For carbon-oxygen white dwarfs accreting hydrogen or helium at rates in the range \sim 1 - 10 \times 10 ^ { -8 } M _ { \odot } y ^ { -1 } , a variety of explosive outcomes is possible well before the star reaches the Chandrasekhar mass .
These outcomes are surveyed for a range of white dwarf masses ( 0.7 - 1.1 M _ { \odot } ) , accretion rates ( 1 - 7 \times 10 ^ { -8 } M _ { \odot } y ^ { -1 } ) , and initial white dwarf temperatures ( 0.01 and 1 L _ { \odot } ) .
The results are particularly sensitive to the convection that goes on during the last few minutes before the explosion .
Unless this convection maintains a shallow temperature gradient , and unless the density is sufficiently high , the accreted helium does not detonate .
Below a critical helium ignition density , which we estimate to be 5 - 10 \times 10 ^ { 5 } g cm ^ { -3 } , either helium novae or helium deflagrations result .
The hydrodynamics , nucleosynthesis , light curves , and spectra of a representative sample of detonating and deflagrating models are explored .
Some can be quite faint indeed , powered at peak for a few days by the decay of ^ { 48 } Cr and ^ { 48 } V. Only the hottest , most massive white dwarfs considered with the smallest helium layers , show reasonable agreement with the light curves and spectra of common Type Ia supernovae .
For the other models , especially those involving lighter white dwarfs , the helium shell mass exceeds 0.05 M _ { \odot } and the mass of the ^ { 56 } Ni that is synthesized exceeds 0.01 M _ { \odot } .
These explosions do not look like ordinary Type Ia supernovae , or any other frequently observed transient .