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

    1. Introduction

    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 [5]. 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 [8].)

    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: evolk@astro.spbu.ru

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    reviews [9].

    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 [2]. 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

    star formation.

    The condition for stability of a cloud with respect to shear can be written in the form [19]

    , 22

    >dr

    dR

    R

    GMcl v(1)

    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

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    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:

    . 2

    3

    pi

    >

    dr

    d

    Gclv

    (2)

    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:

    , 2

    3

    pi

    >

    dr

    d

    G

    RC

    v

    (3)

    or

    . 3

    2-1

    pi (9)

    or, reducing everything to the characteristic magnitudes for this problem,

    ( ) , 3102

    1

    2100

    rncl

    v

    > (10)

    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.

    r (kpc)

    0.5

    R (

    pc)

    10

    1 2 3

    100

    Region of instability

    Region of stability

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    spherical volume with a radius equal to the distance of the cloud from the galactic center:

    ( ) .3

    41

    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

    form of

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