Photoionization of Clustered Halos by the First Stars

We present numerical simulations of the photoevaporation of cosmological halos clustered around a 120 M$_\odot$ primordial star, confining our study to structures capable of hosting Population III star formation. The calculations include self-consistent multifrequency conservative transfer of UV photons together with nine-species primordial chemistry and all relevant radiative processes. The ultimate fates of these halos varies with central density and proximity to the central source but generally fall into one of four categories. Diffuse halos with central densities below 2 - 3 cm$^{-3}$ are completely ionized and evaporated by the central star anywhere in the cluster. More evolved halo cores at densities above 2000 cm$^{-3}$ are impervious to both ionizing and Lyman-Werner flux at most distances from the star and collapse of their cores proceeds without delay. Radiative feedback in halos of intermediate density can be either positive or negative, depending on how the I-front remnant shock both compresses and deforms the core and enriches it with H$_2$. We find that the 120 M$_\odot$ star photodissociates H$_2$ in most halos within the cluster but that catalysis by H- rapidly restores molecular hydrogen within a few hundred Kyr after the death of the star, with little delay in star formation. Our models exhibit significant departures from previous one-dimensional spherically-symmetric simulations, which are prone to serious errors due to unphysical geometric focusing effects.Comment: 5 pages, 5 figures, to appear in "First Stars III", eds. B. O'Shea, A. Heger and T. Abe

How the First Stars Regulated Local Star Formation I: Radiative Feedback

We present numerical simulations of how a 120 M$_\odot$ primordial star regulates star formation in nearby cosmological halos at $z \sim$ 20 by photoevaporation. Our models include nine-species primordial chemistry and self-consistent multifrequency conservative transfer of UV photons with all relevant radiative processes. Whether or not new stars form in halos clustered around a Population III star ultimately depends on their core densities and proximity to the star. Diffuse halos with central densities below 2 - 3 cm$^{-3}$ are completely ionized and evaporated anywhere in the cluster. Evolved halos with core densities above 2000 cm$^{-3}$ are impervious to both ionizing and Lyman-Werner flux at most distances from the star and collapse as quickly as they would in its absence. Star formation in halos of intermediate density can be either promoted or suppressed depending on how the I-front remnant shock compresses, deforms and enriches the core with H$_2$. We find that the 120 M$_\odot$ star photodissociates H$_2$ in most halos in the cluster but that catalysis by H- restores it a few hundred kyr after the death of the star, with little effect on star formation. Our models exhibit significant departures from previous one-dimensional spherically-symmetric simulations, which are prone to serious errors due to unphysical geometric focusing effects.Comment: 20 pages, 19 figures, accepted by ApJ, title and abstract change

Towards Realizability Checking of Contracts using Theories

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. Such proofs build from "leaf-level" assume/guarantee component contracts through architectural layers towards top-level safety properties. The proofs are built upon the premise that each leaf-level component contract is realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. Without engineering support it is all too easy to write leaf-level components that can't be realized. Realizability checking for propositional contracts has been well-studied for many years, both for component synthesis and checking correctness of temporal logic requirements. However, checking realizability for contracts involving infinite theories is still an open problem. In this paper, we describe a new approach for checking realizability of contracts involving theories and demonstrate its usefulness on several examples.Comment: 15 pages, to appear in NASA Formal Methods (NFM) 201

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.Comment: 4 pages, 2 figures. Some revisions, including enhanced discussion of angular momentum issues. Asrophysical Journal, accepte

Conference Series

Civl is a static verifier for concurrent programs designed around the conceptual framework of layered refinement, which views the task of verifying a program as a sequence of program simplification steps each justified by its own invariant. Civl verifies a layered concurrent program that compactly expresses all the programs in this sequence and the supporting invariants. This paper presents the design and implementation of the Civl verifier

Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness

In black-box testing, the tester creates a set of tests to exercise a system under test without regard to the internal structure of the system. Generally, no objective metric is used to measure the adequacy of black-box tests. In recent work, we have proposed three requirements coverage metrics, allowing testers to objectively measure the adequacy of a black-box test suite with respect to a set of requirements formalized as Linear Temporal Logic (LTL) properties. In this report, we evaluate the effectiveness of these coverage metrics with respect to fault finding. Specifically, we conduct an empirical study to investigate two questions: (1) do test suites satisfying a requirements coverage metric provide better fault finding than randomly generated test suites of approximately the same size?, and (2) do test suites satisfying a more rigorous requirements coverage metric provide better fault finding than test suites satisfying a less rigorous requirements coverage metric? Our results indicate (1) only one coverage metric proposed -- Unique First Cause (UFC) coverage -- is sufficiently rigorous to ensure test suites satisfying the metric outperform randomly generated test suites of similar size and (2) that test suites satisfying more rigorous coverage metrics provide better fault finding than test suites satisfying less rigorous coverage metrics

A Flexible and Non-instrusive Approach for Computing Complex Structural Coverage Metrics

Software analysis tools and techniques often leverage structural code coverage information to reason about the dynamic behavior of software. Existing techniques instrument the code with the required structural obligations and then monitor the execution of the compiled code to report coverage. Instrumentation based approaches often incur considerable runtime overhead for complex structural coverage metrics such as Modified Condition/Decision (MC/DC). Code instrumentation, in general, has to be approached with great care to ensure it does not modify the behavior of the original code. Furthermore, instrumented code cannot be used in conjunction with other analyses that reason about the structure and semantics of the code under test. In this work, we introduce a non-intrusive preprocessing approach for computing structural coverage information. It uses a static partial evaluation of the decisions in the source code and a source-to-bytecode mapping to generate the information necessary to efficiently track structural coverage metrics during execution. Our technique is flexible; the results of the preprocessing can be used by a variety of coverage-driven software analysis tasks, including automated analyses that are not possible for instrumented code. Experimental results in the context of symbolic execution show the efficiency and flexibility of our nonintrusive approach for computing code coverage informatio

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.Comment: 25 pages, 16 figures, accepted to ApJ. Minor revisions included. Full resolution PDF available at http://cosmos.ucsd.edu/~dwhalen/downloads/dwhalen_zeusmp_method.pd