Dynamical friction in stratified stellar envelopes

Dynamical friction prescriptions used for common-envelope and planetary engulfment inspirals often assume a homogeneous medium and/or rectilinear perturber motion. A gravitating object embedded in a giant-star envelope instead excites an orbit-scale wake while moving on a curved orbit through a finite, radially stratified medium. We formulate the linear barotropic acoustic response of a weak point perturber on a circular orbit in a hydrostatic, spherically stratified gaseous medium. We apply the formulation to single perturbers in power-law density profiles and giant-star envelope models, and to double perturbers in power-law density backgrounds. We find that stratification affects dynamical friction through the global structure of the wake. The radial component is set by the low-order, orbit-scale wake and can strongly differ in amplitude and sign from the homogeneous-medium result. The azimuthal component is also modified by stratification, but in the supersonic regime it retains the Coulomb-logarithmic sensitivity of the homogeneous problem. In double-perturber systems, the companion wake can substantially change the radial force and reduce the azimuthal drag on a given component, but, unlike the perturber's own wake, it has no local Coulomb-logarithmic contribution. For the adopted giant-star envelope profiles, the azimuthal drag exerted by the stratified wake gives shorter inspiral times than uniform-medium prescriptions evaluated with the same local background quantities. The formulation provides a flexible tool for computing embedded-perturber wakes in prescribed radial stratifications and is a first step toward computationally efficient, self-consistent models of common-envelope and planetary-engulfment inspirals.