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\centerline{\bf {STRUCTURE AND STAR FORMATION}}
\centerline{\bf {IN CIRCUMNUCLEAR REGIONS OF SPIRAL GALAXIES}}

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\begin{abstract}
Photometric and kinematic properties of inner regions of spiral
galaxies are considered. It is shown that the fast rotation of nuclear
gaseous disks  makes them gravitationally stable or
marginally unstable. Their star formation may continue however even
in the absence of large-scale gravitational instability.
\end{abstract}

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{\bf Introduction}

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 Inner parts of galaxies within about 1 kpc from their nuclei in many
cases appears to be peculiar regions by their properties even if we
restrict our attention by normal galaxies without strong nuclear
activity.

First, circumnuclear regions often reveal rather complex -
regular or irregular - photometric structure which may be connected
with general structure of a main disk. It includes spiral
arms (examples: M100, NGC 4314), short nuclear bars or nuclear rings
of resonance nature (see Buta and Crocker 1993) or hot spots (Morgan
1958) which seems to be sites of active star formation. Most of these
features are evidently related to large-scale bars in SB- galaxies,
although in some galaxies a presence of bar is not evident from
optical observations .

 Second, in many galaxies (especially of early types Sa-Sbc), including
our own Galaxy, the central regions accumulate interstellar gas into
dense molecular disk of about 1kpc- size. These central islands (or
sometimes rings or bar-like features) of molecular gas are sooner a
rule than an exception for massive spiral galaxies. In many cases a
dense circumnuclear gas produces strongly enhanced star formation
which is observed as starburst nucleus.

Note that the presence of a large-scale bar is proved to be an
efficient (but not the only one) mechanism for driving interstellar
medium into the nuclear region, to feed starburst or mild star
formation within a few hundred parsecs from the center, and- -under
favorable conditions such as the formation of nuclear bar- to turn on
the action of active nucleus (see for example Friedli and Benz, 1993,
Telesco et al., 1993,  Schlosman et.al.,1989).

Third, as optical and CO - observations have shown, in many normal
galaxies the nuclear gaseous disk is distinguished by rapid
rotation of gas and stars, being often dynamically decoupled from the
rest of the galaxy (Afanasiev et al., 1989, Zasov and Sil'chenko,
1994, Rubin et al.,.1997, Sofue, 1997 and references therein).

A detailed comparison of spectra of nuclear HII- regions with the HII-
regions of main disks which was carried out by Kennicutt et.al., 1993,
and Luis et.al., 1997, showed that they are similar in many respects:
their luminosities, masses of ionized gas and internal color excesses
are within the same ranges, but some properties are systematically
different: as a rule, HII nuclei emit stronger low-ionization
forbidden lines compared to disk HII regions, they also have lower
equivalent widths of Balmer emission lines, which gives evidence of
bright background light of the stellar population. Nuclear emission
regions also have unusually low filling factor (around $10^{-5}$ (Luis
et al., 1997). It is worth mentioning also that the Hubble Space
Telescope observations revealed the presence of unusually bright and
compact young (globular?) stellar clusters in the regions of active
circumnuclear star formation (Barth et.al., 1995). All these
peculiarities show that the conditions of star formation there may
differ from what we observe in spiral arms of galaxies.

In this paper I describe briefly some results of investigations of
nuclear regions of spiral galaxies, related to their structure and star
formation.

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{\bf Rotation of inner discs.}

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For a typical distance to galaxies considered here D = 10 - 20 Mpc a
nuclear disk with diameter of about 1 kpc is seen at the angle 10''
-20''. It is very difficult to get the velocity field or velocity
curve so close to the center. Nevertheless even the long slit
observations gave strict evidences of fast rotation of nuclear regions
of 0.5 - 1 kpc radius in many galaxies (Afanasiev et al., 1989, Rubin
et al.,1997). For the most reliable estimates of velocity gradients it
is necessary to use several cuts passing through a nucleus or two-
dimensional velocity field assuming solid-body rotation. Without using
two- dimensional data it is often impossible to verify rotational
nature of gas velocities. As an example it is worth mentioning that
from 17 galaxies where Rubin et.al. found dynamically detached nuclei
only for a half of them circular rotation of circumnuclear gas fitted
the data.

The other method of seeking  fast rotating dynamically decoupled
nuclei is to measure line- of sight velocity gradient $dV_r / dR $ along the
positional angle PA. This approach appears highly efficient.
Observatons of more than a dosen of normal spiral galaxies obtained
with Fabri-Perot and multipuple spectrograph observations at 6m
telescope of SAO RAS (Laboratory of Spectroscopy and Photometry of
Extragalactic objects, led by S.Dodonov) have shown that such nuclei
may be revealed at distances 1 - 3 arcseconds fron the center (some
examples are given in Zasov, Sil'chenko, 1996). Typical velocity
gradients were found to be several hundreds km/s. They may be even
higher if to take into account that the size of nuclei is comparable
to the seeing during the observations. Note however that in the case
of rigid-body rotation a finite angular resolutuion does not distort
the slope of rotation curve (Fridman et.al., 1994). This method allows not
only io determine velocity gradient in the nucleus, but also to find
the position of dynamical axis (line- of- nodes) and hence to reveal
its agreement or disagreement with the major axis of galaxies.
Happily in most cases the divergence at R $\approx $ several hundreds
parsecs is not too large which gives evidence of approximately
circular rotation of gas (although bright exceptions were also
found, f.e. NGC 895, NGC 972, NGC 7217). In principle, the turn of
dynamical axis may be caused both by non-asymmetrical bar-like
potential and by the inclination of nuclear disk to the plane of the
main disk. To reveal its nature it is necessary to use both kinematic
and photometric data.

  It is curious that unlike nuclear rings, dynamically revealed inner
bars (mini-bars) do not strictly relate to large-
scale optically visible bars: they were found not only in SB-
galaxies, but also in SA-galaxies where the presence of bar is not
evident (NGC 895, NGC 972, NGC 4100, NGC 7217). It means that these
small features are of no resonance nature. Instead they may appear due
to the instability of extended orbits of stars in slowly rotating
stellar components (Lynden-Bell and Polyachenko bar- forming
mechanism, see Polyachenko and Polyachenko, 1994).

 Radio observations of CO-rich nuclei also show fast rotation  within
 inner several hundreds of parsecs with velocity gradients similar to
 those observed in the optically selected galaxies (velocity of
 rotation 200 - 250 km/s reaches within R = 100 - 200 pc (Sofue,
 1997)), so optical and radio samples of nuclear regions are
 non-distinguishable by their gas kinematics.

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 \centerline{\bf Nuclear disc stability and star formation}

\bigskip

As it was pointed in the Introduction, nuclear star formation takes
place in galaxies of all types,  especially those of late Hubble
types. But the intensity of this process differs
by several orders of magnitudes - from weak emission nuclei to
bursting star formation nuclei and further up to ultraluminous far
infrared galaxies galaxies which have both extremaly high luminosity in
far infrared $(10^{11} - 10^{12}~ L_\odot)$ and large surface density
of molecular gas ($10^3 - 10^4 ~M_\odot / pc^2$) in their nuclei (see
f.e.Sanders et.al., 1991). Concerning HII nuclei of normal spiral
galaxies, their properties are in general similar to properties of
giant HII regions in the main disks, with the exception of higher
concentration $n_e$ and very low filling factor $\approx 10^{-5}$
(Luis et.al., 1997). The latter may just be a sequence of large number
density of star forming gas. Indeed, for a given excitation parameter
of single ionizing star a volume filled by ionized gas is proportional
to $n_e^2$, so it must be much lower than in the main disk and hence a
less volume fraction is occupied by HII regions. One can expect that
high resolution observations, if they were available, would show a
presence of thousands of small HII regions related to O-stars,
immersed into the dense non-homogeneous gas medium of nuclear disk.

The other peculiarity of conditions of star formation in moleculal
clouds of circumnuclear disks is  high gas pressure caused by the high
number density of gas (both molecular and HII). A good example is the
nucleus of spiral galaxy NGC 1808 (Aalto et.al., 1994): the analysis of radio
emission in different molecular lines led authors to conclusuion that
$P/k~ \approx 10^8~ cm^{-3} \cdot K$), which is 3 - 4 order of
magnitudes higher than in the disk of the Galaxy. A high pressure  may
be a factor which significantly enhances star formation efficiency in
gas- rich nuclei.

Fast rotation of inner parts of galaxies, especially of dynamically
decoupled nuclei, is a factor, which, on the contrary, reduces star
formation activity (even for rigid body rotation) due to conservation
of angular momentum of collapsing parts of gaseous disks.

For a flat disk a large-scale gravitational instability is absent if
radial velocity dispersion $C_{gas}$ exceeds a critical value

$$
C_{cr}\, =\,Q\,\pi\,G~\sigma_{gas} /\kappa (R).
$$
Here$ \sigma$ is the surface density, $\kappa (R)$ is epicyclic
frequency (for rigid-body rotation $\Omega~= const~\kappa\,=
2\Omega$). Stability parameter $Q$ = 1 for pure radial perturbations
(Toomre' criterion). In  galactic disks, where dispersion velocity of
gas is about 10 km/s,  parameter $Q~ = 1.5 - 2$ (Kennicutt, 1989,
Zasov and Bizyaev, 1994). It agrees with non- WKB analysis of
stability which shows that the threshold for instability reaches for
$Q \approx 1.7$ for flat rotation curve but keeps close to 1 for$
\Omega \approx const$ (Polyachenko, 1990). Hence, as it follows from
the equation, in the region of rigid-body rotation, which usually
coincides with circumnuclear region, a lower value of $C_{cr}$ is
necessary for the disc to be stable due to lower $Q$ and higher
$|kappa/\Omega$.

Note that the strict criterion for three
-dimensional case has not obtained yet, and all  usually adopted conditions
for the instability are still approximate (see the discussion in the book
Horuzhii, Fridman, 1994).

Now the question arise - are circumnuclear disks gravitationally
stable?  The answer is definitely "yes", if  their gas surface density
is less or not much larger than at several kpc from the center in the
main disk where the angular rotation is lower. But there are many
galaxies (including our own) where radio observations in molecular
lines show the presence of dense molecular disks in central kpc
regions. For some of them $ \sigma_{gas}$ often exceeds $10^3~ M_\odot/pc^2$, which
(for the usually adopted conversion factor $2\cdot10^{20}
cm^{-2}(K\cdot km/c)^{-1}$ used here), which makes their self- gravity rather essential. Kinematically
gas-rich nuclear discs (bars, rings) of galaxies are similar to the
optically selected  dynamically detached nuclei having velocity
gradients 300 - 1000 km/s/kpc.

Fig.2 shows histogram of distribution of $C_{cr}$ for galaxies where
both rotation curve and CO intensity map or $\sigma_{gas}$ are
available
for the standard conversion factor
$3\times 10^{20}~K\cdot cm^{-2}$ (for M33 the presence of HI was also
taken into account). Radiuses and general shapes of molecular
"islands" and references are given in the Table. Note that due to
restricted angular observations $\Omega$ may be underestimated which
allows to consider $C_{cr}$ as an upper limit.

Observational estimates of velocity dispersion of molecular clouds in
central parts of galaxies are very scarce and not too reliable. I will adopt 10 km/s as an
lower limit of $C_{gas}$. For gas-rich nuclei it is definitely
higher: direct measurements lead to values $C_{gas}\approx 12-50 km/s
$ (see Kenney et.al. 1997 for NGC 3504, Lo et.al ,1984 for IC 342,
Sofue et.al for NGC 4631, Ishizuki et.al.1990  for NGC 6946 and
Garcia-Burillo, 1992 for NGC 891, Gusten, 1989 for our Galaxy).

 Hence general conclusion which may be done from histogram in Fig 2 is
that a large parts of galaxies which are considered have nuclear discs
which are on the threshold of gravitational stability or definitely stable.
This is especially true for nuclear regions of galaxies poor of gas such NGC
7331 (     ,1997) or NGC 7217 (Zasov, Sil'chenko, 1997).

The problem of lowering of conversion factor used for
transition from the intensity $I_{co}$ to $\sigma_{gas}$ for warm and
dense molecular gas is well known (see Schild, 1994 and references
therein). Here I note that in the nuclear part of nearby actively star
forming galaxy  M 82 observations in different molecular lines
(\raisebox{3pt}{12}CO, \raisebox{3pt}{12}CO) confirm that the
conversion factor is lower with respect to usually adopted one (Wild et.al., 1992).

It is worth noting that  star formation still continues even in the
gravitationally stable disks. A good illustration is NGC 7217, where
the intensity of $H_\alpha$ in this gas-poor galaxy monotonously
rises towards the center of inner disk().

In this galaxy, in spite of the low gas density, star forming regions
do not only exist in the nuclear disk, but apparently have a
surprisingly well-ordered spiral-like structure (Zasov, Sil'chenko,
1997). It is not visible in the original images of this galaxy
because they are swamped by the emission of the substantially brighter
bulge which have unusually high luminosity.

Even if the nuclear disk of this galaxy was marginally unstable (independently on whether it has
gaseous or
stellar nature) the wavelength of perturbations corresponding to the
maximum of instability growth increment would not correspond to the
observed structure. For the observed
velocity gradient $\approx 200 km/s/kpc$ unstable wavelength equals to several hundreds
of parsecs, whereas the observed structure is a sort of "rippled
surface" with a significantly smaller scale (the characteristic
radial distance between neighboring arcs is about 1", or less than 0.1
kpc). Therefore, the observed pattern cannot be due to gravitational
oscillations in either the stellar or the gaseous disk. A possible alternative
is the presence of a hydrodynamical instability in the gaseous disk
that does not require a high surface density to develop. One of the
conditions for such an instability to occur is the presence of a local
maximum in the rotation curve, followed by a region of rapidly
decreasing angular velocity (see the discussion by Fridman in [17,
18]). In this galaxy such a region probably does exist at the boundary
of the dynamically distinct nucleus, where velocity gradient rapidly
changes (Zasov, Sil'chenko, 1994).
Note that similar small-scale inner spiral-like situcture was found by
HST observations of NGC  ()  (Barth et al., 1995).

\centerline{\bf Conclusions}

1.Inner (nuclear) regions of spiral galaxies within several arcseconds from the
center often possess nuclear bars and/or inclined
disks which may be revealed not only from photometric or gas
distribution data, but also from the analysis of gas kinematics.
Nuclear disks are usually distinguished by high angular velocity of gas.

2. In most cases one can epect that the inner molecular disks
$\le 1 kpc$ size are gravitationally stable or marginally unstable.
The dependence of conversion factor on the abundance strengthens this
conclusion.

3. Star formation and some regular structure may be developed even in
gravitationally stable disks and hence there is (are) some
non-gravitational mechanism(s) which regulate(s)  process of star
formation there.

Author is grateful to O.K.Sil'chenko for her key role in the
observational programs and Yu.N. Efremov for valuable discussions.

This work was partially supported by grant RFBI 97-02-17358



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