Witnessing History: Rates and Detectability of Naked-Eye Milky-Way
  Supernovae
  The Milky Way hosts on average a few supernova explosions per century, yet in
the past millennium only five supernovae have been identified confidently in
the historical record. This deficit of naked-eye supernovae is at least partly
due to dust extinction in the Galactic plane. We explore this effect
quantitatively, developing a formalism for the supernova probability
distribution, accounting for dust and for the observer's flux limit. We then
construct a fiducial axisymmetric model for the supernova and dust densities,
featuring an exponential dependence on galactocentric radius and height, with
core-collapse events in a thin disk and Type Ia events including a thick disk
component. When no flux limit is applied, our model predicts supernovae are
intrinsically concentrated in the Galactic plane, with Type Ia events extending
to higher latitudes reflecting their thick disk component. We then apply a flux
limit and include dust effects, to predict the sky distribution of historical
supernovae. We use well-observed supernovae as light-curve templates, and
introduce naked-eye discovery criteria. The resulting sky distributions are
strikingly inconsistent with the locations of confident historical supernovae,
none of which lie near our model's central peaks. Indeed, SN 1054 lies off the
plane almost exactly in the anticenter, and SN 1181 is in the 2nd Galactic
quadrant. We discuss possible explanations for these discrepancies. We
calculate the percentage of all supernovae bright enough for historical
discovery: $\simeq 13\%$ of core-collapse and $\simeq 33\%$ of Type Ia events.
Using these and the confident historical supernovae, we estimate the intrinsic
Galactic supernova rates, finding general agreement with other methods.
Finally, we urge searches for supernovae in historical records from
civilizations in the southern hemisphere.
