We investigate the effect of rotating , triaxial halos on disk galaxies through an extensive set of numerical N -body simulations .
Our simulations use a rigid potential field for the halos and bulges and collisionless particles for the disks .
The triaxiality and the rotation rate of the halo are varied , as well as the masses of all three galaxy components .
We analyze both the bar stability and the spiral response of the disks under these conditions .

We characterize most of our models by the mass ratio of the disk to the halo at 2.3 disk scale lengths , ( M _ { d } / M _ { h } ) _ { R _ { \odot } } .
For models with a mass ratio greater than 0.8 , a halo pattern speed \Omega _ { h } = 6.7 km s ^ { -1 } kpc ^ { -1 } , and a intermediate-to-major axis ratio q _ { b } = 0.85 , a strong bar will develop within 3 Gyr , even for models with a bulge mass M _ { b } = 0.3 M _ { d } .
Models in which the bulge mass is reduced by half develop bars earlier and with lower \Omega _ { h } .

We create an artificial Hubble sequence of disk galaxies by varying the bulge-to-disk ratio of our models from 0 to 2.5 .
The torque induced by a rotating , non-axisymmetric halo creates bisymmetric spiral structure in the disk .
We find that the pitch angle of the spiral arms in these models follows the same general trend found in observations of spiral galaxies , namely that later type galaxies have higher pitch angles .
Our simulations follow closely the observational relation of spiral pitch angle with maximum rotational velocity of the disk , where galaxies with faster rotation have more tightly wound spiral arms .
This relation is followed in our simulations regardless of whether the dominating mass component of the galaxy is the disk , the halo , or the bulge .

\keywords galaxies : spiral – galaxies : stability – methods : numerical