  A generic prediction of the single-degenerate model for Type Ia supernovae
(SNe Ia) is that a significant amount of material will be stripped from the
donor star (~0.5 Msun for a giant donor and ~0.15 Msun for a main sequence
donor) by the supernova ejecta. This material, excited by gamma-rays from
radioactive decay, would then produce relatively narrow (1000 km s-1) emission
features observable once the supernova enters the nebular phase. Such emission
has never been detected, which already provides strong constraints on Type Ia
progenitor models. In this Letter we report the deepest limit yet on the
presence of H-alpha emission originating from the stripped hydrogen in the
nebular spectrum of a Type Ia supernova obtained using a high signal-to-noise
spectrum of the nearby normal SN Ia 2011fe 274 days after B-band maximum light
with the Large Binocular Telescope's Multi-Object Double Spectrograph. We put a
conservative upper limit on the H-alpha flux of 3.14 x 10^-17 erg s-1 cm-2,
which corresponds to a luminosity of 1.57 x 10^35 erg s-1. By scaling models
from the literature, our flux limit translates into an upper limit of 0.001
Msun of stripped material. This is an order of magnitude stronger than previous
limits. SN 2011fe was a typical Type Ia supernova, special only in its
proximity, and we argue that lack of hydrogen emission in its nebular spectrum
adds yet another strong constraint on the single degenerate class of models for
SNe Ia.
