On the generation of asymmetric warps in disk galaxies
  The warps in many spiral galaxies are now known to asymmetric. Recent sensitive observations have revealed that asymmetry of warps may be the norm rather than exception. However there exists no generic mechanism to generate these asymmetries in warps. We have derived the dispersion relation in a compact form for the S-shaped warps(described by the m=1 mode) and the bowl-shaped distribution(described by the m=0 mode) in galactic disk embedded in a dark matter halo. We then performed the numerical modal analysis and used the linear and time-dependent superposition principle to generate asymmetric warps in the disk. On doing the modal analysis we find the frequency of the $m=0$ mode is much larger than that of the $m=1$ mode. The linear and time-dependent superposition of these modes with their unmodulated amplitudes(that is, the coefficients of superposition being unity) results in an asymmetry in warps of ~ 20 - 40 %, whereas a smaller coefficient for the m=0 mode results in a smaller asymmetry. The resulting values agree well with the recent observations. We study the dependence of the asymmetry index on the dark matter halo parameters. This approach can also naturally produce U-shaped warps and L-shaped warps. We show that a rich variety of possible asymmetries in the z-distribution of the spiral galaxies can naturally arise due to a dynamical wave interference between the first two bending modes(i.e. m=0 and m=1) in the disk. This is a simple but general method for generating asymmetric warps that is independent of how the individual modes arise in the disk. 
Kanak Saha and Chanda J. Jog