Scaling relations of supersonic turbulence in star-forming molecular clouds

We present a direct numerical and analytical study of driven supersonic MHD turbulence that is believed to govern the dynamics of star-forming molecular clouds. We describe statistical properties of the turbulence by measuring the velocity difference structure functions up to the fifth order. In particular, the velocity power spectrum in the inertial range is found to be close to E(k) \~ k^{-1.74}, and the velocity difference scales as ~ L^{0.42}. The results agree well with the Kolmogorov--Burgers analytical model suggested for supersonic turbulence in [astro-ph/0108300]. We then generalize the model to more realistic, fractal structure of molecular clouds, and show that depending on the fractal dimension of a given molecular cloud, the theoretical value for the velocity spectrum spans the interval [-1.74 ... -1.89], while the corresponding window for the velocity difference scaling exponent is [0.42 ... 0.78].Comment: 17 pages, 6 figures include

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Dark cloud cores and gravitational decoupling from turbulent flows

We test the hypothesis that the starless cores may be gravitationally bound clouds supported largely by thermal pressure by comparing observed molecular line spectra to theoretical spectra produced by a simulation that includes hydrodynamics, radiative cooling, variable molecular abundance, and radiative transfer in a simple one-dimensional model. The results suggest that the starless cores can be divided into two categories: stable starless cores that are in approximate equilibrium and will not evolve to form protostars, and unstable pre-stellar cores that are proceeding toward gravitational collapse and the formation of protostars. The starless cores might be formed from the interstellar medium as objects at the lower end of the inertial cascade of interstellar turbulence. Additionally, we identify a thermal instability in the starless cores. Under par ticular conditions of density and mass, a core may be unstable to expansion if the density is just above the critical density for the collisional coupling of the gas and dust so that as the core expands the gas-dust coupling that cools the gas is reduced and the gas warms, further driving the expansion.Comment: Submitted to Ap

Flows, Fragmentation, and Star Formation. I. Low-mass Stars in Taurus

The remarkably filamentary spatial distribution of young stars in the Taurus molecular cloud has significant implications for understanding low-mass star formation in relatively quiescent conditions. The large scale and regular spacing of the filaments suggests that small-scale turbulence is of limited importance, which could be consistent with driving on large scales by flows which produced the cloud. The small spatial dispersion of stars from gaseous filaments indicates that the low-mass stars are generally born with small velocity dispersions relative to their natal gas, of order the sound speed or less. The spatial distribution of the stars exhibits a mean separation of about 0.25 pc, comparable to the estimated Jeans length in the densest gaseous filaments, and is consistent with roughly uniform density along the filaments. The efficiency of star formation in filaments is much higher than elsewhere, with an associated higher frequency of protostars and accreting T Tauri stars. The protostellar cores generally are aligned with the filaments, suggesting that they are produced by gravitational fragmentation, resulting in initially quasi-prolate cores. Given the absence of massive stars which could strongly dominate cloud dynamics, Taurus provides important tests of theories of dispersed low-mass star formation and numerical simulations of molecular cloud structure and evolution.Comment: 32 pages, 9 figures: to appear in Ap

A Prediction of Brown Dwarfs in Ultracold Molecular Gas

A recent model for the stellar initial mass function (IMF), in which the stellar masses are randomly sampled down to the thermal Jeans mass from hierarchically structured pre-stellar clouds, predicts that regions of ultra-cold CO gas, such as those recently found in nearby galaxies by Allen and collaborators, should make an abundance of Brown Dwarfs with relatively few normal stars. This result comes from the low value of the thermal Jeans mass, considering that the hierarchical cloud model always gives the Salpeter IMF slope above this lower mass limit. The ultracold CO clouds in the inner disk of M31 have T~3K and pressures that are probably 10 times higher than in the solar neighborhood. This gives a mass at the peak of the IMF equal to 0.01 Msun, well below the Brown Dwarf limit of 0.08 Msun. Using a functional approximation to the IMF, the ultracold clouds would have 50% of the star-like mass and 90% of the objects below the Brown Dwarf limit. The brightest of the Brown Dwarfs in M31 should have an apparent, extinction-corrected K-band magnitude of ~21 mag in their pre-main sequence phase.Comment: 13 pages, 2 figures, to be published in Astrophysical Journal, Vol 522, September 10, 199

Magnetic fields at the periphery of UCHII regions from carbon recombination line observations

Several indirect evidences indicate a magnetic origin for the non-thermal width of spectral lines observed toward molecular clouds. In this letter, I suggest that the origin of the non-thermal width of carbon recombination lines (CRLs) observed from photo-dissociation regions (PDRs) near ultra-compact \HII\ regions is magnetic and that the magnitude of the line width is an estimate of the \alfven speed. The magnetic field strengths estimated based on this suggestion compare well with those measured toward molecular clouds with densities similar to PDR densities. I conclude that multi-frequency CRL observations have the potential to form a new tool to determine the field strength near star forming regions.Comment: To appear in ApJ Letter

Jamming, two-fluid behaviour and 'self-filtration' in concentrated particulate suspensions

We study the flow of model experimental hard sphere colloidal suspensions at high volume fraction $\Phi$ driven through a constriction by a pressure gradient. Above a particle-size dependent limit $\Phi_0$, direct microscopic observations demonstrate jamming and unjamming--conversion of fluid to solid and vice versa--during flow. We show that such a jamming flow produces a reduction in colloid concentration $\Phi_{x}$ downstream of the constriction. We propose that this `self-filtration' effect is the consequence of a combination of jamming of the particulate part of the system and continuing flow of the liquid part, i.e. the solvent, through the pores of the jammed solid. Thus we link the concept of jamming in colloidal and granular media with a 'two-fluid'-like picture of the flow of concentrated suspensions. Results are also discussed in the light of Osborne Reynolds' original experiments on dilation in granular materials.Comment: 4 pages, 3 figure

HCN versus HCO+ as dense molecular gas mass tracer in Luminous Infrared Galaxies

It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas (\rm n\ga 10^4 cm^{-3}) in Luminous Infrared Galaxies (LIRGs: $\rm L_{FIR}> 10^{11} L_{\odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Graci\'a-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.Comment: 16 pages, 4 figures, Accepted for publication in the Astrophysical Journa

Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear

We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicularly oriented lamellae in a uniform, oscillatory, shear flow, and show that the configuration can be hydrodynamically unstable for the constitutive law chosen. It is argued that this instability and the secondary flows it creates can be used to infer a possible mechanism for orientation selection in shear experiments.Comment: 26 pages, 10 figure