Density Power Spectrum in Turbulent Thermally Bi-stable Flows

In this paper we numerically study the behavior of the density power spectrum in turbulent thermally bistable flows. We analyze a set of five three-dimensional simulations where turbulence is randomly driven in Fourier space at a fixed wave-number and with different Mach numbers M (with respect to the warm medium) ranging from 0.2 to 4.5. The density power spectrum becomes shallower as M increases and the same is true for the column density power spectrum. This trend is interpreted as a consequence of the simultaneous turbulent compressions, thermal instability generated density fluctuations, and the weakening of thermal pressure force in diffuse gas. This behavior is consistent with the fact that observationally determined spectra exhibit different slopes in different regions. The values of the spectral indexes resulting from our simulations are consistent with observational values. We do also explore the behavior of the velocity power spectrum, which becomes steeper as M increases. The spectral index goes from a value much shallower than the Kolmogorov one for M=0.2 to a value steeper than the Kolmogorov one for M=4.5.Comment: 16 pages, 11 figures. Accepted for publication in Ap

The physical and the geometrical properties of simulated cold H i structures

The objective of this paper is to help shedding some light on the nature and the properties of the cold structures formed via thermal instability in the magnetized atomic interstellar medium. To this end, we searched for clumps formed in forced (magneto)hydrodynamic simulations with an initial magnetic field ranging from 0 to 8.3 μG. We statistically analysed, through the use of Kernel density estimations, the physical and the morphological properties of a sample containing ∼1500 clumps, as well as the relative alignments between the main direction of clumps and the internal velocity and magnetic field. The density (n ∼50-200 cm-3), the thermal pressure (Pth/k ∼4.9 × 103-104 K cm-3), the mean magnetic field (∼3-11 μG), and the sonic Mach number of the selected clumps have values comparable to those reported in observations. We find, however, that the cloud sample cannot be described by a single regime concerning their pressure balance and their Alfvénic Mach number. We measured the morphological properties of clumps mainly through the asphericity and the prolatness, which appear to be more sensitive than the aspect ratios. From this analysis, we find that the presence of magnetic field, even if it is weak, does qualitatively affect the morphology of the clumps by increasing the probability of having highly aspherical and highly plolate clumps by a factor of two, that is by producing more filamentary clumps. Finally, we find that the angle between the main direction of the clumps and the local magnetic field lies between ∼π/4 and π/2 and shifts to more perpendicular alignments as the intensity of this field increases, while the relative direction between the local density structure and the local magnetic field transits from parallel to perpendicular.Fil: Gazol, Adriana. Universidad Nacional Autónoma de México; MéxicoFil: Villagran Azuara, Marco Adrian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin

The effect of tidal forces on the Jeans instability criterion in star-forming regions

Recent works have proposed the idea of a tidal screening scenario, in which tidal forces determine the mass that a protostar can accrete to explain the IMF. In this scenario, gravitationally unstable fragments will compete for the gas reservoir in a star-forming clump. In this contribution, we propose to properly include the action of an external gravitational potential in the Jeans linear instability analysis as previously proposed by Jog. We have found that an external gravitational potential can reduce the critical mass required for the perturbation to collapse if the tidal force produced is compressive or increase it if it is disruptive. Our analytical treatment provides (a) new mass and length collapse conditions; (b) a simple equation for observers to check whether their observed fragments can collapse; and (c) a simple equation to compute whether collapse-induced turbulence can produce the levels of observed fragmentation. Our results suggest that, given envelopes with similar mass and density, the flatter ones should produce more stars than the steeper ones. If the density profile is a power-law, the corresponding power-law index separating these two regimes should be about 1.5. We finally applied our formalism to 160 fragments identified within 18 massive star-forming cores of previous works. We found that considering tides, 49% of the sample may be gravitationally unstable and that it is unlikely that turbulence acting at the moment of collapse has produced the fragmentation of these cores. Instead, these fragments should have formed earlier when the parent core was substantially flatter.Comment: Accepted MNRAS, 18 pages, 5 figure

The pressure distribution in thermally bistable turbulent flows

We present a systematic numerical study of the effect of turbulent velocity fluctuations on the thermal pressure distribution in thermally bistable flows. The simulations employ a random turbulent driving generated in Fourier space rather than star-like heating. The turbulent fluctuations are characterized by their rms Mach number M and the energy injection wavenumber, k_for. Our results are consistent with the picture that as either of these parameters is increased, the local ratio of turbulent crossing time to cooling time decreases, causing transient structures in which the effective behavior is intermediate between the thermal-equilibrium and adiabatic regimes. As a result, the effective polytropic exponent gamma_ef ranges between ~0.2 to ~1.1. The fraction of high-density zones with P>10^4 Kcm^-3 increases from roughly 0.1% at k_for=2 and M=0.5 to roughly 70% for k_for=16 and M=1.25. A preliminary comparison with the pressure measurements of Jenkins (2004) favors our case with M=0.5 and k_for=2. In all cases, the dynamic range of the pressure summed over the entire density range, typically spans 3-4 orders of magnitude. The total pressure histogram widens as the Mach number is increased, and develops near-power-law tails at high (resp.low) pressures when gamma_ef<~ 0.5 (resp. gamma_ef>~ 1), which occurs at k_for=2 (resp.k_for=16) in our simulations. The opposite side of the pressure histogram decays rapidly, in an approx. lognormal form. Our results show that turbulent advection alone can generate large pressure scatters, with power-law high-P tails for large-scale driving, and provide validation for approaches attempting to derive the shape of the pressure histogram through a change of variable from the known form of the density histogram, such as that performed by MacLow et al.(2004).Comment: to be published in Ap

On the Effects of Projection on Morphology

We study the effects of projection of three-dimensional (3D) data onto the plane of the sky by means of numerical simulations of turbulence in the interstellar medium including the magnetic field, parameterized cooling and diffuse and stellar heating, self-gravity and rotation. We compare the physical-space density and velocity distributions with their representation in position-position-velocity (PPV) space (``channel maps''), noting that the latter can be interpreted in two ways: either as maps of the column density's spatial distribution (at a given line-of-sight (LOS) velocity), or as maps of the spatial distribution of a given value of the LOS velocity (weighted by density). This ambivalence appears related to the fact that the spatial and PPV representations of the data give significantly different views. First, the morphology in the channel maps more closely resembles that of the spatial distribution of the LOS velocity component than that of the density field, as measured by pixel-to-pixel correlations between images. Second, the channel maps contain more small-scale structure than 3D slices of the density and velocity fields, a fact evident both in subjective appearance and in the power spectra of the images. This effect may be due to a pseudo-random sampling (along the LOS) of the gas contributing to the structure in a channel map: the positions sampled along the LOS (chosen by their LOS velocity) may vary significantly from one position in the channel map to the next.Comment: 6 figures. To appear in the March 20th volume in Ap

Molecular cloud evolution. I. Molecular cloud and thin CNM sheet formation

We discuss molecular cloud formation by large-scale supersonic compressions in the diffuse warm neutral medium (WNM). Initially, a shocked layer forms, and within it, a thin cold layer. An analytical model and high-resolution 1D simulations predict the thermodynamic conditions in the cold layer. After $\sim 1$ Myr of evolution, the layer has column density \sim 2.5 \times 10^{19} \psc, thickness $\sim 0.03$ pc, temperature $\sim 25$ K and pressure $\sim 6650$ K \pcc. These conditions are strongly reminiscent of those recently reported by Heiles and coworkers for cold neutral medium sheets. In the 1D simulations, the inflows into the sheets produce line profiles with a central line of width \sim 0.5 \kms and broad wings of width \sim 1 \kms. 3D numerical simulations show that the cold layer develops turbulent motions and increases its thickness, until it becomes a fully three-dimensional turbulent cloud. Fully developed turbulence arises on times ranging from $\sim 7.5$ Myr for inflow Mach number \Mr = 2.4 to $> 80$ Myr for \Mr = 1.03. These numbers should be considered upper limits. The highest-density turbulent gas (HDG, n > 100 \pcc) is always overpressured with respect to the mean WNM pressure by factors 1.5--4, even though we do not include self-gravity. The intermediate-density gas (IDG, $10 < n [{\rm cm}^ {-3}] < 100$) has a significant pressure scatter that increases with \Mr, so that at \Mr = 2.4, a significant fraction of the IDG is at a higher pressure than the HDG. Our results suggest that the turbulence and at least part of the excess pressure in molecular clouds can be generated by the compressive process that forms the clouds themselves, and that thin CNM sheets may be formed transiently by this mechanism, when the compressions are only weakly supersonic.Comment: Accepted for publication in ApJ. For correct display of the tables, download the postscript version. Animations can be downloaded from http://www.astrosmo.unam.mx/~e.vazquez/turbulence/movies.htm

Gravity or turbulence? - II. Evolving column density probability distribution functions in molecular clouds: Column density PDFs

It has been recently shown that molecular clouds do not exhibit a unique shape for the column density probability distribution function (N-PDF). Instead, clouds without star formation seem to possess a lognormal distribution, while clouds with active star formation develop a powerlaw tail at high column densities. The lognormal behaviour of the N-PDF has been interpreted in terms of turbulent motions dominating the dynamics of the clouds, while the power-law behaviour occurs when the cloud is dominated by gravity. In the present contribution, we use thermally bi-stable numerical simulations of cloud formation and evolution to show that, indeed, these two regimes can be understood in terms of the formation and evolution of molecular clouds: a very narrow lognormal regime appears when the cloud is being assembled. However, as the global gravitational contraction occurs, the initial density fluctuations are enhanced, resulting, first, in a wider lognormal N-PDF, and later, in a power-law N-PDF. We thus suggest that the observed N-PDF of molecular clouds are a manifestation of their global gravitationally contracting state. We also show that, contrary to recent suggestions, the exact value of the power-law slope is not unique, as it depends on the projection in which the cloud is being observed

Is Thermal Instability Significant in Turbulent Galactic Gas?

We investigate numerically the role of thermal instability (TI) as a generator of density structures in the interstellar medium (ISM), both by itself and in the context of a globally turbulent medium. Simulations of the instability alone show that the condenstion process which forms a dense phase (``clouds'') is highly dynamical, and that the boundaries of the clouds are accretion shocks, rather than static density discontinuities. The density histograms (PDFs) of these runs exhibit either bimodal shapes or a single peak at low densities plus a slope change at high densities. Final static situations may be established, but the equilibrium is very fragile: small density fluctuations in the warm phase require large variations in the density of the cold phase, probably inducing shocks into the clouds. This result suggests that such configurations are highly unlikely. Simulations including turbulent forcing show that large- scale forcing is incapable of erasing the signature of the TI in the density PDFs, but small-scale, stellar-like forcing causes erasure of the signature of the instability. However, these simulations do not reach stationary regimes, TI driving an ever-increasing star formation rate. Simulations including magnetic fields, self-gravity and the Coriolis force show no significant difference between the PDFs of stable and unstable cases, and reach stationary regimes, suggesting that the combination of the stellar forcing and the extra effective pressure provided by the magnetic field and the Coriolis force overwhelm TI as a density-structure generator in the ISM. We emphasize that a multi-modal temperature PDF is not necessarily an indication of a multi-phase medium, which must contain clearly distinct thermal equilibrium phases.Comment: 18 pages, 11 figures. Submitted to Ap