  What sort of supernova gave rise to the Crab Nebula? There are several
indications that the Crab arose from a sub-energetic explosion of an 8-10 Msun
star, this appears to conflict with the high luminosity indicated by historical
observations. This paper shows that several properties of the Crab are best
suited to Type IIn-P explosions (Type IIn spectra with plateau light curves).
These events probably arise from relatively low-energy (1e50 erg) explosions
with low 56Ni yield resulting from electron-capture SNe (ecSNe), but their high
luminosity and Type IIn spectra are dominated by shock interaction with CSM.
After about 120 days, nearly all of the mass in the CSM and ejecta ends up in a
slow dense shell. In the scenario proposed here for SN1054, this thin shell is
accelerated by the growing pulsar wind nebula, producing the complex network of
filaments seen today. There is no need to invoke the invisible fast SN envelope
hypothesized to reside outside the Crab. SNeIIn-P explain several observed
features of the Crab: (1) No blast wave or rapidly expanding SN envelope
outside the filaments, (2) a total mass of 5 Msun swept up in a thin shell, (3)
a high peak luminosity despite the low kinetic energy, and (4) chemical
abundances consistent with an 8-10 Msun star and low 56Ni yield. A number of
other implications are discussed, concerning other Crab-like remnants, dust in
the Crab filaments, diversity in the initial masses of SNe IIn, and an
association between ecSNe and SN impostors. This model predicts that if light
echoes from SN1054 are discovered, they will be consistent with a Type IIn-P
spectrum.
