Geometrically thick tori around compact objects with a quadrupole moment

TL;DR

This paper investigates thick fluid tori around deformed compact objects with quadrupole moments, revealing unique double torus structures not present in Schwarzschild spacetime, using specific vacuum solutions to Einstein's equations.

Contribution

It introduces the existence of double tori in spacetimes with quadrupole moments, extending the understanding of accretion structures around deformed compact objects.

Findings

Double tori exist for positive quadrupole moments.

Double tori can fill their Roche lobes completely.

Double tori have a fish-shaped cross-section in these spacetimes.

Abstract

We study geometrically thick perfect-fluid tori with constant specific angular momentum, so-called "Polish doughnuts", orbiting deformed compact objects with a quadrupole moment. More specifically, we consider two different asymptotically flat, static and axisymmetric vacuum solutions to Einstein's field equation with a non-zero quadrupole moment, the q-metric and the Erez-Rosen spacetime. It is our main goal to find features of Polish doughnuts in these two spacetimes which qualitatively distinguish them from Polish doughnuts in the Schwarzschild spacetime. As a main result we find that, for both metrics, there is a range of positive (Geroch-Hansen) quadrupole moments which allows for the existence of double tori. If these double tori fill their Roche lobes completely, their meridional cross-section has the shape of a fish, with the body of the fish corresponding to the outer torus and the fish-tail corresponding to the inner torus. Such double tori do not exist in the Schwarzschild spacetime.