Scattering from compact objects: Debye series and Regge-Debye poles

TL;DR

This paper develops a Debye-series decomposition for elastic scattering by compact, horizonless bodies in curved spacetime, revealing distinct pole structures and their contributions to scattering amplitudes, with implications for neutron stars and ultracompact objects.

Contribution

It introduces an exact Debye-series decomposition and analyzes Regge-Debye poles, providing new insights into scattering processes around compact objects in curved spacetime.

Findings

The spectrum shows two pole families for neutron-star-like objects.

Surface-wave branch persists for ultracompact objects, with interior-resonance splitting.

Debye amplitudes are pole dominated in the ultracompact regime.

Abstract

We investigate elastic scattering by a compact, horizonless body in curved spacetime, considering a massless scalar wave incident on a static, spherically symmetric, uniform-density star of radius $R$ and mass $M$ with a Schwarzschild exterior. We introduce an exact Debye-series decomposition of the scattering matrix, in the spirit of Debye expansions in Mie scattering. This decomposition separates direct surface reflection from contributions involving transmission into the interior and subsequent propagation, and admits a natural trajectory interpretation. We then determine the associated Regge-Debye pole spectrum in the complex angular-momentum plane. For neutron-star-like tenuities ($R>3M$), the spectrum exhibits two pole families: a surface-wave branch associated with the surface matching condition and a broad-resonance branch associated with the interior regularity condition. For ultracompact objects ($R<3M$), the surface-wave branch persists, while the interior-resonance sector splits into broad- and narrow-resonance branches. We next reconstruct the scattering amplitude from the Debye partial-wave contributions and find excellent agreement with direct partial-wave calculations. Finally, we develop complex angular-momentum representations order by order in the Debye series, making explicit how the pole families and non-pole sectors contribute to each Debye term. In the neutron-star-like regime, we find a genuine competition between Regge-Debye pole sums and branch-cut contributions, and show that, at high frequency, the rainbow-like enhancement already arises from the first interior-transmission contribution and is dominated by the interior-resonance Regge-Debye poles. By contrast, in the ultracompact regime, the Debye amplitudes are overwhelmingly pole dominated.