ 0.33 yr$^{-1}$ with
timescale $\sim$ 0.8 yr.
While the details of these predictions are quite uncertain,
Alexander concludes that the probability of seeing a resolved lensing
event
with Darwin at
any given time is of order unity. Measurement of the actual lensing
rates,
timescales etc.
can thus confirm that the dark mass is highly concentrated, and so
probably a
black hole, and give valuable information on the properties
of the stellar cluster.

Thus, observations of stars at the Galactic centre will provide rich
information on both genuine stellar proper motions and gravitational
lensing.
Indeed,
as both effects lead to apparent stellar motions, disentanging the two
could be challenging, but the scientific rewards will be substantial.

\subsubsection{Infrared Spectrum of Sgr A$^{*}$}

The spectrum of the ultracompact radio source Sgr A$^{*}$ has been 
measured over a wide range
of radio frequencies (Fig. 2) and the source
has been detected
with VLBI experiments at frequencies as high
as 215 GHz (Krichbaum, Witzel \& Zensus 1999). Recently, Genzel \&
Eckart
(1999) have reported a possible detection of Sgr A$^{*}$ in deep K band
images. They report a source, dubbed S12, detected with m$_{K}$ $\sim$
15
in 1996 and 1997, but undetected in 1992, 1994 and 1998, when the source
was  
fainter than m$_{K}$ $\sim$ 16.3. Source S12 is coincident with
Sgr A$^{*}$ to within the $\pm$ 30 mas uncertainties of the 
radio-infrared reference frames (Menten et al. 1997). This source could
be variable emission from Sgr A$^{*}$ itself, a star which has been
gravitationally lensed by the black hole,
or even a variable star. Alexander \& Sternberg (1999) find that the
probability
that a microlensing event could have been observed during the course of
the
proper motion studies carried out so far is only $\sim$ 0.5\%. The
luminosity of S12 is marked on Fig. 2.

The large gain of sensitivity and resolution to be achieved with Darwin
will
define the spectrum of Sgr A$^{*}$ over the 5 - 28 $\mu$m range if 
appropriate imaging mode observations are possible.. 
The sensitivity I have assumed for Darwin corresponds to log
[$\nu$L$_{\nu}$]
$\simeq$ 10$^{30 - 31}$ erg s$^{-1}$ at the Galactic centre (after
allowing
for an extinction of 1.7 mag at the shorter wavelengths). Fig. 2
shows that this represents a
sensitivity improvement of $\sim$ 4 orders of magnitude over present
upper
limits. Narayan et al.
(1998) have fitted the spectrum of Sgr A$^{*}$ with an Advection
Dominated
Accretion Flow (ADAF) model (solid curve in Fig. 2).
Their model predicts a luminosity of
log [$\nu$L$_{\nu}$] $\simeq$ 10$^{34}$ erg s$^{-1}$ in the Darwin
range, where
the emission is dominated by Compton-scattered synchrotron radiation
plus
the high frequency tail of the thermal synchrotron radiation, both of
which are 
generic features of ADAF models. Thus failure to
detect Sgr A$^{*}$ with
Darwin would pose a severe problem for an ADAF model. Purely
from a phenomenological perspective, it is highly probable Sgr A$^{*}$
will be detected, because non-detection at Darwin sensitivities would
imply a
large drop of 
$\sim$ 10$^{4}$ in flux density between 4 $\times$ 10$^{11}$ and
10$^{13}$ Hz.

\vskip 8.5cm

\noindent
Fig. 2 (adapted from Narayan et al. 1998). Open and filled circles
represent various flux measurements and upper limits of Sgr A$^{*}$.
The filled circles are considered to be more important as model
constraints.
The point with error bars at K band represents the possible detection of
Sgr A$^{*}$ by Genzel \& Eckart (1999) - see text. The curved solid line
is an
ADAF model developed by Narayan et al. The dotted and short-dashed lines
are thin accretion disk models with different mass accretion rates.
The tilted, straight, solid line segment between 10$^{13}$ and
10$^{14}$ Hz represents the projected Darwin sensitivity of 1 $\mu$Jy
for
the Galactic centre assuming an obscuration of A = 1.7 mag at all
wavelengths (the obscuration should be smaller, and the sensitivity
better,
than indicated here
at the longer wavelengths covered by Darwin; no allowance has been made
for confusion by zodiacal light).

\subsubsection{Tidal Disruption of Stars by the Black Hole?}

A star which approaches too closely to the black hole may be tidally
disrupted
by it. Such disruption requires (e.g. Rees 1988)
\begin{equation}
%M_{h} / {r}^{3} > m_{*} / {r_{*}}^{3}
{M_{h}\over{r}^{3}} > {m_{*}\over{r_{*}}^{3}}
\end{equation}
or
\begin{equation}
r_{T} \simeq 5 \times 10^{12} M_{6}^{1/3} \left(r_{*}/r_{\odot}\right)
\left(m_{*}/m_{\odot}\right)^{-1/3} \hspace{1mm} {\rm cm}
\end{equation}

where $r_{T}$ is the tidal radius, $m_{*}$ the stellar mass and $r_{*}$
the stellar radius.
For the Galactic centre, I have estimated the tidal disruption radii of
various
types of stars:

\noindent
Solar, $r_{T} \sim 18 r_{g}$

\noindent
Red giant, $r_{T} \sim 1800 r_{g}$

\noindent
Red supergiant, $r_{T} \sim 6300 r_{g}$

\noindent
Blue main sequence supergiant, $r_{T} \sim 62 _{g}$

Evidence claimed in favor of stellar tidal disruption by massive
black holes includes the 
appearance of double-peaked, broad emission lines in the nuclei of a few
active
galaxies (e.g. NGC 1097, Storchi-Bergmann et al. 1997) and X-ray flares
from `normal' galaxies (e.g. Komossa \& Bade 1999). However, there are
plenty
of other ways to account for such observations. Direct observation of
the tidal
disruption of a star by a black hole would be an extraordinary event and
a major
coup for the telescope which first does it. The key is to have
sufficient
spatial resolution to resolve $r_{T}$, so the star can be separated from
any
nuclear emission. Darwin's best resolution of 600$r_{g}$ would allow
such
separation for the red giant and supergiant stars. The catch is that we
would 
be extremely lucky to see such an event.
While the tidal disruption rates should be recalculated using modern
knowledge of the nuclear ``cusp'' stellar cluster, the disruption rate
for giant stars can be crudely estimated at $\sim$ 5 $\times$ 
10$^{-4}$ yr$^{-1}$ using the work of 
Frank \& Rees (1976), Rees (1988) and Rees (1990); this rate is subject
to
many uncertainties, as these papers point out. It is thus unlikely that
such
an event would be seen in the Galactic centre during Darwin's mission.

\subsubsection{Spatially Resolved Dust Shells} 

IRS 21 is an unusual source in the central parsec of the Galaxy.
Observations reveal polarization, an IR excess and a featureless
spectrum
(see Tanner et al. 1999 and references therein). The object has been
variously
proposed to be a protostar, a dust embedded early-type star, a dusty
Wolf Rayet
star and a high density dust clump. Recent observations by Tanner et al.
(1999) with the Keck telescope at K band have resolved this source
showing
it has an intrinsic size of $\sim$ 1,000 AU. The shape of the infrared
spectrum suggests there are two components - a warm one seen at 2 - 4
$\mu$m
and a cool one seen at 8.7 and 12.4 $\mu$m. Modelling of the spectral
energy distribution suggests the cool
component has T$_{cool}$ = 210 K, R$_{cool}$ = 480 $\pm$ 100 AU and
L$_{cool}$ = 1.8 $\times$ 10$^{4}$ L$_{\odot}$. Tanner et al. (1999)
note 
the agreement
between the measured K-band extent (which applies to the warm component)
and the size inferred for the cool component from the model. They
suggest
that the cool dust is responsible for scattering the 2.2 $\mu$m emission
from the warm component. The waveband of Darwin (5 - 28 $\mu$m) and its
high
spatial
resolution are ideally matched to studying an object of this type.
Darwin
will be able to image the dust in both the warm and cool components and
thus
test the model proposed by Tanner et al. (1999).

\section{M31}

Here I consider the possibilities for studies of the stellar luminosity
function and proper motions in M31, analogous to the above discussion
for the
Galactic centre.
Adopting our canonical sensitivity of m$_{M}$ = 20.65, stars brighter
than
M$_{M}$ = --3.48
will be detectable in M31 (distance 670 kpc). These detectable
stars comprise main sequence O stars, some giants and all supergiants.
For 
comparison, stars which will be just detectable by Darwin in M31 would
have
m$_{K}$ $\simeq$ 14 if transported to the Galactic centre (since
m$_{K}$ $\simeq$ m$_{M}$ for stars, and assuming no obscuration towards
the center of M31 and A$_{K}$ = 3.0 mag to the Galactic centre). This
value
of m$_{K}$ is $\sim$ 2 - 3 mag brighter than the sensitivities currently
reached in ground-based K band imaging on the Galactic centre (Genzel et
al.
1997a; Ghez et al. 1998). However, the {\it linear} resolution to be
achieved
by Darwin on M31 (2 mas angular resolution at a distance of 670 kpc)
will be
similar to that achieved by Genzel et al. (1997a)
on the Galactic centre (150 mas angular resolution at a distance of 8
kpc).
Assuming similar stellar populations in M31 and the Galactic centre,
Darwin's image of the stars in the nuclear regions of M31 could resemble
the image of the Galactic centre shown as Fig. 2 in Genzel \& Eckart
(1999),
but with 2 - 3 mag less sensitivity. The total stellar surface density
would
then 
be $\sim$ 15 - 60 times less than in Genzel \& Eckart's image, so the
mean
projected stellar separation would be 4 - 8 times larger. However,
M$_{h}$ = 3.3 $\times$ 10$^{7}$ M$_{\odot}$ for M31
(Kormendy \& Richstone 1995), a factor of $\sim$ 12 times larger than in
the
Galactic centre. Thus, a given absolute Keplerian velocity should be
found at a 
linear distance from the hole which is $\sim$ 12 times larger in M31
than in the
Galactic centre, compensating for the lower projected stellar
separation. These
crude estimates suggest that stellar proper motion work, leading to an
independent measurement of the nuclear black hole mass in M31, may well
be
possible with Darwin.
  
\section{Nearby Active Galactic Nuclei}
\subsection{Introduction}

The current canonical picture of the nucleus of a Seyfert galaxy is
illustrated
in Fig. 3. The broad line region (blr), composed of gas with densities
$\sim$
10$^{9-11}$ cm$^{-3}$ and velocity spread tens of thousands km s$^{-1}$,
has a
size of $<$ 0.1 - 1 pc. This gas is probably closely connected with the
putative
accretion disk around the black hole, but the precise relationship
remains unclear.
On a larger scale, there is a toroidal structure
of gas and dust that hides our view
of the blr when our line of sight is close to the equatorial plane; the
nucleus is
then classified as a type 2 Seyfert. When viewed from the polar
directions, the blr
is seen directly and the object called a type 1 Seyfert. The precise
geometric form
of the obscuring accretion structure is unclear; although drawn as a
geometrically
thick toroid in Fig. 3, it could equally well be a warped, thin disk.
Ionizing
photons can escape from the nucleus along and around the polar
directions, giving
rise to bi-conical distributions of ionized gas - so called ``ionization
cones'' -
which are seen in emission-line studies of the narrow line regions (nlr)
of some
galaxies. Radio-emitting jets and lobes are ejected along the polar
directions.
These outwardly moving radio components shock and compress ambient
interstellar
gas, enhancing the emission-line emissivity. Jet-driven shocks may also
radiate
ionizing radiation. As a result of these processes, high resolution
images of
Seyfert galaxies in 
emission lines, especially those obtained with HST, usually show close
associations
between radio synchrotron- and optical line-emitting gases in the nlr.

\vskip 9cm

Fig. 3 (from Wilson 1991). A schematic diagram of a Seyfert nucleus,
showing currently recognised components, and their size scales.

Gaseous disks around the nuclear black holes have been 
found in a number of ways.
HST has imaged an ionized gas disk around the nucleus of the radio
galaxy M87
(Ford et al. 1994). A disk of dust with 
extent $\sim$ 125 pc is seen in the radio galaxy NGC 4261
(Jaffe et al. 1996). Lastly, water
vapor maser emission has been found from the nuclei of
about 20 Seyfert and LINER galaxies (Braatz, Wilson \& Henkel 1996).
In NGC 4258 - the best studied case - the maser emission arises from a
thin
annulus of molecular gas that is between 0.13 and 0.25 pc from the black
hole.
The maser emission with the highest velocities w.r.t. systemic defines
an
accurately Keplerian rotation curve, indicating a central mass of 
3.9 $\times$ 10$^{7}$ M$_{\odot}$ (Herrnstein et al. 1999). Some other
galaxies imaged with VLBI in water vapor maser emission also show
rotating
edge-on disk structures (e.g. NGC 1068 - Greenhill 1998), but none has
an
accurately Keplerian rotation curve like NGC 4258.

\subsection{Active Galaxies in the Darwin Band}

The best spectroscopic observations of active galactic nuclei in
Darwin's waveband have been made with the ISO satellite. As examples of
the results, Fig. 4 shows ISO spectra in the 2.5 to 45 $\mu$m band
of the starburst galaxy M82 and the composite Seyfert 2 plus starburst
galaxy Circinus (Moorwood et al. 1996; Genzel et al. 1997b). There
are clear differences between the two galaxies. The emission-line

\vskip 8cm

Fig. 4 (from Genzel et al. 1997b). Full 2.5 - 45 $\mu$m SWS spectra
of the starburst galaxy M82 (upper panel) and the Seyfert 2 plus
starburst galaxy Circinus (Moorwood et al. 1996). The jumps at
$\sim$ 30 $\mu$m are due to a change in aperture.

spectrum of M82 is dominated by fairly low ionization species
(such as [Ar II], [Si II] and [Ne II]), while that of Circinus
shows, in addition, intense high excitation lines (such as 
[Si IX], [Mg VIII] and [Ne VI]). The presence of such high
excitation species is, of course, a characteristic of Seyfert
galaxies. In addition to the ionic fine structure lines,
both galaxies show a number of H$_{2}$ emission lines. There
are also pronounced 3.2 $\mu$m, 6 to 8.5 $\mu$m and 11/12 $\mu$m
emission features from small dust grains and PAHs. 

A study of NGC 4151 with ISO (Sturm et al. 1999), also covering
2.5 - 45 $\mu$m, detected 17 fine structure emission lines from
a wide range of low and high excitation ions, two rotational lines
of molecular hydrogen and the Br$\beta$ HI line. Sturm et al. (1999)
do not detect any PAH features in NGC 4151, consistent with the
finding that such emission features trace star formation regions
and are weak or absent in active galactic nuclei (Roche et al.
1991). The hard radiation from the active nucleus apparently
destroys PAHs.

\subsection{Darwin Programs}

Darwin will probe the distribution of warm dust in galactic nuclei
with excellent spatial resolution (an angular resolution of 2 mas
corresponds to 0.15 pc at a distance of 15 Mpc, which is appropriate
to nearby Seyferts, such as NGC 1068 and NGC 4151). Depending on what
spectroscopic capability is included in the mission, Darwin may also
be able to study the ionic fine structure and molecular hydrogen 
lines discussed above. These capabilities suggest a number of
observational programs:

\noindent
1) {\it Imaging and spectroscopy of warm dust in the accretion disks
in active galactic nuclei.} In NGC 4258 and NGC 1068, the water
masing disks extend $\sim$ 15 mas and 25 mas, respectively, and will
thus be resolved by Darwin. Darwin's image of warm dust will
provide a more reliable measure of the true geometry of the disk than
the water masers, the strength of which is extremely sensitive to
path length and the excitation of the water molecule. More generally,
the issue of whether the obscuring structure is geometrically thin 
or thick could be addressed by Darwin.

\noindent
2) {\it Compact starbursts around active nuclei.} There is
clear evidence that active star formation sometimes
accompanies Seyfert type activity in galactic nuclei (e.g.
Gonz\'alez-Delgado et al. 1998 and references therein).
These starbursts should be strong infrared emitters and
could be imaged with Darwin. They should show strong PAH
emission, unlike the dust heated by the active nucleus.

\noindent
3) {\it Structure of the 8 - 13 $\mu$m silicate absorption.}
This broad feature (e.g. Fig. 4) is common in the spectra of
obscured nuclei.
 
\noindent
4) {\it Stratification of different ionic species.} As noted
above, Seyfert nuclei show a wide range of ionic species
in the infrared, including [Si IX], [Mg VIII], [Ne VI],
[Ne V], [S IV], [S III], [S II] etc. Different photoionization
models (cf. Moorwood et al. 1996; Binette, Wilson \& 
Storchi-Bergmann
 1997) predict different radial distributions of line
emissivity for the different species. Thus spectroscopic 
observations capable of spatially resolving the segregation
of the ions might distinguish between the models.

\noindent
5) {\it Spatial resolution of the broad line region?}
The geometry of the blr is one of the great unknowns of
active galactic nuclei. Darwin might spatially resolve the
broad lines, especially if its coverage could be extended
to shorter wavelengths (e.g. 2 $\mu$m) where stronger hydrogen
lines are present. 

\section{Distant Active Galactic Nuclei}

Darwin's capabilities in the area of high redshift quasars
are quite uncertain. However, hydrogen lines from the Paschen,
Brackett and even Balmer series would be redshifted into
Darwin's band. Fig. 5 gives

\vskip 7.8cm

Fig. 5 (from Voit 1997). Angular sizes of Keplerian orbits. The lines
show
the angular sizes of circular orbits at speed v$_{1000}$ around objects
of mass M$_{9}$, given a Hubble constant h$_{75}$.

the angular sizes of Keplerian
orbits as a function of redshift, z, and density parameter,
$\Omega$, for various values of the parameter combination
M$_{9}$h$_{75}$v$_{1000}^{-2}$, where h$_{75}$ is the Hubble
constant in units of 75 km s$^{-1}$ Mpc$^{-1}$,
and v$_{1000}$ is the velocity in units of 1000 km s$^{-1}$.
Since the Eddington
luminosity of a quasar is $\sim$ 10$^{47}$ M$_{9}$ erg s$^{-1}$,
the Keplerian velocity around the most luminous quasars will exceed
1,000 km s$^{-1}$ at projected separations of 1 mas, independent of the
redshift (Voit 1997). Thus a spectrometer with this velocity resolution
or better could probe
the velocity field in the outskirts of the blr for any sufficiently
luminous quasar. As long as the continuum source in the quasar is
basically pointlike, use of the nulling mode would cancel this source
while allowing extended line emission to leak through. Voit (1997)
presents line profiles observed through a nulling interferometer
for a Keplerian dependence on angular radius and for a velocity law that
is independent of radius. Confirmation of a Keplerian velocity law
would allow the black hole mass to be determined. The distribution of
black hole mass as a function of quasar luminosity and redshift is
fundamental to our understanding of the nature and evolution of
these objects.

\section{Concluding Remarks}

It is clear that Darwin is potentially capable of excellent science in
the
area of galactic nuclei. The actual scientific payoff in this area would
be
enhanced by:

\noindent
1) extending the spectral coverage to shorter wavelengths (2 - 3
$\mu$m),
which would improve observations of stars and hydrogen recombination
lines;

\noindent
2) fast coverage of the uv plane, enabling the complex brightness
distributions of galactic nuclei to be imaged with good fidelity.
Otherwise, these observations
will be confusion limited; and

\noindent
3) good spectral resolution (R $\ge$ 300), which would allow
spectroscopic work on individual gaseous emission lines as well as dust
emission features.

Of course, all of these capabilities come with a price tag!

I thank T. Alexander, D. Figer and E. S. Phinney for discussions.

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