Molecular Cloud Evolution

I describe the scenario of molecular cloud (MC) evolution that has emerged over the past decade or so. MCs can start out as cold atomic clouds formed by compressive motions in the warm neutral medium (WNM) of galaxies. Such motions can be driven by large-scale instabilities, or by local turbulence. The compressions induce a phase transition to the cold neutral medium (CNM) to form growing cold atomic clouds, which in their early stages may constitute thin CNM sheets. Several dynamical instabilities soon destabilize a cloud, rendering it turbulent. For solar neighborhood conditions, a cloud is coincidentally expected to become molecular, magnetically supercritical, and gravitationally dominated at roughly the same column density, N \sim 1.5 \times 10^21 \psc \approx 10 \Msun pc$^{-2}$. At this point, the cloud begins to contract gravitationally. However, before its global collapse is completed ($\sim 10^7$ yr later), the nonlinear density fluctuations within the cloud, which have shorter local free-fall times, collapse first and begin forming stars, a few Myr after the global contraction started. Large-scale fluctuations of lower mean densities collapse later, so the formation of massive star-forming regions is expected to occur late in the evolution of a large cloud complex, while scattered low-mass regions are expected to form earlier. Eventually, the local star formation episodes are terminated by stellar feedback, which disperses the local dense gas, although more work is necessary to clarify the details and characteristic scales of this process.Comment: 15 pages, 7 figure files. Invited review for "The Dynamic ISM: A celebration of the Canadian Galactic Plane Survey," ASP Conference Series, from conference held in Naramata BC, Canada June 6-10, 201

Interstellar Turbulence, Cloud Formation and Pressure Balance

We discuss HD and MHD compressible turbulence as a cloud-forming and cloud-structuring mechanism in the ISM. Results from a numerical model of the turbulent ISM at large scales suggest that the phase-like appearance of the medium, the typical values of the densities and magnetic field strengths in the intercloud medium, as well as Larson's velocity dispersion-size scaling relation in clouds may be understood as consequences of the interstellar turbulence. However, the density-size relation appears to only hold for the densest simulated clouds, there existing a large population of small, low-density clouds, which, on the other hand, are hardest to observe. We then discuss several tests and implications of a fully dynamical picture of interstellar clouds. The results imply that clouds are transient, constantly being formed, distorted and disrupted by the turbulent velocity field, with a fraction of these fluctuations undergoing gravitational collapse. Simulated line profiles and estimated cloud lifetimes are consistent with observational data. In this scenario, we suggest it is quite unlikely that quasi-hydrostatic structures on any scale can form, and that the near pressure balance between clouds and the intercloud medium is an incidental consequence of the density field driven by the turbulence and in the presence of appropriate cooling, rather than a driving or confining mechanism.Comment: 12 pages, 3 postscript figures. Review to appear in the Proceedings of "New Perspectives on the Interstellar Medium", (22-28 August, 1998), eds. A.R. Taylor, T.L. Landecke

Turbulence in Molecular Clouds

In this course we review the theory of incompressible homogeneous turbulence at an elementary level, and discuss the similarities and differences expected in the compressible case, relevant to the interstellar medium and molecular clouds. We stress that a general definition of turbulence applicable to the compressible case should not rely on the Kolmogorov $k^{-5/3}$ spectrum nor on an energy cascade from large to small scales. Instead, we discuss the various possibilities for the energy spectrum of compressible turbulence, which numerical simulations suggest should be $\sim k^{-2}$, and the nature of the cascades, if at all present. We then discuss issues concerning molecular clouds which are likely to be directly related to turbulence, such as cloud formation, cloud structure, and cloud support against gravity.Comment: 24 pages, 1 Latex file, 2 style files. To appear in ``Millimetric and Sub-Millimetric Astronomy. INAOE 1996 Summer School'

The Turbulent Star Formation Model. Outline and Tests

We summarize the current status of the turbulent model of star formation in turbulent molecular clouds. In this model, clouds, clumps and cores form a hierarchy of nested density fluctuations caused by the turbulence, and either collapse or re-expand. Cores that collapse can be either internally sub- or super-sonic. The former cannot further fragment, and can possibly be associated with the formation of a single or a few stars. The latter, instead, can undergo turbulent fragmentation during their collapse, and probably give rise to a cluster of bound objects. The star formation efficiency is low because only a small fraction of the density fluctuations proceed to collapse. Those that do not may constitute a class of ``failed'' cores that can be associated with the observed starless cores. ``Synthetic'' observations of cores in numerical simulations of non-magnetic turbulence show that a large fraction of them have subsonic internal velocity dispersions, can be fitted by Bonnor-Ebert column density profiles, and exhibit ``coherence'' (an apparent independence of linewidth with column density near the projected core centers), in agreement with observed properties of molecular cloud cores.Comment: 8 pages, 2 figures. To appear in the Proceedings of IAU Symposium 221, "Star Formation at High Angular Resolution", Editors M. Burton, R. Jayawardhana & T. Bourke, Astronomical Society of the Pacifi

The Density Probability Distribution Function in Turbulent, Isothermal, Magnetized Flows in Slab Geometry

We investigate the behavior of the magnetic pressure, $b^2$, in fully turbulent MHD flows in ``1+2/3'' dimensions by means of its effect on the probability density function (PDF) of the density field. We start by reviewing our previous results for general polytropic flows, according to which the value of the polytropic exponent $\gamma$ determines the functional shape of the PDF. A lognormal density PDF appears in the isothermal ($\gamma=1$) case, but a power-law tail at either large or small densities appears for large Mach numbers when $\gamma >1$ and $\gamma < 1$, respectively. In the isothermal magnetic case, the relevant parameter is the field fluctuation amplitude, \dbb. A lognormal PDF still appears for small field fluctuations (generally the case for {\it large mean fields}), but a significant low-density excess appears at large fluctuation amplitudes ({\it weak mean fields}), similar to the behavior at $\gamma > 1$ of polytropic flows. We interpret these results in terms of simple nonlinear MHD waves, for which the magnetic pressure behaves linearly with the density in the case of the slow mode, and quadratically in the case of the fast wave. Finally, we discuss some implications of these results, in particular the fact that the effect of the magnetic field in modifying the PDF is strongest when the mean field is weak.Comment: To appear in "Computational Fluid Dynamics": Proceedings of the Fourth UNAM Supercomputing Conference, eds. E. Ramos, G. Cisneros, R. Fernandez-Flores & A. Santillan (Singapore: World Scientific). 8 pages, 2 ps figures. Uses ws-p8-50x6-00.cls style fil

Magnetic Pressure-Density Correlation in Compressible MHD Turbulence

We discuss magnetic pressure and density fluctuations in strongly turbulent isothermal MHD flows in "1+2/3" dimensions. We first consider "simple" nonlinear MHD waves, which allow us show that the slow and fast modes have different asymptotic dependences of the magnetic pressure B^2 vs. rho. For the slow mode, B^2 ~= c_1-c_2 rho, while for the fast mode, B^2 ~= rho^2. We also perform a perturbative analysis to investigate Alfven wave pressure, recovering previous results that B^2 ~= rho^gamma_e, with gamma_e ~= 2, 3/2 and 1/2 at respectively large, moderate and low M_a. This variety of scalings implies that a single polytropic description of magnetic pressure is not possible in general, since the relation between B^2 and rho depends on which mode dominates the density fluctuation production, which in turn depends on the angle between the magnetic field and the direction of wave propagation, and on the Alfvenic Mach number M_a. Typically, at small M_a, the slow mode dominates, and B is ANTIcorrelated with rho. At large M_a, both modes contribute to density fluctuation production, and the magnetic pressure decorrelates from density, exhibiting a large scatter, which however decreases towards higher densities. In this case, the unsystematic behavior of the magnetic pressure causes the density PDF to generally maintain the lognormal shape corresponding to non-magnetic isothermal turbulence, except when the slow mode dominates, in which case the PDF develops an excess at low densities. Our results are consistent with the low values and apparent lack of correlation between the magnetic field strength and density in surveys of the lower-density molecular gas, and also with the recorrelation apparently seen at higher densities, if M_a is relatively large there.Comment: 12 pages, 13 figures (20 postscript files). First page blank for obscure latex reasons. Submitted to A&

Turbulence as an Organizing Agent in the ISM

We discuss HD and MHD compressible turbulence as a cloud-forming and cloud-structuring mechanism in the ISM. Results from a numerical model of the turbulent ISM at large scales suggest that the phase-like appearance of the medium, the typical values of the densities and magnetic field strengths in the intercloud medium, as well as the velocity dispersion-size scaling relation in clouds may be understood as consequences of the interstellar turbulence. However, the density-size relation appears to only hold for the densest clouds, suggesting that low-column density clouds, which are hardest to observe, are turbulent transients. We then explore some properties of highly compressible polytropic turbulence, in one and several dimensions, applicable to molecular cloud scales. At low values of the polytropic index $\gamma$, turbulence may induce the gravitational collapse of otherwise linearly stable clouds, except if they are magnetically subcritical. The nature of the density fluctuations in the high Mach-number limit depends on $\gamma$, and in no case resembles that resulting from Burgers turbulence. In the isothermal ($\gamma=1$) case, the dispersion of $\ln (\rho)$ scales like the turbulent Mach number. The latter case is singular with a lognormal density pdf, while power-law tails develop at high (resp. low) densities for $\gamma 1$).Comment: 9 pages, 4 postscript figures. To appear in "Interstellar Turbulence", eds. P. Franco & A. Carraminana, Cambridge University Pres

Small Ionized and Neutral Structures: A Theoretical Review

The workshop on Small Ionized and Neutral Structures in the Interstellar Medium featured many contributions on the theory of the objects which are responsible for ``Tiny Scale Atomic Structures'' (TSAS) and ``Extreme Scattering Events'' (ESE). The main demand on theory is accounting for objects that have the high densities and small sizes apparently required by the observations, but also persist over a sufficiently long time to be observable. One extensively-discussed mechanism is compressions by transonic turbulence in the warm interstellar medium, followed by thermal instabilities leading to an even more compressed state. In addressing the requirements for overpressured but persistent objects, workshop participants also discussed fundamental topics in the physics of the interstellar medium, such as the timescale for evaporation of cool dense clouds, the relevance of thermodynamically-defined phases of the ISM, the effect of magnetic fields, statistical effects, and the length and time scales introduced by interstellar processes.Comment: Summary of the theory papers presented at the conference "Small Ionized and Neutral Structures in the Diffuse Interstellar Medium", eds. M. Haverkorn and W.M. Goss (ASP Conference Series

Filaments in Simulations of Molecular Cloud Formation

We report on the filaments that develop self-consistently in a new numerical simulation of cloud formation by colliding flows. As in previous studies, the forming cloud begins to undergo gravitational collapse because it rapidly acquires a mass much larger than the average Jeans mass. Thus, the collapse soon becomes nearly pressureless, proceeding along its shortest dimension first. This naturally produces filaments in the cloud, and clumps within the filaments. The filaments are not in equilibrium at any time, but instead are long-lived flow features, through which the gas flows from the cloud to the clumps. The filaments are long-lived because they accrete from their environment while simultaneously accreting onto the clumps within them; they are essentially the locus where the flow changes from accreting in two dimensions to accreting in one dimension. Moreover, the clumps also exhibit a hierarchical nature: the gas in a filament flows onto a main, central clump, but other, smaller-scale clumps form along the infalling gas. Correspondingly, the velocity along the filament exhibits a hierarchy of jumps at the locations of the clumps. Two prominent filaments in the simulation have lengths ~15 pc, and masses ~600 Msun above density n ~ 10^3 cm-3 (~2x10^3 Msun at n > 50 cm-3). The density profile exhibits a central flattened core of size ~0.3 pc and an envelope that decays as r^-2.5, in reasonable agreement with observations. Accretion onto the filament reaches a maximum linear density rate of ~30 Msun Myr^-1 pc^-1.Comment: Revised to address the referee's comments, submitted to ApJ. See related animations in http://www.crya.unam.mx/~g.gomez/publica.htm

Cloud Statistics in Numerical Simulations of the ISM

We present preliminary results on the energy budgets of clouds in two-dimensional numerical simulations of the interstellar medium. Using an automated cloud-identification algorithm, we calculate the gravitational, internal, kinetic and magnetic energies of the clouds. We find that, within a dispersion of roughly one order of magnitude, the gravitational energy in the clouds is balanced by the remaining energies. Furthermore, within the same dispersion, there appears to be equipartition between the kinetic and magnetic energies.Comment: Gzipped, tarred Latex file (4 pages), 6 Postscript figures and one style file. Uses AAS macros. Gzipped Postscript file also available at ftp://kepler.astroscu.unam.mx/incoming/enro/papers/cloudstat.ps.g