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Michael L. Norman

Publications and source records attributed to Michael L. Norman.

At least 127 records · Page 7Linked to original sources

Forming a Primordial Star in a Relic HII Region

There has been considerable theoretical debate over whether photoionization and supernova feedback from the first Population III stars facilitate or suppress the formation of the next generation of stars. We present results from an Eulerian adaptive mesh refinement simulation demonstrating the formation of a primordial star within a region ionized by an earlier nearby star. Despite the higher temperatures of the ionized gas and its flow out of the dark matter potential wells, this second star formed within 23 million years of its neighbor's death. The enhanced electron fraction within the HII region catalyzes rapid molecular hydrogen formation that leads to faster cooling in the subsequent star forming halos than in the first halos. This "second generation" primordial protostar has a much lower accretion rate because, unlike the first protostar, it forms in a rotationally supported disk of approx. 10-100 solar masses. This is primarily due to the much higher angular momentum of the halo in which the second star forms. In contrast to previously published scenarios, such configurations may allow binaries or multiple systems of lower mass stars to form. These first high resolution calculations offer insight into the impact of feedback upon subsequent populations of stars and clearly demonstrate how primordial chemistry promotes the formation of subsequent generations of stars even in the presence of the entropy injected by the first stars into the IGM.

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Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence

We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 1024^3 zones. Our experiments describe non-magnetized driven supersonic turbulent flows with an isothermal equation of state. Mesh refinement on shocks and shear is implemented to cover dynamically important structures with the highest resolution subgrids and calibrated to match the turbulence statistics obtained from the equivalent uniform grid simulations. We found that at a level of resolution slightly below 512^3, when a sufficient integral/dissipation scale separation is first achieved, the fraction of the box volume covered by the AMR subgrids first becomes smaller than unity. At the higher AMR levels subgrids start covering smaller and smaller fractions of the whole volume, which scale with the Reynolds number as Re^{-1/4}. We demonstrate the consistency of this scaling with a hypothesis that the most dynamically important structures in intermittent supersonic turbulence are strong shocks with a fractal dimension of two. We show that turbulence statistics derived from AMR simulations and simulations performed on uniform grids agree surprisingly well, even though only a fraction of the volume is covered by AMR subgrids. Based on these results, we discuss the signature of dissipative structures in the statistical properties of supersonic turbulence and their role in overall flow dynamics.

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Comparing AMR and SPH Cosmological Simulations: I. Dark Matter & Adiabatic Simulations

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: The SPH code GADGET, and the Eulerian AMR code ENZO. Both codes represent dark matter with the N-body method, but use different gravity solvers and fundamentally different approaches to hydrodynamics. We compare the GADGET `entropy conserving' SPH formulation with two ENZO methods: The piecewise parabolic method (PPM), and the artificial viscosity-based scheme used in the ZEUS code. In this paper we focus on a comparison of cosmological simulations that follow either only dark matter, or also adiabatic baryonic gas. The dark matter-only runs agree generally quite well, provided ENZO is run with a comparatively fine root grid and a low overdensity threshold for mesh refinement, otherwise the abundance of low-mass halos is suppressed. This is due to the hierarchical particle-mesh method used to compute gravitational forces in ENZO, which tends to deliver lower force resolution than the tree algorithm of GADGET. At comparable force resolution, we find that the latter offers substantially better performance and lower memory consumption than the present gravity solver in ENZO. In simulations that include adiabatic gas dynamics, we find general agreement in the distribution functions of temperature, entropy, and density for gas of moderate to high overdensity, as found inside dark matter halos. However, there are some significant differences at lower overdensities. We argue that these discrepancies are presumably owing to differences in the shock-capturing abilities of the different methods. In particular, ZEUS hydro leads to some unphysical heating at early times in preshock regions. Overall, the GADGET hydro results are bracketed by those for ENZO/ZEUS and ENZO/PPM. (abridged)

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The H I opacity of the intergalactic medium at redshifts 1.6 < z < 3.2

We use high quality echelle spectra of 24 QSOs to provide a calibrated measurement of the total amount of Lyman-alpha forest absorption (DA) over the redshift range 2.2 < z < 3.2. Our measurement of DA excludes absorption from metal lines or the Lyman-alpha lines of Lyman limit systems and damped Lyman-alpha systems. We use artificial spectra with realistic flux calibration errors to show that we are able to place continuum levels that are accurate to better than 1%. When we combine our results with our previous results between 1.6 < z < 2.2, we find that the redshift evolution of DA is well described over 1.6 < z < 3.2 as A*(1+z)^gamma, where A = 0.0062 and gamma = 2.75. We detect no significant deviations from a smooth power law evolution over the redshift range studied. We find less H I absorption than expected at z=3, implying that the UV background is about 40% higher than expected. Our data appears to be consistent with an H I ionization rate of Gamma ~ 1.4E-12 1/s.

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The Integrated Sunyaev-Zeldovich Effect as the Superior Method for Measuring the Mass of Clusters of Galaxies

We investigate empirical scaling relations between the thermal Sunyaev-Zeldovich effect (SZE) and cluster mass in simulated clusters of galaxies. The simulated clusters have been compiled from four different samples that differ only in their assumed baryonic physics. We show that the strength of the thermal SZE integrated over a significant fraction of the virialized region of the clusters is relatively insensitive to the detailed heating and cooling processes in the cores of clusters by demonstrating that the derived scaling relations are nearly identical between the four cluster samples considered. For our synthetic images, the central Comptonization parameter shows significant boosting during transient merging events, but the integrated SZE appears to be relatively insensitive to these events. Most importantly, the integrated SZE closely tracks the underlying cluster mass. Observations through the thermal SZE allow a strikingly accurate mass estimation from relatively simple measurements that do not require either parametric modeling or geometric deprojection and thus avoid assumptions regarding the physics of the ICM or the symmetry of the cluster. This result offers significant promise for precision cosmology using clusters of galaxies.

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A Solution to the Protostellar Accretion Problem

Accretion rates of order 10^-8 M_\odot/yr are observed in young protostars of approximately a solar mass with evidence of circumstellar disks. The accretion rate is significantly lower for protostars of smaller mass, approximately proportional to the second power of the stellar mass, \dot{M}_accr\propto M^2. The traditional view is that the observed accretion is the consequence of the angular momentum transport in isolated protostellar disks, controlled by disk turbulence or self--gravity. However, these processes are not well understood and the observed protostellar accretion, a fundamental aspect of star formation, remains an unsolved problem. In this letter we propose the protostellar accretion rate is controlled by accretion from the large scale gas distribution in the parent cloud, not by the isolated disk evolution. Describing this process as Bondi--Hoyle accretion, we obtain accretion rates comparable to the observed ones. We also reproduce the observed dependence of the accretion rate on the protostellar mass. These results are based on realistic values of the ambient gas density and velocity, as inferred from numerical simulations of star formation in self--gravitating turbulent clouds.

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A Statistical Analysis of Intergalactic Medium Transmission Approaching Reionization

We use hydrodynamic cosmological simulations in a 9.6 Mpc box to explore the evolution of the intergalactic medium (IGM) transmissivity from z=2 through the epoch of reionization. Reionization is achieved through an ultraviolet background (UVB) that includes evolving stellar and QSO source populations. We construct and analyze noiseless synthetic HI Lya absorption spectra along lines of sight through our continuously evolving box and find a smooth evolution of the effective optical depth under a power law up to the epoch of reionization. Crossing into the epoch of reionization, both the mean transmitted flux (MTF) and variance to the mean transmitted flux sharply deviate from a smooth evolution and hence such observables have large margins of error. Despite the statistical uncertainty in inferring the reionization profile from spectra, the end of an opacity phase transition of the IGM correlates well with the redshift when both the mean and variance of the transmitted flux rapidly deviate from the post-reionization profile. However, an unobtainable number of lines of sight is needed to allow an estimate of the MTF with less than 10% relative margin of error. In addition to optical transmission, we compare the predicted dark gap length distribution with observations. We show that this statistic is sensitive to spectral resolution at reionization redshifts, but overall in agreement with results by Songaila and Cowie (2002). Finally, we derive a positive correlation between the mean optical depth within a gap and the size of the gap, in attempt to relate "transmission statistics" to "dark gap statistics" in high redshift studies of the IGM.

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Cosmological parameters sigma_8, the baryon density, and the UV background intensity from a calibrated measurement of H I Lyman-alpha absorption at z = 1.9

We identify a concordant model for the intergalactic medium (IGM) at redshift z=1.9 that uses popular values for cosmological and astrophysical parameters and accounts for all baryons with an uncertainty of 6%. We have measured the amount of absorption, DA, in the Ly-alpha forest at redshift 1.9 in spectra of 77 QSO from the Kast spectrograph. We calibrated the continuum fits with realistic artificial spectra, and we found that averaged over all 77 QSOs the mean continuum level is within 1-2% of the correct value. Absorption from all lines in the Ly-alpha forest at z=1.9 removes DA=15.1 +/- 0.7% of the flux between 1070 and 1170 (rest) Angstroms. This is the first measurement using many QSOs at this z, and the first calibrated measurement at any redshift. Metal lines absorb 2.3 +/- 0.5%, and LLS absorb 1.0 +/- 0.4% leaving 11.8 +/- 1.0% from the lower density bulk of the IGM. Averaging over Delta z=0.1 or 154 Mpc, the dispersion is 6.1 +/- 0.3% including LLS and metal lines, or 3.9 (+0.5, -0.7)% for the lower density IGM alone, consistent with the usual description of large scale structure. LLS and metal lines are major contributors to the variation in the mean flux, and they make the flux field significantly non-Gaussian. We find that a hydrodynamic simulation on a 1024 cubed grid in a 75.7 Mpc box reproduces the observed DA from the low density IGM with parameters values H_o=71 km/s/Mpc, Omega_Lambda=0.73, Omega_m=0.27, Omega_b=0.044, sigma_8=0.9 and a UV background that has an ionization rate that is 1.08 +/- 0.08 times the prediction by Madau, Haardt & Rees (1999).

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Scaling Relations for Turbulence in the Multiphase Interstellar Medium

We employ a generalization of the She & Leveque model to study velocity scaling relations based on our simulations of thermal instability--induced turbulence. Being a by-product of the interstellar phase transition, such multiphase turbulence tends to be more intermittent than compressible isothermal turbulence. Due to radiative cooling, which promotes nonlinear instabilities in supersonic flows, the Hausdorff dimension of the most singular dissipative structures, D, can be as high as 2.3, while in supersonic isothermal turbulence D is limited by shock dissipation to D < 2. We also show that single-phase velocity statistics carry only incomplete information on the turbulent cascade in a multiphase medium. We briefly discuss the possible implications of these results on the hierarchical structure of molecular clouds and on star formation.

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Cosmological Simulations of X-ray Clusters: The Quest for Higher Resolution and Essential Physics

I review cosmological simulations of X-ray clusters. Simulations have increased in resolution dramatically and the effects of radiative cooling, star formation feedback, and chemical enrichment on the ICM are being simulated. The structure and evolution of non-radiative X-ray clusters is now well characterized. Such models fail to reproduce the observed L_x-T relation, implying the need for additional physics. Simulations adding radiative cooling produce too much cool gas and unreasonably high X-ray luminosities. Simulations including star formation and feedback appear more promising, but need further refinement. New observations should help in this regard.

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Radiation Hydrodynamical Evolution of Primordial H II Regions

We simulate the ionization environment of z ~ 20 luminous objects formed within the framework of the current CDM cosmology and compute their UV escape fraction. These objects are likely single very massive stars that are copious UV emitters. We present analytical estimates as well as one--dimensional radiation hydrodynamical calculations of the evolution of these first HII regions in the universe. The initially D--type ionization front evolves to become R--type within $\lesssim 10^5$ yrs at a distance $\sim1$ pc. This ionization front then completely overruns the halo, accelerating an expanding shell of gas outward to velocities in excess of 30 km s$^{-1}$, about ten times the escape velocity of the confining dark matter halo. We find that the evolution of the HII region depends only weakly on the assumed stellar ionizing luminosities. Consequently, most of the gas surrounding the first stars will leave the dark halo whether or not the stars produce supernovae. If they form the first massive seed black holes these are unlikely to accrete within a Hubble time after they formed until they are incorporated into larger dark matter halos that contain more gas. Because these I--fronts exit the halo on timescales much shorter than the stars' main sequence lifetimes their host halos have UV escape fractions of $\gtrsim 0.95$, fixing an important parameter for theoretical studies of cosmological hydrogen reionization.

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Introducing Enzo, an AMR Cosmology Application

In this paper we introduce Enzo, a 3D MPI-parallel Eulerian block-structured adaptive mesh refinement cosmology code. Enzo is designed to simulate cosmological structure formation, but can also be used to simulate a wide range of astrophysical situations. Enzo solves dark matter N-body dynamics using the particle-mesh technique. The Poisson equation is solved using a combination of fast fourier transform (on a periodic root grid) and multigrid techniques (on non-periodic subgrids). Euler's equations of hydrodynamics are solved using a modified version of the piecewise parabolic method. Several additional physics packages are implemented in the code, including several varieties of radiative cooling, a metagalactic ultraviolet background, and prescriptions for star formation and feedback. We also show results illustrating properties of the adaptive mesh portion of the code. Enzo is publicly available and can be downloaded at http://cosmos.ucsd.edu/enzo/ .

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The Impact of AMR in Numerical Astrophysics and Cosmology

I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell refinement, and patch refinement, otherwise known as block-structured adaptive mesh refinement (SAMR). In this survey, no attempt is made to assess the relative merits of these two approaches. Rather, the discussion focuses on how AMR is being used and how AMR is making a scientific impact in a diverse set of fields from space physics to the cosmology of the early universe. The increased adoption of AMR techniques in the past decade is driven in part by the public availability of AMR codes and frameworks. I provide a partial list of resources for those interested in learning more about AMR simulations.

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Did Massive Primordial Stars Preenrich the Lyman Alpha Forest?

We examine the dynamical evolution and statistical properties of the supernova ejecta of massive primordial stars in a cosmological framework to determine whether this first population of stars could have enriched the universe to the levels and dispersions seen by the most recent observations of the Lyman-Alpha forest. We evolve a lambda CDM model in a 1 Mpc^3 volume to a redshift of z = 15 and add ``bubbles'' of metal corresponding to the supernova ejecta of the first generation of massive stars in all dark matter halos with masses greater than 5 times 10^5 solar masses. These initial conditions are then evolved to z = 3 and the distribution and levels of metals are compared to observations. In the absence of further star formation the primordial metal is initially contained in halos and filaments. Photoevaporation of metal-enriched gas due to the metagalactic ultraviolet background radiation at the epoch of reionization (z ~ 6) causes a sharp increase of the metal volume filling factor. At z = 3, ~ 2.5% of the simulation volume (approx. 20% of the total gas mass) is filled with gas enriched above a metallicity of 10^-4 Z_solar, and less than 0.6% of the volume is enriched above a metallicity of 10^-3 Z_solar. This suggests that, even with the most optimistic prescription for placement of primordial supernova and the amount of metals produced by each supernova, this population of stars cannot entirely be responsible for the enrichment of the Lyman-$α$ forest to the levels and dispersions seen by current observations unless we have severely underestimated the duration of the Pop III epoch. However, comparison to observations show that Pop III supernovae can be significant contributors to the very low overdensity Lyman-Alpha forest.

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The Formation of Self-Gravitating Cores in Turbulent Magnetized Clouds

We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256^3 and 512^3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows that: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power law relation between central magnetic field strength and density B_c propto rho_c^{1/2} is observed despite the cores being strongly supercritical. (3) Specific angular momentum j propto R^{3/2} for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie et al.

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On the Detectability of Turbulence and Bulk Flows in X-ray Clusters

Cooling flows, cluster mergers and motions of galaxies through the cluster gas with supersonic and sonic velocities must lead to large scale motions of the intracluster medium (ICM). A high-resolution numerical simulation of X-ray cluster formation by Norman and Bryan predicts cluster-wide turbulence with v_turb ~ 300-600 ~km/s and eddy scales l_outer ~ 100-500 kpc, the larger numbers being characteristic of turbulence near the virial radius, while the smaller numbers pertain to the core. The simulation also predicts the existence of ordered bulk flows in the core with v ~ 400 km/s on scales of several hundred kpc. In this paper we consider the observability of such fluid motions via the distortions it induces in the CMB via the kinematic SZ effect, as well as via Doppler broadening and shifting of metal lines in the X-ray spectrum. We estimate |ΔT/T|_kinematic < few X 10^{-6} -- at or below current limits of detectability. However, we find that an energy resolution of a few eV is sufficient to detect several Doppler shifted components in the 6.7 keV Fe line in the core of the cluster.

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Temperature Bias in Measurements of The Hubble Constant Using The Sunyaev-Zeldovich Effect

Measurements of the Hubble constant to distant galaxy clusters using the Sunyaev-Zeldovich effect are systematically low in comparison to values obtained by other means. These measurements usually assume a spherical isothermal $β$ model for the intracluster medium (ICM). We present the results of a statistical analysis of {\em temperature bias} in $H_0$ determinations in a sample of 27 numerically simulated X-ray clusters drawn from a $Λ$CDM model at z=0.5. We employ adaptive mesh refinement to provide high resolution (15.6 h$^{-1} kpc$) in cluster cores which dominate the X-ray and radio signals. Fitting synthetic X-ray and y-parameter maps to the standard isothermal beta model, we find a broad, skewed distribution in $f\equiv H_0(SZ)/H_0(actual)$ with a mean, median, and standard deviation of 0.89, 0.83 and 0.32 respectively, where $H_0(SZ)$ is the value of $H_0$ derived by using Sunyaev-Zeldovich effect method and $H_0(actual)$ is the value used in the cosmological simulation. We find that the clusters' declining temperature profiles systematically lower estimates of $H_0$ by 10% to 20%. The declining temperature profile of our adiabatic system is consistent with the result including radiative cooling and supernovae feedback (Loken et al. 2002). We thereby introduce a non-isothermal $β$ model as an improvement. Applying the non-isothermal $β$ model to the refined sample with well-fitted temperature profile, the value of f improves 9% relative to the actual value. The study of the morphology and the clumping effects conclude that these two factors combine to induce scatter in f of $\pm$ 30 %.

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Formation of Cool Cores in Galaxy Clusters via Hierarchical Mergers

We present a new scenario for the formation of cool cores in rich galaxy clusters based on results from recent high spatial dynamic range, adaptive mesh Eulerian hydrodynamic simulations of large-scale structure formation. We find that cores of cool gas, material that would be identified as a classical cooling flow based on its X-ray luminosity excess and temperature profile, are built from the accretion of discrete, stable subclusters. Any ``cooling flow'' present is overwhelmed by the velocity field within the cluster - the bulk flow of gas through the cluster typically has speeds up to about 2,000 km s^-1 and significant rotation is frequently present in the cluster core. The inclusion of consistent initial cosmological conditions for the cluster within its surrounding supercluster environment is crucial when simulating the evolution of cool cores in rich galaxy clusters. This new model for the hierarchical assembly of cool gas naturally explains the high frequency of cool cores in rich galaxy clusters despite the fact that a majority of these clusters show evidence of substructure which is believed to arise from recent merger activity. Furthermore, our simulations generate complex cluster cores in concordance with recent X-ray observations of cool fronts, cool ``bullets'', and filaments in a number of galaxy clusters. Our simulations were computed with a coupled N-body, Eulerian, adaptive mesh refinement, hydrodynamics cosmology code that properly treats the effects of shocks and radiative cooling by the gas. We employ up to seven levels of refinement to attain a peak resolution of 15.6 h^-1 kpc within a volume 256 h-1 Mpc on a side and assume a standard LambdaCDM cosmology.

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