<commit_before>\documentclass[twocolumn,numberedappendix]{../aastex6}

% these lines seem necessary for pdflatex to get the paper size right
\pdfpagewidth 8.5in
\pdfpageheight 11.0in

% for the red MarginPars
\usepackage{color}

% some extra math symbols
\usepackage{mathtools}

% allows Greek symbols to be bold
\usepackage{bm}

% allows us to force the location of a figure
\usepackage{float}

% allows comment sections
\usepackage{verbatim}

% Override choices in \autoref
\def\sectionautorefname{Section}
\def\subsectionautorefname{Section}
\def\subsubsectionautorefname{Section}

% MarginPars
\setlength{\marginparwidth}{0.75in}
\newcommand{\MarginPar}[1]{\marginpar{\vskip-\baselineskip\raggedright\tiny\sffamily\hrule\smallskip{\color{red}#1}\par\smallskip\hrule}}

\newcommand{\msolar}{\mathrm{M}_\odot}

% Software names
\newcommand{\amrex}{\texttt{AMReX}}
\newcommand{\boxlib}{\texttt{BoxLib}}
\newcommand{\castro}{\texttt{CASTRO}}
\newcommand{\microphysics}{\texttt{Microphysics}}
\newcommand{\wdmerger}{\texttt{wdmerger}}
\newcommand{\python}{\texttt{Python}}
\newcommand{\matplotlib}{\texttt{matplotlib}}
\newcommand{\yt}{\texttt{yt}}
\newcommand{\vode}{\texttt{VODE}}
\newcommand{\isoseven}{\texttt{iso7}}
\newcommand{\aproxthirteen}{\texttt{aprox13}}
\newcommand{\aproxnineteen}{\texttt{aprox19}}
\newcommand{\aproxtwentyone}{\texttt{aprox21}}

\begin{document}

%==========================================================================
% Title
%==========================================================================
\title{White Dwarf Mergers on Adaptive Meshes\\ II. Nuclear Reactions}

\shorttitle{WD Mergers. II. Nuclear Reactions}
\shortauthors{Katz et al. (2017)}

\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{1,2}}
\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{3}}
\author{Weiqun Zhang\altaffilmark{3}}
\author{<NAME>\altaffilmark{4,5}}

\altaffiltext{1}
{
  Department of Physics and Astronomy,
  Stony Brook University, Stony Brook, NY, 11794-3800, USA
}

\altaffiltext{2}
{
  Institute for Advanced Computational Sciences,
  Stony Brook University, Stony Brook, NY, 11794-5250, USA
}

\altaffiltext{3}
{
  Center for Computational Sciences and Engineering,
  Lawrence Berkeley National Laboratory, Berkeley, CA 94720
}

\altaffiltext{4}
{
  The Joint Institute for Nuclear Astrophysics, USA
}

\altaffiltext{5}
{
  School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA
}



%==========================================================================
% Abstract
%==========================================================================
\begin{abstract}
Simulations of white dwarf mergers and collisions that attempt to answer the
question of whether these events are progenitors of Type Ia supernovae must
confront the question of how nuclear detonations form and whether observed
detonations in a numerical simulation are realistic. We address this question
by performing simulations of collisions of white dwarfs, a subset of white
dwarf mergers that occur when the stars approach each other nearly head-on.
These have the potential for explosive nucleosynthesis, leading to a thermonuclear
detonation that disrupts both stars, possibly causing a Type Ia supernova.
While this story is intuitively plausible, demonstrating this in a reacting
hydrodynamics simulation is challenging due to the rapid evolution of the
nuclear burning, posing numerical challenges related to both spatial and
temporal resolution. In this study we explore a number of the algorithms
that affect the outcome of reacting hydrodynamics simulations that lead
to explosive burning and address the question of what can be done to ensure
that these simulations are properly converged. We find that achieving a
converged simulation in the code \castro\ is very difficult for a standard
approach with uniform resolution. The typical timesteps taken by hydrodynamics
codes are too large and the spatial resolution is too low, while increasing
either to the point required to actually obtain a converged simulation is
prohibitive. However, we have identified a criterion for adaptive mesh refinement
that substantially improves the situation: by targeting for extra sptial resolution
only those regions that are likely to undergo numerically unstable burning,
we can significantly reduce the effects of numerically spurious detonations.
This result is a possible path forward for obtaining reliable numerical
simulations of Type Ia supernova involving thermonuclear detonations.
\end{abstract}
\keywords{supernovae: general - white dwarfs}

%==========================================================================
% Introduction
%==========================================================================
\section{Introduction}
\label{sec:introduction}

Binary white dwarf (WD) systems are a promising progenitor candidate for Type
Ia supernovae (SNe Ia) for observational reasons, but from the simulation
perspective there is still significant uncertainty regarding how nuclear
detonations form in an exploding white dwarf. There is uncertainty in the<commit_msg>Another stab at the abstract<commit_after>\documentclass[twocolumn,numberedappendix]{../aastex6}

% these lines seem necessary for pdflatex to get the paper size right
\pdfpagewidth 8.5in
\pdfpageheight 11.0in

% for the red MarginPars
\usepackage{color}

% some extra math symbols
\usepackage{mathtools}

% allows Greek symbols to be bold
\usepackage{bm}

% allows us to force the location of a figure
\usepackage{float}

% allows comment sections
\usepackage{verbatim}

% Override choices in \autoref
\def\sectionautorefname{Section}
\def\subsectionautorefname{Section}
\def\subsubsectionautorefname{Section}

% MarginPars
\setlength{\marginparwidth}{0.75in}
\newcommand{\MarginPar}[1]{\marginpar{\vskip-\baselineskip\raggedright\tiny\sffamily\hrule\smallskip{\color{red}#1}\par\smallskip\hrule}}

\newcommand{\msolar}{\mathrm{M}_\odot}

% Software names
\newcommand{\amrex}{\texttt{AMReX}}
\newcommand{\boxlib}{\texttt{BoxLib}}
\newcommand{\castro}{\texttt{CASTRO}}
\newcommand{\microphysics}{\texttt{Microphysics}}
\newcommand{\wdmerger}{\texttt{wdmerger}}
\newcommand{\python}{\texttt{Python}}
\newcommand{\matplotlib}{\texttt{matplotlib}}
\newcommand{\yt}{\texttt{yt}}
\newcommand{\vode}{\texttt{VODE}}
\newcommand{\isoseven}{\texttt{iso7}}
\newcommand{\aproxthirteen}{\texttt{aprox13}}
\newcommand{\aproxnineteen}{\texttt{aprox19}}
\newcommand{\aproxtwentyone}{\texttt{aprox21}}

\begin{document}

%==========================================================================
% Title
%==========================================================================
\title{White Dwarf Mergers on Adaptive Meshes\\ II. Nuclear Reactions}

\shorttitle{WD Mergers. II. Nuclear Reactions}
\shortauthors{Katz et al. (2017)}

\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{1,2}}
\author{<NAME>\altaffilmark{1}}
\author{<NAME>\altaffilmark{3}}
\author{<NAME>\altaffilmark{3}}
\author{<NAME>\altaffilmark{4,5}}

\altaffiltext{1}
{
  Department of Physics and Astronomy,
  Stony Brook University, Stony Brook, NY, 11794-3800, USA
}

\altaffiltext{2}
{
  Institute for Advanced Computational Sciences,
  Stony Brook University, Stony Brook, NY, 11794-5250, USA
}

\altaffiltext{3}
{
  Center for Computational Sciences and Engineering,
  Lawrence Berkeley National Laboratory, Berkeley, CA 94720
}

\altaffiltext{4}
{
  The Joint Institute for Nuclear Astrophysics, USA
}

\altaffiltext{5}
{
  School of Earth and Space Exploration, Arizona State University, Tempe, AZ, USA
}



%==========================================================================
% Abstract
%==========================================================================
\begin{abstract}
Simulations of white dwarf mergers that include thermonuclear reactions must
confront the question of how nuclear detonations form and whether observed
detonations in a numerical simulation are realistic. We address this question
by performing simulations of collisions of white dwarfs, a subset of white
dwarf mergers that occur when the stars approach each other nearly head-on.
These have the potential for explosive nucleosynthesis, leading to a thermonuclear
detonation that disrupts both stars, possibly causing a Type Ia supernova.
While this story is intuitively plasible, demonstrating this in a reacting
hydrodynamics simulation is challenging due to the rapid evolution of the
nuclear burning, posing numerical challenges related to both spatial and
temporal resolution. In this study we explore a number of the algorithmic choices
that affect the outcome of reacting hydrodynamics simulations, and address
the question of what is required to ensure that these simulations are properly
converged. We find that achieving a converged white dwarf collision simulation
in the code \castro\ is very difficult. The typical timesteps taken by hydrodynamics
codes are too large, and the achievable spatial resolution is too low, while increasing
either to the point required to actually obtain a converged simulation is
prohibitive. We have identified a criterion for adaptive mesh refinement
that covers the most important regions in the simulation and allows us to
achieve very high resolution in the burning region. However, even in our
highest resolution simulations, we do not find a converged result, and
detonations seem to occur stochastically. Our results point to a path forward
for astrophysical simulations with thermonuclear detonations, but for now
they encourage severe caution in interpreting observed detonations in previous
and current simulations.
\end{abstract}
\keywords{supernovae: general - white dwarfs}

%==========================================================================
% Introduction
%==========================================================================
\section{Introduction}
\label{sec:introduction}

Binary white dwarf (WD) systems are a promising progenitor candidate for Type
Ia supernovae (SNe Ia) for observational reasons, but from the simulation
perspective there is still significant uncertainty regarding how nuclear
detonations form in an exploding white dwarf. There is uncertainty in the
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