Spectro-polarimetric study to constrain accretion-ejection properties of MCG-5-23-16 using IXPE and NuSTAR observations

We conducted a study on the X-ray polarization properties of MCG-5-23-16 by analyzing long-term monitoring data from {\it NuSTAR} jointly with {\it IXPE} observations made in May and November 2022. The re-analysis of {\it IXPE} data gives model-dependent polarization degree, PD (\%) = $1.08\pm0.66$ in the energy band $2-8$ keV. The model-independent analysis of PD poses an upper limit of $\leq3.8$ ($1\sigma$ level) for the same energy band. The observed upper limit of PD, along with broadband spectral analysis ($2-79$ keV) using an accretion-ejection based model, allowed us to derive the corona geometry (i.e. radius and height) and the accretion disk inclination ($\sim 33^\circ$). Additional {\it NuSTAR} observations were also analyzed to gain insights into the accretion flow properties of the source and to estimate the expected polarization during those epochs with PD $\sim 4.3\%$. The radius and height of the corona varies between $28.2\pm3.1 - 39.8\pm4.6$ r$_s$ and $14.3\pm1.7-21.4\pm1.9$ r$_s$ respectively, with a mass outflow rate from the corona measuring $0.14\pm0.03-0.2\pm0.03$ Eddington rate ($\dot m_{\rm Edd}$). The spectral analysis further provided an estimate for the mass of the central black hole $\sim 2\times 10^7$ M$_\odot$ and the velocity of the outflowing gas $\sim 0.16-0.19c$. A comparative broadband spectral study using reflection-based models estimates the disk inclination between $\sim 31^\circ\pm8^\circ-45^\circ\pm7^\circ$, and yields an expected PD of 3.4-6.0\%. The expected PD measured using accretion-ejection and reflection models is less compared to the expected PD measured for a given disk inclination of $45^\circ$. Our modeling of the disk-corona-outflows and polarization connection can be extended and validated with data from the recently launched \textit{XPoSat}, India's first X-ray Polarimeter Satellite, offering potential applications to other sources.