Relativistic Scattering in the Funnel of Cygnus X-3

TL;DR

This paper introduces a relativistic scattering model within a funnel-shaped geometry to explain the high polarization degrees observed in Cygnus X-3's different states, unifying the polarization data with a variable outflow velocity.

Contribution

The model demonstrates that a single funnel-outflow with variable bulk velocity can reproduce polarization observations in both soft and hard states of Cygnus X-3.

Findings

Reproduces 12% polarization in soft state with static scattering.

Achieves 23% polarization in hard state with mildly relativistic velocities.

Supports a super-Eddington luminosity estimate of ~10^{40} erg s^{-1}.

Abstract

Cygnus X-3 presents significant challenges to standard accretion models. Recent polarimetric observations by IXPE reveal high polarization degrees (PD) in the hard state ($\sim 23\%$) and unexpectedly significant polarization in the soft state ($\sim 12\%$), which are difficult to reconcile with static scattering models at low inclination ($i \approx 30^\circ$). We present a relativistic scattering model within a funnel-shaped geometry that resolves this discrepancy. We show that a single funnel-outflow configuration with variable bulk velocity $\beta$ can reproduce both polarization states, with lower velocities ($\beta \approx 0$) yielding $\sim 12\%$ polarization (soft state) and mildly relativistic velocities ($\beta \lesssim 0.4$) producing $\sim 23\%$ polarization (hard state) at $i \approx 30^\circ$ for half funnel opening angles of $\sim 13^\circ$-$16^\circ$. Relativistic aberration modifies the effective scattering angle in the comoving frame, enhancing polarization in the hard state while recovering the static limit in the soft state. The model also yields a consistent estimate of the intrinsic luminosity, of order $\sim 10^{40}$ erg s$^{-1}$, supporting a super-Eddington interpretation. This framework provides a unified explanation of the observed polarization properties of Cygnus X-3.