Gilberto C. Gómez

Molecular Cloud Evolution. II. From Cloud Formation to the Early Stages of Star Formation in Decaying Conditions

We study the formation of giant dense cloud complexes and of stars within them using SPH numerical simulations of the collision of gas streams (‘‘inflows’’) in the WNM at moderately supersonic velocities. The collisions cause compression,cooling,andturbulencegenerationinthegas,formingacloudthatthenbecomesself-gravitatingandbeginsto collapse globally. Simultaneously, the turbulent, nonlinear density fluctuations induce fast, local collapse events. The simulationsshowthat(1)Thecloudsarenotinastateofequilibrium.Instead,theyundergosecularevolution.Duringits early stages, the cloud’s mass and gravitational energy jEgj increase steadily, while the turbulent energy Ek reaches a plateau.(2)When jEgjbecomescomparabletoEk,globalcollapsebegins,causingasimultaneousincreasein jEgjandEk that maintains a near-equipartition condition jEg j� 2Ek. (3) Longer inflow durations delay the onset of global and local collapsebymaintainingahigherturbulentvelocitydispersioninthecloudoverlongertimes.(4)Thestarformationrate islargefrom the beginning,without any periodofslow and acceleratingstar formation.(5) The column densities of the local star-forming clumps closely resemble reported values of the column density required for molecule formation, suggesting that locally molecular gas and star formation occur nearly simultaneously. The MC formation mechanism discussedherenaturallyexplainstheapparent‘‘virialized’’stateofMCsandtheubiquityofHihalosaroundthem.Also, within their assumptions, our simulations support the scenario of rapid star formation after MCs are formed, although long (k15 Myr) accumulation periods do occur during which the clouds build up their gravitational energy, and which are expected to be spent in the atomic phase.

Molecular cloud evolution – IV. Magnetic fields, ambipolar diffusion and the star formation efficiency

We investigate the formation and evolution of giant molecular clouds (GMCs) by the collision of convergent warm neutral medium (WNM) streams in the interstellar medium, in the presence of magnetic fields and ambipolar diffusion (AD), focusing on the evolution of the star formation rate (SFR) and efficiency (SFE), as well as of the mass-to-magnetic-flux ratio (M2FR) in the forming clouds. We find that: 1) Clouds formed by supercritical inflow streams proceed directly to collapse, while clouds formed by subcritical streams first contract and then re-expand, oscillating on the scale of tens of Myr. 2) Our suite of simulations with initial magnetic field strength of 2, 3, and 4�G show that only supercritical or marginal critical streams lead to reasonable star forming rates. This result is not altered by the inclusion of ambipolar diffusion. 3) The GMC’s M2FR is a generally increasing function of time, whose growth rate depends on the details of how mass is added to the GMC from the WNM. 4) The M2FR is a highly fluctuating function of position in the clouds. This implies that a significant fraction of a cloud’s mass may remain magnetically supported, while SF occurs in the supercritical regions that are not supported. 5) In our simulations, the SFE approaches stationarity, because mass is added to the GMC at a similar rate at which it converts mass to stars. In such an approximately stationary regime, we find that the SFE provides a proxy of the supercritical mass fraction in the cloud. 6) We observe the occurrence of buoyancy of the low-M2FR regions within the gravitationally-contracting GMCs, so that the latter naturally segregate into a high-density, high-M2FR “core” and a low-density, low-M2FR “envelope”, without the intervention of AD.

HIGH- AND LOW-MASS STAR-FORMING REGIONS FROM HIERARCHICAL GRAVITATIONAL FRAGMENTATION. HIGH LOCAL STAR FORMATION RATES WITH LOW GLOBAL EFFICIENCIES

We investigate the properties of star-forming regions in a previously published numerical simulation of molecular cloud formation out of compressive motions in the warm neutral atomic interstellar medium, neglecting magnetic fields and stellar feedback. We study the properties (density, total gas + stars mass, stellar mass, velocity dispersion, and star formation rate (SFR)) of the cloud hosting the first local, isolated star formation event and compare them with those of the cloud formed by the central, global collapse event. In this simulation, the velocity dispersions at all scales are caused primarily by infall motions rather than by random turbulence. We suggest that the small-scale isolated collapses may be representative of low- to intermediate-mass star-forming regions, with gas masses (M gas) of hundreds of solar masses, velocity dispersions σ v ~ 0.7 km s–1, and SFRs ~3 × 10–5 M ☉ yr–1, while the large-scale, massive ones may be representative of massive star-forming regions, with M gas of thousands of solar masses, σ v ~ a few km s–1, and SFRs ~3 × 10–4 M ☉ yr–1. We also compare the statistical distributions of the physical properties of the dense cores appearing in the central region of massive collapse with those from a recent survey of the massive star-forming region in the Cygnus X molecular cloud, finding that the observed and simulated distributions are in general very similar. However, we find that the star formation efficiency per free-fall time (SFEff) of the high mass region, similar to that of OMC-1, is low, ~0.04. In the simulated cloud, this is not a consequence of a slow SFR in a nearly hydrostatic cloud supported by turbulence, but rather of the region accreting mass at a high rate. Thus, we find that measuring a low SFEff may be incorrectly interpreted as implying a lifetime much longer than the cores local free-fall time, and an SFR much slower than that given by the free-fall rate, if the accretion is not accounted for. We suggest that rather than requiring a low value of the SFEff everywhere in the Galaxy, attaining a globally low specific SFR requires star formation to be a spatially intermittent process, so that most of the mass in a giant molecular cloud (GMC) is not participating in the SF process at any given time. Locally, the specific SFR of a star-forming region can be much larger than the global GMCs average.

Molecular cloud evolution - V. Cloud destruction by stellar feedback

We present a numerical study of the evolution of molecular clouds, from their formation by converging flows in the warm ISM, to their destruction by the ionizing feedback of the massive stars they form. We improve with respect to our previous simulations by including a different stellar-particle formation algorithm, which allows them to have masses corresponding to single stars rather than to small clusters, and with a mass distribution following a near-Salpeter stellar IMF. We also employ a simplified radiative-transfer algorithm that allows the stellar particles to feed back on the medium at a rate that depends on their mass and the local density. Our results are as follows: a) Contrary to the results from our previous study, where all stellar particles injected energy at a rate corresponding to a star of � 10 M⊙, the dense gas is now completely evacuated from 10-pc regions around the stars within 10–20 Myr, suggesting that this feat is accomplished essentially by the most massive stars. b) At the scale of the whole numerical simulations, the dense gas mass is reduced by up to an order of magnitude, although star formation (SF) never shuts off completely, indicating that the feedback terminates SF locally, but new SF events continue to occur elesewhere in the clouds. c) The SF efficiency (SFE) is maintained globally at the � 10% level, although locally, the cloud with largest degree of focusing of its accretion flow reaches SFE � 30%. d) The virial parameter of the clouds approaches unity before the stellar feedback begins to dominate the dynamics, becoming much larger once feedback dominates, suggesting that clouds become unbound as a consequence of the stellar feedback, rather than unboundness being the cause of a low SFE. e) The erosion of the filaments that feed the star-forming clumps produces chains of isolated dense blobs reminiscent of those observed in the vicinity of the dark globule B68.

ASPECT RATIO DEPENDENCE OF THE FREE-FALL TIME FOR NON-SPHERICAL SYMMETRIES

We investigate the collapse of non-spherical substructures, such as sheets and filaments, which are ubiquitous in molecular clouds. Such non-spherical substructures collapse homologously in their interiors but are influenced by an edge effect that causes their edges to be preferentially accelerated. We analytically compute the homologous collapse timescales of the interiors of uniform-density, self-gravitating filaments and find that the homologous collapse timescale scales linearly with the aspect ratio. The characteristic timescale for an edge-driven collapse mode in a filament, however, is shown to have a square-root dependence on the aspect ratio. For both filaments and circular sheets, we find that selective edge acceleration becomes more important with increasing aspect ratio. In general, we find that lower dimensional objects and objects with larger aspect ratios have longer collapse timescales. We show that estimates for star formation rates, based upon gas densities, can be overestimated by an order of magnitude if the geometry of a cloud is not taken into account.

THE EFFECT OF THE CORIOLIS FORCE ON KELVIN-HELMHOLTZ-DRIVEN MIXING IN PROTOPLANETARY DISKS

We study the stability of protoplanetary disks with vertical velocity gradients in their equilibrium rotation rates; such gradients are expected to develop when dust settles into the midplane. Using a linear stability analysis of a simple three-layer model, we show that the onset of instability occurs at a larger value of the Richardson number, and therefore for a thicker layer, when the effects of Coriolis forces are included. This analysis also shows that even-symmetry (midplane crossing) modes develop faster than odd-symmetry ones. These conclusions are corroborated by a large number of nonlinear numerical simulations with two different parameterized prescriptions for the initial (continuous) dust distributions. Based on these numerical experiments, the Richardson number required for marginal stability is more than an order of magnitude larger than the traditional value. The dominant modes that grow have horizontal wavelengths of several initial dust scale heights and in nonlinear stages mix solids fairly homogeneously over a comparable vertical range. We conclude that gravitational instability may be more difficult to achieve than previously thought and that the vertical distribution of matter within the dust layer is likely globally, rather than locally, determined.

FORMATION AND COLLAPSE OF QUIESCENT CLOUD CORES INDUCED BY DYNAMIC COMPRESSIONS

We present numerical hydrodynamic simulations of the formation, evolution, and gravitational collapse of isothermal molecular cloud cores in spherical geometry. A compressive wave is set up in a constant sub-Jeans density distribution of radius r ¼1 pc. As the wave travels through the simulation grid, a shock-bounded spherical shell is formed. The inner shockof thisshellreachesandbouncesoffthecenter,leavingbehindacentralcorewithaninitiallyalmostuniformdensity distribution,surroundedbyanenvelopeconsistingof thematerialintheshock-boundedshell,whichatlatetimesdevelops al ogarithmic slope close to� 2, even in noncollapsing cases. The central core and the envelope are separated by a mild shock. The central core grows to sizes of � 0.1 pc and resembles a Bonnor-Ebert (BE) sphere, although it has significant dynamical differences: its self-gravity is initially negligible, and it is confined by the ram pressure of the infalling material, thusgrowingcontinuouslyinmassandsize.Withtheappropriateparameters,thecoremasseventuallyreachesaneffective Jeans mass, at which time the core begins to collapse. Thus, the core evolves from a stable regime to an unstable one, implying the existence of a time delay between the appearance of the core and the onset of its collapse, but due to its growth in mass, rather than to the dissipation of its internal turbulence, as is often believed. These results suggest that prestellar cores may approximate BE structures, which are, however, of variable mass and may or may not experience gravitational collapse, in qualitative agreement with the large observed frequency of cores with BE-like profiles. Subject headingg ISM: clouds — ISM: evolution — ISM: structure — stars: formation — turbulence Online material: mpeg animations

Three-Dimensional Magnetohydrodynamic Modeling of the Gaseous Structure of the Galaxy: Description of the Simulations

As we have discussed previously, the extra stiffness that a magnetic field adds to the interstellar medium (ISM) changes the way the ISM reacts to the presence of a spiral perturbation. At intermediate to high z, the gas shoots up before the arm, then flows over and falls behind the arm as it approaches the next arm. This generates a multicell circulation pattern, within each of which the net radial mass flux is positive near the midplane and negative at higher z. The flow distorts the magnetic field lines. In the arm region, the gas flows nearly parallel to the arm, and therefore the magnetic field adopts a similar pitch angle. Between the arms, the gas flows out in radius, generating a negative pitch angle in the magnetic field. The intensity and direction of the field yield synthetic synchrotron maps that reproduce some features of the synchrotron maps of external galaxies, such as the islands of emission and the displacement between the gaseous and synchrotron arms. When comparing the magnitude of the field with the local gas density, two distinctive relations appear, depending on whether the magnetic pressure is dominant. Above the plane, the density structure develops a shape resembling a breaking wave. This structure collapses and rises again with a period of about 60 Myr, similar to that of a vertical oscillation mode. The falling gas plays an important part in the overall hydrostatics, since its deceleration compresses the low-z gas, raising the average midplane pressure in the interarm region above that provided by the weight of the material above.

Errors in Kinematic Distances and Our Image of the Milky Way Galaxy

Errors in the kinematic distances, under the assumption of circular gas orbits, were estimated by performing synthetic observations of a model disk galaxy. It was found that the error is <0.5 kpc for most of the disk when the measured rotation curve is used, but larger if the real rotation curve is applied. In both cases, the error is significantly larger at the positions of the spiral arms. The error structure is such that, when kinematic distances are used to develop a picture of the large-scale density distribution, the most significant features of the numerical model are significantly distorted or absent, while spurious structure appears. By considering the full velocity field in the calculation of the kinematic distances, most of the original density structures can be recovered.

Tidal forces as a regulator of star formation in Taurus

Only a few molecular clouds in the solar neighbourhood exhibit the formation of only low-mass stars. Traditionally, these clouds have been assumed to be supported against more vigorous collapse by magnetic fields. The existence of strong magnetic fields in molecular clouds, however, poses serious problems for the formation of stars and of the clouds themselves. In this Letter, we review the three-dimensional structure and kinematics of Taurus – the archetype of a region forming only low-mass stars – as well as its orientation within the Milky Way. We conclude that the particularly low star formation efficiency in Taurus may naturally be explained by tidal forces from the Galaxy, with no need for magnetic regulation or stellar feedback.