Motivated by their gravitational wave driven instability, we investigate the influence of the crust on $r$-mode oscillations in a neutron star. Using a simplistic model of an elastic neutron star crust with constant shear modulus, we carry out an analytic calculation with the main objective of deriving an expression for the slippage between the core and the crust. Our analytic estimates support previous numerical results and provide useful insights into the details of the problem.

• Received 11 April 2006

DOI:https://doi.org/10.1103/PhysRevD.74.044040