  Radiative transfer studies of Type Ia supernovae (SNe Ia) hold the promise of
constraining both the time-dependent density profile of the SN ejecta and its
stratification by element abundance which, in turn, may discriminate between
different explosion mechanisms and progenitor classes. Here we present a
detailed analysis of Hubble Space Telescope ultraviolet (UV) and ground-based
optical spectra and light curves of the SN Ia SN 2010jn (PTF10ygu). SN 2010jn
was discovered by the Palomar Transient Factory (PTF) 15 days before maximum
light, allowing us to secure a time-series of four UV spectra at epochs from
-11 to +5 days relative to B-band maximum. The photospheric UV spectra are
excellent diagnostics of the iron-group abundances in the outer layers of the
ejecta, particularly those at very early times. Using the method of 'Abundance
Tomography' we have derived iron-group abundances in SN 2010jn with a precision
better than in any previously studied SN Ia. Optimum fits to the data can be
obtained if burned material is present even at high velocities, including
significant mass fractions of iron-group elements. This is consistent with the
slow decline rate (or high 'stretch') of the light curve of SN 2010jn, and
consistent with the results of delayed-detonation models. Early-phase UV
spectra and detailed time-dependent series of further SNe Ia offer a promising
probe of the nature of the SN Ia mechanism.
