  We present data for LSQ14bdq, a hydrogen-poor super-luminous supernova (SLSN)
discovered by the La Silla QUEST survey and classified by the Public ESO
Spectroscopic Survey of Transient Objects. The spectrum and light curve are
very similar to slow-declining SLSNe such as PTF12dam. However, detections
within ~1 day after explosion show a bright and relatively fast initial peak,
lasting for ~15 days, prior to the usual slow rise to maximum light. The
broader, main peak can be fit with either central engine or circumstellar
interaction models. We discuss the implications of the precursor peak in the
context of these models. It is too bright and narrow to be explained as a
normal 56Ni-powered SN, and we suggest that interaction models may struggle to
fit the two peaks simultaneously. We propose that the initial peak may arise
from the post-shock cooling of extended stellar material, and reheating by a
central engine drives the second peak. In this picture, we show that an
explosion energy of ~2x10^{52} erg and a progenitor radius of a few hundred
solar radii would be required to power the early emission. The competing engine
models involve rapidly spinning magnetars (neutron stars) or fall-back
accretion onto a central black hole. The prompt energy required may favour the
black hole scenario. The bright initial peak effectively rules out a compact
Wolf-Rayet star as a progenitor, since the inferred energies and ejected masses
become unphysical.
