Shadow of quadrupole-deformed compact objects in a local dark-matter shell

¹ University of Bremen, Center of Applied Space Technology and Microgravity (ZARM), 28359 Bremen, Germany
² Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
³ Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, N2L 3G1 Waterloo, Canada
⁴ Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Canada
⁵ Institute of Theoretical Physics and Astrophysics, University of Gdańsk, Jana Bażyńskiego 8, 80-309 Gdańsk, Poland
⁶ Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia

^⋆ Corresponding authors: s3faraji@uwaterloo.ca, joaoluis92@gmail.com

Received: 10 March 2024
Accepted: 7 April 2025

Abstract

This work investigated observational properties, namely the shadow and photon ring structure, of emission profiles originating near compact objects. In particular, we considered a distorted and deformed compact object characterized by two quadrupole parameters and surrounded by an optically thin and geometrically thin accretion disk with different emission profiles modeled by Johnson's standard-unbound (SU) distribution in the reference frame of the emitter. Under these assumptions, we produced the observed intensity profiles and shadow images for a face-on observer. Our results indicate that, due to the fact that modifications of the quadrupole parameters affect the radius of the innermost stable circular orbit (ISCO) and the unstable photon orbits on the equatorial plane, the observed shadow images and their properties are significantly influenced by the quadrupole parameters and emission profiles. Furthermore, we analyzed the impact of the presence of a dark-matter halo in the observational imprints considered and verified that both the increase in the matter contained in the halo or the decrease in the length-scale of the halo led to an increase in the size of the observed shadow. Our results indicate potential degeneracies between the observational features of distorted and deformed compact objects with those of spherically symmetric black holes, which could be assessed by a comparison with the current and future generation of optical experiments in gravitational physics.