arXiv subjects

Paolo Padoan

Publications and source records attributed to Paolo Padoan.

At least 91 records · Page 5Linked to original sources

arXiv2003

The Spectral Correlation Function of Molecular Clouds: A Statistical Test for Theoretical Models

We compute the spectral correlation function (SCF) of 13CO J=1--0 maps of molecular cloud complexes. The SCF is a power law over approximately an order of magnitude in spatial separation in every map. The power law slope of the SCF, alpha, its normalization, S_0(1pc), and the spectral line width averaged over the whole map, sigma_v, are computed for all the observational maps. The values of alpha, S_0(1pc) and sigma_v are combined to obtain empirical correlations to be used as tests for theoretical models of molecular clouds. Synthetic spectral maps are computed from different theoretical models, including solutions of the magneto-hydrodynamic (MHD) equations with different values of the rms Mach number of the flow and stochastic models with different power spectra of the velocity field. In order to compute the radiative transfer from the MHD models it is necessary to assign the models a physical scale and a physical density. When these assignments are made according to Larson type relations the best fit to the observational correlations is obtained. Unphysical stochastic models are instead ruled out by the empirical correlations. MHD models with equipartition of magnetic and kinetic energy of turbulence do not reproduce the observational data when their average magnetic field is oriented approximately parallel to the line of sight.

astro-ph↗

arXiv2002

Star Formation and the Initial Mass Function

Supersonic turbulence fragments the interstellar medium into dense sheets, filaments, cores and large low density voids. The turbulence is driven on large scales, probably predominantly by supernovae. The scaling properties of supersonic turbulence are well described by a new analytical theory. The distribution of proto-stellar core masses depends primarily on the power spectrum of the turbulent flow, and on the jump conditions for near isothermal shocks in a magnetized gas. For the predicted velocity power spectrum index beta=1.74, consistent with results of numerical experiments of supersonic turbulence as well as with Larson's velocity-size relation, one obtains by scaling arguments a power law mass distribution of dense cores with a slope equal to 3/(4-beta) = 1.33, consistent with the slope of the Salpeter stellar initial mass function (IMF). Results from numerical simulations confirm this scaling. Both the analytical model for the stellar IMF and its numerical estimate show that turbulent fragmentation can also explain the origin of brown dwarfs.

astro-ph↗

arXiv2002

Structure Function Scaling of a 2MASS Extinction Map of Taurus

We compute the structure function scaling of a 2MASS extinction map of the Taurus molecular cloud complex. The scaling exponents of the structure functions of the extinction map follow the Boldyrev's velocity structure function scaling of supersonic turbulence. This confirms our previous result based on a spectral map of 13CO J=1-0 covering the same region and suggests that supersonic turbulence is important in the fragmentation of this star--forming cloud.

astro-ph↗

arXiv2002

Structure Function Scaling in the Taurus and Perseus Molecular Cloud Complexes

We compute the structure function scaling of the integrated intensity images of two J=1-0 13CO maps of Taurus and Perseus. The scaling exponents of the structure functions follow the velocity scaling of supersonic turbulence, suggesting that turbulence plays an important role in the fragmentation of cold interstellar clouds. The data also allows to verify the validity of the two basic assumptions of the hierarchical symmetry model, originally proposed for the derivation of the velocity structure function scaling. This shows that the same hierarchical symmetry holds for the projected density field of cold interstellar clouds.

astro-ph↗

arXiv2002

The Stellar IMF from Turbulent Fragmentation

The morphology and kinematics of molecular clouds (MCs) are best explained as the consequence of super--sonic turbulence. Super--sonic turbulence fragments MCs into dense sheets, filaments and cores and large low density ``voids'', via the action of highly radiative shocks. We refer to this process as "turbulent fragmentation". In this work we derive the mass distribution of gravitationally unstable cores generated by the process of turbulent fragmentation. The mass distribution above one solar mass depends primarily on the power spectrum of the turbulent flow and on the jump conditions for isothermal shocks in a magnetized gas. For a power spectrum index β=-1.74, consistent with Larson's velocity dispersion--size relation as well as with new numerical and analytic results on super--sonic turbulence, we obtain a power law mass distribution of dense cores with a slope equal to 3/(4-β) = 1.33, consistent with the slope of the stellar IMF. Below one solar mass, the mass distribution flattens and turns around at a fraction of a solar mass, as observed for the stellar IMF in a number of stellar clusters, because only the densest cores are gravitationally unstable. The mass distribution at low masses is determined by the probability distribution of the gas density, which is known to be approximately Log--Normal for an isothermal turbulent gas. The intermittent nature of the turbulent density distribution is thus responsible for the existence of a significant number of small collapsing cores, even of sub--stellar mass. Since turbulent fragmentation is unavoidable in super--sonically turbulent molecular clouds, and given the success of the present model in predicting the observed shape of the stellar IMF, we conclude that turbulent fragmentation is essential to the origin of the stellar IMF.

astro-ph↗

arXiv2002

Supersonic turbulence and structure of interstellar molecular clouds

The interstellar medium (ISM) provides a unique laboratory for highly supersonic, driven hydrodynamics turbulence. We present a theory of such turbulence, confirm it by numerical simulations, and use the results to explain observational properties of interstellar molecular clouds, the regions where stars are born.

astro-ph↗

arXiv2001

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 <|Δu|>~ 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].

astro-ph↗

arXiv2001

Theoretical Models of Polarized Dust Emission from Protostellar Cores

We model the polarized thermal dust emission from protostellar cores that are assembled by super-sonic turbulent flows in molecular clouds. Self-gravitating cores are selected from a three dimensional simulation of super-sonic and super-Alfvenic magneto-hydrodynamic (MHD) turbulence. The polarization is computed in two ways. In model A it is assumed that dust properties and grain alignment efficiency are uniform; in model B it is assumed that grains are not aligned at visual extinction larger than 3 mag. The main results of this work are: i) Values of the degree of polarization P between 1 and 10% are typical, despite the super-Alfvenic nature of the turbulence; ii) A steep decrease of P with increasing values of the sub-mm dust continuum intensity I is always found in self--gravitating cores selected from the MHD simulations, if grains are not aligned above a certain value of visual extinction (model B); iii) The same behavior is hard to reproduce if grains are aligned independently of visual extinction (model A); iv) The Chandrasekhar-Fermi formula, corrected by a factor f=0.4, provides an approximate estimate of the average magnetic field strength in the cores. Sub-mm dust continuum polarization maps of quiescent protostellar cores and Bok globules always show a decrease in P with increasing value of I consistent with the predictions of our model B. We therefore conclude that sub-mm polarization maps of quiescent cores do not map the magnetic field inside the cores at visual extinction larger than approximately 3 mag. There is no inconsistency between the results from optical and near-IR polarized absorption of background stars, and the observed polarization of sub-mm dust continuum from quiescent cores. In both cases, grains at large visual extinction appear to be virtually unaligned.

astro-ph↗

arXiv2001

A New Method to Measure and Map the Gas Scale-Height of Disk Galaxies

We propose a new method to measure and map the gas scale height of nearby disk galaxies. This method is applied successfully to the Australia Telescope Compact Array interferometric HI survey of the Large Magellanic Cloud (LMC); it could also be applied to a significant number of nearby disk galaxies, thanks to the next generation of interferometric facilities, such as the extended VLA and CARMA. The method consists of computing the Spectral Correlation Function (SCF) for a spectral-line map of a face-on galaxy. The SCF quantifies the correlation between spectra at different map positions as a function of their separation, and is sensitive to the properties of both the gas mass distribution and the gas velocity field. It is likely that spatial correlation properties of the gas density and velocity fields in a galactic disk are sensitive to the value of the scale height of the gas disk. A scale-free turbulent cascade is unlikely to extend to scales much larger than the disk scale height, as the disk dynamics on those larger scales should be dominated by two dimensional motions. We find a clear feature in the SCF of the LMC HI disk, on the scale of approximately 180 pc, which we identify as the disk scale height. We are also tentatively able to map variations of the scale height over the disk.

astro-ph↗

arXiv2000

Turbulent Fragmentation and the Initial Conditions for Star Formation

Super-sonic turbulence fragments molecular clouds (MC) into a very complex density field with density contrasts of several orders of magnitude. A fraction of the gas is locked into dense and gravitationally bound cores, which collapse as proto-stars. This process can be studied with numerical simulations of super-sonic self-gravitating turbulence. In this work, we use numerical simulations of magneto-hydrodynamic (MHD), super-sonic, super-Alfvénic and self-gravitating turbulence to compute the mass distribution of collapsing proto-stellar cores, which are selected as local density maxima. We find that the mass distribution of collapsing cores is consistent with the stellar initial mass function (IMF), suggesting that super-sonic turbulence may be responsible for the generation of the IMF. To support this conclusion we also show that the physical properties of the numerically selected cores are in agreement with the properties of observed NH$_3$ cores and that their magnetic field strength is consistent with Zeeman splitting measurements. In turbulent MCs, star formation occurs via the gravitational collapse of super-critical cores, formed by the turbulent flow, sub-critical cores being irrelevant for the process of star formation.

astro-ph↗

arXiv2000

The Turbulent Shock Origin of Proto--Stellar Cores

The fragmentation of molecular clouds (MC) into protostellar cores is a central aspect of the process of star formation. Because of the turbulent nature of super-sonic motions in MCs, it has been suggested that dense structures such as filaments and clumps are formed by shocks in a turbulent flow. In this work we present strong evidence in favor of the turbulent origin of the fragmentation of MCs. The most generic result of turbulent fragmentation is that dense post shock gas traces a gas component with a smaller velocity dispersion than lower density gas, since shocks correspond to regions of converging flows, where the kinetic energy of the turbulent motion is dissipated. Using synthetic maps of spectra of molecular transitions, computed from the results of numerical simulations of super--sonic turbulence, we show that the dependence of velocity dispersion on gas density generates an observable relation between the rms velocity centroid and the integrated intensity (column density), Sigma(V_0)-I, which is indeed found in the observational data. The comparison between the theoretical model (maps of synthetic 13CO spectra), with 13CO maps from the Perseus, Rosette and Taurus MC complexes, shows excellent agreement in the Sigma(V_0)-I relation. The Sigma(V_0)-I relation of different observational maps with the same total rms velocity are remarkably similar, which is a strong indication of their origin from a very general property of the fluid equations, such as the turbulent fragmentation process.

astro-ph↗

arXiv2000

The Effects of Noise and Sampling on the Spectral Correlation Function

The effects of noise and sampling on the ``Spectral Correlation Function'' (SCF) introduced by Rosolowsky et al. 1999 are studied using observational data, numerical simulations of magneto-hydrodynamic turbulence, and simple models of Gaussian spectral line profiles. The most significant innovations of this paper are: i) the normalization of the SCF based on an analytic model for the effect of noise; ii) the computation of the SCF as a function of the spatial lag between spectra within a map. By computing of the dependence of the SCF on the spatial lag, S_o(dr), we have been able to conclude that: 1) S_o(dr) is a power law, with slope in the range of scales l_i-l_o. 2) The correlation outer scale, l_o, is determined by the size of the map, and no evidence for a true departure from self-similarity on large scales has been found. 3) The correlation inner scale, l_i, is a true estimate of the smallest self-similar scale in a map. 4) The spectral slope in a given region, is independent of velocity resolution (above a minimum resolution threshold), spatial resolution, and average spectrum quality. 5) Molecular transitions which trace higher gas density yield larger values of the spectral slope than transitions tracing lower gas density. 6) Nyquist sampling, bad pixels in detector arrays, and reference sharing data acquisition need to be taken into account for a correct determination of the SCF at lag dr=1. The value of the spectral slope, however, can be computed correctly without a detailed knowledge of observational procedures.

astro-ph↗

arXiv1999

Primordial Proto-Galaxies

The first stars to form in protogalaxies must have primordial chemical composition. We refer to a protogalaxy that is forming stars of primordial composition, or very low metallicity ($Z\le 0.01 Z_{\odot}$), as ``Primordial Proto-Galaxy'' (PPG). PPGs contain little or no dust, and therefore their spectral energy distribution can be modelled from the rest-frame ultraviolet to the infrared without accounting for dust extinction and emission. We present the results of computing the photometric properties of high redshift PPGs at near-d-to-mid infrared wavelengths, that will soon be available with the new generation of infrared space telescopes, such as SIRTF and the NGST. We show that: i) PPGs at very high redshift (5<z<10) should be easily selected from deep near/mid IR surveys with a colour-colour criterion; ii) PPGs at redshift 5<z<10 can be detected at 8 $μ$m with the NGST, if they have a constant star formation rate of at least 100 M$_{\odot}/$yr; iii) once the redshift of a PPG photometric candidate is determined, its near-to-mid infrared colors should provide strong constraints on the stellar IMF at zero or very low metallicity.

astro-ph↗

arXiv1999

Proto-Galactic Starbursts at High Redshift

We have computed the evolving ultraviolet-millimeter spectral energy distribution (SED) produced by proto-galactic starbursts at high redshift, incorporating the chemical evolution of the interstellar medium in a consistent manner. Dust extinction is calculated in a novel way, that is not based on empirical calibrations of extinction curves, but rather on the lifetime of molecular clouds which delays the emergence of each successive generation of stars at ultraviolet wavelengths by typically 15 Myr. The predicted rest-frame far-infrared to millimeter-wave emission includes the calculation of molecular emission-line luminosities ($^{12}$CO and O$_{2}$ among other molecules) consistent with the evolving chemical abundances. Here we present details of this new model, along with the results of comparing its predictions with several high-redshift observables, namely: the ultraviolet SEDs of Lyman-limit galaxies, the high-redshift radiogalaxies 4C41.17 and 8C1435, the SCUBA sub-millimeter survey of the Hubble Deep Field (HDF), and the SEDs of intermediate-redshift elliptical galaxies. With our new reddening method, we are able to fit the spectrum of the Lyman-limit galaxy 1512-cB58, and we find an extinction of about 1.9 magnitudes at 1600 Å. The model also predicts that most Lyman-limit galaxies should have a value of $α$ inside that range, as it is observed. The 850 $μ$m flux density of a typical Lyman-limit galaxy is expected to be only $\simeq 0.5$ mJy, and therefore the optical counterparts of the most luminous sub-mm sources in the HDF (or any other currently feasible sub-mm survey) are unlikely to be Lyman-break galaxies.

astro-ph↗

arXiv1999

Ambipolar Drift Heating in Turbulent Molecular Clouds

Although thermal pressure is unimportant dynamically in most molecular gas, the temperature is an important diagnostic of dynamical processes and physical conditions. This is the first of two papers on thermal equilibrium in molecular clouds. We present calculations of frictional heating by ion-neutral (or ambipolar) drift in three-dimensional simulations of turbulent, magnetized molecular clouds. We show that ambipolar drift heating is a strong function of position in a turbulent cloud, and its average value can be significantly larger than the average cosmic ray heating rate. The volume averaged heating rate per unit volume due to ambipolar drift, H_AD ~ |JxB|^2 ~ B^4/L_B^2, is found to depend on the rms Alfvenic Mach number, M_A, and on the average field strength, as H_AD ~ M_A^2<|B|>^4. This implies that the typical scale of variation of the magnetic field, L_B, is inversely proportional to M_A, which we also demonstrate.

astro-ph↗

arXiv1999

The Chemical Evolution of the Galaxy with Variable IMFs

In this work we explore the effects of adopting initial mass functions (IMFs) variable in time on the chemical evolution of the Galaxy. In order to do that we adopt a chemical evolution model which assumes two main infall episodes for the formation of the Galaxy and which proved to be successful in reproducing the majority of the observational constraints, at least for the case of a constant IMF. Different variable IMFs are tested with this model, all assuming that massive stars are preferentially formed in ambients of low metallicity. This implies that massive stars are formed preferentially at early times and at large galactocentric distances. Our numerical results have shown that all the variable IMFs proposed so far are unable to reproduce all the relevant observational constraints in the Galaxy and that a constant IMF still reproduces better the observations. In particular, variable IMFs of the kind explored here are unable to reproduce the observed abundance gradients even when allowing for changes in other chemical evolution model parameters as, for instance, the star formation rate. As a consequence of this we conclude that the G-dwarf metallicity distribution is best explained by infall with a large timescale and a constant IMF, since it is possible to find variable IMFs of the kind studied here, reproducing the G-dwarf metallicity but this worsen the agreement with other observational constraints.

astro-ph↗

arXiv1999

Super-Sonic Turbulence in the Perseus Molecular Cloud

We compare the statistical properties of J=1-0 13CO spectra observed in the Perseus Molecular Cloud with synthetic J=1-0 13CO spectra, computed solving the non-LTE radiative transfer problem for a model cloud obtained as solutions of the three dimensional magneto-hydrodynamic (MHD) equations. The model cloud is a randomly forced super-Alfvenic and highly super-sonic turbulent isothermal flow. The purpose of the present work is to test if idealized turbulent flows, without self-gravity, stellar radiation, stellar outflows, or any other effect of star formation, are inconsistent or not with statistical properties of star forming molecular clouds. We present several statistical results that demonstrate remarkable similarity between real data and the synthetic cloud. Statistical properties of molecular clouds like Perseus are appropriately described by random super-sonic and super-Alfvenic MHD flows. Although the description of gravity and stellar radiation are essential to understand the formation of single protostars and the effects of star formation in the cloud dynamics, the overall description of the cloud and of the initial conditions for star formation can apparently be provided on intermediate scales without accounting for gravity, stellar radiation, and a detailed modeling of stellar outflows. We also show that the relation between equivalent line width and integrated antenna temperature indicates the presence of a relatively strong magnetic field in the core B1, in agreement with Zeeman splitting measurements.

astro-ph↗

arXiv1999

A Super-Alfvenic Model of Dark Clouds

Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfven waves, but the possibility that these motions are super-Alfvenic has not been ruled out. In this work we report the results of numerical experiments in two opposite regimes; M_a ~ 1 and M_a >> 1, where M_a is the initial Alfvenic Mach number --the ratio of the rms velocity to the Alfven speed. Our results show that models with M_a >> 1 are consistent with the observed properties of molecular clouds that we have tested --statistics of extinction measurements, Zeeman splitting measurements of magnetic field strength, line width versus integrated antenna temperature of molecular emission line spectra, statistical B-n relation, and scatter in that relation-- while models with M_a ~ 1 have properties that are in conflict with the observations. We find that both the density and the magnetic field in molecular clouds may be very intermittent. The statistical distributions of magnetic field and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B ~ n^{0.4}. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out, and also cores with weak field can be generated, by mass accretion along magnetic field lines.

astro-ph↗