of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, U.K.\
    $^2$School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, KY16 9SS, U.K.\
    $^3$ETH Zürich, Institut für Astronomie, HIT J 11.3, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland\
    $^4$Gemini Observatory, Northern Operations Center, 670 N. A’ohuku Place, Hilo, HI96720, USA\
    $^5$Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, U.K.\
date: 'Accepted 2017 July 28. Received 2017 July 24; in original form 2016 February 3.'
title: 'Massive post-starburst galaxies at $z>1$ are compact proto-spheroids'
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galaxies: evolution – galaxies: formation – galaxies: fundamental parameters – galaxies: structure – galaxies: high-redshift

Introduction {#sec:intro}
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Galaxies in the local Universe display a striking bimodality in their morphological and spectral characteristics; massive galaxies (M$_{\ast}> 10^{10.5} ~$M$_{\sun}$) are typically spheroidal with old stellar populations, while lower mass galaxies are typically disc-dominated with blue, younger stellar populations (e.g. Strateva et al. 2001; Hogg et al. 2002). Deep surveys have revealed that the most massive galaxies were formed at high redshift ($z>1$; e.g. Fontana et al. 2004; Kodama et al. 2004; Cirasuolo et al. 2010), but we still do not understand why their star formation was abruptly 