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Michael L. Norman

Publications and source records attributed to Michael L. Norman.

At least 109 records · Page 6Linked to original sources
arXiv2007

The Statistics of Supersonic Isothermal Turbulence

We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512^3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the first time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1.95 compared to -5/3 in the incompressible case. The exponent of the third-order velocity structure function is 1.28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov's phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v=ρ^{1/3}u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the exponent of the third-order structure function of v is unity. We also directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m = 2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.

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arXiv2007

Scaling Laws and Intermittency in Highly Compressible Turbulence

We use large-scale three-dimensional simulations of supersonic Euler turbulence to study the physics of a highly compressible cascade. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We find that the inertial range velocity scaling deviates strongly from the incompressible Kolmogorov laws. We propose an extension of Kolmogorov's K41 phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that low-order statistics of 'v' are invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69 and the third-order structure function of 'v' scales linearly with separation. We directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m=2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.

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arXiv2007

Simulating Cosmological Evolution with Enzo

In this paper we describe our massively parallel version of Enzo, a multiphysics, parallel, AMR application for simulating cosmological structure formation developed at UCSD and Columbia. We describe its physics, numerical algorithms, implementation, and performance on current terascale platforms. We also discuss our future plans and some of the challenges we face as we move to the petascale.

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arXiv2007

The Beta-Model Problem: The Incompatibility of X-ray and Sunyaev-Zeldovich Effect Model Fitting for Galaxy Clusters

We have analyzed a large sample of numerically simulated clusters to demonstrate the adverse effects resulting from use of X-ray fitted beta-model parameters with Sunyaev-Zeldovich effect (SZE) data. There is a fundamental incompatibility between model fits to X-ray surface brightness profiles and those done with SZE profiles. Since observational SZE radial profiles are in short supply, the X-ray parameters are often used in SZE analysis. We show that this leads to biased estimates of the integrated Compton y-parameter inside r_{500} calculated from clusters. We suggest a simple correction of the method, using a non-isothermal beta-model modified by a universal temperature profile, which brings these calculated quantities into closer agreement with the true values.

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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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arXiv2006

The Power Spectrum of Supersonic Turbulence in Perseus

We test a method of estimating the power spectrum of turbulence in molecular clouds based on the comparison of power spectra of integrated intensity maps and single-velocity-channel maps, suggested by Lazarian and Pogosyan. We use synthetic 13CO data from non-LTE radiative transfer calculations based on density and velocity fields of a simulation of supersonic hydrodynamic turbulence. We find that the method yields the correct power spectrum with good accuracy. We then apply the method to the Five College Radio Astronomy Observatory 13CO map of the Perseus region, from the COMPLETE website. We find a power law power spectrum with slope beta=1.81+-0.10. The values of beta as a function of velocity resolution are also confirmed using the lower resolution map of the same region obtained with the AT&T Bell Laboratories antenna. Because of its small uncertainty, this result provides a useful constraint for numerical codes used to simulate molecular cloud turbulence.

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arXiv2006

Beyond the Cool Core: The Formation of Cool Core Galaxy Clusters

Why do some clusters have cool cores while others do not? In this paper, cosmological simulations, including radiative cooling and heating, are used to examine the formation and evolution of cool core (CC) and non-cool core (NCC) clusters. Numerical CC clusters at z=0 accreted mass more slowly over time and grew enhanced cool cores via hierarchical mergers; when late major mergers occurred, the CCs survived the collisions. By contrast, NCC clusters of similar mass experienced major mergers early in their evolution that destroyed embryonic cool cores and produced conditions that prevent CC re-formation. We discuss observational consequences.

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arXiv2006

AMR Simulations of the Cosmological Light Cone: SZE Surveys of the Synthetic Universe

We present preliminary results from simulated large sky coverage (~100 square degrees) Sunyaev-Zeldovich effect (SZE) cluster surveys using the cosmological adaptive mesh refinement N-body/hydro code Enzo. We have generated simulated light cones to match the resolution and sensitivity of current and future SZE instruments. These simulations are the most advanced calculations of their kind. The simulated sky surveys allow a direct comparison of large N-body/hydro cosmological simulations to current and pending sky surveys. Our synthetic surveys provide an indispensable guide for observers in the interpretation of large area sky surveys, and will develop the tools necessary to discriminate between models for cluster baryonic physics, and to accurately determine cosmological parameters.

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arXiv2006

Population III star formation in a Lambda CDM universe, I: The effect of formation redshift and environment on protostellar accretion rate

(abridged) We perform 12 extremely high resolution adaptive mesh refinement cosmological hydrodynamic simulations of Population III star formation in a Lambda CDM universe, varying the box size and large-scale structure, to understand systematic effects in the formation of primordial protostellar cores. We find results that are qualitatively similar to those observed previously. We observe that the threshold halo mass for formation of a Population III protostar does not evolve significantly with time in the redshift range studied (33 > z > 19) but exhibits substantial scatter due to different halo assembly histories: Halos which assembled more slowly develop cooling cores at lower mass than those that assemble more rapidly, in agreement with Yoshida et al. (2003). We do, however, observe significant evolution in the accretion rates of Population III protostars with redshift, with objects that form later having higher maximum accretion rates, with a variation of two orders of magnitude (10^-4 - 10^-2 Msolar/year). This can be explained by considering the evolving virial properties of the halos with redshift and the physics of molecular hydrogen formation at low densities. Our result implies that the mass distribution of Population III stars inferred from their accretion rates may be broader than previously thought, and may evolve with redshift. Finally, we observe that our collapsing protostellar cloud cores do not fragment, consistent with previous results, which suggests that Population III stars which form in halos of mass 10^5 - 10^6 Msun always form in isolation.

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arXiv2006

High Resolution Simulations of Supersonic Turbulence in Molecular Clouds

We present the results of three-dimensional simulations of supersonic Euler turbulence with grid resolutions up to 1024^3 points. Our numerical experiments describe nonmagnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We demonstrate that the inertial range scaling properties of turbulence in this strongly compressible regime deviate substantially from a Kolmogorov-like behavior previously recovered for mildly compressible transonic flows.

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arXiv2006

Can We Trust the Dust? Evidence of Dust Segregation in Molecular Clouds

Maps of estimated dust column density in molecular clouds are usually assumed to reliably trace the total gas column density structure. In this work we present results showing a clear discrepancy between the dust and the gas distribution in the Taurus molecular cloud complex. We compute the power spectrum of a 2MASS extinction map of the Taurus region and find it is much shallower than the power spectrum of a 13CO map of the same region previously analyzed. This discrepancy may be explained as the effect of grain growth on the grain extinction efficiency. However, this would require a wide range of maximum grain sizes, which is ruled out based on constraints from the extinction curve and the available grain models. We show that major effects due to CO formation and depletion are also ruled out. Our result may therefore suggest the existence of intrinsic spatial fluctuations of the dust to gas ratio, with amplitude increasing toward smaller scales. Preliminary results of numerical simulations of trajectories of inertial particles in turbulent flows illustrate how the process of clustering of dust grains by the cloud turbulence may lead to observable effects. However, these results cannot be directly applied to large scale supersonic and magnetized turbulence at present.

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arXiv2006

Population III Star Formation in a Lambda WDM Universe

In this paper we examine aspects of primordial star formation in a gravitino warm dark matter universe with a cosmological constant. We compare a set of simulations using a single cosmological realization but with a wide range of warm dark matter particle masses which have not yet been conclusively ruled out by observations. The addition of a warm dark matter component to the initial power spectrum results in a delay in the collapse of high density gas at the center of the most massive halo in the simulation and, as a result, an increase in the virial mass of this halo at the onset of baryon collapse. Both of these effects become more pronounced as the warm dark matter particle mass becomes smaller. A cosmology using a gravitino warm dark matter power spectrum assuming a particle mass of m_{WDM} ~ 40keV is effectively indistinguishable from the cold dark matter case, whereas the m_{WDM} ~ 15 keV case delays star formation by approx. 10^8 years. There is remarkably little scatter between simulations in the final properties of the primordial protostar which forms at the center of the halo, possibly due to the overall low rate of halo mergers which is a result of the WDM power spectrum. The detailed evolution of the collapsing halo core in two representative WDM cosmologies is described. At low densities (n_{b} <= 10^5 cm^{-3}), the evolution of the two calculations is qualitatively similar, but occurs on significantly different timescales, with the halo in the lower particle mass calculation taking much longer to evolve over the same density range and reach runaway collapse. Once the gas in the center of the halo reaches relatively high densities (n_{b} >= 10^5 cm^{-3}) the overall evolution is essentially identical in the two calculations.

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arXiv2006

Challenges for Precision Cosmology with X-ray and Sunyaev-Zeldovich Effect Gas Mass Measurements of Galaxy Clusters

We critically analyze the measurement of galaxy cluster gas masses, which is central to cosmological studies that rely on the galaxy cluster gas mass fraction. Using synthetic observations of numerically simulated clusters viewed through their X-ray emission and thermal Sunyaev-Zeldovich effect (SZE), we reduce the observations to obtain measurements of the cluster gas mass. We are thus able to quantify the possible sources of uncertainty and systematic bias associated with the common simplifying assumptions used in reducing real cluster observations including isothermality and hydrostatic equilibrium. We find that intrinsic variations in clusters limit the precision of observational gas mass estimation to ~10% to 1 sigma confidence excluding instrumental effects. Gas mass estimates performed via all methods surprisingly show little or no trending in the scatter as a function of cluster redshift. For the full cluster sample, methods that use SZE profiles out to roughly the virial radius are the simplest, most accurate, and unbiased way to estimate cluster mass. X-ray methods are systematically more precise mass estimators than are SZE methods if merger and cool core systems are removed, but X-ray methods slightly overestimate (5-10%) the cluster gas mass on average. We find that cool core clusters in our samples are particularly poor candidates for observational mass estimation, even when excluding emission from the core region. The effects of cooling in the cluster gas alter the radial profile of the X-ray and SZE surface brightness outside the cool core region, leading to poor gas mass estimates in cool core clusters. Finally, we find that methods using a universal temperature profile estimate cluster masses to higher precision than those assuming isothermality.

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arXiv2006

Adaptive Mesh Refinement Simulations of the Ionization Structure and Kinematics of Damped Ly$α$ Systems with Self-consistent Radiative Transfer

We use high resolution Eulerian hydrodynamics simulations to study kinematic properties of the low ionization species in damped Ly-alpha systems at redshift z=3. Our adaptive mesh refinement simulations include most key ingredients relevant for modeling neutral gas in high-column density absorbers: hydrodynamics, gravitational collapse, continuum radiative transfer and gas chemistry, but no star formation. We model high-resolution Keck spectra with unsaturated low ion transitions in two Si II lines (1526 and 1808 A), and compare simulated line profiles to the data from the SDSS DLA survey. We find that with increasing grid resolution the models show a trend in convergence towards the observed distribution of HI column densities. While in our highest resolution model we recover the cumulative number of DLAs per unit absorption distance, none of our models predicts DLA velocity widths as high as indicated by the data, suggesting that feedback from star formation might be important. At z=3 a non-negligible fraction of DLAs with column densities below 10^21 cm^-2 is caused by tidal tails due to galaxy-galaxy interactions in more massive halo environments. Lower column density absorbers with N_HI < 10^21.4 cm^-2 are sensitive to changes in the UV background resulting in a 10% reduction of the cumulative number of DLAs for twice the quasar background relative to the fiducial value. We find that the mass cut-off below which a large fraction of dwarf galaxies cannot retain gas after reionization is 7*10^7 msun, lower than the previous estimates. Finally, we show that models with self-shielding commonly used in the literature produce significantly lower DLA velocity widths than the full radiative transfer runs.

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arXiv2006

Cosmological Radiative Transfer Codes Comparison Project I: The Static Density Field Tests

Radiative transfer simulations are now at the forefront of numerical astrophysics. They are becoming crucial for an increasing number of astrophysical and cosmological problems; at the same time their computational cost has come to the reach of currently available computational power. Further progress is retarded by the considerable number of different algorithms (including various flavours of ray-tracing and moment schemes) developed, which makes the selection of the most suitable technique for a given problem a non-trivial task. Assessing the validity ranges, accuracy and performances of these schemes is the main aim of this paper, for which we have compared 11 independent RT codes on 5 test problems: (0) basic physics, (1) isothermal H II region expansion and (2) H II region expansion with evolving temperature, (3) I-front trapping and shadowing by a dense clump, (4) multiple sources in a cosmological density field. The outputs of these tests have been compared and differences analyzed. The agreement between the various codes is satisfactory although not perfect. The main source of discrepancy appears to reside in the multi-frequency treatment approach, resulting in different thicknesses of the ionized-neutral transition regions and different temperature structure. The present results and tests represent the most complete benchmark available for the development of new codes and improvement of existing ones. To this aim all test inputs and outputs are made publicly available in digital form.

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arXiv2005

Hot Gas in Galaxy Clusters: Theory and Simulations

We review the theory of the formation of galaxy clusters and discuss their role as cosmological probes. We begin with the standard cosmological framework where we discuss the origin of the CDM matter power spectrum and the growth of density fluctuations in the linear regime. We then summarize the spherical top-hat model for the nonlinear growth of fluctuations from which scaling relations and halo statistics are derived. Numerical methods for simulating gas in galaxy clusters are then overviewed with an emphasis on multiscale hydrodynamic simulations of cluster ensembles. Results of hydrodynamic AMR simulations are described which compare cluster internal and statistical properties as a function of their assumed baryonic processes. Finally, we compare various methods of measuring cluster masses using X-ray and the thermal Sunyaev-Zeldovich effect (SZE). We find that SZE offers great promise for precision measurements in raw samples of high-z clusters.

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arXiv2005

A Multistep Algorithm for the Radiation Hydrodynamical Transport of Cosmological Ionization Fronts and Ionized Flows

Radiation hydrodynamical transport of ionization fronts in the next generation of cosmological reionization simulations holds the promise of predicting UV escape fractions from first principles as well as investigating the role of photoionization in feedback processes and structure formation. We present a multistep integration scheme for radiative transfer and hydrodynamics for accurate propagation of I-fronts and ionized flows from a point source in cosmological simulations. The algorithm is a photon-conserving method which correctly tracks the position of I-fronts at much lower resolutions than non-conservative techniques. The method applies direct hierarchical updates to the ionic species, bypassing the need for the costly matrix solutions required by implicit methods while retaining sufficient accuracy to capture the true evolution of the fronts. We review the physics of ionization fronts in power-law density gradients, whose analytical solutions provide excellent validation tests for radiation coupling schemes. The advantages and potential drawbacks of direct and implicit schemes are also considered, with particular focus on problem timestepping which if not properly implemented can lead to morphologically plausible I-front behavior that nonetheless departs from theory. We also examine the effect of radiation pressure from very luminous central sources on the evolution of I-fronts and flows.

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