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Fall-back crust around a quark-nova compact remnant I: The degenerate shell case with applications to SGRs, AXPs and XDINs

We explore the formation and evolution of debris ejected around quark stars in the Quark Nova scenario, and the application to Soft Gamma-ray Repeaters (SGRs) and Anomolous X-ray Pulsars (AXPs). If an isolated neutron star explodes as a Quark Nova, an Iron-rich shell of degenerate matter forms out of the fall-back (crust) material. Our model can account for many of the observed features of SGRs and AXPs such as: (i) the two types of bursts (giant and regular); (ii) the spin-up and spin-down episodes during and following the bursts with associated persistant increases in $\dot{P}$; (iii) the energetics of the boxing day burst, SGR1806$+$20; (iv) the presence of an Iron line as observed in SGR1900$+$14; (v) the correlation between the far-Infrared and the X-ray fluxes during the bursting episode and the quiescent phase; (vi) the hard X-ray component observed in SGRs during the giant bursts, and (vii) the discrepancy between the ages of SGRs/AXPs and their supernova remnants. We also find a natural evolutionary relationship between SGRs and AXPs in our model which predicts that only the youngest SGRs/AXPs are most likely to exhibit strong bursting. Many features of X-ray Dim Isolated Neutron stars (XDINs) are also accounted for in our model such as, (i) the two-component blackbody spectra; (ii) the absorption lines around 300 eV; and (iii) the excess optical emission.