peculiarities in the formation of molecular clouds in the central regions of spiral galaxies
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PECULIARITIES IN THE FORMATION OF MOLECULAR CLOUDS IN THE CEN-TRAL REGIONS OF SPIRAL GALAXIES
E. V. Volkov UDC: 524.726
The limitations imposed by the shear instability on the formation of gigantic molecular clouds in the centralregions of spiral galaxies are examined. The criteria obtained here are illustrated using the example of sixgalaxies for which the detailed rotation curves are known. The different mechanisms for formation of molecu-lar clouds which apply in the central and edge regions of disk galaxies are evaluated.
Keywords: molecular clouds: shear instability
At present in astrophysics it is generally accepted that star formation in spiral galaxies is closely associated with
cold regions with a high density of gas, i.e., giant molecular clouds (GMCs). The conclusions regarding the mechanisms
leading to the formation of objects of this sort are not so unambiguous. There is also no unique opinion regarding the
lifetime of GMCs, nor regarding the details of the processes which ultimately lead to the appearance with time of star
clusters and groups of clusters at the site of a parent cloud.
Another, equally interesting problem is resolving the many questions associated with the radial distribution of the
molecular gas in the disks of different spiral galaxies. The importance of understanding the behavior leading to one or
another distribution of cold gas along the radius is perfectly evident, if only because this determines the radial distribution
of the newly developing stars in galaxies. In the beginning of the 1980s, observations with radio telescopes having
diameters on the order of 10 m showed that a number of spiral galaxies, mainly of a later type, have a radiation peak
in the central region with a subsequent exponential drop in the surface density of molecular gas [1-4]. At the same time,
some galaxies are observed to have a central dip in the distribution of this gas . Finally, some other spiral galaxies
are observed to have yet another peak in the radial distribution of molecular gas at some distance from the center, in
addition to the central peak [6,7]. (It should be noted this kind of behavior is characteristic or our galaxy, as well .)
The first classifications of galaxies in terms of the type of distribution of molecular gas observed in them appeared in
Astrophysics, Vol. 47, No. 3, 2004
0571-7256/04/4703-0335 '2004 Plenum Publishing Corporation
Translated from Astrofizika, Vol. 47, No. 3, pp. 393-402 (July-September 2004). Original article submitted Decem-ber 5, 2003; accepted for publication May 19, 2004.
V. V. Sobolev Scientific Research Institute for Astronomy, St. Petersburg University, Russia, e-mail: firstname.lastname@example.org
Over the last 20 years there have been numerous attempts to explain the annular distribution of the GMC in the
galaxy, as well as the different distributions of molecular gas in other galaxies. The following mechanisms for restructuring
of the cold component of galactic disks have been proposed: dynamic friction [10,11], viscosity [12-14], simultaneous
action of dynamic friction and viscosity [15,16], and exhaust of the gas in the inner regions of galaxies in the formation
of a bulge . Despite the interesting results obtained in the framework of these models, the main question, about the
nature of the observed distribution of GMCs in spiral galaxies, remains as yet unanswered.
The picture has been somewhat clarified (although made more complicated at the same time) as a result of some
new observations made by Japanese astronomers on the 45 m NRO radio telescope [17,18]. As was perfectly correctly
emphasized in their papers, a valid study of the spatial distribution of the molecular gas in spiral galaxies lying beyond
the confines of the local group and the construction of more or less reliable classifications based on this kind of
measurements are impossible using instruments with a diameter on the order of 10 m. In fact, they have an angular
resolution of about 1, which for a distance of 10 Mpc implies a spatial resolution of roughly 3 kpc. The resolution
attained in Refs. 17 and 18, on the other hand, is roughly 4 times better, so their results essentially provide us with the
first possibility of a valid analysis of the distribution of the cold gas in the disks of spiral galaxies. Equally importantly,
the spatial distributions of the molecular gas in galaxies obtained in Refs. 17 and 18 are compared with the rotation curves
of these galaxies. The main conclusion reached in Ref. 18 is that the principal factor determining one or another profile
of the distribution of H2 in spiral galaxies is the presence or absence of a bar in a disk galaxy.
In this paper we analyze some important limitations imposed by the shape of the rotation curve of spiral galaxies
on the structure of GMCs and on the very possibility of forming clouds with a given mass in different regions of a galaxy.
At the end of the article we discuss the consequences of these limitations and of the results of the above-cited papers
for the behavior of the distribution of molecular gas in the disks of spiral galaxies.
2. Effect of the shear instability on the formation of GMCs
The shear instability, which is directly associated with the form of the rotation curve in a galaxy and develops
only in the presence of differential rotation, has a significant influence on the possible existence of GMCs as coherent
structures. If, over characteristic spatial scales on the order of the cloud size, the forces induced by differential rotation
exceed the gravitational forces maintaining a cloud as a unified whole, then a cloud of this size (and the corresponding
mass) cannot survive. This can have a significant effect on the mass spectrum of GMCs and, ultimately, on the rate of
The condition for stability of a cloud with respect to shear can be written in the form 
where R is the cloud radius, r is the distance form the center of the galaxy to the center of the cloud, is the angular
velocity, is the linear velocity of rotation at distance from the center of the galaxy, and Mcl is the mass of the cloud.
This criterion has been used previously for evaluating the significance of the shear instability in spiral galaxies. It should
be noted, however, that the transition to a surface density of the interstellar gas using the criterion (1), as done in Ref.
20, is unacceptable: the surface density operates with the integral characteristics of the gas along the line of sight
regardless of whether clouds of a given size and mass contribute to it. The criterion, on the other hand, should be applied
to individual clouds and not to the interstellar medium as a whole.
It is easy to see that when it is assumed that the cloud density cl is independent of its mass, the cloud radius
disappears from the above criterion:
In this case it turns out that clouds of arbitrary mass (size), for which this inequality holds, are stable with respect
to the galactic shear. Observational data [21-24], however, indicate that in molecular clouds with different masses it is
not the three-dimensional density that remains constant, but the concentration integrated along the radius: CRcl = ,where C = const. In this case, we obtain the following limitation:
or, reducing everything to the characteristic magnitudes for this problem,
( ) , 3102
where ncl is the concentration of particles in the cloud, 100v is the rotation velocity in units of 100 km/s, and r1 is the
distance from the center in kiloparsecs. It is clear from this last inequality that on going closer to the center of the galaxy,
the rotation velocity increases and that as the local rotation differs more strongly from rigid body rotation, the require-
ments imposed by instability on the parameters of the cloud become more stringent.
We obtain yet another curious relationship if we introduce the total density of galactic matter averaged over a
Fig. 1. The limiting radius of a cloud as afunction of distance to the center of a galaxyassuming a constant linear rotation velocityfor the galaxy.
1 2 3
Region of instability
Region of stability
spherical volume with a radius equal to the distance of the cloud from the galactic center:
( ) .3
pi= rMr GG (11)
Then the ratio of the two characteristic densities of the problem cl and ( )rG must satisfy the inequality( ) , 3 > rGcl (12)
or, transforming to concentrations and assuming that a particle in a GMC is, on average, twice as heavy as a particle of
galactic matter, we obtain
( ) . 32 >rnn Gcl (13)We emphasize once again that in this last formula, n
cl refers to an isolated cloud, while ( )rnG characterizes the
concentration of the matter in the galaxy averaged over the volume 3r .
3. The stability criterion for the case of several specific galaxies
The inequalities (5)-(7) and (9)-(13) cited in the preceding section use one or another assumption regarding the