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I am writing a letter with an APA-style bibliography, and I want to center the bibliography heading. There are no hooks in apacite for controlling its formatting, so I'm going to have to renew \section (which isn't defined in the letter environment, but which I am defining for the body anyway). So I have written this code:

\documentclass[12pt]{letter}

\usepackage{microtype}          % better spacing
\usepackage[margin=1in]{geometry} % nice margins
\usepackage[utf8]{inputenc}     % utf-8 encoding
\usepackage{block}              % left-align everything
\usepackage[natbibapa]{apacite} % citations
\usepackage[english]{babel}     % correct line breaks
\usepackage{setspace}           % double spacing

%\addto{\captionsenglish}{\renewcommand{\refname}{}}
\newcommand{\section}[1]{{\bf #1}\hfill\break}

\begin{document}
\begin{letter}{}

\bibliographystyle{apacite}
\doublespacing
\newcommand{\newblock}{}
\renewcommand{\section}[1]{\begin{center}#1\end{center}}
\bibliography{bibliography.bib}
\singlespacing

\end{letter}
\end{document}

But instead of centering my header, it does this:

A centered asterisk appears before the title, but the title itself is not centered.

What does this mean? How do I prevent this?

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The answer is obvious once you see it. apacite is supplying two arguments to \section, one being the asterisk, and the other being the title. (I had my own battles with changing the title; it turned out to be an interaction with the babel package, documented here.) So the correct code for the redefinition of \section is:

\renewcommand{\section}[2]{\begin{center}#2\end{center}}

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