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LSQ14bdq and SN 2006oz are super-luminous, hydrogen-poor, SNe withdouble-humped light curves. We show that a Quark-Nova (QN; explosive transitionof the neutron star to a quark star) occurring in a massive binary,experiencing two Common Envelope (CE) phases, can quantitatively explain thelight curves of LSQ14bdq and SN 2006oz. The more massive component (A) explodesfirst as a normal SN, yielding a Neutron Star which ejects the hydrogenenvelope of the companion when the system enters its first CE phase. During thesecond CE phase, the NS spirals into and inflates the second He-rich CE. In theprocess it gains mass and triggers a Quark-Nova, outside of the CO core,leaving behind a Quark Star. The first hump in our model is the QN shockre-energizing the expanded He-rich CE. The QN occurs when the He-rich envelopeis near maximum size (~ 1000R_sun) and imparts enough energy to unbind andeject the envelope. Subsequent merging of the Quark Star with the CO core ofcomponent B, driven by gravitational radiation, turns the Quark star to a BlackHole. The ensuing Black Hole accretion provides sufficient power for the secondbrighter and long lasting hump. Our model suggests a possible connectionbetween SLSNe-I and type Ic-BL SNe which occur when the Quark Nova is triggeredinside the CO core. We estimate the rate of QNe in massive binaries during thesecond CE phase to be ~ 5x10^(-5) of that of core-collapse SNe.

Quark-Novae in massive binaries : a model for double-humped, hydrogen-poor, superluminous Supernovae