Near-infrared ( NIR ) spectra of the subluminous Type Ia supernova SN 1999by are presented which cover the time evolution from about 4 days before to 2 weeks after maximum light .
Analysis of these data was accomplished through the construction of an extended set of delayed detonation ( DD ) models covering the entire range of normal to subluminous SNe Ia .
The explosion , light curves ( LC ) , and the time evolution of the synthetic spectra were calculated self-consistently for each model with the only free parameters being the initial structure of the white dwarf ( WD ) and the description of the nuclear burning front during the explosion .
From these , one model was selected for SN 1999by by matching the synthetic and observed optical light curves , principly the rapid brightness decline .
DD models require a minimum amount of burning during the deflagration phase which implies a lower limit for the ^ { 56 } Ni mass of about 0.1 M _ { \odot } and consequently a lower limit for the SN brightness .
The models which best match the optical light curve of SN 1999by were those with a ^ { 56 } Ni production close to this theoretical minimum .
The data are consistent with little or no interstellar reddening ( E ( B - V ) \leq 0.12 ^ { m } ) and we derive a distance or 11 \pm 2.5 Mpc for SN 1999by in agreement with other estimates .

Without any modification , the synthetic spectra from this subluminous model match reasonably well the observed IR spectra taken on May 6 , May 10 , May 16 and May 24 , 1999 .
These dates correspond roughly to -4 d , 0 d , and 6 d and 14 d after maximum light .
Prior to maximum , the NIR spectra of SN 1999by are dominated by products of explosive carbon burning ( O , Mg ) , and Si .
Spectra taken after maximum light are dominated by products of incomplete Si burning .
Unlike the behavior of normal Type Ia SNe , lines from iron-group elements only begin to show up in our last spectrum taken about two weeks after maximum light .
The implied distribution of elements in velocity space agrees well with the DD model predictions for a subluminous SN Ia .
Regardless of the explosion model , the long duration of the phases dominated by layers of explosive carbon and oxygen burning argues that SN 1999by was the explosion of a white dwarf at or near the Chandrasekhar mass .

The good agreement between the observations and the models without fine-tuning a large number of free parameters suggests that DD models are a good description of at least subluminous Type Ia SNe .
Pure deflagration scenarios or mergers are unlikely and helium-triggered explosions can be ruled out .
However , problems for DD models still remain , as the data seem to be at odds with recent 3-D models of the deflagration phase which predict significant mixing of the inner layers of the white dwarf prior to detonation .
Possible solutions include the effects of rapid rotation on the propagation of nuclear flames during the explosive phase of burning , or extensive burning of carbon just prior to the runaway .