  Left-over, ablated material from a possible non-degenerate companion can
reveal itself after about one year in spectra of Type Ia SNe (SNe Ia). We have
searched for such material in spectra of SN 2011fe (at 294 days after the
explosion) and for SN 2014J (315 days past explosion). The observations are
compared with numerical models simulating the expected line emission. The
spectral lines sought for are H-alpha, [O I] 6300 and [Ca II] 7291,7324, and
the expected width of these lines is about 1000 km/s. No signs of these lines
can be traced in any of the two supernovae. When systematic uncertainties are
included, the limits on hydrogen-rich ablated gas in SNe 2011fe and 2014J are
0.003 M_sun and 0.0085 M_sun, respectively, where the limit for SN 2014J is the
second lowest ever, and the limit for SN 2011fe is a revision of a previous
limit. Limits are also put on helium-rich ablated gas. These limits are used,
in conjunction with other data, to argue that these supernovae can stem from
double-degenerate systems, or from single-degenerate systems with a spun
up/spun down super-Chandrasekhar white dwarf. For SN 2011fe, other types of
hydrogen-rich donors can likely be ruled out, whereas for SN 2014J a
main-sequence donor system with large intrinsic separation is still possible.
Helium-rich donor systems cannot be ruled out for any of the two supernovae,
but the expected short delay time for such progenitors makes this possibility
less likely, especially for SN 2011fe. The broad [Ni II] 7378 emission in SN
2014J is redshifted by about +1300 km/s, as opposed to the known blueshift of
roughly -1100 km/s for SN 2011fe. [Fe II] 7155 is also redshifted in SN 2014J.
SN 2014J belongs to a minority of SNe Ia that both have a nebular redshift of
[Fe II] 7155 and [Ni II] 7378, and a slow decline of the Si II 6355 absorption
trough just after B-band maximum.
