Revisiting the analysis of HW Vir eclipse timing data I. A frequentist data modeling approach and a dynamical stability analysis

HW Vir is a short-period binary that presents eclipse timing variations. Circumbinary planets have been proposed as a possible explanation, although the properties of the planets differ in each new study. Our aim is to perform robust model selection methods for eclipse timing variations (ETV) and error calculation techniques based on a frequentist approach for the case of the HW Vir system. We initially performed simultaneous light and radial velocity curve analysis to derive the masses of the binary. We then analyzed the eclipse timing variation of the system by fitting multiple models. To select the best model, we searched the confidence levels for the best model by creating an \(\chi^2\) surface grid and bootstrap methods for each pair of parameters. We searched for stable orbital configurations for our adopted ETV model. The masses of the binary are found as 0.413 \(\pm\) 0.008 \(M_\odot\) and 0.128 \(\pm\) 0.004 \(M_\odot\). Under the assumption of two light time effects superimposed on a secular change, the minimum masses of the circumbinary objects are calculated as \(25.0_{-2.2}^{+3.5} \ M_{Jup}\) and \(13.9_{-0.45}^{+0.60}\ M_{Jup}\). The projected semi-major axes are found to be \(7.8_{-1.0}^{+1.4}\ au\) and \(4.56_{-0.22}^{+0.27}\ au\) in respective order. We find that this configuration is unstable within a 3\(\sigma\) range on the semi-major axis and eccentricity of the outer circumbinary object.