arXiv subjects

AAke Nordlund

Publications and source records attributed to AAke Nordlund.

At least 19 recordsLinked to original sources

arXiv2025

The Formation of Protoplanetary Disks through Pre-Main Sequence Bondi-Hoyle Accretion

Protoplanetary disks are traditionally described as finite mass reservoirs left over by the gravitational collapse of the protostellar core, a view that strongly constrains both disk evolution and planet formation models. We propose a different scenario where protoplanetary disks of pre-main sequence stars are primarily assembled by Bondi-Hoyle accretion from the parent gas cloud. We demonstrate that Bondi-Hoyle accretion can supply not only the mass, but also the angular momentum necessary to explain the observed size of protoplanetary disks. Additionally, we predict how the specific angular momentum of protoplanetary disks scales with stellar mass. Our conclusions are based on a new analytical derivation of the scaling of the angular momentum in turbulent flows, which we confirm with a numerical simulation of supersonic turbulence. A key outcome of our analysis is the recognition that density fluctuations in supersonic turbulence--previously overlooked in studies of cloud and core rotation--lead to a significant increase in angular momentum at disk-forming scales. This revised understanding of disk formation and evolution alleviates several longstanding observational discrepancies and compels substantial revisions to current models of disk and planet formation.

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arXiv2017

Microscopic Processes in Global Relativistic Jets Containing Helical Magnetic Fields: Dependence on Jet Radius

In this study we investigate jet interaction at a microscopic level in a cosmological environment, which responds to a key open question in the study of relativistic jets. Using small simulation systems during prior research, we initially studied the evolution of both electron-proton and electron-positron relativistic jets containing helical magnetic fields, by focusing on their interactions with an ambient plasma. Here, using larger jet radii, we have performed simulations of global jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). We found that the evolution of global jets strongly depends on the size of the jet radius. For example, phase bunching of jet electrons, in particular in the electron-proton jet, is mixed with larger jet radius due to the more complicated structures of magnetic fields with excited kinetic instabilities. In our simulation study these kinetic instabilities lead to new types of instabilities in global jets. In the electron-proton jet simulation a modified recollimation occurs and jet electrons are strongly perturbed. In the electron-positron jet simulation mixed kinetic instabilities occur at early times followed by a turbulence-like structure. Simulations using much larger (and longer) systems are further required in order to thoroughly investigate the evolution of global jets containing helical magnetic fields.

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arXiv2016

Microscopic Processes in Global Relativistic Jets Containing Helical Magnetic Fields

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron$-$proton ($e^{-}-p^{+}$) and electron$-$positron ($e^{\pm}$) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of "global" jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the $e^{-}-p^{+}$ jet simulation a recollimation-like instability occurs and jet electrons are strongly perturbed. In the $e^{\pm}$ jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.

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arXiv2012

A Simple Law of Star Formation

We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds (MCs), for characteristic values of the free-fall time divided by the dynamical time, $t_{\rm ff}/t_{\rm dyn}$, the alfvénic Mach number, ${\cal M}_{\rm a}$, and the sonic Mach number, ${\cal M}_{\rm s}$. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, $ε_{\rm ff}$, on the above parameters. Our main results are: i) $ε_{\rm ff}$ decreases exponentially with increasing $t_{\rm ff}/t_{\rm dyn}$, but is insensitive to changes in ${\cal M}_{\rm s}$, for constant values of $t_{\rm ff}/t_{\rm dyn}$ and ${\cal M}_{\rm a}$. ii) Decreasing values of ${\cal M}_{\rm a}$ (stronger magnetic fields) reduce $ε_{\rm ff}$, but only to a point, beyond which $ε_{\rm ff}$ increases with a further decrease of ${\cal M}_{\rm a}$. iii) For values of ${\cal M}_{\rm a}$ characteristic of star-forming regions, $ε_{\rm ff}$ varies with ${\cal M}_{\rm a}$ by less than a factor of two. We propose a simple star-formation law, based on the empirical fit to the minimum $ε_{\rm ff}$, and depending only on $t_{\rm ff}/t_{\rm dyn}$: $ε_{\rm ff} \approx ε_{\rm wind} \exp(-1.6 \,t_{\rm ff}/t_{\rm dyn})$. Because it only depends on the mean gas density and rms velocity, this law is straightforward to implement in simulations and analytical models of galaxy formation and evolution.

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arXiv2011

The observable prestellar phase of the IMF

The observed similarities between the mass function of prestellar cores (CMF) and the stellar initial mass function (IMF) have led to the suggestion that the IMF is already largely determined in the gas phase. However, theoretical arguments show that the CMF may differ significantly from the IMF. In this Letter, we study the relation between the CMF and the IMF, as predicted by the IMF model of Padoan and Nordlund. We show that 1) the observed mass of prestellar cores is on average a few times smaller than that of the stellar systems they generate; 2) the CMF rises monotonically with decreasing mass, with a noticeable change in slope at approximately 3-5 solar masses, depending on mean density; 3) the selection of cores with masses larger than half their Bonnor-Ebert mass yields a CMF approximately consistent with the system IMF, rescaled in mass by the same factor as our model IMF, and therefore suitable to estimate the local efficiency of star formation, and to study the dependence of the IMF peak on cloud properties; 4) only one in five pre-brown-dwarf core candidates is a true progenitor to a brown dwarf.

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arXiv2010

The Star Formation Rate of Supersonic MHD Turbulence

This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, alpha_vir, the rms sonic Mach number, M_S,0, and the ratio of mean gas pressure to mean magnetic pressure, beta_0. The SFR is predicted to decrease with increasing alpha_vir (stronger turbulence relative to gravity), to increase with increasing M_S,0 (for constant values of alpha_vir), and to depend weakly on beta_0 for values typical of star forming regions (M_S,0 ~ 4-20 and beta_0 ~ 1-20). In the unrealistic limit of beta_0 -> infinity, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on alpha_vir, and almost the same dependence on M_S,0, as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on alpha_vir and M_S,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions.

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arXiv2007

Two regimes of Turbulent Fragmentation and the stellar IMF from Primordial to Present Day Star Formation

The Padoan and Nordlund model of the stellar initial mass function (IMF) is derived from low order statistics of supersonic turbulence, neglecting gravity (e.g. gravitational fragmentation, accretion and merging). In this work the predictions of that model are tested using the largest numerical experiments of supersonic hydrodynamic (HD) and magneto-hydrodynamic (MHD) turbulence to date (~1000^3 computational zones) and three different codes (Enzo, Zeus and the Stagger Code). The model predicts a power law distribution for large masses, related to the turbulence energy power spectrum slope, and the shock jump conditions. This power law mass distribution is confirmed by the numerical experiments. The model also predicts a sharp difference between the HD and MHD regimes, which is recovered in the experiments as well, implying that the magnetic field, even below energy equipartition on the large scale, is a crucial component of the process of turbulent fragmentation. These results suggest that the stellar IMF of primordial stars may differ from that in later epochs of star formation, due to differences in both gas temperature and magnetic field strength. In particular, we find that the IMF of primordial stars born in turbulent clouds may be narrowly peaked around a mass of order 10 solar masses, as long as the column density of such clouds is not much in excess of 10^22 cm^-2.

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arXiv2004

The "Mysterious" Origin of Brown Dwarfs

Hundreds of brown dwarfs (BDs) have been discovered in the last few years in stellar clusters and among field stars. BDs are almost as numerous as hydrogen burning stars and so a theory of star formation should also explain their origin. The ``mystery'' of the origin of BDs is that their mass is two orders of magnitude smaller than the average Jeans' mass in star--forming clouds, and yet they are so common. In this work we investigate the possibility that gravitationally unstable protostellar cores of BD mass are formed directly by the process of turbulent fragmentation. Supersonic turbulence in molecular clouds generates a complex density field with a very large density contrast. As a result, a fraction of BD mass cores formed by the turbulent flow are dense enough to be gravitationally unstable. We find that with density, temperature and rms Mach number typical of cluster--forming regions, turbulent fragmentation can account for the observed BD abundance.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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arXiv1998

Density PDFs of Super-Sonic Turbulence

The question of the shape of the density PDF for supersonic turbulence is addressed, using both analytical and numerical methods. For isothermal supersonic turbulence, the PDF is Log-Normal, with a width that scales approximately linearly with the Mach number. For a polytropic equation of state, with an effective gamma smaller than one, the PDF becomes skewed and reminiscent of (but not equal to) a power law on the high density side.

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arXiv1997

Synthetic Molecular Clouds from Supersonic MHD and Non-LTE Radiative Transfer Calculations

The dynamics of molecular clouds is characterized by supersonic random motions in the presence of a magnetic field. We study this situation using numerical solutions of the three-dimensional compressible magneto-hydrodynamic (MHD) equations in a regime of highly supersonic random motions. The non-LTE radiative transfer calculations are performed through the complex density and velocity fields obtained as solutions of the MHD equations, and more than 5x10^5 synthetic molecular spectra are obtained. We use a numerical flow without gravity or external forcing. The flow is super-Alfvenic and corresponds to model A of Padoan and Nordlund (1997). Synthetic data consist of sets of 90x90 synthetic spectra with 60 velocity channels, in five molecular transitions: J=1-0 and J=2-1 for 12CO and 13CO, and J=1-0 for CS. Though we do not consider the effects of stellar radiation, gravity, or mechanical energy input from discrete sources, our models do contain the basic physics of magneto-fluid dynamics and non-LTE radiation transfer and are therefore more realistic than previous calculations. As a result, these synthetic maps and spectra bear a remarkable resemblance to the corresponding observations of real clouds.

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arXiv1997

Supersonic Random Flows 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 from a 5 pc model cloud. The synthetic spectra are computed solving the non-LTE radiative transfer problem for a model cloud obtained as solutions of the 3-D magneto-hydrodynamic (MHD) equations in both the highly supersonic and super-Alfvenic regimes of random flows. We present several statistical results that demonstrate remarkable similarity between real data and the synthetic cloud. The three-dimensional structure and dynamics of molecular clouds like Perseus are appropriately described by random supersonic 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 described on intermediate scales without accounting for gravity and stellar radiation.

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