arXiv subjects

Aake Nordlund

Publications and source records attributed to Aake Nordlund.

At least 19 recordsLinked to original sources

arXiv2018

The stellar IMF from Isothermal MHD Turbulence

We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwarfs to massive stars. Our simulations represent a generic 4 pc region within a typical Galactic molecular cloud, with a mass of 3000 Msun and an rms velocity 10 times the isothermal sound speed and 5 times the average Alfven velocity, in agreement with observations. We achieve a maximum resolution of 50 au and a maximum duration of star formation of 4.0 Myr, forming up to a thousand sink particles whose mass distribution closely matches the observed stellar IMF. A large set of medium-size simulations is used to test the sink particle algorithm, while larger simulations are used to test the numerical convergence of the IMF and the dependence of the IMF turnover on physical parameters predicted by the turbulent fragmentation model. We find a clear trend toward numerical convergence and strong support for the model predictions, including the initial time evolution of the IMF. We conclude that the physics of isothermal MHD turbulence is sufficient to explain the origin of the IMF.

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arXiv2016

Supernova Driving. II. Compressive Ratio in Molecular-Cloud Turbulence

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value $\approx 0.3$, lower than the equilibrium value of $\approx 0.5$ found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.

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arXiv2016

Tracking the distribution of $^{26}$Al and $^{60}$Fe during the early phases of star and disk evolution

The short-lived $^{26}$Al and $^{60}$Fe radionuclides are synthesized and expelled in the interstellar medium by core-collapse supernova events. The solar system's first solids, calcium-aluminium refractory inclusions (CAIs), contain evidence for the former presence of the $^{26}$ Al nuclide defining the canonical $^{26}$Al/$^{27}$ Al ratio of $\sim5 \times10^{-5}$. A different class of objects temporally related to canonical CAIs are CAIs with fractionation and unidentified nuclear effects (FUN CAIs), which record a low initial $^{26}$Al/$^{27}$Al of $10^{-6}$. The contrasting level of $^{26}$Al between these objects is often interpreted as reflecting the admixing of the $^{26}$Al nuclide during the early formative phase of the Sun. We use giant molecular cloud (GMC) scale adaptive mesh-refinement numerical simulations to trace the abundance of $^{26}$Al and $^{60}$Fe in star-forming gas during the early stages of accretion of individual low mass protostars. We find that the $^{26}$Al/$^{27}$Al and $^{60}$Fe/$^{56}$Fe ratios of accreting gas within a vicinity of 1000 AU of the stars follow the predicted decay curves of the initial abundances at time of star formation without evidence of spatial or temporal heterogeneities for the first 100 kyr of star formation. Therefore, the observed differences in $^{26}$Al/$^{27}$Al ratios between FUN and canonical CAIs are likely not caused by admixing of supernova material during the early evolution of the proto-Sun. Selective thermal processing of dust grains is a more viable scenario to account for the heterogeneity in $^{26}$Al/$^{27}$Al ratios at the time of solar system formation.

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arXiv2013

Abundance of 26Al and 60Fe in evolving Giant Molecular Clouds

The nucleosynthesis and ejection of radioactive $^{26}$Al (t$_{1/2} \sim$ 0.72\,Myr) and $^{60}$Fe, (t$_{1/2} \sim$ 2.5\,Myr) into the interstellar medium is dominated by the stellar winds of massive stars and supernova type II explosions. Studies of meteorites and their components indicate that the initial abundances of these short-lived radionuclides in the solar protoplanetary disk were higher than the background levels of the galaxy inferred from $γ$--ray astronomy and models of the galactic chemical evolution. This observation has been used to argue for a late-stage addition of stellar debris to the Solar System's parental molecular cloud or, alternatively, the solar protoplanetary disk, thereby requiring a special scenario for the formation of our Solar System. Here, we use supercomputers to model---from first principles---the production, transport and admixing of freshly synthesized $^{26}$Al and $^{60}$Fe in star-forming regions within giant molecular clouds. Under typical star-formation conditions, the levels of $^{26}$Al in most star-forming regions are comparable to that deduced from meteorites, suggesting that the presence of short-lived radionuclides in the early Solar System is a generic feature of the chemical evolution of giant molecular clouds. The $^{60}$Fe/$^{26}$Al yield ratio of $\approx 0.2$ calculated from our simulations is consistent with the galactic value of 0.15 $\pm$ 0.06 inferred from $γ$--ray astronomy but is significantly higher than most current Solar System measurements indicate. We suggest that estimates based on differentiated meteorites and some chondritic components may not be representative of the initial $^{60}$Fe abundance of the bulk Solar System.

astro-ph.EP↗

arXiv2012

Photon-Plasma: a modern high-order particle-in-cell code

We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation scheme for particle-to-cell interpolation and charge deposition. It includes powerful diagnostics tools with on-the-fly particle tracking, synthetic spectra integration, 2D volume slicing, and a new method to correctly account for radiative cooling in the simulations. A robust technique for imposing (time-dependent) particle and field fluxes on the boundaries is also presented. Using a hybrid OpenMP and MPI approach the code scales efficiently from 8 to more than 250.000 cores with almost linear weak scaling on a range of architectures. The code is tested with the classical benchmarks particle heating, cold beam instability, and two-stream instability. We also present particle-in-cell simulations of the Kelvin-Helmholtz instability, and new results on radiative collisionless shocks.

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arXiv2011

Radiation from sub-Larmor scale magnetic fields

Spontaneous rapid growth of strong magnetic fields is rather ubiquitous in high-energy density environments ranging from astrophysical sources (e.g., gamma-ray bursts and relativistic shocks), to reconnection, to laser-plasma interaction laboratory experiments, where they are produced by kinetic streaming instabilities of the Weibel type. Relativistic electrons propagating through these sub-Larmor-scale magnetic fields radiate in the jitter regime, in which the anisotropy of the magnetic fields and the particle distribution have a strong effect on the produced radiation. Here we develop the general theory of jitter radiation, which includes (i) anisotropic magnetic fields and electron velocity distributions, (ii) the effects of trapped electrons and (iii) extends the description to large deflection angles of radiating particles thus establishing a cross-over between the classical jitter and synchrotron regimes. Our results are in remarkable agreement with the radiation spectra obtained from particle-in-cell simulations of the classical Weibel instability. Particularly interesting is the onset of the field growth, when the transient hard synchrotron-violating spectra are common as a result of the dominant role of the trapped population. This effect can serve as a distinct observational signature of the violent field growth in astrophysical sources and lab experiments. It is also interesting that a system with small-scale fields tends to evolve toward the small-angle jitter regime, which can, under certain conditions, dominate the overall emission of a source.

astro-ph.HE↗

arXiv2011

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.

astro-ph.SR↗

arXiv2011

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.

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arXiv2010

Radiation Spectral Synthesis of Relativistic Filamentation

Radiation from many astrophysical sources, e.g. gamma-ray bursts and active galactic nuclei, is believed to arise from relativistically shocked collisionless plasmas. Such sources often exhibit highly transient spectra evolving rapidly, compared with source lifetimes. Radiation emitted from these sources is typically associated with non-linear plasma physics, complex field topologies and non-thermal particle distributions. In such circumstances a standard synchrotron paradigm may fail to produce accurate conclusions regarding the underlying physics. Simulating spectral emission and spectral evolution numerically in various relativistic shock scenarios is then the only viable method to determine the detailed physical origin of the emitted spectra. In this Letter we present synthetic radiation spectra representing the early stage development of the filamentation (streaming) instability of an initially unmagnetized plasma, which is relevant for both collisionless shock formation and reconnection dynamics in relativistic astrophysical outflows, as well as for laboratory astrophysics experiments. Results were obtained using a highly efficient "in situ" diagnostics method, based on detailed particle-in-cell modeling of collisionless plasmas. The synthetic spectra obtained here are compared with those predicted by a semi-analytical model for jitter radiation from the filamentation instability, the latter including self-consistent generated field topologies and particle distributions obtained from the simulations reported upon here. Spectra exhibit dependence on the presence - or absence - of an inert plasma constituent, when comparing baryonic plasmas (i.e. containing protons) with pair plasmas. The results also illustrate that considerable care should be taken when using lower-dimensional models to obtain information about the astrophysical phenomena generating observed spectra.

astro-ph.HE↗

arXiv2008

A grid of MARCS model atmospheres for late-type stars I. Methods and general properties

We have constructed a grid of about 10,000 spherically symmetric and plane-parallel models with the MARCS program, and make it available for public use. Parameter ranges are: Teff=2500 to 8000 K, log g =log(GM/R2)= -1 to 5 (cgs) with various masses and radii, [Me/H]=-5 to +1, with [Alpha/Fe] = 0.0 and 0.4 and different choices of C and N abundances to also represent stars of types R, S and N, and with microturbulence parameters from 1 to 5 km/s. We also list fluxes in approximately 108,000 wavelength points. Underlying assumptions in addition to 1D stratification include hydrostatic equilibrium, MLT convection and LTE. A number of general properties of the models are discussed, in relation to the effects of changing blanketing and sphericity. Models are compared with other available grids and excellent agreement is found with plane-parallel models of Castelli and Kurucz within the overlapping parameter range. Although there are departures from the spherically symmetric NextGen models, the agreement with more recent PHOENIX models is gratifying. The models of the grid show regularities, but some interesting departures from general patterns occur for the coolest models due to the molecular opacities. We have tested rules of thumb concerning effects of blanketing and sphericity and found them to often be astonishingly accurate. Some interesting new phenomena have been discovered, such as the intricate coupling between blanketing and sphericity, and the strong effects of carbon enhancement on metal-poor models. We give further details of models and comparisons with observations in subsequent papers.

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arXiv2008

The Formation of Distributed and Clustered Stars in Molecular Clouds

During the last two decades, the focus of star formation research has shifted from understanding the collapse of a single dense core into a star to studying the formation hundreds to thousands of stars in molecular clouds. In this chapter, we overview recent observational and theoretical progress toward understanding star formation on the scale of molecular clouds and complexes, i.e the macrophysics of star formation. We begin with an overview of recent surveys of young stellar objects (YSOs) in molecular clouds and embedded clusters, and we outline an emerging picture of cluster formation. We then discuss the role of turbulence to both support clouds and create dense, gravitationally unstable structures, with an emphasis on the role of magnetic fields (in the case of distributed stars) and feedback (in the case of clusters) to slow turbulent decay and mediate the rate and density of star formation. The discussion is followed by an overview of how gravity and turbulence may produce observed scaling laws for the properties of molecular clouds, stars and star clusters, and how the observed, low star formation rate may result from self regulated star formation. We end with some concluding remarks, including a number of questions to be addressed by future observations and simulations.

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arXiv2007

3D Radiative Hydrodynamics for Disk Stability Simulations: A Proposed Testing Standard and New Results

Recent three-dimensional radiative hydrodynamics simulations of protoplanetary disks report disparate disk behaviors, and these differences involve the importance of convection to disk cooling, the dependence of disk cooling on metallicity, and the stability of disks against fragmentation and clump formation. To guarantee trustworthy results, a radiative physics algorithm must demonstrate the capability to handle both the high and low optical depth regimes. We develop a test suite that can be used to demonstrate an algorithm's ability to relax to known analytic flux and temperature distributions, to follow a contracting slab, and to inhibit or permit convection appropriately. We then show that the radiative algorithm employed by Mejiá (2004) and Boley et al. (2006) and the algorithm employed by Cai et al. (2006) and Cai et al. (2007, in prep.) pass these tests with reasonable accuracy. In addition, we discuss a new algorithm that couples flux-limited diffusion with vertical rays, we apply the test suite, and we discuss the results of evolving the Boley et al. (2006) disk with this new routine. Although the outcome is significantly different in detail with the new algorithm, we obtain the same qualitative answers. Our disk does not cool fast due to convection, and it is stable to fragmentation. We find an effective $α\approx 10^{-2}$. In addition, transport is dominated by low-order modes.

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arXiv2006

PPV Chapter - The Formation of Brown Dwarfs

We review five mechanisms for forming brown dwarfs: (i) turbulent fragmentation of molecular clouds, producing very low-mass prestellar cores by shock compression; (ii) collapse and fragmentation of more massive prestellar cores; (iii) disc fragmentation; (iv) premature ejection of protostellar embryos from their natal cores; and (v) photo-erosion of pre-existing cores overrun by HII regions. These mechanisms are not mutually exclusive. Their relative importance probably depends on environment, and should be judged by their ability to reproduce the brown-dwarf IMF, the distribution and kinematics of newly formed brown dwarfs, the binary statistics of brown dwarfs, the ability of brown dwarfs to retain discs, and hence their ability to sustain accretion and outflows. This will require more sophisticated numerical modelling than is presently possible, in particular more realistic initial conditions and more realistic treatments of radiation transport, angular momentum transport and magnetic fields. We discuss the minimum mass for brown dwarfs, and how brown dwarfs should be distinguished from planets.

astro-ph↗

arXiv2004

Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence

Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfvénic turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with numerical simulations that the scaling can be described with the She--Lévêque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of \ms. Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.

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arXiv2004

The Average Magnetic Field Strength in Molecular Clouds: New Evidence of Super-Alfvenic Turbulence

The magnetic field strength in molecular clouds is a fundamental quantity for theories of star formation. It is estimated by Zeeman splitting measurements in a few dense molecular cores, but its volume--averaged value within large molecular clouds (over several parsecs) is still uncertain. In this work we provide a new method to constrain the average magnetic field strength in molecular clouds. We compare the power spectrum of gas density of molecular clouds with that of two $350^3$ numerical simulations of supersonic MHD turbulence. The numerical simulation with approximate equipartition of kinetic and magnetic energies (model A) yields the column density power spectrum $P(k)\propto k^{-2.25\pm 0.01}$, the super--Alfvénic simulation (model B) $P(k)\propto k^{-2.71\pm 0.01}$. The column density power spectrum of the Perseus, Taurus and Rosetta molecular cloud complexes is found to be well approximated by a power law, $P_{\rm o}(k)\propto k^{-a}$, with $a=2.74\pm 0.07$, $2.74\pm 0.08$ and $2.76\pm 0.08$ respectively. We conclude that the observations are consistent with the presence of super--Alfvénic turbulence in molecular clouds (model B) while model A is inconsistent (more than 99% confidence) with the observations.

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arXiv2003

Self-regulating supernova heating in interstellar medium simulations

Numerical simulations of the multi-phase interstellar medium have been carried out, using a 3D, nonlinear, magnetohydrodynamic, shearing-box model, with random motions driven by supernova explosions. These calculations incorporate the effects of magnetic fields and rotation in 3D; these play important dynamical roles in the galaxy, but are neglected in many other simulations. The supernovae driving the motions are not arbitrarily imposed, but occur where gas accumulates into cold, dense clouds; their implementation uses a physically motivated model for the evolution of such clouds. The process is self-regulating, and produces mean supernova rates as part of the solution. Simulations with differing mean density show a power law relation between the supernova rate and density, with exponent 1.7; this value is within the range suggested from observations (taking star formation rate as a proxy for supernova rate). The global structure of the supernova driven medium is strongly affected by the presence of magnetic fields; e.g. for one solution the filling factor of hot gas is found to vary from 0.19 (with no field) to 0.12 (with initial mid-plane field B_0=6 muG).

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arXiv2003

Dynamo action in turbulent flows

We present results from numerical simulations of nonlinear MHD dynamo action produced by three-dimensional flows that become turbulent for high values of the fluid Reynolds number. The magnitude of the forcing function driving the flow is allowed to evolve with time in such way as to maintain an approximately constant velocity amplitude (and average kinetic energy) when the flow becomes hydrodynamically unstable. It is found that the saturation level of the dynamo increases with the fluid Reynolds number (at constant magnetic Prandtl number), and that the average growth rate approaches an asymptotic value for high fluid Reynolds number. The generation and destruction of magnetic field is examined during the laminar and turbulent phase of the flow and it is found that in the neighborhood of strong magnetic "flux cigars" Joule dissipation is balanced by the work done against the Lorentz force, while the steady increase of magnetic energy occurs mainly through work done in the weak part of the magnetic field.

astro-ph↗

arXiv2002

The effects of spiral arms on the multi-phase ISM

Statistical parameters of the ISM driven by thermal energy injections from supernova explosions have been obtained from 3D, nonlinear, magnetohydrodynamic, shearing-box simulations for spiral arm and interarm regions. The density scale height obtained for the interarm regions is 50% larger than within the spiral arms because of the higher gas temperature. The filling factor of the hot gas is also significantly larger between the arms and depends sensitively on magnetic field strength.

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