Peculiarities in the Formation of Molecular Clouds in the Central Regions of Spiral Galaxies

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<ul><li><p>335</p><p>PECULIARITIES IN THE FORMATION OF MOLECULAR CLOUDS IN THE CEN-TRAL REGIONS OF SPIRAL GALAXIES</p><p>E. V. Volkov UDC: 524.726</p><p>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.</p><p>Keywords: molecular clouds: shear instability</p><p>1. Introduction</p><p>At present in astrophysics it is generally accepted that star formation in spiral galaxies is closely associated with</p><p>cold regions with a high density of gas, i.e., giant molecular clouds (GMCs). The conclusions regarding the mechanisms</p><p>leading to the formation of objects of this sort are not so unambiguous. There is also no unique opinion regarding the</p><p>lifetime of GMCs, nor regarding the details of the processes which ultimately lead to the appearance with time of star</p><p>clusters and groups of clusters at the site of a parent cloud.</p><p>Another, equally interesting problem is resolving the many questions associated with the radial distribution of the</p><p>molecular gas in the disks of different spiral galaxies. The importance of understanding the behavior leading to one or</p><p>another distribution of cold gas along the radius is perfectly evident, if only because this determines the radial distribution</p><p>of the newly developing stars in galaxies. In the beginning of the 1980s, observations with radio telescopes having</p><p>diameters on the order of 10 m showed that a number of spiral galaxies, mainly of a later type, have a radiation peak</p><p>in the central region with a subsequent exponential drop in the surface density of molecular gas [1-4]. At the same time,</p><p>some galaxies are observed to have a central dip in the distribution of this gas [5]. Finally, some other spiral galaxies</p><p>are observed to have yet another peak in the radial distribution of molecular gas at some distance from the center, in</p><p>addition to the central peak [6,7]. (It should be noted this kind of behavior is characteristic or our galaxy, as well [8].)</p><p>The first classifications of galaxies in terms of the type of distribution of molecular gas observed in them appeared in</p><p>Astrophysics, Vol. 47, No. 3, 2004</p><p>0571-7256/04/4703-0335 '2004 Plenum Publishing Corporation</p><p>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.</p><p>V. V. Sobolev Scientific Research Institute for Astronomy, St. Petersburg University, Russia, e-mail: evolk@astro.spbu.ru</p></li><li><p>336</p><p>reviews [9].</p><p>Over the last 20 years there have been numerous attempts to explain the annular distribution of the GMC in the</p><p>galaxy, as well as the different distributions of molecular gas in other galaxies. The following mechanisms for restructuring</p><p>of the cold component of galactic disks have been proposed: dynamic friction [10,11], viscosity [12-14], simultaneous</p><p>action of dynamic friction and viscosity [15,16], and exhaust of the gas in the inner regions of galaxies in the formation</p><p>of a bulge [2]. Despite the interesting results obtained in the framework of these models, the main question, about the</p><p>nature of the observed distribution of GMCs in spiral galaxies, remains as yet unanswered.</p><p>The picture has been somewhat clarified (although made more complicated at the same time) as a result of some</p><p>new observations made by Japanese astronomers on the 45 m NRO radio telescope [17,18]. As was perfectly correctly</p><p>emphasized in their papers, a valid study of the spatial distribution of the molecular gas in spiral galaxies lying beyond</p><p>the confines of the local group and the construction of more or less reliable classifications based on this kind of</p><p>measurements are impossible using instruments with a diameter on the order of 10 m. In fact, they have an angular</p><p>resolution of about 1, which for a distance of 10 Mpc implies a spatial resolution of roughly 3 kpc. The resolution</p><p>attained in Refs. 17 and 18, on the other hand, is roughly 4 times better, so their results essentially provide us with the</p><p>first possibility of a valid analysis of the distribution of the cold gas in the disks of spiral galaxies. Equally importantly,</p><p>the spatial distributions of the molecular gas in galaxies obtained in Refs. 17 and 18 are compared with the rotation curves</p><p>of these galaxies. The main conclusion reached in Ref. 18 is that the principal factor determining one or another profile</p><p>of the distribution of H2 in spiral galaxies is the presence or absence of a bar in a disk galaxy.</p><p>In this paper we analyze some important limitations imposed by the shape of the rotation curve of spiral galaxies</p><p>on the structure of GMCs and on the very possibility of forming clouds with a given mass in different regions of a galaxy.</p><p>At the end of the article we discuss the consequences of these limitations and of the results of the above-cited papers</p><p>for the behavior of the distribution of molecular gas in the disks of spiral galaxies.</p><p>2. Effect of the shear instability on the formation of GMCs</p><p>The shear instability, which is directly associated with the form of the rotation curve in a galaxy and develops</p><p>only in the presence of differential rotation, has a significant influence on the possible existence of GMCs as coherent</p><p>structures. If, over characteristic spatial scales on the order of the cloud size, the forces induced by differential rotation</p><p>exceed the gravitational forces maintaining a cloud as a unified whole, then a cloud of this size (and the corresponding</p><p>mass) cannot survive. This can have a significant effect on the mass spectrum of GMCs and, ultimately, on the rate of</p><p>star formation.</p><p>The condition for stability of a cloud with respect to shear can be written in the form [19]</p><p>, 22 </p><p>&gt;dr</p><p>dR</p><p>R</p><p>GMcl v(1)</p><p>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</p><p>velocity, is the linear velocity of rotation at distance from the center of the galaxy, and Mcl is the mass of the cloud.</p><p>This criterion has been used previously for evaluating the significance of the shear instability in spiral galaxies. It should</p><p>be noted, however, that the transition to a surface density of the interstellar gas using the criterion (1), as done in Ref.</p><p>20, is unacceptable: the surface density operates with the integral characteristics of the gas along the line of sight</p></li><li><p>337</p><p>regardless of whether clouds of a given size and mass contribute to it. The criterion, on the other hand, should be applied</p><p>to individual clouds and not to the interstellar medium as a whole.</p><p>It is easy to see that when it is assumed that the cloud density cl is independent of its mass, the cloud radius</p><p>disappears from the above criterion:</p><p>. 2</p><p>3 </p><p>pi</p><p>&gt;</p><p>dr</p><p>d</p><p>Gclv</p><p>(2)</p><p>In this case it turns out that clouds of arbitrary mass (size), for which this inequality holds, are stable with respect</p><p>to the galactic shear. Observational data [21-24], however, indicate that in molecular clouds with different masses it is</p><p>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:</p><p>, 2</p><p>3 </p><p>pi</p><p>&gt;</p><p>dr</p><p>d</p><p>G</p><p>RC</p><p>v</p><p>(3)</p><p>or</p><p>. 3</p><p>2-1</p><p>pi (9)</p><p>or, reducing everything to the characteristic magnitudes for this problem,</p><p>( ) , 3102</p><p>1</p><p>2100</p><p>rncl</p><p>v</p><p>&gt; (10)</p><p>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</p><p>distance from the center in kiloparsecs. It is clear from this last inequality that on going closer to the center of the galaxy,</p><p>the rotation velocity increases and that as the local rotation differs more strongly from rigid body rotation, the require-</p><p>ments imposed by instability on the parameters of the cloud become more stringent.</p><p>We obtain yet another curious relationship if we introduce the total density of galactic matter averaged over a</p><p>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.</p><p>r (kpc)</p><p>0.5</p><p>R (</p><p>pc)</p><p>10</p><p>1 2 3</p><p>100</p><p>Region of instability</p><p>Region of stability</p></li><li><p>339</p><p>spherical volume with a radius equal to the distance of the cloud from the galactic center:</p><p>( ) .3</p><p>41</p><p>3</p><p>pi= rMr GG (11)</p><p>Then the ratio of the two characteristic densities of the problem cl and ( )rG must satisfy the inequality( ) , 3 &gt; rGcl (12)</p><p>or, transforming to concentrations and assuming that a particle in a GMC is, on average, twice as heavy as a particle of</p><p>galactic matter, we obtain</p><p>( ) . 32 &gt;rnn Gcl (13)We emphasize once again that in this last formula, n</p><p>cl refers to an isolated cloud, while ( )rnG characterizes the</p><p>concentration of the matter in the galaxy averaged over the volume 3r .</p><p>3. The stability criterion for the case of several specific galaxies</p><p>The inequalities (5)-(7) and (9)-(13) cited in the preceding section use one or another assumption regarding the</p><p>form of the rotation curve ( )rv . In addition, it would be interesting to see how the stability criterion (4) limits theparameters of GMCs in real galaxies, for which data exist on their rotation curves, especially in their central regions. In</p><p>recent years radio observations have made it possible to construct these curves for several dozen relatively nearby objects.</p><p>Thus, for example, detailed rotation curves have been obtained for 52 spiral galaxies by Sofue et al. [25,26] They have</p><p>pointed out, in particular, that in the overwhelming majority of the galaxies which they analyzed, the rotation curve rises</p><p>sharply while still in the very central region of the galaxy (100-500 pc), reaches a maximum, and then often either has</p><p>a local minimum or enters a plateau.</p><p>This behavior of the rotation curve in a region immediately adjacent to the center of a galaxy creates</p><p>Fig. 2. The limiting mass of a cloud as afunction of distance to the center of a galaxyassuming a constant linear rotation velocityfor the galaxy.</p><p>r (kpc)0.5</p><p>M</p><p>/M</p><p>104</p><p>1 2 3</p><p>Region of instability</p><p>Region of stability</p><p>105</p><p>106</p><p>107</p></li><li><p>340</p><p>extremely favorable conditions for the development of the shear instability. As an example, we have chosen 6 objects</p><p>(including our galaxy) for which curves have been constructed that isolate the region of stability with respect to the cloud</p><p>mass as a function of distance to the galactic center. Here it was assumed that GMCs with a mass of M</p><p>610 have a</p><p>concentration of 30 cm-3 and that the integral of the density along the radius is constant for clouds with different masses.</p><p>The rotation curves for the chosen galaxies are shown in Fig. 3, and the results of a calculation using the criterion (4)</p><p>are shown in Fig. 4.</p><p>We see that for the concentration we have chosen for the most massive GMCs, within the confines of a region</p><p>Fig. 3. Rotation curves for galaxies from the sample used in thispaper [26].</p><p>Fig. 4. The limiting mass of a cloud as a function of the distance tothe center of the galaxies in the sample used in this paper.</p><p>r (kpc)</p><p>V (</p><p>km/s</p><p>)</p><p>0</p><p>50</p><p>GalaxyNGC 224NGC 660NGC 2841NGC 5236NGC 6946</p><p>0.5 1 1.5 2</p><p>100</p><p>150</p><p>350</p><p>300</p><p>250</p><p>200</p><p>Galaxy</p><p>NGC 224</p><p>NGC 660</p><p>NGC 2841</p><p>NGC 5236</p><p>NGC 6946</p><p>r (kpc)</p><p>0 0.5 1 1.5 2</p><p>M</p><p>/M 104</p><p>105</p><p>106</p><p>107</p><p>1000</p><p>100</p><p>10</p></li><li><p>341</p><p>of size 1 kpc from the center, clouds with masses of M</p><p>510 or more cannot exist for any of the galaxies in our sample,</p><p>while clouds with masses of M</p><p>610 do not survive in a region of size roughly 2 kpc around the center for five of the</p><p>six galaxies in this example.</p><p>4. Discussion and conclusion</p><p>In the above estimates we have repeatedly taken an average concentration in the GMCs of 30-100 particles per</p><p>cm3. This choice was made because, in the many papers devoted to the properties of GMCs located in the galaxy, densities</p><p>in this range [27] or even less (e.g., in Ref. 28 the average concentration for the most massive clouds from the sample</p><p>of GMCs used in this paper is 18 cm-3) are cited, except in the central region of the galaxy. And, as the analysis in the</p><p>preceding sections shows, clouds with these concentrations simply cannot survive in the central regions of massive spiral</p><p>galaxies.</p><p>Nevertheless, as noted in the Introduction, observations indicate the presence of substantial masses of molecular</p><p>gas in the central regions of the galaxy. The point is that the molecular clouds in the center of the galaxy have</p><p>significantly different properties from those lying in the main body of the galaxy. The main difference that we wish to</p><p>point out is that the central clouds have a gas density that is 2-3 orders of magnitude higher than the analogous</p><p>characteristic of GMCs far from the center [29,30]. This may be caused by a number of factors: an elevated overall pressure</p><p>of the gas in the interstellar medium in the center of the galaxy, manifestations of activity in the center, the action of</p><p>tidal forces, etc. However, it is possible to go somewhat further: it is entirely plausible that the mechanisms for formation</p><p>of GMCs which are effective in the center of the galaxy and at distance of 2 kpc or more from it are different. The dip</p><p>observed in the distribution of molecular gas between 2 and roughly 4 kpc may, at least partially, be related to the fact</p><p>that one mechanism (central) has already ceased to act, while the other is not yet fully effective.</p><p>It is also possible that in those spiral galaxies where a deficit in the molecular gas is observed in the central regions,</p><p>the alternative (central) mechanism does not work at all for some reason, while the formation of GMCs by the standard</p><p>(characteristic of the peripheral regions) scenario is suppressed by the shear instability. Whatever may be the case, the</p><p>present analysis allows us to conclude that the existence of large scale coherent structures (GMCs and gas-dust complexes</p><p>surrounded by a shell of neutral hydrogen), which are characteristic of the noncentral regions of the disks of galaxies,</p><p>is significantly restricted by the action of the shear instability in the center of massive spiral galaxies.</p><p>This work was partially supported by a grant from the President of the Russian Federation for the support of</p><p>Leading Scientific Schools, No. NSh-1088.2003.2.</p><p>REFERENCES</p><p>1. L. J. Rickard and P. Palmer, Astron. Astrophys. 102, L13 (1981).</p><p>2. J. S. Young and N. Scoville, Astrophys. J. 258, 467 (1982).</p><p>3. N. Z. Scoville and J. Young, Astrophys. J. 265, 148 (1983).</p><p>4. P. M. Solomon, J. Barrett, D. B. Sanders, and R. de Zafra, Astrophys. J. 266, L103 (1983).</p><p>5. J. S. Young and N. Scoville, Astrophys. J. 260, L41 (1982).</p></li><li><p>342</p><p>6. F. Verter, Astrophys. J. Suppl. Ser. 57, 261 (1985).</p><p>7. N. Nakai, Publ. Astron. Soc. Japan 44, L27 (1992).</p><p>8. W. B. Burton, M. A. Gordon, T. M. Bania, and F. J. Lockman, Astrophys. J. 202, 30 (1975).</p><p>9. M. Morris and L. J. Rickard, Ann. Rev. Astron. Astrophys....</p></li></ul>