\newcommand{\LCDM}{$\Lambda$CDM} \newcommand{\kms}{\, {\rm km}\, {\rm s}^{-1}} % \providecommand{\farcm}{\mbox{\ensuremath{.\mkern-4mu^\prime}}}% % fractional arcminute symbol: 0.'0 % \providecommand{\farcs}{\mbox{\ensuremath{.\!\!^{\prime\prime}}}}% % fractional arcsecond symbol: 0.''0 % \providecommand{\fdg}{\mbox{\ensuremath{.\!\!^\circ}}}% % fractional degree symbol: 0.°0 % \providecommand{\arcdeg}{\ensuremath{^{\circ}}}% % degree symbol: ° \providecommand{\farcm}{.\mkern-4mu^\prime}% % fractional arcminute symbol: 0.'0 \providecommand{\farcs}{.\!\!^{\prime\prime}}% % fractional arcsecond symbol: 0.''0 \providecommand{\fras}{.\!\!^{s}}% % fractional seconds of ra symbol: 0.s0 \providecommand{\fdg}{.\!\!^\circ}% % fractional degree symbol: 0.°0 \providecommand{\arcdeg}{^{\circ}}% % degree symbol: ° \documentclass[apjl]{emulateapj} \usepackage{amsfonts,amsmath,amssymb} \usepackage{graphicx} \usepackage{color} \usepackage{url} \bibliographystyle{apj}