arXiv subjects

Åke Nordlund

Publications and source records attributed to Åke Nordlund.

At least 37 records · Page 2Linked to original sources

arXiv2020

The Effect of Supernovae on the Turbulence and Dispersal of Molecular Clouds

While the importance of supernova feedback in galaxies is well established, its role on the scale of molecular clouds is still debated. In this work, we focus on the impact of supernovae on individual clouds, using a high-resolution magneto-hydrodynamic simulation of a region of 250 pc where we resolve the formation of individual massive stars. The supernova feedback is implemented with real supernovae that are the natural evolution of the resolved massive stars, so their position and timing are self-consistent. We select a large sample of molecular clouds from the simulation to investigate the supernova energy injection and the resulting properties of molecular clouds. We find that molecular clouds have a lifetime of a few dynamical times, less then half of them contract to the point of becoming gravitationally bound, and the dispersal time of bound clouds, of order one dynamical time, is a factor of two shorter than that of unbound clouds. We stress the importance of internal supernovae, that is massive stars that explode inside their parent cloud, in setting the cloud dispersal time, and their huge overdensity compared to models where the supernovae are randomly distributed. We also quantify the energy injection efficiency of supernovae as a function of supernova distance to the clouds. We conclude that intermittent driving by supernovae can maintain molecular-cloud turbulence and may be the main process of cloud dispersal. The role of supernovae in the evolution of molecular clouds cannot be fully accounted for without a self-consistent implementation of their feedback.

astro-ph.GA↗

arXiv2019

The Probability Distribution of Density Fluctuations in Supersonic Turbulence

We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $\mathcal{M}$, up to $\mathcal{M}\sim30$. The PDF width, $σ_{s}$, follows the relation $σ_{s}^2 = \ln (1+b^2 {\mathcal M}^2)$, with $b\approx0.38$. However, the PDF exhibits a negative skewness that increases with increasing $\mathcal{M}$, so much of the growth of $σ_{s}$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $\mathcal{M}$, which may have a significant impact on theoretical models of star formation.

astro-ph.GA↗

arXiv2019

Inaccuracy of Spatial Derivatives in Simulations of Supersonic Turbulence

We examine the accuracy of spatial derivatives computed from numerical simulations of supersonic turbulence. Two sets of simulations, carried out using a finite-volume code that evolves the hydrodynamic equations with an approximate Riemann solver and a finite-difference code that solves the Navier-Stokes equations, are tested against a number of criteria based on the continuity equation, including exact results at statistically steady state. We find that the spatial derivatives in the Navier-Stokes runs are accurate and satisfy all the criteria. In particular, they satisfy our exact results that the conditional mean velocity divergence, $\langle \nabla \cdot {\bs u}|s\rangle$, where $s$ is the logarithm of density, and the conditional mean of the advection of $s$, $\langle {\bs u} \cdot \nabla s|s\rangle$, vanish at steady state for all density values, $s$. On the other hand, the Riemann solver simulations fail all the tests that require accurate evaluation of spatial derivatives, resulting in apparent violation of the continuity equation, even if the solver enforces mass conservation. In particular, analysis of the Riemann simulations may lead to the incorrect conclusion that the $\pdv$ work tends to preferentially convert kinetic energy into thermal energy, inconsistent with the exact result that the energy exchange by $\pdv$ work is symmetric in barotropic supersonic turbulence at steady state. The inaccuracy of spatial derivatives is a general problem in the post-processing of simulations of supersonic turbulence with Riemann solvers. Solutions from such simulations must be used with caution in post-processing studies concerning the spatial gradients.

physics.flu-dyn↗

arXiv2018

Pebble dynamics and accretion onto rocky planets. II. Radiative models

We investigate the effects of radiative energy transfer on a series of nested-grid, high-resolution hydrodynamic simulations of gas and particle dynamics in the vicinity of an Earth-mass planetary embryo. We include heating due to the accretion of solids and the subsequent convective motions. Using a constant embryo surface temperature, we show that radiative energy transport results in a tendency to reduce the entropy in the primordial atmosphere, but this tendency is alleviated by an increase in the strength of convective energy transport, triggered by a correspondingly increased super-adiabatic temperature gradient. As a consequence, the amplitude of the convective motions increase by roughly an order of magnitude in the vicinity of the embryo. In the cases investigated here, where the optical depth towards the disk surface is larger than unity, the reduction of the temperature in the outer parts of the Hill sphere relative to cases without radiative energy transport is only $\sim$100K, while the mass density increase is on the order of a factor of two in the inner parts of the Hill sphere. Our results demonstrate that, unless unrealistically low dust opacities are assumed, radiative cooling in the context of primordial rocky planet atmospheres can only become important after the disk surface density has dropped significantly below minimum-mass-solar-nebula values.

astro-ph.EP↗

arXiv2018

Detailed Balance and Exact Results for Density Fluctuations in Supersonic Turbulence

The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in compressible turbulence in two forms: a first-order partial differential equation involving the average divergence conditioned on the flow density, $\langle \nabla \cdot {\bs u} | s\rangle$, and a Fokker-Planck equation with the drift and diffusion coefficients equal to $-\langle {\bs u} \cdot \nabla s | s\rangle$ and $\langle {\bs u} \cdot \nabla s | s\rangle$, respectively. Assuming statistical homogeneity only, the detailed balance at steady state leads to two exact results, $\langle \nabla \cdot {\bs u} | s \rangle =0$, and $\langle {\bs u} \cdot \nabla s | s\rangle=0$. The former indicates a balance of the flow divergence over all expanding and contracting regions at each given density. The exact results provide an objective criterion to judge the accuracy of numerical codes with respect to the density statistics in supersonic turbulence. We also present a method to estimate the effective numerical diffusion as a function of the flow density and discuss its effects on the shape of the density PDF.

astro-ph.GA↗

arXiv2017

The benchmark halo giant HD 122563: CNO abundances revisited with three-dimensional hydrodynamic model stellar atmospheres

We present an abundance analysis of the low-metallicity benchmark red giant star HD 122563 based on realistic, state-of-the-art, high-resolution, three-dimensional (3D) model stellar atmospheres including non-grey radiative transfer through opacity binning with four, twelve, and 48 bins. The 48-bin 3D simulation reaches temperatures lower by ~ 300 - 500 K than the corresponding 1D model in the upper atmosphere. Small variations in the opacity binning, adopted line opacities, or chemical mixture can cool the photospheric layers by a further ~ 100 - 300 K and alter the effective temperature by ~ 100 K. A 3D local thermodynamic equilibrium (LTE) spectroscopic analysis of Fe I and Fe II lines gives discrepant results in terms of derived Fe abundance, which we ascribe to non-LTE effects and systematic errors on the stellar parameters. We also determine C, N, and O abundances by simultaneously fitting CH, OH, NH, and CN molecular bands and lines in the ultraviolet, visible, and infrared. We find a small positive 3D-1D abundance correction for carbon (+0.03 dex) and negative ones for nitrogen (-0.07 dex) and oxygen (-0.34 dex). From the analysis of the [O I] line at 6300.3 Å, we derive a significantly higher oxygen abundance than from molecular lines (+0.46 dex in 3D and +0.15 dex in 1D). We rule out important OH photodissociation effects as possible explanation for the discrepancy and note that lowering the surface gravity would reduce the oxygen abundance difference between molecular and atomic indicators.

astro-ph.SR↗

arXiv2017

Accounting for the diversity in stellar environments

Stars and their corresponding protoplanetary disks form in diverse environments. To account for these natural variations, we investigate the formation process around nine solar mass stars with a maximum resolution of 2 AU in a Giant Molecular Cloud of (40 pc)$^3$ in volume by using the adaptive mesh refinement code \ramses. The magnetohydrodynamic simulations reveal that the accretion process is heterogeneous in time, in space, and among protostars of otherwise similar mass. During the first roughly 100 kyr of a protostar evolving to about a solar mass, the accretion rates peak around $10^{-5}$ to $10^{-4}$ M$_{\odot}$ yr$^{-1}$ shortly after its birth, declining with time after that. The different environments also affect the spatial accretion, and infall of material to the star-disk system is mostly through filaments and sheets. Furthermore, the formation and evolution of disks varies significantly from star to star. We interpret the variety in disk formation as a consequence of the differences in the combined effects of magnetic fields and turbulence that may cause differences in the efficiency of magnetic braking, as well as differences in the strength and distribution of specific angular momentum.

astro-ph.GA↗

arXiv2017

Early formation of planetary building blocks inferred from Pb isotopic ages of chondrules

The most abundant components of primitive meteorites (chondrites) are millimeter-sized glassy spherical chondrules formed by transient melting events in the solar protoplanetary disk. Using Pb-Pb dates of 22 individual chondrules, we show that primary production of chondrules in the early solar system was restricted to the first million years after formation of the Sun and that these existing chondrules were recycled for the remaining lifetime of the protoplanetary disk. This is consistent with a primary chondrule formation episode during the early high-mass accretion phase of the protoplanetary disk that transitions into a longer period of chondrule reworking. An abundance of chondrules at early times provides the precursor material required to drive the efficient and rapid formation of planetary objects via chondrule accretion.

astro-ph.EP↗

arXiv2017

Zoom-Simulations of Protoplanetary Disks starting from GMC scales

We investigate the formation of protoplanetary disks around nine solar mass stars formed in the context of a (40 pc)$^3$ Giant Molecular Cloud model, using RAMSES adaptive-mesh refinement simulations extending over a scale range of about 4 million, from an outer scale of 40 pc down to cell sizes of 2 AU. Our most important result is that the accretion process is heterogeneous in multiple ways; in time, in space, and among protostars of otherwise similar mass. Accretion is heterogeneous in time, in the sense that accretion rates vary during the evolution, with generally decreasing profiles, whose slopes vary over a wide range, and where accretion can increase again if a protostar enters a region with increased density and low speed. Accretion is heterogeneous in space, because of the mass distribution, with mass approaching the accreting star-disk system in filaments and sheets. Finally, accretion is heterogeneous among stars, since the detailed conditions and dynamics in the neighborhood of each star can vary widely. We also investigate the sensitivity of disk formation to physical conditions, and test their robustness by varying numerical parameters. We find that disk formation is robust even when choosing the least favorable sink particle parameters, and that turbulence cascading from larger scales is a decisive factor in disk formation. We also investigate the transport of angular momentum, finding that the net inward mechanical transport is compensated for mainly by an outward directed magnetic transport, with a contribution from gravitational torques usually subordinate to the magnetic transport.

astro-ph.SR↗

arXiv2017

Supernova Driving. IV. The Star Formation Rate of Molecular Clouds

We compute the star formation rate (SFR) in molecular clouds (MCs) that originate {\it ab initio} in a new, higher-resolution simulation of supernova-driven turbulence. Because of the large number of well-resolved clouds with self-consistent boundary and initial conditions, we obtain a large range of cloud physical parameters with realistic statistical distributions, an unprecedented sample of star-forming regions to test SFR models and to interpret observational surveys. We confirm the dependence of the SFR per free-fall time, $SFR_{\rm ff}$, on the virial parameter, $α_{\rm vir}$, found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, ${\cal M}$, gas to magnetic pressure ratio, $β$, and compressive to solenoidal power ratio, $χ$ at fixed $α_{\rm vir}$ are not well constrained, because of random scatter due to time and cloud-to-cloud variations in $SFR_{\rm ff}$. We find that $SFR_{\rm ff}$ in MCs can take any value in the range $0 \le SFR_{\rm ff} \lesssim 0.2$, and its probability distribution peaks at a value $SFR_{\rm ff}\approx 0.025$, consistent with observations. The values of $SFR_{\rm ff}$ and the scatter in the $SFR_{\rm ff}$--$α_{\rm vir}$ relation are consistent with recent measurements in nearby MCs and in clouds near the Galactic center. Although not explicitly modeled by the theory, the scatter is consistent with the physical assumptions of our revised model and may also result in part from a lack of statistical equilibrium of the turbulence, due to the transient nature of MCs.

astro-ph.GA↗

arXiv2016

Particle-in-cell Simulations of Global Relativistic Jets with Helical Magnetic Fields

We study the interaction of relativistic jets with their environment, using 3-dimensional relativistic particle-in-cell simulations for two cases of jet composition: (i) electron-proton ($e^{-}-p^{+}$) and (ii) electron-positron ($e^{\pm}$) plasmas containing helical magnetic fields. 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 and the Mushroom instability. We have found that these kinetic instabilities are suppressed and new types of instabilities can grow. For the $e^{-}-p^{+}$ jet, a recollimation-like instability occurs and jet electrons are strongly perturbed, whereas for the $e^{\pm}$ jet, a recollimation-like instability occurs at early times followed by kinetic instability and the general structure is similar to a simulation without a helical magnetic field. We plan to perform further simulations using much larger systems to confirm these new findings.

astro-ph.HE↗

arXiv2016

Supernova Driving. III. Synthetic Molecular Cloud Observations

We present a comparison of molecular clouds (MCs) from a simulation of supernova-driven interstellar medium (ISM) turbulence with real MCs from the Outer Galaxy Survey. The radiative transfer calculations to compute synthetic CO spectra are carried out assuming the CO relative abundance depends only on gas density, according to four different models. Synthetic MCs are selected above a threshold brightness temperature value, $T_{\rm B,min}=1.4$ K, of the $J=1-0$ $^{12}$CO line, generating 16 synthetic catalogs (four different spatial resolutions and four CO abundance models), each containing up to several thousands MCs. The comparison with the observations focuses on the mass and size distributions and on the velocity-size and mass-size Larson relations. The mass and size distributions are found to be consistent with the observations, with no significant variations with spatial resolution or chemical model, except in the case of the unrealistic model with constant CO abundance. The velocity-size relation is slightly too steep for some of the models, while the mass-size relation is a bit too shallow for all models only at a spatial resolution $dx\approx 1$ pc. The normalizations of the Larson relations show a clear dependence on spatial resolution, for both the synthetic and the real MCs. The comparison of the velocity-size normalization suggests that the SN rate in the Perseus arm is approximately 70\% or less of the rate adopted in the simulation. Overall, the realistic properties of the synthetic clouds confirm that supernova-driven turbulence can explain the origin and dynamics of MCs.

astro-ph.GA↗

arXiv2014

Infall-Driven Protostellar Accretion and the Solution to the Luminosity Problem

We investigate the role of mass infall in the formation and evolution of protostars. To avoid ad hoc initial and boundary conditions, we consider the infall resulting self-consistently from modeling the formation of stellar clusters in turbulent molecular clouds. We show that infall rates in turbulent clouds are comparable to accretion rates inferred from protostellar luminosities or measured in pre-main-sequence stars. They should not be neglected in modeling the luminosity of protostars and the evolution of disks, even after the embedded protostellar phase. We find large variations of infall rates from protostar to protostar, and large fluctuations during the evolution of individuals protostars. In most cases, the infall rate is initially of order 10$^{-5}$\msun\ yr$^{-1}$, and may either decay rapidly in the formation of low-mass stars, or remain relatively large when more massive stars are formed. The simulation reproduces well the observed characteristic values and scatter of protostellar luminosities and matches the observed protostellar luminosity function. The luminosity problem is therefore solved once realistic protostellar infall histories are accounted for, with no need for extreme accretion episodes. These results are based on a simulation of randomly-driven magneto-hydrodynamic turbulence on a scale of 4pc, including self-gravity, adaptive-mesh refinement to a resolution of 50AU, and accreting sink particles. The simulation yields a low star formation rate, consistent with the observations, and a mass distribution of sink particles consistent with the observed stellar initial mass function during the whole duration of the simulation, forming nearly 1,300 sink particles over 3.2 Myr.

astro-ph.SR↗

arXiv2014

Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation

We perform a calibration of the mixing length of convection in stellar structure models against realistic 3D radiation-coupled hydrodynamics (RHD) simulations of convection in stellar surface layers, determining the adiabat deep in convective stellar envelopes. The mixing-length parameter $α$ is calibrated by matching averages of the 3D simulations to 1D stellar envelope models, ensuring identical atomic physics in the two cases. This is done for a previously published grid of solar-metallicity convection simulations, covering from 4200 K to 6900 K on the main sequence, and 4300-5000 K for giants with logg=2.2. Our calibration results in an $α$ varying from 1.6 for the warmest dwarf, which is just cool enough to admit a convective envelope, and up to 2.05 for the coolest dwarfs in our grid. In between these is a triangular plateau of $α$ ~ 1.76. The Sun is located on this plateau and has seen little change during its evolution so far. When stars ascend the giant branch, they largely do so along tracks of constant $α$, with $α$ decreasing with increasing mass.

astro-ph.SR↗

arXiv2014

Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. $T(τ)$-Relations

Relations between temperature, T, and optical depth, tau, are often used for describing the photospheric transition from optically thick to optically thin in stellar structure models. We show that this is well justified, but also that currently used T(tau) relations are often inconsistent with their implementation. As an outer boundary condition on the system of stellar structure equations, T(tau) relations have an undue effect on the overall structure of stars. In this age of precision asteroseismology, we need to re-assess both the method for computing and for implementing T(tau) relations, and the assumptions they rest on. We develop a formulation for proper and consistent evaluation of T(tau) relations from arbitrary 1D or 3D stellar atmospheres, and for their implementation in stellar structure and evolution models. We extract radiative T(tau) relations, as described by our new formulation, from 3D simulations of convection in deep stellar atmospheres of late-type stars from dwarfs to giants. These simulations employ realistic opacities and equation of state, and account for line-blanketing. For comparison, we also extract T(tau) relations from 1D MARCS model atmospheres using the same formulation. T(tau)-relations from our grid of 3D convection simulations display a larger range of behaviours with surface gravity, compared with those of conventional theoretical 1D hydrostatic atmosphere models. Based on this, we recommend no longer to use scaled solar T(tau) relations. Files with T(tau) relations for our grid of simulations are made available to the community, together with routines for interpolating in this irregular grid. We also provide matching tables of atmospheric opacity, for consistent implementation in stellar structure models.

astro-ph.SR↗

arXiv2013

The Star Formation Rate of Molecular Clouds

We review recent advances in the analytical and numerical modeling of the star formation rate in molecular clouds and discuss the available observational constraints. We focus on molecular clouds as the fundamental star formation sites, rather than on the larger-scale processes that form the clouds and set their properties. Molecular clouds are shaped into a complex filamentary structure by supersonic turbulence, with only a small fraction of the cloud mass channeled into collapsing protostars over a free-fall time of the system. In recent years, the physics of supersonic turbulence has been widely explored with computer simulations, leading to statistical models of this fragmentation process, and to the prediction of the star formation rate as a function of fundamental physical parameters of molecular clouds, such as the virial parameter, the rms Mach number, the compressive fraction of the turbulence driver, and the ratio of gas to magnetic pressure. Infrared space telescopes, as well as ground-based observatories have provided unprecedented probes of the filamentary structure of molecular clouds and the location of forming stars within them.

astro-ph.GA↗

arXiv2013

A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion

Present grids of stellar atmosphere models are the workhorses in interpreting stellar observations, and determining their fundamental parameters. These models rely on greatly simplified models of convection, however, lending less predictive power to such models of late type stars. We present a grid of improved and more reliable stellar atmosphere models of late type stars, based on deep, 3D, convective, stellar atmosphere simulations. This grid is to be used in general for interpreting observations, and improve stellar and asteroseismic modeling. We solve the Navier Stokes equations in 3D and concurrent with the radiative transfer equation, for a range of atmospheric parameters, covering most of stellar evolution with convection at the surface. We emphasize use of the best available atomic physics for quantitative predictions and comparisons with observations. We present granulation size, convective expansion of the acoustic cavity, asymptotic adiabat, as function of atmospheric parameters. These and other results are also available in electronic form.

astro-ph.SR↗

arXiv2012

On the Formation of Active Regions

Magneto-convection can produce an active region without an initial coherent flux tube. A simulation was performed where uniform, untwisted, horizontal magnetic field of 1 kG strenght was advected into the bottom of a computational domain 48 Mm wide by 20 Mm deep. The up and down convective motions produce a hierarchy of magnetic loops with a wide range of scales, with smaller loops riding "piggy back" in a serpentine fashion on larger loops. When a large loop approaches the surface it produces an small active region with a compact leading spot and more diffuse following spots.

astro-ph.SR↗