Sonic Mach Number Research Articles

Probes of turbulent driving mechanisms in molecular clouds from fluctuations in synchrotron intensity

Previous studies have shown that star formation depends on the driving of molecular cloud turbulence, and differences in the driving can produce an order of magnitude difference in the star formation rate. The turbulent driving is characterised by the parameter $\zeta$, with $\zeta=0$ for compressive, curl-free driving (e.g. accretion or supernova explosions), and $\zeta=1$ for solenoidal, divergence-free driving (e.g. Galactic shear). Here we develop a new method to measure $\zeta$ from observations of synchrotron emission from molecular clouds. We calculate statistics of mock synchrotron intensity images produced from magnetohydrodynamic simulations of molecular clouds, in which the driving was controlled to produce different values of $\zeta$. We find that the mean and standard deviation of the log-normalised synchrotron intensity are sensitive to $\zeta$, for values of $\zeta$ between $0$ (curl-free driving) and $0.5$ (naturally-mixed driving). We quantify the dependence of zeta on the direction of the magnetic field relative to the line of sight. We provide best-fit formulae for $\zeta$ in terms of the log-normalised mean and standard deviation of synchrotron intensity, with which $\zeta$ can be determined for molecular clouds that have similar Alfv\'enic Mach number to our simulations. These formulae are independent of the sonic Mach number. Signal-to-noise ratios larger than $5$, and angular resolutions smaller than $5\%$ of the cloud diameter, are required to apply these formulae. Although there are no firm detections of synchrotron emission from molecular clouds, by combining Green Bank Telescope and Very Large Array observations it should be possible to detect synchrotron emission from molecular clouds, thereby constraining the value of $\zeta$.

DENSITY-MAGNETIC FIELD CORRELATION IN MAGNETOHYDRODYNAMIC TURBULENCE DRIVEN BY DIFFERENT DRIVING SCHEMES WITH DIFFERENT CORRELATION TIMES

ABSTRACT Turbulent motions naturally produce density and magnetic-field fluctuations. Correlation between the two fluctuations is important for interpretation of observations, such as observations of the rotation measure (RM). In this paper, we study the effect of driving schemes on the density-magnetic-field correlation. In particular, we numerically investigate how the correlation time of driving affects the correlation between density and magnetic field. We perform compressible magnetohydrodynamic turbulence simulations at different sonic Mach numbers (M s ), using two different driving schemes—a finite-correlated driving and a delta-correlated driving. In the former, the forcing vectors change continuously with a correlation time comparable to the large-eddy turnover time. In the latter, the direction (and amplitude) of driving changes in a very short timescale. The finite-correlated driving results in strong anti-correlation between two fields when the sonic and the Alfvénic Mach numbers are similar to unity (i.e., when M s ∼ 1 and M A ∼ 1, respectively). However, the anti-correlation becomes weaker and approaches zero for higher values of M s or M A. The delta-correlated driving produces virtually no correlation between two fields when M s ∼ 1 and M A ∼ 1, and produces more and more positive correlations as M s or M A increases. We conjecture that two competing effects, tendency for achieving balance between the gas and the magnetic pressure and simultaneous compression of fluid and magnetic field, determine the correlation behavior. We also investigate how different driving schemes affect the Probability Density Function of three-dimensional density, dispersion measure, and RM.

SHOCKFIND - an algorithm to identify magnetohydrodynamic shock waves in turbulent clouds

The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetised turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks --- fast, intermediate and slow --- distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here we introduce the publicly available algorithm, SHOCKFIND, to extract and characterise the mixture of shock families in MHD turbulence. The algorithm is applied to a 3-dimensional simulation of a magnetised turbulent molecular cloud, and we find that both fast and slow MHD shocks are present in the simulation. We give the first prediction of the mixture of turbulence-driven MHD shock families in this molecular cloud, and present their distinct distributions of sonic and Alfvenic Mach numbers. Using subgrid one-dimensional models of MHD shocks we estimate that ~0.03 % of the volume of a typical molecular cloud in the Milky Way will be shock heated above 50 K, at any time during the lifetime of the cloud. We discuss the impact of this shock heating on the dynamical evolution of molecular clouds.

THE PHASE COHERENCE OF INTERSTELLAR DENSITY FLUCTUATIONS

ABSTRACT Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here, we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM column density maps: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create three-dimensional density and two-dimensional column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide range of sonic and Alfvénic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the k 1 or k 2 axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfvénic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfvénic turbulence and near the shock scale. This suggests that nonlinear interactions with correlated phases are strongest in shock-dominated regions, in agreement with findings from the solar wind. Our results suggest that the phase information contained in the bispectrum and PCI can be used to find the turbulence parameters in column density maps.

NUMERICAL SIMULATIONS OF KELVIN–HELMHOLTZ INSTABILITY: A TWO-DIMENSIONAL PARAMETRIC STUDY

ABSTRACT Using two-dimensional simulations, we numerically explore the dependences of Kelvin–Helmholtz (KH) instability upon various physical parameters, including viscosity, the width of the sheared layer, flow speed, and magnetic field strength. In most cases, a multi-vortex phase exists between the initial growth phase and the final single-vortex phase. The parametric study shows that the evolutionary properties, such as phase duration and vortex dynamics, are generally sensitive to these parameters, except in certain regimes. An interesting result is that for supersonic flows, the phase durations and saturation of velocity growth approach constant values asymptotically as the sonic Mach number increases. We confirm that the linear coupling between magnetic field and KH modes is negligible if the magnetic field is weak enough. The morphological behavior suggests that the multi-vortex coalescence might be driven by the underlying wave–wave interaction. Based on these results, we present a preliminary discussion of several events observed in the solar corona. The numerical models need to be further improved to perform a practical diagnostic of the coronal plasma properties.

A nonlinear structural subgrid-scale closure for compressible MHD. II. A priori comparison on turbulence simulation data

Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics. We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number Ms=0.2–20 as reference data for the most extensive a priori tests performed so far in literature. In these tests, we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicity flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and the direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value > 0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.

RE-ACCELERATION MODEL FOR RADIO RELICS WITH SPECTRAL CURVATURE

ABSTRACT Most of the observed features of radio gischt relics, such as spectral steepening across the relic width and a power-law-like integrated spectrum, can be adequately explained by a diffusive shock acceleration (DSA) model in which relativistic electrons are (re-)accelerated at shock waves induced in the intracluster medium. However, the steep spectral curvature in the integrated spectrum above ∼2 GHz detected in some radio relics, such as the Sausage relic in cluster CIZA J2242.8+5301, may not be interpreted by the simple radiative cooling of postshock electrons. In order to understand such steepening, we consider here a model in which a spherical shock sweeps through and then exits out of a finite-size cloud with fossil relativistic electrons. The ensuing integrated radio spectrum is expected to steepen much more than predicted for aging postshock electrons, since the re-acceleration stops after the cloud-crossing time. Using DSA simulations that are intended to reproduce radio observations of the Sausage relic, we show that both the integrated radio spectrum and the surface brightness profile can be fitted reasonably well, if a shock of speed ∼ 2.5–2.8 × and a sonic Mach number ∼ 2.7–3.0 traverses a fossil cloud for ∼45 Myr, and the postshock electrons cool further for another ∼10 Myr. This attempt illustrates that steep curved spectra of some radio gischt relics could be modeled by adjusting the shape of the fossil electron spectrum and adopting the specific configuration of the fossil cloud.

Supersonic Jet Control with Air-Tabs

A Mach 2 jet controlled with two air-tabs at subsonic, correctly and underexpanded sonic Mach numbers, located diametrically opposite at distances of 0.38D, 1.15D and 1.92 D, downstream of the nozzle exit has been studied. The air-tab effect on the jet mixing, in the presence of adverse pressure gradient corresponding to nozzle pressure ratios 2, 3 and 4 were investigated. The results show that air-tab can be used to control the jet mixing. The mixing modification caused by the air-tab is found to be strong function of the pressure gradient of the jet, air-tab Mach number and the location. The underexpansion level of the air-tab also influences the mixing promoting capability of the sonic air-tab. As high as 56% reduction in the jet core length has been obtained with sonic air-tab at NPR 4 positioned at 1.92 D downstream of the nozzle exit.

Effect of Mach number, valve angle and length to diameter ratio on thermal performance in flow of air through Ranque Hilsch vortex tube

Ranque Hilsch vortex tube is a device that can produce cold and hot air streams simultaneously from pressurized air. Performance of vortex tube is influenced by a number of geometrical and operational parameters. In this study parametric analysis of vortex tube is carried out. Air is used as the working fluid and geometrical parameters like length to diameter ratio (15, 16, 17, 18), exit valve angles (30°–90°), orifice diameters (5, 6 and 7 mm), 2 entry nozzles and tube divergence angle 4° is used for experimentation. Operational parameters like pressure (200–600 kPa), cold mass fraction (0–1) is varied and effect of Mach number at the inlet of the tube is investigated. The vortex tube is tested at sub sonic (0 < Ma < 1), sonic (Ma = 1) and supersonic (1 < Ma < 2) Mach number, and its effect on thermal performance is analysed. As a result it is observed that, higher COP and low cold end temperature is obtained at subsonic Ma. As CMF increases, COP rises and cold and temperature drops. Optimum performance of the tube is observed for CMF up to 0.5. Experimental correlations are proposed for optimum COP. Parametric correlation is developed for geometrical and operational parameters.

Slow modes in the Hermean magnetosphere: Effect of the solar wind hydrodynamic parameters and IMF orientation

The aim of this study is to simulate the slow mode structures in the Hermean magnetosphere. We use a single fluid MHD model and a multipolar expansion of the Northward displaced Hermean magnetic field, to perform simulations with different solar wind parameters to foreseen the most favorable configuration for the formation of slow modes, attending to the solar wind density, velocity, temperature and the interplanetary magnetic field orientation. If the interplanetary magnetic field is aligned with the Mercury-Sun direction, the magnetic axis of Mercury in the Northward direction or the planet orbital plane, slow mode structures are observed nearby the South pole. If the orientation is in the Sun-Mercury or Northward directions, slow mode structures are observed nearby the North pole, but smaller compared with the structures near the South pole. Increasing the density or the solar wind velocity avoids the formation of slow modes structures, not observed for a dynamic pressure larger than 6.25·10−9Pa in the case of a Northward interplanetary magnetic field orientation, due to the enhancement of the bow shock compression. If the solar wind temperature increases, the slow mode structures are wider because the sonic Mach number is smaller and the bow shock is less compressed.

PROPERTIES OF THE FAST FORWARD SHOCK DRIVEN BY THE 2012 JULY 23 EXTREME CORONAL MASS EJECTION

ABSTRACT Late on 2012 July 23, the STEREO-A spacecraft encountered a fast forward shock driven by a coronal mass ejection (CME) launched from the Sun earlier that same day. The estimated travel time of the disturbance (∼20 hr), together with the massive magnetic field strengths measured within the ejecta (&gt;100 nT), made it one of the most extreme events observed during the space era. In this study, we examine the properties of the shock wave. Because of an instrument malfunction, plasma measurements during the interval surrounding the CME were limited, and our approach has been modified to capitalize on the available measurements and suitable proxies, where possible. We were able to infer the following properties. First, the shock normal was pointing predominantly in the radial direction ( n = 0.97 e r &minus; 0.09 e t &minus; 0.23 e n ?> ). Second, the angle between n ?> and the upstream magnetic field, θ Bn, was estimated to be ≈34°, making the shock “quasi-parallel,” and supporting the idea of an earlier “preconditioning” ICME. Third, the shock speed was estimated to be ≈3300 km s−1. Fourth, the sonic Mach number, M s , for this shock was ∼28. We support these results with an idealized numerical simulation of the ICME. Finally, we estimated the change in ram pressure upstream of the shock to be ∼5 times larger than the pressure from the energetic particles, suggesting that this cosmic-ray modified shock had not reached steady-state, but instead, had been caught in an early, transient phase in its evolution.

PRINCIPAL COMPONENT ANALYSIS STUDIES OF TURBULENCE IN OPTICALLY THICK GAS

ABSTRACT In this work we investigate the sensitivity of principal component analysis (PCA) to the velocity power spectrum in high-opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic position–position–velocity (PPV) cubes of fractional Brownian motion and magnetohydrodynamics (MHD) simulations, post-processed to include radiative transfer effects from CO. We find that PCA analysis is very different from the tools based on the traditional power spectrum of PPV data cubes. Our major finding is that PCA is also sensitive to the phase information of PPV cubes and this allows PCA to detect the changes of the underlying velocity and density spectra at high opacities, where the spectral analysis of the maps provides the universal −3 spectrum in accordance with the predictions of the Lazarian &amp; Pogosyan theory. This makes PCA a potentially valuable tool for studies of turbulence at high opacities, provided that proper gauging of the PCA index is made. However, we found the latter to not be easy, as the PCA results change in an irregular way for data with high sonic Mach numbers. This is in contrast to synthetic Brownian noise data used for velocity and density fields that show monotonic PCA behavior. We attribute this difference to the PCA's sensitivity to Fourier phase information.

STUDYING THE INTERSTELLAR MAGNETIC FIELD FROM ANISOTROPIES IN VELOCITY CHANNELS

Turbulence in the interstellar medium is anisotropic due to the ubiquitous magnetic fields. This anisotropy depends on the strength of the magnetic field and leaves an imprint on observations of spectral line maps. We use a grid of ideal magnetohydrodynamic simulations of driven turbulence and produce synthetic position–position–velocity maps to study the turbulence anisotropy in velocity channels of various resolutions. We found that the average structure function of velocity channels is aligned with the projection of the magnetic field on the plane of the sky. We also found that the degree of such anisotropy increases with the magnitude of the magnetic field. For thick velocity channels (low velocity resolution), the anisotropy is dominated by density, and the degree of anisotropy in these maps allows one to distinguish sub-Alfvenic and super-Alfvenic turbulence regimes, but it also depends strongly on the sonic Mach number. For thin channels (high velocity resolution), we find that the anisotropy depends less on the sonic Mach number. An important limitation of this technique is that it only gives a lower limit on the magnetic field strength because the anisotropy is related only to the magnetic field component on the plane of the sky. It can, and should, be used in combination with other techniques to estimate the magnetic field, such as the Fermi-Chandrasekhar method, anisotropies in centroids, Faraday rotation measurements, or direct line-of-sight determinations of the field from Zeeman effect observations.

THE LOGNORMAL PROBABILITY DISTRIBUTION FUNCTION OF THE PERSEUS MOLECULAR CLOUD: A COMPARISON OF HI AND DUST

The shape of the probability distribution function (PDF) of molecular clouds is an important ingredient for modern theories of star formation and turbulence. Recently, several studies have pointed out observational difficulties with constraining the low column density (i.e. Av <1) PDF using dust tracers. In order to constrain the shape and properties of the low column density probability distribution function, we investigate the PDF of multiphase atomic gas in the Perseus molecular cloud using opacity-corrected GALFA-HI data and compare the PDF shape and properties to the total gas PDF and the N(H2) PDF. We find that the shape of the PDF in the atomic medium of Perseus is well described by a lognormal distribution, and not by a power-law or bimodal distribution. The peak of the atomic gas PDF in and around Perseus lies at the HI-H2 transition column density for this cloud, past which the N(H2) PDF takes on a powerlaw form. We find that the PDF of the atomic gas is narrow and at column densities larger than the HI-H2 transition the HI rapidly depletes, suggesting that the HI PDF may be used to find the HI-H2 transition column density. We also calculate the sonic Mach number of the atomic gas by using HI absorption line data, which yields a median value of Ms=4.0 for the CNM, while the HI emission PDF, which traces both the WNM and CNM, has a width more consistent with transonic turbulence.

CURVED RADIO SPECTRA OF WEAK CLUSTER SHOCKS

In order to understand certain observed features of arc-like giant radio relics such as the rareness, uniform surface brightness, and curved integrated spectra, we explore a diffusive shock acceleration (DSA) model for radio relics in which a spherical shock impinges on a magnetized cloud containing fossil relativistic electrons. Toward this end, we perform DSA simulations of spherical shocks with the parameters relevant for the Sausage radio relic in cluster CIZA J2242.8+5301, and calculate the ensuing radio synchrotron emission from re-accelerated electrons. Three types of fossil electron populations are considered: a delta-function like population with the shock injection momentum, a power-law distribution, and a power-law with an exponential cutoff. The surface brightness profile of radio-emitting postshock region and the volume-integrated radio spectrum are calculated and compared with observations. We find that the observed width of the Sausage relic can be explained reasonably well by shocks with speed $u_s \sim 3\times 10^3 \kms$ and sonic Mach number $M_s \sim 3$. These shocks produce curved radio spectra that steepen gradually over $(0.1-10) \nu_{\rm br}$ with break frequency $ \nu_{\rm br}\sim 1$ GHz, if the duration of electron acceleration is $\sim 60 - 80$ Myr. However, the abrupt increase of spectral index above $\sim 1.5$ GHz observed in the Sausage relic seems to indicate that additional physical processes, other than radiative losses, operate for electrons with $\gamma_e \gtrsim 10^4$.

Self-similar hierarchical energetics in the ICM of massive galaxy clusters

AbstractMassive galaxy clusters (GC) are filled with a hot, turbulent and magnetised intra-cluster medium (ICM). They are still forming under the action of gravitational instability, which drives supersonic mass accretion flows. These partially dissipate into heat through a complex network of large scale shocks, and partly excite giant turbulent eddies and cascade. Turbulence dissipation not only contributes to heating of the ICM but also amplifies magnetic energy by way of dynamo action. The pattern of gravitational energy turning into kinetic, thermal, turbulent and magnetic is a fundamental feature of GC hydrodynamics but quantitative modelling has remained a challenge. In this contribution we present results from a recent high resolution, fully cosmological numerical simulation of a massive Coma-like galaxy cluster in which the time dependent turbulent motions of the ICM are resolved (Miniati 2014) and their statistical properties are quantified for the first time (Miniati 2015, Beresnyak &amp; Miniati 2015). We combine these results with independent state-of-the art numerical simulations of MHD turbulence (Beresnyak 2012), which shows that in the nonlinear regime of turbulent dynamo (for magnetic Prandtl numbers≳ 1) the growth rate of the magnetic energy corresponds to a fraction CE ≃ 4 − 5 × 10−2 of the turbulent dissipation rate. We thus determine without adjustable parameters the thermal, turbulent and magnetic history of giant GC (Miniati &amp; Beresnyak 2015). We find that the energy components of the ICM are ordered according to a permanent hierarchy, in which the sonic Mach number at the turbulent injection scale is of order unity, the beta of the plasma of order forty and the ratio of turbulent injection scale to Alfvén scale is of order one hundred. These dimensionless numbers remain virtually unaltered throughout the cluster's history, despite evolution of each individual component and the drive towards equipartition of the turbulent dynamo, thus revealing a new type of self-similarity in cosmology. Their specific values, while consistent with current data, indicate that thermal energy dominates the ICM energetics and the turbulent dynamo is always far from saturation, unlike the condition in other familiar astrophysical fluids (stars, interstellar medium of galaxies, compact objects, etc.). In addition, they have important physical meaning as their specific values encodes information about the efficiency of turbulent heating (the fraction of ICM thermal energy produced by turbulent dissipation) and the efficiency of dynamo action in the ICM (CE).

A UNIVERSAL, TURBULENCE-REGULATED STAR FORMATION LAW: FROM MILKY WAY CLOUDS TO HIGH-REDSHIFT DISK AND STARBURST GALAXIES

While the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes that determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation (SF) laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation () by the gas column density (), we develop a new universal SF law based on the multi-freefall prescription of gas. This new SF law relies predominantly on the probability density function and on the sonic Mach number of the turbulence in the star-forming clouds. By doing so we derive a relation where the SFR correlates with the molecular gas mass per multi-freefall time, whereas previous models had used the average, single-freefall time. We define a new quantity called maximum (multi-freefall) gas consumption rate (MGCR) and show that the actual SFR is only about 0.4% of this maximum possible SFR, confirming the observed low efficiency of SF. We show that placing observations in this new framework ( versus MGCR) yields a significantly improved correlation with 3–4 times reduced scatter compared to previous SF laws and a goodness-of-fit parameter . By inverting our new relationship, we provide sonic Mach number predictions for kiloparsec-scale observations of Local Group galaxies as well as unresolved observations of local and high-redshift disk and starburst galaxies that do not have independent, reliable estimates for the turbulent cloud Mach number.

On the electron-ion temperature ratio established by collisionless shocks

Astrophysical shocks are often collisionless shocks. An open question about collisionless shocks is whether electrons and ions each establish their own post-shock temperature, or whether they quickly equilibrate in the shock region. Here we provide simple relations for the minimal amount of equilibration to expect. The basic assumption is that the enthalpy-flux of the electrons is conserved separately, but that all particle species should undergo the same density jump across the the shock. This assumption results in an analytic treatment of electron-ion equilibration that agrees with observations of collisionless shocks: at low Mach numbers ($<2$) the electrons and ions are close to equilibration, whereas for Mach numbers above $M \sim 60$ the electron-ion temperature ratio scales with the particle masses $T_e/T_i = m_e/m_i$. In between these two extremes the electron-ion temperature ratio scales as $T_e/T_i \propto 1/M_s^2$. This relation also hold if adiabatic compression of the electrons is taken into account. For magnetised plasmas the compression is governed by the magnetosonic Mach number, whereas the electron-ion temperatures are governed by the sonic Mach number. The derived equations are in agreement with observational data at low Mach numbers, but for supernova remnants the relation requires that the inferred Mach numbers for the observations are over- estimated, perhaps as a result of upstream heating in the cosmic-ray precursor. In addition to predicting a minimal electron/ion temperature ratio, we also heuristically incorporate ion-electron heat exchange at the shock, quantified with a dimensionless parameter ${\xi}$. Comparing the model to existing observations in the solar system and supernova remnants suggests that the data are best described by ${\xi} \sim 5$ percent. (Abridged abstract.)

The density variance–Mach number relation in isothermal and non-isothermal adiabatic turbulence

The density variance { Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, eciency, and the initial mass function of stars. Here we use high-resolution hydrodynamical simulations with grid resolutions of up to 1024 3 cells to model compressible turbulence in a regime similar to the observed interstellar medium. We use Fyris Alpha, a shock-capturing code employing a high-order Godunov scheme to track large density variations induced by shocks. We investigate the robustness of the standard relation between the logarithmic density variance ( 2 ) and the sonic Mach number (M) of isothermal interstellar turbulence, in the non-isothermal regime. Specically, we test ideal gases with diatomic molecular ( = 7=5) and monatomic ( = 5=3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fullydeveloped turbulent medium. We nd that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance { Mach number plane, but deviates signicantly from the standard expression for isothermal gases. Our main

ON THE FUNCTIONAL FORM OF THE UNIVERSAL STAR-FORMATION LAW

We study the functional form of the star formation law, using the Vaschy-Buckingham Pi theorem. We find that that it should have a form $\rm \dot{\Sigma}_{\star} \propto \sqrt{\frac{G}{L}}\Sigma_{gas}^{3/2}$, where L is a characteristic length that is related with an integration scale. With a reasonable estimation for L, we find that galaxies from different types and redshifts, including Low Surface Brightness galaxies, and individual star-forming regions in our galaxy, obey this single star formation law. We also find that depending on the assumption for L, this star formation law adopt different formulations of $\rm \dot{\Sigma}_{\star}$ scaling, that are widely studied in the literature: $\rm \Sigma_{gas}^{3/2}, \Sigma_{gas}/t_{orb}, \Sigma_{gas}/t_{ff} \, and \, \Sigma_{gas}^{2}/v_{turb}$. We also study secondary controlling parameters of the star formation law, based on the current evidence from numerical simulations and find that for galaxies, the star formation efficiency should be controlled, at least, by the turbulent Toomre parameter, the sonic and Alfvenic Mach numbers.