Response of a galactic disc to vertical perturbations: Strong dependence on density distribution

We study the self-consistent, linear response of a galactic disc to non-axisymmetric perturbations in the vertical direction as due to a tidal encounter, and show that the density distribution near the disc mid-plane has a strong impact on the radius beyond which distortions like warps develop. The self-gravity of the disc resists distortion in the inner parts. Applying this approach to a galactic disc with an exponential vertical profile, Saha & Jog showed that warps develop beyond 4-6 disc scalelengths, which could hence be only seen in HI. The real galactic discs, however, have less steep vertical density distributions that lie between a sech and an exponential profile. Here we calculate the disc response for such a general sec h2/n density distribution, and show that the warps develop from a smaller radius of 2-4 disc scalelengths. This naturally explains why most galaxies show stellar warps that start within the optical radius. Thus, a qualitatively different picture of ubiquitous optical warps emerges for the observed less steep density profiles. The surprisingly strong dependence on the density profile is due to the fact that the disc self-gravity depends crucially on its mass distribution close to the mid-plane. General results for the radius of onset of warps, obtained as a function of the disc scalelength and the vertical scaleheight, are presented as contour plots which can be applied to any galaxy.