The Cataclysmic Variable ( CV ) population harbors a diverse range of donor stars and accreting white dwarfs ( WDs ) .
A range of WD masses is expected , from low mass Helium core WDs , to massive WDs which have previously accreted at rates high enough for Hydrogen to burn steadily .
Furthermore , a wide range of Helium enrichment is expected in the accreted material depending on the degree to which the donor star is evolved .
We investigate the impact of this diversity on the range of effective temperatures ( T _ { eff } ) for which g-modes are unstable .
Motivated by earlier theoretical studies , we use a simple criterion for g-mode excitation : that the thermal time at the base of the convection zone becomes longer than ( some multiple of ) a fiducial shortest g-mode period .
The critical T _ { eff } below which modes are unstable ( “ blue edge ” ) then depends on both surface gravity , g , and He abundance , Y .
The Hydrogen/first Helium ionization instability strip is more sensitive to g than Y .
We find that ( for solar composition envelopes ) , relative to a fiducial WD mass 0.6 M _ { \odot } , the blue edge for a 0.4 M _ { \odot } He core WD shifts downward by \approx 1000 { K } , while that for a massive \approx 1.2 M _ { \odot } WD shifts upward by \approx 2000 { K } .
The second Helium ionization instability strip exhibits strong dependences on both g and Y .
Surprisingly , increasing Y by only 10 \% relative to solar creates an instability strip near 15 , 000 { K } .
Hence CV ’ s below the period gap with evolved donor stars of Y \gtrsim 0.4 may have an “ intermediate ” instability strip well outside of the isolated DA and DB variables .
This “ intermediate ” instability strip also occurs for low mass He WD with solar composition envelopes .
The lack of pulsations in CV ’ s with T _ { eff } in the pure Hydrogen ZZ Ceti instability strip is also easily explained .