We present late-time ($200-400$ days) near-infrared spectral evolution for the Type Ia supernova SN 2005df. The spectra show numerous strong emission features of [CoII], [CoIII], and [FeII] throughout the $0.8-1.8$��m region. As the spectrum ages, the cobalt features fade as would be expected from the decay of $^{56}$Co to $^{56}$Fe. We show that the strong and isolated [FeII] emission line at $1.644$��m provides a unique tool to analyze near-infrared spectra of Type Ia supernovae. Normalization of spectra to this line allows separation of features produced by stable versus unstable isotopes of iron group elements. We develop a new method of determining the initial central density, $��_c$, and the magnetic field, $B$, of the white dwarf using the width of the $1.644$��m line. The line width is sensitive because of electron capture in the early stages of burning, which increases as a function of density. The sensitivity of the line width to $B$ increase with time and the effects of the magnetic field shift towards later times with decreasing $��_c$. The initial central density for SN 2005df is measured as $��_c=0.9(\pm0.2)$ (in $10^9$g/cm$^3$), which corresponds to a white dwarf close to the Chandrasekhar mass ($\rm M_{Ch}$) with $\rm M_{WD}=1.313(\pm0.034)$M$_{\odot}$ and systematic error less than $0.04$M$_{\odot}$. Within $\rm M_{Ch}$ explosions, however, the central density found for SN 2005df is very low for a H-accretor, possibly suggesting a helium star companion or a tidally-disrupted white dwarf companion. As an alternative, we suggest mixing of the central region. We find some support for high initial magnetic fields of strength $10^6$G for SN 2005df, however, $0$G cannot be ruled out because of noise in the spectra combined with low $��_c$.

13 pages, 14 figures, submitted to ApJ