# Astrometric and polarimetric imprints of hot-spots orbiting parametrized black holes

## TL;DR

This study simulates hot-spot orbits around parametrized black holes to identify observable differences in astrometric and polarimetric signals, highlighting the need for more precise measurements to distinguish between models.

## Contribution

It introduces a comprehensive simulation framework for hot-spot observables around various parametrized black hole spacetimes, comparing their signatures to Schwarzschild black holes.

## Key findings

- At low inclination, observables are similar to Schwarzschild with minor deviations.
- At high inclination, polarimetric differences are visible only during part of the orbit.
- JP parametrized models show more deviation from Schwarzschild than KZ models.

## Abstract

We analyze the observational features of hot-spots orbiting parametrized black hole (BH) spacetimes. We select a total of four BH spacetimes, two from the Johanssen-Psaltis (JP) parametrization, and two from the Konoplya-Zhidenko (KZ) parametrization, corresponding to the most extreme configurations whose shadow sizes are within the $2\sigma$-constraints of the Event Horizon Telescope (EHT). We use the ray-tracing software GYOTO to simulate the orbit of a spherically symmetric hot-spot emitting synchrotron radiation close to a central parametrized BH object, in a vertical magnetic field configuration, and we extract the corresponding astrometric and polarimetric observables for the Stokes parameters I, Q and U, namely the time integrated fluxes, temporal fluxes and magnitudes, temporal centroid, temporal QU-loops, and temporal Electric Field Position Angle (EVPA). Our results indicate that at low inclination the astrometric observables extracted from the parametrized BH spacetimes considered are qualitatively similar to those extracted from the Schwarzschild one, with minor quantitative deviations caused by differences in the size and position of the secondary images. On the other hand, the polarimetric observables at high inclination present qualitative differences, but these are only visible for a short portion of the whole hot-spot orbit. Furthermore, the observables extracted from the JP parametrized BH models deviate more prominently from those of the Schwarzschild model than the ones extracted from the KZ parametrized BH models, with the JP model with a positive free parameter deviating the most among all models tested. Given the strong similarity among the observables extracted from all models tested, we point out that more precise observations are needed to successfully impose constraints on parametrized BH models via this method.