Density waves in protoplanetary discs excited by eccentric planets: linear theory

Spiral density waves observed in protoplanetary discs have often been used to infer the presence of embedded planets. This inference relies both on simulations as well linear theory planet-disc interaction developed for planets circular orbits predict morphology wake. In this work we develop and implement a framework calculating structure wave gaseous disc driven by an eccentric planet. Our approach takes into account essential azimuthal temporal periodicities problem, allowing us treat any periodic perturbing potential (i.e. not only that planet). We test our excited eccentric, low-mass planet globally isothermal compare results recent direct numerical (and heuristic wavelet analysis) same problem Zhu Zhang. find excellent agreement with simulations, capturing all complex features including spiral bifurcations, crossings planet-wave detachments, improved accuracy detail compared method. illustrates power reproducing complicated time-dependent wakes, presenting it valuable tool future studies interactions.