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Daniel Whalen

Publications and source records attributed to Daniel Whalen.

At least 19 recordsLinked to original sources
arXiv2023

The Evolution of Population III and Extremely Metal-Poor Binary Stars

Numerical simulations have now shown that Population III (Pop III) stars can form in binaries and small clusters and that these stars can be in close proximity to each other. If so, they could be subject to binary interactions such as mass exchange that could profoundly alter their evolution, ionizing UV and Lyman-Werner (LW) photon emission and explosion yields, with important consequences for early cosmological reionization and chemical enrichment. Here we investigate the evolution of Pop III and extremely metal-poor binary stars with the MESA code. We find that interactions ranging from stable mass transfer to common envelope evolution can occur in these binaries for a wide range of mass ratios and initial separations. Mass transfer can nearly double UV photon yields in some of these binaries with respect to their individual stars by extending the life of the companion star, which in turn can enhance early cosmological reionization but also suppress the formation of later generations of primordial stars. Binary interactions can also have large effects on the nucleosynthetic yields of the stars by promoting or removing them into or out of mass ranges for specific SN types. We provide fits to total photon yields for the binaries in our study for use in cosmological simulations.

astro-ph.SR↗
arXiv2021

The Birth Mass Function of Pop III Stars

Population III (Pop III) stars ended the cosmic Dark Ages and began early cosmological reionization and chemical enrichment. However, in spite of their importance to the evolution of the early Universe, their properties remain uncertain because of limitations to previous numerical simulations and the lack of any observational constraints. Here we investigate Pop III star formation in five primordial halos with 3D radiation-hydrodynamical cosmological simulations. We find that multiple stars form in each minihalo and that their numbers increase over time, with up to 23 stars forming in one of the halos. Radiative feedback from the stars generates strong outflows, deforms the surrounding protostellar disk, and delays star formation for a few thousand years. Star formation rates vary with halo and depend on mass accretion onto the disk, halo spin number, and the fraction of massive stars in the halo. Stellar masses in our models range from 0.1-37 $\rm M_{\odot}$, and of the 55 stars that form in our models twelve are $\rm > 10~ M_{\odot}$ and most of the others are 1-10 $\rm M_{\odot}$. Our simulations thus suggest that Pop III stars have characteristic masses of 1-10 $\rm M_{\odot}$ and a top-heavy IMF with dN/dM $\propto M_*^{-1.18}$. Up to 70\% of the stars are ejected from their disks by three-body interactions which, along with ionizing UV feedback, limits their final masses.

astro-ph.GA↗
arXiv2020

How the Population III Initial Mass Function Governs the Properties of the First Galaxies

The properties of Population III (Pop III) stars impact many aspects of primeval structure formation such as the onset of cosmological reionization and early chemical enrichment. However, in spite of over twenty years of numerical simulations and attempts to constrain the Pop III initial mass function (IMF) by stellar archaelogy, little is known of the masses of the first stars for certain. Here, we model the effect of Pop III IMF on the properties of primeval galaxies with a suite of high-resolution radiation-hydrodynamical simulations with ENZO. We find that a top-heavy Pop III IMF results in earlier star formation but dimmer galaxies than a more conventional Salpeter-type IMF because explosions of massive Pop III stars produce more turbulence that suppresses high-mass second-generation star formation. Our models suggest that the Pop III IMF could therefore be inferred from detections of primordial galaxies, which will be principal targets of the James Webb Space Telescope and extremely large telecopes on the ground in the coming decade.

astro-ph.GA↗
arXiv2020

The Birth of Binary Direct-Collapse Black Holes

Supermassive primordial stars forming during catastrophic baryon collapse in atomically-cooling halos at $z \sim$ 15 - 20 may be the origin of the first quasars in the universe. However, no simulation to date has followed the evolution of these halos at resolutions that are high enough or for times that are long enough to determine if collapse actually produces SMSs. Here we report new cosmological simulations of baryon collapse in atomically-cooled halos for times that are long enough for SMSs to form and die as direct-collapse black holes (DCBHs). We find that the high infall rates required to build up such stars do persist until the end of their lives and could fuel the rapid growth of their BHs thereafter. Our simulations also demonstrate that binary and even small multiples of SMSs can form in low-spin and high-spin halos, respectively. This discovery raises the exciting prospect of detecting gravitational waves from DCBH mergers with LISA and tidal disruption events in the near infrared with the {\em James Webb Space Telescope} and ground-based telescopes in the coming decade.

astro-ph.GA↗
arXiv2019

The Quantum Double Model with Boundary: Condensations and Symmetries

Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S_3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry.

quant-ph↗
arXiv2016

Holophrasm: a neural Automated Theorem Prover for higher-order logic

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a neural-network-augmented bandit algorithm and a sequence-to-sequence model for action enumeration. The system proves 14% of its test theorems from Metamath's set.mm module.

cs.AI↗
arXiv2015

On the elliptic genera of manifolds of Spin(7) holonomy

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The $\mathcal{N}=1$ superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a $c=12$ realization of the symmetry group $\mathcal{SW}(3/2,2)$. In this paper, we compute the characters of this supergroup, and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. We find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

hep-th↗
arXiv2015

Exceptional Algebra and Sporadic Groups at c=12

In earlier works, it was seen that a ${\mathbb Z}/2$ orbifold of the theory of 24 free two-dimensional chiral fermions admits various sporadic finite simple groups as global symmetry groups when viewed as an ${\cal N}=1$, ${\cal N}=2$, or ${\cal N}=4$ superconformal field theory. In this note, we show that viewing the same theory as an SCFT with extended ${\cal N}=1$ symmetry -- where the extension is the same one which arises in string compactification on manifolds of exceptional Spin$(7)$ holonomy -- yields theories which have global symmetry given by the sporadic groups $M_{24}, Co_2$ or $Co_3$. The partition functions twined by these symmetries, when decomposed into characters of the Spin(7) algebra, give rise to two-component vector-valued mock modular forms encoding an infinite-dimensional module for the corresponding sporadic groups.

hep-th↗
arXiv2015

Pair-Instability Supernovae of Non-Zero Metallicity Stars

Observational evidence suggests that some very massive stars in the local Universe may die as pair-instability supernovae. We present 2D simulations of the pair-instability supernova of a non-zero metallicity star. We find that very little mixing occurs in this explosion because metals in the stellar envelope drive strong winds that strip the hydrogen envelope from the star prior to death. Consequently, a reverse shock cannot form and trigger fluid instabilities during the supernova. Only weak mixing driven by nuclear burning occurs in the earliest stages of the supernova, and it is too weak to affect the observational signatures of the explosion.

astro-ph.HE↗
arXiv2014

Pair Instability Supernovae of Very Massive Population III Stars

Numerical studies of primordial star formation suggest that the first stars in the universe may have been very massive. Stellar models indicate that non-rotating Population III stars with initial masses of 140-260 Msun die as highly energetic pair-instability supernovae. We present new two-dimensional simulations of primordial pair-instability supernovae done with the CASTRO code. Our simulations begin at earlier times than previous multidimensional models, at the onset of core collapse, to capture any dynamical instabilities that may be seeded by collapse and explosive burning. Such instabilities could enhance explosive yields by mixing hot ash with fuel, thereby accelerating nuclear burning, and affect the spectra of the supernova by dredging up heavy elements from greater depths in the star at early times. Our grid of models includes both blue supergiants and red supergiants over the range in progenitor mass expected for these events. We find that fluid instabilities driven by oxygen and helium burning arise at the upper and lower boundaries of the oxygen shell $\sim$ 20 - 100 seconds after core bounce. Instabilities driven by burning freeze out after the SN shock exits the helium core. As the shock later propagates through the hydrogen envelope, a strong reverse shock forms that drives the growth of Rayleigh--Taylor instabilities. In red supergiant progenitors, the amplitudes of these instabilities are sufficient to mix the supernova ejecta.

astro-ph.HE↗
arXiv2014

General Relativistic Instability Supernova of a Supermassive Population III Star

The formation of supermassive Population III stars with masses $\gtrsim$ 10,000 Msun in primeval galaxies in strong UV backgrounds at $z \sim$ 15 may be the most viable pathway to the formation of supermassive black holes by $z \sim$ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. But we have now discovered that non-rotating primordial stars with masses close to 55,000 Msun can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 10$ ^{55}$ erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at $z \lesssim$ 20 to {\it Euclid} and the Wide-Field Infrared Survey Telescope (WFIRST), perhaps signaling the birth of supermassive black hole seeds and the first quasars.

astro-ph.HE↗
arXiv2014

Two-Dimensional Simulations of Pulsational Pair-Instability Supernovae

Massive stars that end their lives with helium cores in the range of 35 to 65 Msun are known to produce repeated thermonuclear outbursts due to a recurring pair-instability. In some of these events, solar masses of material are ejected in repeated outbursts of several times 10$^{50}$ erg each. Collisions between these shells can sometimes produce very luminous transients that are visible from the edge of the observable universe. Previous 1D studies of these events produce thin, high-density shells as one ejection plows into another. Here, in the first multidimensional simulations of these collisions, we show that the development of a Rayleigh-Taylor instability truncates the growth of the high density spike and drives mixing between the shells. The progenitor is a 110 Msun solar-metallicity star that was shown in earlier work to produce a superluminous supernova. The light curve of this more realistic model has a peak luminosity and duration that are similar to those of 1D models but a structure that is smoother.

astro-ph.HE↗
arXiv2012

Indistinguishable Chargeon-Fluxion Pairs in the Quantum Double of Finite Groups

We consider the category of finite dimensional representations of the quantum double of a finite group as a modular tensor category. We study auto-equivalences of this category whose induced permutations on the set of simple objects (particles) are of the special form of PJ, where J sends every particle to its charge conjugation and P is a transposition of a chargeon-fluxion pair. We prove that if the underlying group is the semidirect product of the additive and multiplicative groups of a finite field, then such an auto-equivalence exists. In particular, we show that for S_3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. Conversely, by considering such permutations as modular invariants, we show that a transposition of a chargeon-fluxion pair forms a modular invariant if and only if the corresponding group is isomorphic to the semidirect product of the additive and multiplicative groups of a finite near-field.

quant-ph↗
arXiv2010

The Early Evolution of Primordial Pair-Instability Supernovae

The observational signatures of the first cosmic explosions and their chemical imprint on second-generation stars both crucially depend on how heavy elements mix within the star at the earliest stages of the blast. We present numerical simulations of the early evolution of Population III pair-instability supernovae with the new adaptive mesh refinement code CASTRO. In stark contrast to 15 - 40 Msun core-collapse primordial supernovae, we find no mixing in most 150 - 250 Msun pair-instability supernovae out to times well after breakout from the surface of the star. This may be the key to determining the mass of the progenitor of a primeval supernova, because vigorous mixing will cause emission lines from heavy metals such as Fe and Ni to appear much sooner in the light curves of core-collapse supernovae than in those of pair-instability explosions. Our results also imply that unlike low-mass Pop III supernovae, whose collective metal yields can be directly compared to the chemical abundances of extremely metal-poor stars, further detailed numerical simulations will be required to determine the nucleosynthetic imprint of very massive Pop III stars on their direct descendants.

astro-ph.CO↗
arXiv2010

The Nucleosynthetic Imprint of 15-40 Solar Mass Primordial Supernovae on Metal-Poor Stars

The inclusion of rotationally-induced mixing in stellar evolution can alter the structure and composition of presupernova stars. We survey the effects of progenitor rotation on nucleosynthetic yields in Population III and II supernovae using the new adaptive mesh refinement (AMR) code CASTRO. We examine spherical explosions in 15, 25 and 40 solar mass stars at Z = 0 and 10^-4 solar metallicity with three explosion energies and two rotation rates. Rotation in the Z = 0 models resulted in primary nitrogen production and a stronger hydrogen burning shell which led all models to die as red supergiants. On the other hand, the Z=10^-4 solar metallicity models that included rotation ended their lives as compact blue stars. Because of their extended structure, the hydrodynamics favors more mixing and less fallback in the metal free stars than the Z = 10^-4 models. As expected, higher energy explosions produce more enrichment and less fallback than do lower energy explosions, and less massive stars produce more enrichment and leave behind smaller remnants than do more massive stars. We compare our nucleosynthetic yields to the chemical abundances in the three most iron-poor stars yet found and reproduce the abundance pattern of one, HE 0557-4840, with a zero metallicity 15 solar mass, 2.4 x 10^51 erg supernova. A Salpeter IMF averaged integration of our yields for Z=0 models with explosion energies of 2.4x10^51 ergs or less is in good agreement with the abundances observed in larger samples of extremely metal-poor stars, provided 15 solar mass stars are included. Since the abundance patterns of extremely metal-poor stars likely arise from a representative sample of progenitors, our yields suggest that low-mass supernovae contributed the bulk of the metals to the early universe.

astro-ph.CO↗
arXiv2009

Cosmological Radiative Transfer Comparison Project II: The Radiation-Hydrodynamic Tests

The development of radiation hydrodynamical methods that are able to follow gas dynamics and radiative transfer self-consistently is key to the solution of many problems in numerical astrophysics. Such fluid flows are highly complex, rarely allowing even for approximate analytical solutions against which numerical codes can be tested. An alternative validation procedure is to compare different methods against each other on common problems, in order to assess the robustness of the results and establish a range of validity for the methods. Previously, we presented such a comparison for a set of pure radiative transfer tests (i.e. for fixed, non-evolving density fields). This is the second paper of the Cosmological Radiative Transfer (RT) Comparison Project, in which we compare 9 independent RT codes directly coupled to gasdynamics on 3 relatively simple astrophysical hydrodynamics problems: (5) the expansion of an H II region in a uniform medium; (6) an ionization front (I-front) in a 1/r^2 density profile with a flat core, and (7), the photoevaporation of a uniform dense clump. Results show a broad agreement between the different methods and no big failures, indicating that the participating codes have reached a certain level of maturity and reliability. However, many details still do differ, and virtually every code has showed some shortcomings and has disagreed, in one respect or another, with the majority of the results. This underscores the fact that no method is universal and all require careful testing of the particular features which are most relevant to the specific problem at hand.

astro-ph.CO↗