arXiv subjects

Ralf S. Klessen

Publications and source records attributed to Ralf S. Klessen.

At least 397 records · Page 22Linked to original sources

arXiv2014

Hierarchical Bayesian analysis of the velocity power spectrum in supersonic turbulence

Turbulence is a dominant feature operating in gaseous flows across nearly all scales in astrophysical environments. Accordingly, accurately estimating the statistical properties of such flows is necessary for developing a comprehensive understanding of turbulence. We develop and employ a hierarchical Bayesian fitting method to estimate the parameters describing the scaling relationships of the velocity power spectra of supersonic turbulence. We demonstrate the accuracy and other advantages of this technique compared with ordinary linear regression methods. Using synthetic power spectra, we show that the Bayesian method provides accurate parameter and error estimates. Commonly used normal linear regression methods can provide estimates that fail to recover the underlying slopes, up to 70% of the instances, even when considering the 2std.dev. uncertainties. Additionally, we apply the Bayesian methods to analyse the statistical properties of compressible turbulence in 3D numerical simulations. We model driven, isothermal, turbulence with rms Mach numbers in the highly supersonic regime M~15. We study the influence of purely solenoidal (divergence-free) and purely compressive (curl-free) forcing on the scaling exponent of the power spectrum. In simulations with solenoidal forcing and 1024^3 resolution, our results indicate that there is no extended inertial range with a constant scaling exponent. The bottleneck effect results in a curved power spectrum at all wave numbers and is more pronounced in the transversal modes compared with the longitudinal modes. Therefore, this effect is stronger in stationary turbulent flows driven by solenoidal forcing compared to the compressive one. The longitudinal spectrum driven with compressive forcing is the only spectrum with constant scaling exponent z=-1.94 +- 0.01, corresponding to slightly shallower slopes than the Burger's prediction.

astro-ph.SR↗

arXiv2014

A new approach to determine optically thick H2 cooling and its effect on primordial star formation

We present a new method for estimating the H2 cooling rate in the optically thick regime in simulations of primordial star formation. Our new approach is based on the TreeCol algorithm, which projects matter distributions onto a spherical grid to create maps of column densities for each fluid element in the computational domain. We have improved this algorithm by using the relative gas velocities, to weight the individual matter contributions with the relative spectral line overlaps, in order to properly account for the Doppler effect. We compare our new method to the widely used Sobolev approximation, which yields an estimate for the column density based on the local velocity gradient and the thermal velocity. This approach generally underestimates the photon escape probability, because it neglects the density gradient and the actual shape of the cloud. We present a correction factor for the true line overlap in the Sobolev approximation and a new method based on local quantities, which fits the exact results reasonably well during the collapse of the cloud, with the error in the cooling rates always being less than 10%. Analytical fitting formulae fail at determining the photon escape probability after formation of the first protostar (error of 40%) because they are based on the assumption of spherical symmetry and therefore break down once a protostellar accretion disc has formed. Our method yields lower temperatures and hence promotes fragmentation for densities above 10^{10}/ccm at a distance of 200AU from the first protostar. Since the overall accretion rates are hardly affected by the cooling implementation, we expect Pop III stars to have lower masses in our simulations, compared to the results of previous simulations that used the Sobolev approximation.

astro-ph.SR↗

arXiv2014

Centroid Velocity Statistics of Molecular Clouds

We compute structure functions and Fourier spectra of 2D centroid velocity (CV) maps in order to study the gas dynamics of typical molecular clouds (MCs) in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H2 number density, 12CO number density as well as the integrated intensity of 12CO (J=1-0) and 13CO (J=1-0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.

astro-ph.SR↗

arXiv2014

The $^{12}$CO/$^{13}$CO ratio in turbulent molecular clouds

The $^{13}$CO molecule is often used as a column density tracer in regions where the $^{12}$CO emission saturates. The $^{13}$CO column density is then related to that of $^{12}$CO by a uniform isotopic ratio. A similar approximation is frequently used when deriving $^{13}$CO emission maps from numerical simulations of molecular clouds. To test this assumption we calculate the $^{12}$CO/$^{13}$CO ratio self-consistently, taking the isotope selective photodissociation and the chemical fractionation of CO into account. We model the coupled chemical, thermal and dynamical evolution and the emergent $^{13}$CO emission of isolated, starless molecular clouds in various environments. Selective photodissociation has a minimal effect on the ratio, while the chemical fractionation causes a factor of 2-3 decrease at intermediate cloud depths. The variation correlates with both the $^{12}$CO and the $^{13}$CO column densities. Neglecting the depth dependence results in $\leq$60 per cent error in $^{12}$CO column densities derived from $^{13}$CO. The same assumption causes $\leq$50 per cent disparity in the $^{13}$CO emission derived from simulated clouds. We show that the discrepancies can be corrected by a fitting formula. The formula is consistent with millimetre-wavelength isotopic ratio measurements of dense molecular clouds, but underestimates the ratios from the ultraviolet absorption of diffuse regions.

astro-ph.GA↗

arXiv2014

Line Profiles of Cores within Clusters. III. What is the most reliable tracer of core collapse in dense clusters?

Recent observational and theoretical investigations have emphasised the importance of filamentary networks within molecular clouds as sites of star formation. Since such environments are more complex than those of isolated cores, it is essential to understand how the observed line profiles from collapsing cores with non-spherical geometry are affected by filaments. In this study, we investigate line profile asymmetries by performing radiative transfer calculations on hydrodynamic models of three collapsing cores that are embedded in filaments. We compare the results to those that are expected for isolated cores. We model the five lowest rotational transition line (J = 1-0, 2-1, 3-2, 4-3, and 5-4) of both optically thick (HCN, HCO$^+$) as well as optically thin (N$_2$H$^+$, H$^{13}$CO$^+$) molecules using constant abundance laws. We find that less than 50% of simulated (1-0) transition lines show blue infall asymmetries due to obscuration by the surrounding filament. However, the fraction of collapsing cores that have a blue asymmetric emission line profile rises to 90% when observed in the (4-3) transition. Since the densest gas towards the collapsing core can excite higher rotational states, upper level transitions are more likely to produce blue asymmetric emission profiles. We conclude that even in irregular, embedded cores one can trace infalling gas motions with blue asymmetric line profiles of optically thick lines by observing higher transitions. The best tracer of collapse motions of our sample is the (4-3) transition of HCN, but the (3-2) and (5-4) transitions of both HCN and HCO$^+$ are also good tracers.

astro-ph.SR↗

arXiv2014

Modeling jet and outflow feedback during star cluster formation

Powerful jets and outflows are launched from the protostellar disks around newborn stars. These outflows carry enough mass and momentum to transform the structure of their parent molecular cloud and to potentially control star formation itself. Despite their importance, we have not been able to fully quantify the impact of jets and outflows during the formation of a star cluster. The main problem lies in limited computing power. We would have to resolve the magnetic jet-launching mechanism close to the protostar and at the same time follow the evolution of a parsec-size cloud for a million years. Current computer power and codes fall orders of magnitude short of achieving this. In order to overcome this problem, we implement a subgrid-scale (SGS) model for launching jets and outflows, which demonstrably converges and reproduces the mass, linear and angular momentum transfer, and the speed of real jets, with ~ 1000 times lower resolution than would be required without SGS model. We apply the new SGS model to turbulent, magnetized star cluster formation and show that jets and outflows (1) eject about 1/4 of their parent molecular clump in high-speed jets, quickly reaching distances of more than a parsec, (2) reduce the star formation rate by about a factor of two, and (3) lead to the formation of ~ 1.5 times as many stars compared to the no-outflow case. Most importantly, we find that jets and outflows reduce the average star mass by a factor of ~ 3 and may thus be essential for understanding the characteristic mass of the stellar initial mass function.

astro-ph.SR↗

arXiv2014

Low-metallicity star formation: Relative impact of metals and magnetic fields

Low-metallicity star formation poses a central problem of cosmology, as it determines the characteristic mass scale and distribution for the first and second generations of stars forming in our Universe. Here, we present a comprehensive investigation assessing the relative impact of metals and magnetic fields, which may both be present during low-metallicity star formation. We show that the presence of magnetic fields generated via the small-scale dynamo stabilises the protostellar disc and provides some degree of support against fragmentation. In the absence of magnetic fields, the fragmentation timescale in our model decreases by a factor of ~10 at the transition from Z=0 to Z>0, with subsequently only a weak dependence on metallicity. Similarly, the accretion timescale of the cluster is set by the large-scale dynamics rather than the local thermodynamics. In the presence of magnetic fields, the primordial disc can become completely stable, therefore forming only one central fragment. At Z>0, the number of fragments is somewhat reduced in the presence of magnetic fields, though the shape of the mass spectrum is not strongly affected in the limits of the statistical uncertainties. The fragmentation timescale, however, increases by roughly a factor of 3 in the presence of magnetic fields. Indeed, our results indicate comparable fragmentation timescales in primordial runs without magnetic fields and Z>0 runs with magnetic fields.

astro-ph.GA↗

arXiv2014

Statistical properties of dark matter mini-haloes at z >= 15

Understanding the formation of the first objects in the universe critically depends on knowing whether the properties of small dark matter structures at high-redshift (z > 15) are different from their more massive lower-redshift counterparts. To clarify this point, we performed a high-resolution N-body simulation of a cosmological volume 1 Mpc/h comoving on a side, reaching the highest mass resolution to date in this regime. We make precision measurements of various physical properties that characterize dark matter haloes (such as the virial ratio, spin parameter, shape, and formation times, etc.) for the high-redshift (z > 15) dark matter mini-haloes we find in our simulation, and compare them to literature results and a moderate-resolution comparison run within a cube of side-length 100 Mpc/h. We find that dark matter haloes at high-redshift have a log-normal distribution of the dimensionless spin parameter centered around λ $\sim$ 0.03, similar to their more massive counterparts. They tend to have a small ratio of the length of the shortest axis to the longest axis (sphericity), and are highly prolate. In fact, haloes of given mass that formed recently are the least spherical, have the highest virial ratios, and have the highest spins. Interestingly, the formation times of our mini-halos depend only very weakly on mass, in contrast to more massive objects. This is expected from the slope of the linear power spectrum of density perturbations at this scale, but despite this difference, dark matter structures at high-redshift share many properties with their much more massive counterparts observed at later times.

astro-ph.CO↗

arXiv2014

CO-dark gas and molecular filaments in Milky Way type galaxies

We use the moving mesh code AREPO coupled to a time-dependent chemical network to investigate the formation and destruction of molecular gas in simulated spiral galaxies. This allows us to determine the characteristics of the gas that is not traced by CO emission. Our extremely high resolution AREPO simulations allow us to capture the chemical evolution of the disc, without recourse to a parameterised `clumping factor'. We calculate H2 and CO column densities through our simulated disc galaxies, and estimate the CO emission and CO-H2 conversion factor. We find that in conditions akin to those in the local interstellar medium, around 42% of the total molecular mass should be in CO-dark regions, in reasonable agreement with observational estimates. This fraction is almost insensitive to the CO integrated intensity threshold used to discriminate between CO-bright and CO-dark gas, as long as this threshold is less than 10 K km/s. The CO-dark molecular gas primarily resides in extremely long (>100 pc) filaments that are stretched between spiral arms by galactic shear. Only the centres of these filaments are bright in CO, suggesting that filamentary molecular clouds observed in the Milky Way may only be small parts of much larger structures. The CO-dark molecular gas mainly exists in a partially molecular phase which accounts for a significant fraction of the total disc mass budget. The dark gas fraction is higher in simulations with higher ambient UV fields or lower surface densities, implying that external galaxies with these conditions might have a greater proportion of dark gas.

astro-ph.GA↗

arXiv2014

Interpreting the sub-linear Kennicutt-Schmidt relationship: The case for diffuse molecular gas

Recent statistical analysis of two extragalactic observational surveys strongly indicate a sublinear Kennicutt-Schmidt (KS) relationship between the star formation rate (Sigsfr) and molecular gas surface density (Sigmol). Here, we consider the consequences of these results in the context of common assumptions, as well as observational support for a linear relationship between Sigsfr and the surface density of dense gas. If the CO traced gas depletion time (tau_mol) is constant, and if CO only traces star forming giant molecular clouds (GMCs), then the physical properties of each GMC must vary, such as the volume densities or star formation rates. Another possibility is that the conversion between CO luminosity and Sigmol, the XCO factor, differs from cloud-to-cloud. A more straightforward explanation is that CO permeates the hierarchical ISM, including the filaments and lower density regions within which GMCs are embedded. A number of independent observational results support this description, with the diffuse gas comprising at least 30% of the total molecular content. The CO bright diffuse gas can explain the sublinear KS relationship, and consequently leads to an increasing tau_mol with Sigmol. If Sigsfr linearly correlates with the dense gas surface density, a sublinear KS relationship indicates that the fraction of diffuse gas fdiff grows with Sigmol. In galaxies where Sigmol falls towards the outer disk, this description suggests that fdiff also decreases radially.

astro-ph.GA↗

arXiv2014

Collective outflow from a small multiple stellar system

The formation of high-mass stars is usually accompanied by powerful protostellar outflows. Such high-mass outflows are not simply scaled-up versions of their lower-mass counterparts, since observations suggest that the collimation degree degrades with stellar mass. Theoretically, the origins of massive outflows remain open to question because radiative feedback and fragmentation of the accretion flow around the most massive stars, with M > 15 M_Sun, may impede the driving of magnetic disk winds. We here present a three-dimensional simulation of the early stages of core fragmentation and massive star formation that includes a subgrid-scale model for protostellar outflows. We find that stars that form in a common accretion flow tend to have aligned outflow axes, so that the individual jets of multiple stars can combine to form a collective outflow. We compare our simulation to observations with synthetic H_2 and CO observations and find that the morphology and kinematics of such a collective outflow resembles some observed massive outflows, such as Cepheus A and DR 21. We finally compare physical quantities derived from simulated observations of our models to the actual values in the models to examine the reliability of standard methods for deriving physical quantities, demonstrating that those methods indeed recover the actual values to within a factor of 2-3.

astro-ph.SR↗

arXiv2014

X-Ray Emission from Star-Forming Galaxies - Signatures of Cosmic Rays and Magnetic Fields

The evolution of magnetic fields in galaxies is still an open problem in astrophysics. In nearby galaxies the far-infrared-radio correlation indicates the coupling between magnetic fields and star formation. The correlation arises from the synchrotron emission of cosmic ray electrons traveling through the interstellar magnetic fields. However, with an increase of the interstellar radiation field (ISRF), inverse Compton scattering becomes the dominant energy loss mechanism of cosmic ray electrons with a typical emission frequency in the X-ray regime. The ISRF depends on the one hand on the star formation rate and becomes stronger in starburst galaxies, and on the other hand increases with redshift due to the evolution of the cosmic microwave background. With a model for the star formation rate of galaxies, the ISRF, and the cosmic ray spectrum, we can calculate the expected X-ray luminosity resulting from the inverse Compton emission. Except for galaxies with an active galactic nucleus the main additional contribution to the X-ray luminosity comes from X-ray binaries. We estimate this contribution with an analytical model as well as with an observational relation, and compare it to the pure inverse Compton luminosity. Using data from the Chandra Deep Field Survey and far-infrared observations from ALMA we then determine upper limits for the cosmic ray energy. Assuming that the magnetic energy in a galaxy is in equipartition with the energy density of the cosmic rays, we obtain upper limits for the magnetic field strength. Our results suggest that the mean magnetic energy of young galaxies is similar to the one in local galaxies. This points toward an early generation of galactic magnetic fields, which is in agreement with current dynamo evolution models.

astro-ph.GA↗

arXiv2014

Principal Component Analysis of Molecular Clouds: Can CO reveal the dynamics?

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical MCs. Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry. We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n_0 = 30, 100, 300 cm^{-3} that span the range of values typical for MCs in the solar neighbourhood and investigate the slope α_{PCA} of the pseudo structure function computed by PCA for several components: the total density, H2 density, 12CO density, 12CO J = 1 -> 0 intensity and 13CO J = 1 -> 0 intensity. We estimate power-law indices α_{PCA} for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ~ +/- 0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

astro-ph.SR↗

arXiv2014

The Complex Distribution of Recently Formed Stars. Bimodal Stellar Clustering in the Star-Forming Region NGC 346

We present a detailed stellar clustering analysis with the application of the two-point correlation function on distinct young stellar ensembles. Our aim is to understand how stellar systems are assembled at the earliest stages of their formation. Our object of interest is the star-forming region NGC 346 in the Small Magellanic Cloud. It is a young stellar system well-revealed from its natal environment, comprising complete samples of pre--main-sequence and upper main-sequence stars, very close to their formation. We apply a comprehensive characterization of the autocorrelation function for both centrally condensed stellar clusters and self-similar stellar distributions through numerical simulations of stellar ensembles. We interpret the observed autocorrelation function of NGC 346 on the basis of these simulations. We find that it can be best explained as the combination of two distinct stellar clustering designs, a centrally concentrated, dominant at the central part of the star-forming region, and an extended self-similar distribution of stars across the complete observed field. The cluster component, similar to non-truncated young star clusters, is determined to have a core radius of ~2.5 pc and a density profile index of ~2.3. The extended fractal component is found with our simulations to have a fractal dimension of ~2.3, identical to that found for the interstellar medium, in agreement to hierarchy induced by turbulence. This suggests that the stellar clustering at a time very near to birth behaves in a complex manner. It is the combined result of the star formation process regulated by turbulence and the early dynamical evolution induced by the gravitational potential of condensed stellar clusters.

astro-ph.GA↗

arXiv2014

The CO-to-H2 Conversion Factor across the Perseus Molecular Cloud

We derive the CO-to-H2 conversion factor, X_CO = N(H2)/I_CO, across the Perseus molecular cloud on sub-parsec scales by combining the dust-based N(H2) data with the I_CO data from the COMPLETE Survey. We estimate an average X_CO ~ 3 x 10^19 cm^-2 K^-1 km^-1 s and find a factor of ~3 variations in X_CO between the five sub-regions in Perseus. Within the individual regions, X_CO varies by a factor of ~100, suggesting that X_CO strongly depends on local conditions in the interstellar medium. We find that X_CO sharply decreases at Av < 3 mag but gradually increases at Av > 3 mag, with the transition occurring at Av where I_CO becomes optically thick. We compare the N(HI), N(H2), I_CO, and X_CO distributions with two models of the formation of molecular gas, a one-dimensional photodissociation region (PDR) model and a three-dimensional magnetohydrodynamic (MHD) model tracking both the dynamical and chemical evolution of gas. The PDR model based on the steady state and equilibrium chemistry reproduces our data very well but requires a diffuse halo to match the observed N(HI) and I_CO distributions. The MHD model generally matches our data well, suggesting that time-dependent effects on H2 and CO formation are insignificant for an evolved molecular cloud like Perseus. However, we find interesting discrepancies, including a broader range of N(HI), likely underestimated I_CO, and a large scatter of I_CO at small Av. These discrepancies likely result from strong compressions/rarefactions and density fluctuations in the MHD model.

astro-ph.GA↗

arXiv2014

On the evolution of the density pdf in strongly self-gravitating systems

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple appoximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form $\mathrm{P}_v(ρ)\proptoρ^{-1.54}$ for the (volume-weighted) PDF and $\mathrm{P}_m(ρ)\proptoρ^{-0.54}$ for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates. Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured star formation rates are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.

astro-ph.GA↗

arXiv2013

Magnetic Field Amplification in Young Galaxies

The Universe at present is highly magnetized, with fields of the order of a few 10^-5 G and coherence lengths larger than 10 kpc in typical galaxies like the Milky Way. We propose that the magnetic field was amplified to this values already during the formation and the early evolution of the galaxies. Turbulence in young galaxies is driven by accretion as well as by supernova (SN) explosions of the first generation of stars. The small-scale dynamo can convert the turbulent kinetic energy into magnetic energy and amplify very weak primordial magnetic seed fields on short timescales. The amplification takes place in two phases: in the kinematic phase the magnetic field grows exponentially, with the largest growth on the smallest non-resistive scale. In the following non-linear phase the magnetic energy is shifted towards larger scales until the dynamo saturates on the turbulent forcing scale. To describe the amplification of the magnetic field quantitatively we model the microphysics in the interstellar medium (ISM) of young galaxies and determine the growth rate of the small-scale dynamo. We estimate the resulting saturation field strengths and dynamo timescales for two turbulent forcing mechanisms: accretion-driven turbulence and SN-driven turbulence. We compare them to the field strength that is reached, when only stellar magnetic fields are distributed by SN explosions. We find that the small-scale dynamo is much more efficient in magnetizing the ISM of young galaxies. In the case of accretion-driven turbulence a magnetic field strength of the order of 10^-6 G is reached after a time of 24-270 Myr, while in SN-driven turbulence the dynamo saturates at field strengths of typically 10^-5 G after only 4-15 Myr. This is considerably shorter than the Hubble time. Our work can help to understand why present-day galaxies are highly magnetized.

astro-ph.GA↗

arXiv2013

Morphologies of protostellar outflows: An ALMA view

The formation of stars is usually accompanied by the launching of protostellar outflows. Observations with the Atacama Large Millimetre/sub-millimetre Array (ALMA) will soon revolutionalise our understanding of the morphologies and kinematics of these objects. In this paper, we present synthetic ALMA observations of protostellar outflows based on numerical magnetohydrodynamic collapse simulations. We find significant velocity gradients in our outflow models and a very prominent helical structure within the outflows. We speculate that the disk wind found in the ALMA Science Verification Data of HD 163296 presents a first instance of such an observation.

astro-ph.SR↗