Robert Fisher – Statement of Research Accomplishments

1. Overview The incorporation of turbulent processes into theoretical and computational models has enabled remarkable progress on a wide range of topics in fundamental science. This has par- ticularly been true in astrophysics, where turbulence is now understood to play an essential role in processes ranging from the formation of stars to supernovae explosions. Despite the apparent complexity of the turbulent flows at work in these disparate phenomena, the tur- bulent cascade concept originally proposed by Kolmogorov endows them with a deep under- lying universal scale-invariant structure within the inertial range, independent of the driving mechanism [1]. Zwicky, von Weizsäcker, and later authors (in particular Larson) noted the significance of this powerful concept, and applied it within an astrophysical context to galax- ies and clusters of galaxies, the interstellar medium, and accretion disks [2, 3, 4, 5]. Their seminal work has provided an overarching framework with which we can begin to understand the role turbulence plays in astrophysical processes. Thanks to the monumental advances in parallel supercomputers over the past decade, we can now directly simulate turbulent processes in astrophysics in fully three-dimensional cal- culations, coupled with other key physics, such as self-gravity, radiative transfer, and nuclear burning. These advances in computing come at the same time as a powerful new genera- tion of observational instruments across the entire spectrum – including SCUBA, IRAM, CARMA, SMA, ALMA, Spitzer, SOFIA, LMT, James Webb, and Chandra. As the result of this tremendous progress, we are in a now at an exciting point in time where we can now begin to address how turbulence plays a crucial role in answering fundamental, long-standing questions which have long vexed astrophysicists. My own work has focused on two endpoints of stellar evolution – star formation and su- pernovae. In the context of star formation, these outstanding questions include : How is turbulence within star-forming giant molecular clouds (GMCs) generated and sustained? What sets the stellar initial mass function (IMF)? What sets the rate at which stars are formed? How are brown dwarfs formed? How are binary stars formed? In the context of su- pernovae, these questions include : How does a Chandrasekhar-mass white dwarf first ignite and initiate a subsonic deflagration front that becomes a type Ia supernova? What is the nature of turbulent deflagration within Ia supernovae? Does the deflagration front transi- tion into a supersonic detonation, and if so, how? What is the origin of the Phillips relation, and is it possible to obtain an even-tighter relation using first principles simulations of Ia supernovae, and thereby provide even tighter constraints on the properties of dark energy? Successfully addressing these fundamental questions though computation hinges crucially upon efficient, scalable parallel algorithms to treat the essential physics; a portion of my research is devoted to the development of such algorithms. In addition, computation at the petascale and beyond leads to challenging informatics problems in the analysis of large-scale datasets, which must be solved in order to produce scientific results. I outline our research accomplishments in §2.

2. Key Accomplishments to Date Fisher Research Statement 2

(a) (b) (c) Figure 1: The sequence of events leading up to a type Ia supernova in our recent 3D sim- ulations. (a) Carbon burning on the interior of a Chadrasekhar-mass white dwarf leads to the ignition of a nuclear flame bubble, slightly offset from the center of the star. (b) The bubble rises from the point of ignition, buoyed by the hot nuclear ash, becomes turbulent, and breaks out of the surface of the star about one second later. (c) The hot ash remains gravitationally confined to the surface of the star, generating a surface flow which rushes over the surface of the star in another 1-2 seconds, setting off a detonation.

3D Simulations of Type Ia Supernovae. Type Ia supernovae have received increased in- terest because of their importance as “standard candles” for cosmology. Observations using type Ia supernovae as standard candles have revealed that the ex- pansion rate of the universe is accelerating and have led to the discovery of dark energy. However, the basic explosion mechanism of type Ia supernovae is not fully understood. A fundamental question is how the transi- tion from a subsonic deflagration to a super- sonic detonation occurs in a white dwarf [6]. In collaboration with colleagues (C. Jor- dan, D. Townsley, A. Calder, C. Graziani, S. Asida, D. Lamb, & J. Truran), we were the first to demonstrate successful self- consistent detonations in three-dimensional Figure 2: A close-up demonstrating the GCD simulations of type Ia supernovae [7]. We mechanism in detail. The white dwarf sur- began our simulations with ignition at an face is shown as an isocontour of density, while off-center point in the white dwarf interior, the heated material in the incoming jet gener- resulting in a turbulent burning bubble of ated by the convergence of swept-up unburned hot ash that rose rapidly, broke through surface flow is volume-rendered temperature. the surface of the star, and collided at a The intersection of these two surfaces satisfies point opposite breakout on the stellar sur- a conservative detonation criterion. face – a “gravitationally-confined detona- tion” (GCD). We found that detonation conditions were robustly reached in our three-dimensional simu- Fisher Research Statement 3

lations for a range of initial conditions and resolutions. These conditions were achieved as the result of an inwardly-directed jet that is produced by the compression of unburnt surface material when the surface flow collides with itself (figure 2). Observations of type Ia super- novae imply properties that are consistent with those expected from these 3D simulations of the GCD model.

Eulerian and Lagrangian Properties of Homogeneous, Isotropic Weakly Com- pressible Turbulence. Recent experiments involving tracer particles within turbulent flows have sparked considerable interest in the topic of Lagrangian properties of turbulence. Beginning in December 2005, I have led a large, interdisciplinary, international group of over twenty-five computer scientists, applied mathematicians, and physicists at the University of Chicago, Argonne National Laboratory, and the Università di Roma on a project studying the Eulerian and Lagrangian properties of weakly-compressible turbulence through numerical simulation. Our largest simulation was run at a grid resolution of 18563 on the Lawrence Liv- ermore BG/L supercomputer, and utilized 2563 Lagrangian tracer particles. Approximately one week of CPU time on 65,536 processors was used to complete our highest-resolution simulation, which produced over 100 TB of data.

Figure 3: A nonlinear mapping of the density gradient within a single cut plane of our large-scale homogeneous isotropic turbulence simulation, revealing the rich network of vortex filament cores in weakly-compressible turbulence.

When we initiated this project, we had the vision to release the full dataset under an open data model, allowing open access to any and all interested parties. Designing the hardware Fisher Research Statement 4 and software systems to meet this vision was a major challenge which we successfully ad- dressed in collaboration with a team of computer scientists from the joint Argonne/University of Chicago Computation Institute (CI) [8]. We chose to collocate storage and analysis com- putation, which is the natural solution for a large dataset. The full dataset is served to the community from the CI’s mass datastore, which was custom-designed to meet our specifi- cations. The system currently is a scalable high-performance storage resource that has 75 TB of raw storage configured in an 8+2 RAID array, allowing up to 48 drives to fail with no impact to performance, stability, or reliability. It can deliver a sustained throughput of 3 GB/s. It can also be scaled to 480 TB of raw storage. Five I/O servers are connected to storage system by five fiber channels and then connected to the outside world via 1 Gb/s Ethernet connections to the CI’s 10 Gb/s I-WIRE link. Collocated with the storage resource is the CI’s TeraPort compute resource; a 244-processor AMD Opteron cluster that is used for local processing of the data. Custom parallel software tools were written to handle the data analysis. Over 1015 points were computed when determining the Eulerian structure functions while writing the first papers from this run. In a recent paper we have examined the Eulerian scaling properties within this weakly- compressible flow [9]. One remarkable property of weakly-compressible turbulence emerged during our analysis of the scaling exponents of the pth order density structure function p Sp(r) [δρ(r)] (where ρ(x) is the spatial density field, δρ(r) = ρ(x + r) ρ(x), and ≡ " # − denotes average over points x in the volume and over time). In the inertial regime, the "# ζp structure functions are scale-invariant and therefore follow the power-law Sp(r) r . We ∝ have shown that although no shock waves are produced in the simulation, the density fluc- tuations are characterized by front-like structures that determine the tail of the probability distribution of density increments δρ(r). Accordingly, the scaling exponents ζp of the density structure functions saturate at large moments p. An additional paper currently in prepara- tion compares the scaling properties of the Lagrangian structure functions of this simulation against those obtained both by several experimental groups and by other simulations.

Ideal MHD Algorithmic Development and Sub-Alfvénic Non-Ideal MHD Tur- bulence With Ambipolar Diffusion. One of the challenges in developing realistic sim- ulations is the design of accurate, robust numerical algorithms which can treat the physics of a problem accurately. In the case of astrophysical simulations, these physical processes are governed by several fundamental partial differential equations of the hyperbolic (hydro- dynamic / magnetohydrodynamic), elliptic (self-gravity), and mixed parabolic/elliptic types (radiative transfer). Beginning with the pioneering work of Boris, Book, Van Leer, Colella, Woodward, and others in the 1970s and 1980s, the state-of-the-art in direct simulation of strongly-compressible hyperbolic systems of equations has centered on higher-order Godunov methods, which extend Godunov’s method beyond first order by adding a small amount of dissipation (using geometric slope limiters, artificial viscosity, slope steepeners, filtering, and other techniques) in the vicinity of shocks. In a recent paper (in collaboration with Rob Crockett, Phil Colella, Richard Klein, and Christopher McKee) we have described the development of a highly-accurate and robust higher-order Godunov method for ideal magnetohydroynamics (MHD). Our algorithm built upon and extended the work of previous authors, eliminating prior limitations such as high dissipation rates or first-order convergence in one or more wave families. [10] These are im- Fisher Research Statement 5

portant issues in astrophysical simulations, since many of the most widely-studied processes deal with the magnetized processes whose evolution is set by the growth and decay rates of instabilities (Balbus-Hawley / MRI, photon bubble, magnetoconvection) and turbulence. In each case, numerical dissipation and reconnection can mimic physical dissipation and reconnection, and therefore a simulation with insufficient resolution can lead to a qualita- tively different outcome than one with sufficient resolution. This issue becomes particularly acute in three dimensions, where only a very limited spatial dynamic range can typically be afforded. Most of the numerical investigations on the role of magnetic fields on turbulent molecular clouds to date have based on ideal MHD. However, molecular clouds are weakly-ionized, and the time scale required for the magnetic field to diffuse through the neutral component of the plasma is set by ambipolar diffusion (AD), which can be comparable to the dynam- ical time scale. In collaboration with my colleagues (PS Li, Christopher McKee, Richard Klein), we have performed a series of 2563 and 5123 simulations on supersonic, sub-Alfvénic turbulent systems using the heavy-ion approximation, which extends our ideal MHD algo- rithmic development to treat non-ideal effects due to ambipolar diffusion [11]. We found that ambipolar diffusion steepens the velocity and magnetic power spectra compared to the ideal MHD case. We also found that the power spectra for the neutral gas properties of a strongly-magnetized medium with a low AD Reynolds number are similar to those of a weakly-magnetized medium.

Interactions of Shocks with Clouds with Smooth Boundaries. For decades, re- searchers have pursued the goal of understanding the physical processes which govern the dynamics of the interstellar medium (ISM). One outstanding issue is how turbulence is cre- ated and maintained in the ISM. Turbulence is a ubiqituous phenemonon in the ISM across many decades in lengthscale, despite the fact that it decays very rapidly (of order a crossing time) – why should this be the case? In collaboration with Fumitaka Nakamura, Richard Klein, and Christopher McKee, we set out to understand the general behavior of whether a shock driven into a cloud can generate turbulence within it without destroying the cloud. The shock-cloud system is a well-studied model system which serves as a conceptual laboratory in which one can explore the In this paper, we set up a more realistic and general initial condition with a power-law density profile in the envelope of the cloud. The stratification of the cloud leads to some remarkable differences. Figure 4a depicts the interaction of a shock with a cloud with a power-law density profile 2 going as r− in the envelope. Figure 4b depicts the interaction of the same shock with a 8 cloud with a teeper density profile, this time going as r− in the envelope. In both cases, the Kelvin-Helmholtz instability arising at the shear interface between the passing shock and the outer boundary of the cloud eventually grows, leading to the destruction of the cloud itself 2 through mixing with the ambient medium. Remarkably, however, the r− envelope cloud delays the development of the Kelvin-Helmholtz instability for a significantly longer time. One of the key contributions of this paper is a simple physical explanation of this effect, based on the growth rate of the Kelvin-Helmholtz instability in a stratified medium. These results have significant implications for current models of supernova-driven formation Fisher Research Statement 6 of GMCs. One of the features of these models is an explanation for observed GMC turbulence as the result of supernovae-driven shocks on large scales. However, our results suggest that shock-driven turbulence will rapidly destroy the parent cloud on a timescale of a few shock- crossing times, and is therefore unlikely to sustain turbulence within the cloud.

(a) (b)

Figure 4: (a) The interaction of a shock with a cloud with a power-law density profile going 2 as r− in the envelope. The Kelvin-Helmholtz instability generated by the shear in the post- shock flow causes the cloud to mix and disrupt. (b) The same shock interacting with a cloud 8 with a steeper density profile, going as r− in the envelope. The sharper stratification leads to a more rapid development of Kelvin-Helmholtz and a more rapid disruption.

Turbulent Interstellar Medium Origin of the Binary Period Distribution. Most G-type and earlier stars in the solar neighborhood exist in gravitationally-bound binary and low-order multiple systems [12, 13]. Moreover, many nearby observations of nearby star- forming regions (including Taurus, Orion, Scorpius-Centaurus OB, Chameleon, Lupus, and Corona Australis) indicate that the fraction of binary systems seen is at least that of the field in every region, and up to twice that of the field in some regions (such as Taurus) [14]. Because multiple star formation is ubiquitous, our knowledge of it is central to our understanding of the star formation process, and has enormous significance for the study of the formation of planetary systems as well. Binary star systems offer crucial clues about the distribution and evolution of angular momentum in dense star-forming gas in giant molecular clouds (GMCs). The observed period distribution of binaries is remarkably broad – spanning some 10 decades – and is consistent with a log-normal distribution (figure 5b). Explaining the broad distribution of binary periods presented a significant challenge to the- orists. Indeed, previously, despite significant contributions by a number of authors [15, 16], the binary period distribution had not been explained by theory. Our main contribution was to connect the stellar binary period to the idea that turbulence, which endows star-forming giant molecular cloud cores with a non-thermal linewidth, also endows them with a net angular momentum [17]. Our model begins with a binary system whose masses are randomly drawn from the stellar initial mass function (IMF) [18]. We then connect this model binary to a parent turbulent Fisher Research Statement 7 giant molecular cloud core whose mass is consistent with the binary and the star formation efficiency, and whose velocity field is a turbulent realization of a Gaussian random field with linewidth and spectrum consistent with observation. The predicted binary period distribu- tion is consistent with the observed period distribution for both field stars and young stellar objects (YSOs). In addition, the model also predicts three correlations similar to those observed — a robust anticorrelation of binary period and mass ratio, a robust, positive cor- relation of binary period and eccentricity, and a robust prediction that the binary separation of low-mass systems should be less than that of solar-mass or larger systems.

(a) (b)

Figure 5: (a) Binary period distribution resulting from our turbulent model, drawn for 200 binary systems. The distribution is plotted versus the log of period, in days. (b) The binary period distribution of stars in the field (dashed line) and pre-main sequence stars (solid line).

Fragmentation and Star Formation in Turbulent Cores. One of the key oustanding problems in low-mass star-formation is the origin of binary and multiple star systems. We know from observation that the majority of G-type and earlier stars (both pre-main sequence and main sequence) are located in binary star systems. In addition, the binarity in young star-forming regions is generally observed to be in excess of that of older background field stars, indicating that the dynamical processes leading to multiple systems must arise early in the process of star formation. Indeed, in some cases, embedded binaries are seen directly in observations. These basic observational facts alone provide demanding constraints on dynamical models of star formation. Numerous early theoretical studies failed to explain why binary systems should be so commonplace in nature. Almost inevtiably, models formed a single star un- less the initial conditions were very highly unstable – and therefore highly unphysical – to gravitational collapse initially. Furthermore, the models typically included only isothermal self-gravitating hydrodynamics, and therefore could not tie the degree of multiplicity to the mass of the core, contrary to observation. Lastly, centrally-condensed initial GMC cores did not generally lead to fragmentation, against contrary to observation. For part of my thesis dissertation, I formulated a physically-motivated set of initial condi- tions for star formation in turbulent, isolated GMC cores [19]. These models began with an Fisher Research Statement 8

(a) (b)

Figure 6: The results of two turbulent GMC core models. (a) A core with 3D rms-Mach number 1, resulting in the formation of a single star. (b) A core with rms-Mach number 3, resulting in a binary system. All other parameters specifying the runs, including the realization of turbulence, are held fixed. These simulations demonstrate that transonic turbulence produces multiple systems in centrally-condensed cores. equilibrium isothermal sphere. Superposed on the background equilibrium sphere, I intro- duced a turbulent velocity field with a power spectrum consistent with Larson’s linewidth-size relation. The resulting set of models had only a single free physical parameter – the tur- bulent Mach number. The addition of the turbulent Mach number naturally allows one to tie increased multiplicity to higher levels of turbulence and higher core masses, unlike the non-turbulent case. The resulting GMC cores matched a number of key properties of obser- vations – including masses, radii, non-thermal linewidths, projected radial density profiles, and aspect ratios. I then evolved these initial models in fully three-dimensional simulations using the ORION adaptive mesh refinement code, using an adaptive parallel multigrid Poisson solver which I wrote for this purpose. I discovered that while subsonic cores typically produced single stars, transonic to mildly supersonic cores produced binary and multiple systems (see figure 6). These turbulent simulations were the first to tie the origin of multiple systems to a physically-plausible mechanism, rather than arbitrarily-imposed initial conditions.

The Effect of Barotropic Approximation to Radiative Transfer in Low-Mass Star Formation. For densities, temperatures, and metallicities typical of nearby star forming regions, dust is the primary source of opacity. The collapse of a molecular cloud core begins optically thin to its own thermal radiation, but as the collapse proceeds, the optical depth becomes of order unity, and the collapsing core may no longer radiate away its gravitational binding energy as efficiently. While the full treatment of this process requires a fully-coupled radiative-hydrodynamics solution, the approximate barotropic method is commonly used to Fisher Research Statement 9

specify the pressure of the gas as a function of density. Through a series of comparison cal- culations in collaboration with Alan Boss, Richard Klein, and Chris McKee, we computed simulations which incorporated both the grey flux-limited diffusion and the barotropic ap- proximation. We concluded that the barotropic approximation is a coarse approximation to the underlying radiative transfer. In some situations, such as the collapse of a filamentary spindle, the optical depths in different directions (say, along the axis, and in the radial direc- tion) are very different, and the temperature of the gas is not well-approximated by a single value of the density at a given point, which may lead to significantly different outcomes in the fragmentation pattern in some circumstances. However, the dramatically increased cost of the fully-coupled radiation hydrodynamics solutions still makes the barotropic ap- proximation a useful first-cut on problems involving a large dynamical range or parameter space.

(a) (b)

Figure 7: (a) Results from a radiative transfer simulation in log density, drawn in contours in the equatorial plane at two successive times. (b) Raster images of the log density of the barotropic simulation, taken at the same physical times, and at the same domain scale. There is a close correspondence between the two sets of results at the earlier time at which the peak density is just beginning to enter into the optically thick regime (on left). Both sets of simulations have produced a very tight filamentary binary, with its ends nearly touching. However, a short time later, the radiative calculation has produced two fragments, whereas in the barotropic calculation, these have merged and produced only a single object.

Realistic Initial Conditions for Star-Formation Simulations. Our thesis work on star formation in turbulent low-mass cores was based on models which began with a smooth Bonnor-Ebert density profile describing an isolated core, and a turbulent velocity field super- posed upon the core. While these models were consistent with a broad range of observational properties, including masses, radii, turbulent linewidths, density profiles, and aspect ratios, they lack self-consistent density fluctuations initially. These density fluctuations are rapidly built up over a crossing-time, but because the turbulent support itself decays on the same crossing-time timescale, there is never a chance for the density fluctuations to fully develop before the onset of gravitational collapse of an isolated core. In this collaborative effort, I worked with Mark Krumholz, Richard Klein, and Chris McKee to develop a more realistic initial condition for isolated turbulent GMC cores by beginning with a smooth density profile within a single isolated core and superposing a turbulent Fisher Research Statement 10

Figure 8: Shown above is the log of the column density of a sample model core, proceessed with a beam-smearing appropriate to a core at the distance of Taurus.

velocity field [20]. Thereafter we drove the turbulent velocity field until a self-consistent set of density perturbations was established. These results were then post-processed with a synthetic beam-smearing technique to simulate observational resolution effects – see figure 8.

References

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[2] Zwicky, F. 1941, The Astrophysical Journal, 93, 411

[3] von Weizsäcker, C. F. 1951, The Astrophysical Journal, 114, 165

[4] Larson, R. B. 1979, Monthly Notices of the Royal Astronomical Society, 186, 479

[5] Larson, R. B. 1981, Monthly Notices of the Royal Astronomical Society, 194, 809

[6] Niemeyer, J. C. 1999, Astrophysical Journal Letters, 523, L57

[7] Jordan, G. I., Fisher, R., Townsley, D., Calder, A., Graziani, C, Asida, S, Lamb, D., & Truran, J. 2007, Submitted to Astrophysical Journal Letters, ArXiv Astrophysics e-prints, arXiv:astro-ph/0703573

[8] Fisher, R., Abarzhi, S., Antypas, K., Asida, S., Calder, A., Cattaneo, F., Constantin, P., Dubey, A., Foster, I., Gallagher, J., Ganapathy, M., Glendenin, C., Kadanoff, L., Lamb, D., Needham, S., Papka, M., Plewa, T., Reid, L., Rich, P., Riley, K., and Sheeler, D., accepted to IBM Research Journal Special Issue on Applications of Massively Parallel Systems

[9] Benzi, R., Biferale, L., Fisher, R., Kadanoff, L., Lamb, D., Toschi, F. 2007, Submitted to Physical Review Letters, ArXiv Nonlin e-prints, arXiv:astro-ph/0703573

[10] Crockett, R. K., Colella, P., Fisher, R. T., Klein, R. I., & McKee, C. F. 2005, Journal of Computational Physics, 203, 422 Fisher Research Statement 11

[11] Li, P. S., Klein, R. I., McKee, C. F., & Fisher, R. .T., The Astrophysical Journal, submitted.

[12] Abt, H. A., & Levy, S. G. 1976, The Astrophysical Journal Supplement, 30, 273

[13] Lada, C. J. 2006, The Astrophysical Journal Letters, 640, L63

[14] Ghez, A. M., McCarthy, D. W., Patience, J. L., & Beck, T. L. 1997, The Astrophysical Journal, 481, 378

[15] Mouschovias, T. C. 1977, The Astrophysical Journal, 211, 147

[16] Kroupa, P., & Burkert, A. 2001, The Astrophysical Journal, 555, 945

[17] Burkert, A., & Bodenheimer, P. 2000, The Astrophysical Journal, 543, 822

[18] Fisher, R. T. 2004, The Astrophysical Journal, 600, 769

[19] Fisher, R. T. 2002, Ph.D. Thesis, University of California at Berkeley.

[20] Krumholz, M. R., Fisher, R. T., Klein, R. I., & McKee, C. F. 2003, Revista Mexicana de Astronomia y Astrofisica Conference Series, 15, 138