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198Oapj. . .238. .158N the Astrophysical Journal, 238:158-174 .158N .238. The Astrophysical Journal, 238:158-174, 1980 May 15 . © 1980. The American Astronomical Society. All rights reserved. Printed in U.S.A. 198OApJ. CLUMPY MOLECULAR CLOUDS: A DYNAMIC MODEL SELF-CONSISTENTLY REGULATED BY T TAURI STAR FORMATION Colin Norman Huygens Laboratory, University of Leiden AND Joseph Silk Department of Astronomy, University of California, Berkeley Received 1978 December 11; accepted 1979 October 31 ABSTRACT A new model is proposed which can account for the longevity, energetics, and dynamical structure of dark molecular clouds. It seems clear that the kinetic and gravitational energy in macroscopic cloud motions cannot account for the energetics of many molecular clouds. A stellar energy source must evidently be tapped, and infrared observations indicate that one cannot utilize massive stars in dark clouds. Recent observations of a high space density of T Tauri stars in some dark clouds provide the basis for our assertion that high-velocity winds from these low-mass pre- main-sequence stars provide a continuous dynamic input into molecular clouds. The T Tauri winds sweep up shells of gas, the intersections or collisions of which form dense clumps embedded in a more rarefied interclump medium. Observations constrain the clumps to be ram-pressure confined, but at the relatively low Mach numbers, continuous leakage occurs. This mass input into the interclump medium leads to the existence of two phases ; a dense, cold phase (clumps of density ~ 104-105 cm-3 and temperature ~ 10 K) and a warm, more diffuse, interclump medium (ICM, of density ~ 103-104 cm-3 and temperature ~30 K). Clump collisions lead to coalescence, and the evolution of the mass spectrum of clumps is studied. We postulate that as clumps are driven above the Jeans mass, both by coalescence and the enhancement of ram pressure through continuing acceleration by protostellar winds, collapse is followed by the formation of low-mass stars that generate additional protostellar winds. We find that this continuing feedback is primarily due to the adopted form of the clump mass spectrum. If most of the mass in clumps is at the high-mass end \_N(m) ~ ra_v; v < 2], catastrophic bursts of star formation occur. Long-lived clouds (with lifetimes ~ 107-108 yr) must possess steeper clump mass spectra (v > 2). In this case, continuous recycling occurs between clumps, ICM, and low-mass stars. We find that star formation occurs on a relatively slow time scale, comparable to the cloud lifetime. The cloud will not be disrupted by the formation of low-mass stars. However, initiation of sequential OB star formation is likely to modify severely the cloud evolution after ~ 107-108 yr. We envisage that such an event will lead to rapid disruption of the cloud. Specific predictions of our model are that high spatial resolution mapping will reveal the presence of dense clumps coexisting with a warmer ICM. Because of the ram-pressure confinement, broad emission wings are predominantly produced by the densest clumps. Two further consequences of this model are that T Tauri stars should occur frequently (space density - 3 > 10 pc in dark clouds) and may be detectable by observations of H2, strong far-infrared lines, notably [O i] 63 ¡im and [O m] 88 ¿an, and other molecular line emission from the dense shocked circumstellar gas. The shocked-wind gas also provides an internal source of ultraviolet radiation longward of 912 Â that is equivalent to an average interstellar flux with a visual extinction ^4^ æ 4. This may lead to a significant degree of photo-ejection of molecules and electrons from interstellar grains. Subject headings: interstellar: molecules — nebulae: general — stars: formation — stars: pre-main-sequence I. INTRODUCTION ~ 2 pc, and mean molecular hydrogen density Considerable evidence has accumulated that dense ~104cm~3, and should be distinguished from the molecular clouds may be inhomogeneous in density more extensive and diffuse molecular cloud complexes and possess complex velocity fields. The clouds that we in which they may be embedded. We shall cite in § II a 4 consider here have a typical mass ~10 M0, radius number of observations of several different molecules 158 © American Astronomical Society • Provided by the NASA Astrophysics Data System .158N .238. CLUMPY MOLECULAR CLOUDS . 159 that support the hypothesis that molecular clouds are characteristic Lbol ^ 1 L0) which are presumably em- clumpy. While the ultimate test of this hypothesis bedded within the clouds and that are found in optical awaits the completion of high-resolution maps, it surveys of the outer regions of the clouds. The 198OApJ. appears that the existing evidence is sufficiently com- intersecting dense shells swept up by the winds form pelling to justify exploration of the astrophysical clumps, and the lower-density material interior to the plausibility and possible implications of a clumpy shells permeates the ICM. cloud model (Townes 1976). The simplest such model While details of this model are described in § III, we consists of many small, dense, cold clumps immersed note here a simple argument demonstrating that T in a more diffuse interclump medium (ICM). Tauri stellar winds can provide an adequate energy Alternative possibilities are that the observed supply. This stellar energy source can exceed that emission-line widths are due to systematic motions, available in the gravitational binding energy of the such as radial infall (Goldreich and Kwan 1974) or cloud, and is moreover in a usable form. In fact, the rotation (Field 1978a). Systematic motions may be energy available in T Tauri winds (velocity Vw) relative inadequate to account for the observed line profiles, to that in cloud potential energy (random velocity v) is and a more complex velocity and/or density structure -10(^0.01) (UJtOOkms-1)2 (Bkms"1/^2, (where is probably required (Kwan 1978). £ (~ 0.01) is the ratio of mass ejected in winds In a clumpy cloud model, the most straightforward cloud mass. That an energy source which exceeds that interpretation of the emission profiles is that the line available in cloud gravitational potential energy is widths are in fact a superposition of emission profiles often required has previously been noted by Goldreich from a number of cold clumps that are moving and Kwan (1974). While applicable in certain regions, randomly in the cloud gravitational potential well. the solution offered by these authors requires the This type of model should be distinguished from the presence of luminous OB stars, and is not compatible more phenomenological models of molecular clouds with infrared observations of many dark molecular involving a few massive fragments (Zuckerman and clouds. It seems clear that an energy source tapping the Evans 1974; Elmegreen 1978). However, individual reservoir of stellar binding energy is required, and T massive fragments may well be constrained on grounds Tauri winds from the low-mass stars that can be of energetics and stability to contain complex clumpy present in dark clouds seem the most plausible substructure as discussed here. candidates. A multiple cloudlet model clearly possesses a num- Although clump-clump collisions occur (typically ber of serious problems, notably clump containment on the order of a cloud crossing time), such collisions and clump survival against dissipation and coalescence are not disruptive because of strong postshock cooling. by collisions and by interaction with the ICM. We shall In fact, we shall argue that colliding clumps coalesce discuss in detail the formation and destruction of and eventually become Jeans unstable. This yields a clumps, and demonstrate that a plausible clumpy specific mode of star formation on a relatively slow cloud model can be constructed if a suitable dynamical time scale that can considerably exceed the cloud source is present. We shall concentrate here on dark crossing time. Enhanced star formation may occur on molecular clouds; many of our arguments can be a more rapid time scale as a consequence of a secular extended to consider warm clouds containing OB increase in the ambient pressure of the ICM that stars. In fact, a natural source of cloud inhomogeneity confines the clumps. Such an increase in ICM pressure is available via the interaction of embedded T Tauri provides positive feedback by lowering the Jeans mass stars with their immediate environment. We shall show and therefore triggering further star formation. A that winds from T Tauri stars can form bubbles with fundamental assumption in our model is that chimp typical radii ~ 1017 cm if there is no significant relative coalescence and compression by the ICM leads only to motion <lkms_1 between gas and stars, and we low-mass star formation and drives T Tauri winds. shall hereafter refer to this as the static model. Provided that a certain condition on the clump mass Observational evidence discussed by Herbig (1977) spectrum is satisfied, molecular clouds are therefore supports the use of such a model, at least at the edges of stabilized and heated in this manner until an external molecular clouds. Since the space density of T Tauri trigger stimulates massive star formation. Specific stars in dark clouds may approach > 10 pc-3 (Cohen triggers may be the initiation of sequential OB star and Kuhi 1979a) it seems possible that the bubbles can formation in the surrounding molecular cloud com- intersect. If there is a relative motion between the stars plex by either spiral density wave shocks or a nearby and ICM then the bubbles will have a radius supernova blast wave: the time scale for a cloud to 1016~17 cm and bubble-bubble collisions will occur on undergo catastrophic energy input from either mech- the order of a crossing time (~106yr). We shall anism is ^ 107-108 yr. The final stages in a cloud’s hereafter refer to this as the moving bubble model ; this lifetime would therefore find it undergoing OB star limiting case is where the stars have acquired the virial formation in the outer regions and continuing T Tauri velocity of the gravitational potential well of the cloud star formation in the dense core.
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