Larson's Law Research Articles

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles – II. Contribution of the turbulent term and the potential of the outer shells

In this paper we continue to investigate the energy conservation equation obtained in our previous work. We set ourselves three new goals. The first one is to rewrite the main equations in terms of density profile in order to give more physical insight. The second one is to investigate the significance of two new terms in the energy conservation equation. They originate from the gravity of the outer shells of cloud and the masses outer to the cloud, respectively. The third goal is to investigate the main equation in the case when the kinetic turbulent term scales according to Larson's law and it is independent, formally, of the accretion, in contrast to the previous work. The combination of supersonic turbulence and spherical symmetry raises a caveat which is commented in our conclusions. We obtained two solutions for the density profile. They scale with slopes -2 and -3/2, respectively. The energy balance for the second solution is the same as in the previous paper: this is a free-fall. For the first solution there are two cases. The first one: if the turbulent term does not scale, then it could be important for the energy balance of the cloud. The second one: if the turbulent term does scale, then it is not important for the energy balance of the cloud. The two new gravitational terms don't affect the existence of the two solutions, but the gravitation of the outer masses calibrate the energy balance for the first solution.

An analysis of the turbulence in the central region of M 42 through structure functions

Here, we analyse the character of the turbulence of the Huygens Region in the Orion Nebula (M 42) using structure functions. We compute the second order structure function of a high resolution velocity map in H$\alpha$ obtained through the {\emph MUSE} instrument. Ours is one of the few works that follows a mathematically sound methodology for calculating the second order structure function of astronomical velocity fields. Because of that our results will be useful for future comparisons with other studies of M 42 or other regions. We first analyse the Probability Distribution Function (PDF) and found it consistent with those resulting from numerical simulations of solenoidal turbulence. After a further analysis of the data, we found two possible separate motions or at least regimes in the region. This is confirmed later through the calculation of several filtered structure functions. We found that the turbulence in the Huygens Region is between the Kolmogorov regime ($S_2\propto\delta r^{2/3}$) and the Burgers regime ($S_2\propto\delta r$). We found that the turbulence in the region consists on two flow regimes that reproduce a generalised Larson's Law, $S_2\sim\delta r^{0.74-0.76}$.

Impact of galactic shear and stellar feedback on star formation

Context. Feedback processes and the galactic shear regulate star formation. Aims. We investigate the effects of differential galactic rotation and stellar feedback on the interstellar medium (ISM) and on the star formation rate (SFR). Methods. A numerical shearing box is used to perform three-dimensional simulations of a 1 kpc stratified cubic box of turbulent and self-gravitating interstellar medium (in a rotating frame) with supernovae and H II feedback. We vary the value of the velocity gradient induced by the shear and the initial value of the galactic magnetic field. Finally, the different star formation rates and the properties of the structures associated with this set of simulations are computed. Results. We first confirm that the feedback has a strong limiting effect on star formation. The galactic shear has also a great influence: the higher the shear, the lower the SFR. Taking the value of the velocity gradient in the solar neighbourhood, the SFR is too high compared to the observed Kennicutt law, by a factor approximately three to six. This discrepancy can be solved by arguing that the relevant value of the shear is not the one in the solar neighbourhood, and that in reality the star formation efficiency within clusters is not 100%. Taking into account the fact that star-forming clouds generally lie in spiral arms where the shear can be substantially higher (as probed by galaxy-scale simulations), the SFR is now close to the observed one. Different numerical recipes have been tested for the sink particles, giving a numerical incertitude of a factor of about two on the SFR. Finally, we have also estimated the velocity dispersions in our dense clouds and found that they lie below the observed Larson law by a factor of about two. Conclusions. In our simulations, magnetic field, shear, H II regions, and supernovae all contribute significantly to reduce the SFR. In this numerical setup with feedback from supernovae and H II regions and a relevant value of galactic shear, the SFRs are compatible with those observed, with a numerical incertitude factor of about two.

Warm CO Gas Generated by Possible Turbulent Shocks in a Low-mass Star-forming Dense Core in Taurus

Abstract We report ALMA Cycle 3 observations in CO isotopes toward a dense core, MC27/L1521F in Taurus, which is considered to be at an early stage of multiple star formation in a turbulent environment. Although most of the high-density parts of this core are considered to be as cold as ∼10 K, high-angular resolution (∼20 au) observations in 12CO (J = 3–2) revealed complex warm (>15–60 K) filamentary/clumpy structures with the sizes from a few tens of astronomical units to ∼1000 au. The interferometric observations of 13CO and C18O show that the densest part with arc-like morphologies associated with the previously identified protostar and condensations are slightly redshifted from the systemic velocity of the core. We suggest that the warm CO clouds may be consequences of shock heating induced by interactions among the different density/velocity components that originated from the turbulent motions in the core. However, such a small-scale and fast turbulent motion does not correspond to a simple extension of the line–width–size relation (i.e., Larson's law), and thus the actual origin remains to be studied. The high-angular resolution CO observations are expected to be essential in detecting small-scale turbulent motions in dense cores and to investigate protostar formation therein.

Connecting the Cosmic Star Formation Rate with the Local Star Formation

Abstract We present a model that unifies the cosmic star formation rate (CSFR), obtained through the hierarchical structure formation scenario, with the (Galactic) local star formation rate (SFR). It is possible to use the SFR to generate a CSFR mapping through the density probability distribution functions commonly used to study the role of turbulence in the star-forming regions of the Galaxy. We obtain a consistent mapping from redshift z ∼ 20 up to the present (z = 0). Our results show that the turbulence exhibits a dual character, providing high values for the star formation efficiency ( 〈 ε 〉 ∼ 0.32 ) in the redshift interval z ∼ 3.5 – 20 and reducing its value to 〈 ε 〉 = 0.021 at z = 0. The value of the Mach number (  crit ), from which 〈 ε 〉 rapidly decreases, is dependent on both the polytropic index (Γ) and the minimum density contrast of the gas. We also derive Larson’s first law associated with the velocity dispersion ( 〈 V rms 〉 ) in the local star formation regions. Our model shows good agreement with Larson’s law in the ∼ 10 – 50 pc range, providing typical temperatures T 0 ∼ 10 – 80 K for the gas associated with star formation. As a consequence, dark matter halos of great mass could contain a number of halos of much smaller mass, and be able to form structures similar to globular clusters. Thus, Larson’s law emerges as a result of the very formation of large-scale structures, which in turn would allow the formation of galactic systems, including our Galaxy.

On the impact of the magnitude of Interstellar pressure on physical properties of Molecular Cloud

Recently reported variations in the typical physical properties of Galactic and extra-Galactic molecular clouds (MCs), and in their ability to form stars have been attributed to local variations in the magnitude of interstellar pressure. Inferences from these surveys have called into question two long-standing beliefs that the MCs : 1 are Virialised entities and (2) have approximately constant surface density i.e., the validity of the Larson's third law. In this work we invoke the framework of cloud-formation via collisions between warm gas flows. Post-collision clouds forming in these realisations cool rapidly and evolve primarily via the interplay between the Non-linear Thin Shell Instability (NTSI), and the self-gravity. Over the course of these simulations we traced the temporal evolution of the surface density of the assembled clouds, the fraction of dense gas, the distribution of gas column density (NPDF), and the Virial nature of the assembled clouds. We conclude, these physical properties of MCs not only exhibit temporal variation, but their respective peak-magnitude also increases in proportion with the magnitude of external pressure, $P_{ext}$. The velocity dispersion in assembled clouds appears to follow the power-law, $\sigma_{gas}\propto P_{ext}^{0.23}$. Also, the power-law tail at higher densities becomes shallower with increasing magnitude of external pressure, for magnitudes, $P_{ext}/k_{B}\lesssim 10^{7}$ K cm$^{-3}$, at higher magnitudes such as those typically found in the Galactic CMZ ($P_{ext}/k_{B} > 10^{7}$ K cm$^{-3}$), the power-law shows significant steepening. Thus while our results are broadly consistent with inferences from various recent observational surveys, it appears, MCs hardly exhibit a unique set of properties, but rather a wide variety, that can be reconciled with a range of magnitudes of pressure between 10$^{4}$ K cm$^{-3}$ - 10$^{8}$ K cm$^{-3}$.

A UNIFORM CATALOG OF MOLECULAR CLOUDS IN THE MILKY WAY

ABSTRACT The all-Galaxy CO survey of Dame et al. is by far the most uniform, large-scale Galactic CO survey. Using a dendrogram-based decomposition of this survey, we present a catalog of 1064 massive molecular clouds throughout the Galactic plane. This catalog contains 2.5 × 108 solar masses, or 25 − 5.8 + 10.7 % of the Milky Way's estimated H2 mass. We track clouds in some spiral arms through multiple quadrants. The power index of Larson's first law, the size-linewidth relation, is consistent with 0.5 in all regions—possibly due to an observational bias—but clouds in the inner Galaxy systematically have significantly (∼30%) higher linewidths at a given size, indicating that their linewidths are set in part by the Galactic environment. The mass functions of clouds in the inner Galaxy versus the outer Galaxy are both qualitatively and quantitatively distinct. The inner Galaxy mass spectrum is best described by a truncated power law with a power index of γ = −1.6 ± 0.1 and an upper truncation mass of M 0 = (1.0 ± 0.2) × 107 M ⊙, while the outer Galaxy mass spectrum is better described by a non-truncating power law with γ = −2.2 ± 0.1 and an upper mass of M 0 = (1.5 ± 0.5) × 106 M ⊙, indicating that the inner Galaxy is able to form and host substantially more massive GMCs than the outer Galaxy. Additionally, we have simulated how the Milky Way would appear in CO from extragalactic perspectives, for comparison with CO maps of other galaxies.

STAR FORMATION IN SELF-GRAVITATING TURBULENT FLUIDS

We present a model of star formation in self-gravitating turbulent gas. We treat the turbulent velocity $v_T$ as a dynamical variable, and assume that it is adiabatically heated by the collapse. The theory predicts the run of density, infall velocity, and turbulent velocity, and the rate of star formation in compact massive gas clouds. The turbulent pressure is dynamically important at all radii, a result of the adiabatic heating. The system evolves toward a coherent spatial structure with a fixed run of density, $\rho(r,t)\to\rho(r)$; mass flows through this structure onto the central star or star cluster. We define the sphere of influence of the accreted matter by $m_*=M_g(r_*)$, where $m_*$ is the stellar plus disk mass in the nascent star cluster and $M_g(r)$ is the gas mass inside radius $r$. The density is given by a broken power law with a slope $-1.5$ inside $r_*$ and $\sim -1.6$ to $-1.8$ outside $r_*$. Both $v_T$ and the infall velocity $|u_r|$ decrease with decreasing $r$ for $r>r_*$; $v_T(r)\sim r^p$, the size-linewidth relation, with $p\approx0.2-0.3$, explaining the observation that Larson's Law is altered in massive star forming regions. The infall velocity is generally smaller than the turbulent velocity at $r>r_*$. For $r<r_*$, the infall and turbulent velocities are again similar, and both increase with decreasing $r$ as $r^{-1/2}$, with a magnitude about half of the free-fall velocity. The accreted (stellar) mass grows super-linearly with time, $\dot M_*=\phi M_{\rm cl}(t/\tau_{ff})^2$, with $\phi$ a dimensionless number somewhat less than unity, $M_{\rm cl}$ the clump mass and $\tau_{ff}$ the free-fall time of the clump. We suggest that small values of p can be used as a tracer of convergent collapsing flows.

Age, size, and position of H ii regions in the Galaxy

This work aims at improving the current understanding of the interaction between H ii regions and turbulent molecular clouds. We propose a new method to determine the age of a large sample of OB associations by investigating the development of their associated H ii regions in the surrounding turbulent medium. Using analytical solutions, one-dimensional (1D), and three-dimensional (3D) simulations, we constrained the expansion of the ionized bubble depending on the turbulent level of the parent molecular cloud. A grid of 1D simulations was then computed in order to build isochrone curves for H ii regions in a pressure-size diagram. This grid of models allowed to date large sample of OB associations and was used on the H ii Region Discovery Survey (HRDS). Analytical solutions and numerical simulations showed that the expansion of H ii regions is slowed down by the turbulence up to the point where the pressure of the ionized gas is in a quasi-equilibrium with the turbulent ram pressure. Based on this result, we built a grid of 1D models of the expansion of H ii regions in a profile based on Larson laws. The 3D turbulence is taken into account by an effective 1D temperature profile. The ages estimated by the isochrones of this grid agree well with literature values of well-known regions such as Rosette, RCW 36, RCW 79, and M16. We thus propose that this method can be used to give ages of young OB associations through the Galaxy such as the HRDS survey and also in nearby extra-galactic sources.

Larson's scaling laws, and the gravitational instability of clumpy discs at high redshift

Gravitational instabilities play a primary role in shaping the clumpy structure and powering the star formation activity of gas-rich high-redshift galaxies. Here we analyse the stability of such systems, focusing on the size and mass ranges of unstable regions in the disc. Our analysis takes into account the mass-size and linewidth-size scaling relations observed in molecular gas, originally discovered by Larson. We show that such relations can have a strong impact on the size and mass of star-forming clumps, as well as on the stability properties of the disc at all observable scales, making the classical Toomre parameter a highly unreliable indicator of gravitational instability. For instance, a disc with Q=1 can be far from marginal instability, while a disc with Q<<1 can be marginally unstable. Our work raises an important caveat: if clumpy discs at high redshift have scale-dependent surface densities and velocity dispersions, as implied by the observed clump scaling relations, then we cannot thoroughly understand their stability and star formation properties unless we perform multi-scale observations. This will soon be possible thanks to dedicated ALMA surveys, which will explore the physical properties of super-giant molecular clouds at the peak of cosmic star formation and beyond.

A supersonic turbulence origin of Larson's laws

We revisit the origin of Larson's scaling laws describing the structure and kinematics of molecular clouds. Our analysis is based on recent observational measurements and data from a suite of six simulations of the interstellar medium, including effects of self-gravity, turbulence, magnetic field, and multiphase thermodynamics. Simulations of isothermal supersonic turbulence reproduce observed slopes in linewidth-size and mass-size relations. Whether or not self-gravity is included, the linewidth-size relation remains the same. The mass-size relation, instead, substantially flattens below the sonic scale, as prestellar cores start to form. Our multiphase models with magnetic field and domain size 200 pc reproduce both scaling and normalization of the first Larson law. The simulations support a turbulent interpretation of Larson's relations. This interpretation implies that: (i) the slopes of linewidth-size and mass-size correlations are determined by the inertial cascade; (ii) none of the three Larson laws is fundamental; (iii) instead, if one is known, the other two follow from scale invariance of the kinetic energy transfer rate. It does not imply that gravity is dynamically unimportant. The self-similarity of structure established by the turbulence breaks in star-forming clouds due to the development of gravitational instability in the vicinity of the sonic scale. The instability leads to the formation of prestellar cores with the characteristic mass set by the sonic scale. The high-end slope of the core mass function predicted by the scaling relations is consistent with the Salpeter power-law index.

Turbulent magnetic field amplification from the smallest to the largest magnetic Prandtl numbers

The small-scale dynamo provides a highly efficient mechanism for the conversion of turbulent into magnetic energy. In astrophysical environments, such turbulence often occurs at high Mach numbers, implying steep slopes in the turbulent spectra. It is thus a central question whether the small-scale dynamo can amplify magnetic fields in the interstellar or intergalactic media, where such Mach numbers occur. To address this long-standing issue, we employ the Kazantsev model for turbulent magnetic field amplification, systematically exploring the effect of different turbulent slopes, as expected for Kolmogorov, Burgers, the Larson laws and results derived from numerical simulations. With the framework employed here, we give the first solution encompassing the complete range of magnetic Prandtl numbers, including Pm ≪ 1, Pm ∼ 1 and Pm ≫ 1. We derive scaling laws of the growth rate as a function of hydrodynamic and magnetic Reynolds number for Pm ≪ 1 and Pm ≫ 1 for all types of turbulence. A central result concerns the regime of Pm ∼ 1, where the magnetic field amplification rate increases rapidly as a function of Pm. This phenomenon occurs for all types of turbulence we have explored. We further find that the dynamo growth rate can be decreased by a few orders of magnitude for turbulence spectra steeper than Kolmogorov. We calculate the critical magnetic Reynolds number Rmc for magnetic field amplification, which is highest for the Burgers case. As expected, our calculation shows a linear behaviour of the amplification rate close to the threshold proportional to (Rm − Rmc). On the basis of the Kazantsev model, we therefore expect the existence of the small-scale dynamo for a given value of Pm as long as the magnetic Reynolds number is above the critical threshold.

13CO CORES IN THE TAURUS MOLECULAR CLOUD

Young stars form in molecular cores, which are dense condensations within molecular clouds. We have searched for molecular cores traced by $^{13}$CO $J=1\to 0$ emission in the Taurus molecular cloud and studied their properties. Our data set has a spatial dynamic range (the ratio of linear map size to the pixel size) of about 1000 and spectrally resolved velocity information, which together allow a systematic examination of the distribution and dynamic state of $^{13}$CO cores in a large contiguous region. We use empirical fit to the CO and CO$_2$ ice to correct for depletion of gas-phase CO. The $^{13}$CO core mass function ($^{13}$CO CMF) can be fitted better with a log-normal function than with a power law function. We also extract cores and calculate the $^{13}$CO CMF based on the integrated intensity of $^{13}$CO and the CMF from 2MASS. We demonstrate that there exists core blending, i.e.\ combined structures that are incoherent in velocity but continuous in column density. The core velocity dispersion (CVD), which is the variance of the core velocity difference $\delta v$, exhibits a power-law behavior as a function of the apparent separation $L$:\ CVD (km/s) $\propto L ({\rm pc})^{0.7}$. This is similar to Larson's law for the velocity dispersion of the gas. The peak velocities of $^{13}$CO cores do not deviate from the centroid velocities of the ambient $^{12}$CO gas by more than half of the line width. The low velocity dispersion among cores, the close similarity between CVD and Larson's law, and the small separation between core centroid velocities and the ambient gas all suggest that molecular cores condense out of the diffuse gas without additional energy from star formation or significant impact from converging flows.

Molecular Cores in Taurus: Evolution and Dynamics

AbstractThe evolution and dynamics of the molecular cores traced by 13CO J = 1 → 0 emission in the Taurus molecular cloud are studied. We performed a systematic examination of the distribution and dynamic state of cores in a large contiguous region, as well as the core ages, which lie between 106 and 107 years. The core velocity dispersion (CVD), which is the variance of the core velocity difference δ v, exhibits a power-law behavior as a function of the apparent separation L, i.e. CVD (km/s) ∝ L (pc)0.7, with similarities to Larson's law for the velocity dispersion of the gas.

Occupational Health Nursing Interventions to Reduce Third-Party Liability in Workplace Injuries

This aRticle explores general principles of workers' compensation law and the ability to sue third parties for employee injuries by using case law and the treatise Larson's Workers' Compensation Law. This overview provides occupational health nurses with a background on workers' compensation law, who is liable for employee injuries, and how recovery from third parties is distributed between the employer or insurer and the employee. The author then explores interventions that occupational health nurses can implement to reduce employee injury and employer costs for providing workers' compensation. The goal of this article is to stimulate occupational health nurses' critical-thinking and problem-solving skills so they may identify risks and implement cost-effective solutions that will prevent injuries to employees.

Occupational Health Nursing Interventions to Reduce Third-Party Liability in Workplace Injuries

This article explores general principles of workers' compensation law and the ability to sue third parties for employee injuries by using case law and the treatise Larson's Workers' Compensation Law. This overview provides occupational health nurses with a background on workers' compensation law, who is liable for employee injuries, and how recovery from third parties is distributed between the employer or insurer and the employee. The author then explores interventions that occupational health nurses can implement to reduce employee injury and employer costs for providing workers' compensation. The goal of this article is to stimulate occupational health nurses' critical-thinking and problem-solving skills so they may identify risks and implement cost-effective solutions that will prevent injuries to employees.

Larson's third law and the universality of molecular cloud structure

Larson (1981) first noted a scaling relation between masses and sizes in molecular clouds that implies that these objects have approximately constant column densities. This original claim, based upon millimeter observations of carbon monoxide lines, has been challenged by many theorists, arguing that the apparent constant column density observed is merely the result of the limited dynamic range of observations, and that in reality clouds have column density variations over two orders of magnitudes. In this letter we investigate a set of nearby molecular clouds with near-infrared excess methods, which guarantee very large dynamic ranges and robust column density measurements, to test the validity of Larson's third law. We verify that different clouds have almost identical average column densities <i>above a given extinction threshold <i/>; this holds regardless of the extinction threshold, but the actual average surface mass density is a function of the specific threshold used. We show that a second version of Larson's third law, involving the mass-radius relation for single clouds and cores, does not hold in our sample, indicating that individual clouds are not objects that can be described by constant column density. Our results instead indicate that molecular clouds are characterized by a universal structure. Finally we point out that this universal structure can be linked to the log-normal nature of cloud column density distributions.

THE MASS-SIZE RELATION FROM CLOUDS TO CORES. II. SOLAR NEIGHBORHOOD CLOUDS

We measure the mass and size of cloud fragments in several molecular clouds continuously over a wide range of spatial scales (0.05 < r / pc < 3). Based on the recently developed "dendrogram-technique", this characterizes dense cores as well as the enveloping clouds. "Larson's 3rd Law" of constant column density, m(r) = C*r^2, is not well suited to describe the derived mass-size data. Solar neighborhood clouds not forming massive stars (< 10 M_sun; Pipe Nebula, Taurus, Perseus, and Ophiuchus) obey m(r) < 870 M_sun (r / pc)^1.33 . In contrast to this, clouds forming massive stars (Orion A, G10.15$-$0.34, G11.11$-$0.12) do exceed the aforementioned relation. Thus, this limiting mass-size relation may approximate a threshold for the formation of massive stars. Across all clouds, cluster-forming cloud fragments are found to be---at given radius---more massive than fragments devoid of clusters. The cluster-bearing fragments are found to roughly obey a mass-size law m = C*r^1.27 (where the exponent is highly uncertain in any given cloud, but is certainly smaller than 1.5).

THE EFFECT OF PROJECTION ON DERIVED MASS-SIZE AND LINEWIDTH-SIZE RELATIONSHIPS

Power law mass-size and linewidth-size correlations, two of "Larson's laws," are often studied to assess the dynamical state of clumps within molecular clouds. Using the result of a hydrodynamic simulation of a molecular cloud, we investigate how geometric projection may affect the derived Larson relationships. We find that large scale structures in the column density map have similar masses and sizes to those in the 3D simulation (PPP). Smaller scale clumps in the column density map are measured to be more massive than the PPP clumps, due to the projection of all emitting gas along lines of sight. Further, due to projection effects, structures in a synthetic spectral observation (PPV) may not necessarily correlate with physical structures in the simulation. In considering the turbulent velocities only, the linewidth-size relationship in the PPV cube is appreciably different from that measured from the simulation. Including thermal pressure in the simulated linewidths imposes a minimum linewidth, which results in a better agreement in the slopes of the linewidth-size relationships, though there are still discrepancies in the offsets, as well as considerable scatter. Employing commonly used assumptions in a virial analysis, we find similarities in the computed virial parameters of the structures in the PPV and PPP cubes. However, due to the discrepancies in the linewidth- and mass- size relationships in the PPP and PPV cubes, we caution that applying a virial analysis to observed clouds may be misleading due to geometric projection effects. We speculate that consideration of physical processes beyond kinetic and gravitational pressure would be required for accurately assessing whether complex clouds, such as those with highly filamentary structure, are bound.

A Catalog of H i Clouds in the Large Magellanic Cloud

A 21 cm neutral hydrogen interferometric survey of the Large Magellanic Cloud (LMC) combined with the Parkes multi-beam HI single-dish survey clearly shows that the HI gas is distributed in the form of clumps or clouds. The HI clouds and clumps have been identified using a thresholding method with three separate brightness temperature thresholds ($T_b$). Each catalog of HI cloud candidates shows a power law relationship between the sizes and the velocity dispersions of the clouds roughly following the Larson Law scaling $\sigma_v \propto R^{0.5}$, with steeper indices associated with dynamically hot regions. The clouds in each catalog have roughly constant virial parameters as a function mass suggesting that that the clouds are all in roughly the same dynamical state, but the values of the virial parameter are significantly larger than unity showing that turbulent motions dominate gravity in these clouds. The mass distribution of the clouds is a power law with differential indices between -1.6 and -2.0 for the three catalogs. In contrast, the distribution of mean surface densities is a log-normal distribution.