Estimates of the Dynamic Characteristics of Binary Systems for Traversable Wormholes Search

Abstract

The work is devoted to the study of the possibilities of observational manifestations of traversable wormholes (WHs). The simplest binary system model consisting of a traversable WH candidate (black hole (BH), supermassive BH) and a companion star, whose motion is perturbed by a massive object (star) located on the other side of the wormhole throat, is considered. In the first case of supermassive BH as WH candidate the perturbing acceleration is analyzed and compared with a competing effect in the form of the stochastic influence of stars adjacent to the companion star. In the second case the features of the change in the radial velocity of the companion star in the model of a wide binary system with a WH are also analyzed in order to distinguish it from the following models: 1) a binary system with a BH, and 2) a triple system. For the observational accuracy in radial velocity expected in the near future, at the level of 1.5 km/s the radial velocity perturbations are detectable for all considered observation time spans. For a more realistic accuracy of 10 km/s, the spectral analysis methods become statistically significant after approximately 17 years of data accumulation. The application of spectral and non-parametric methods significantly decreases the required accumulation time compared to matched-filtering applied in isolation.

Figures (9)

• Figure 1: Schematic of the system model. The observed star orbits on side 1; the perturbing star orbits on side 2, connected to side 1 via the WH throat.
• Figure 2: The computed normalized perturbation template $u(t)$. Impulse amplitudes are modulated by the inverse square of the star's radial coordinate $r_1^{-2}$. The template is dimensionless after normalization and x-axis shows the index of the time-step.
• Figure 3: Left: integrated trajectory of the star in the orbital plane. Right: $x$-component of the stellar velocity. The inset demonstrates how small the sought perturbations are even when artificially amplified by a factor of 1000 in the simulation.
• Figure 4: a) Top: the ideal signal $s(t)=v^{o}-v_{0}$ (where $v_{0}$ is the Keplerian component and $v^{o}$ is the observed line-of-sight velocity of the star) as a function of orbital phase and orbit number; bottom: $s(t)$ as a function of observation time, with the $\pm 1$ km/s observational noise shown in the background. b) Top: the matched filter statistic $\rho^2$ for the noisy observed signal in the phase-domain representation; bottom: in the time-domain representation, with the running mean overlaid. Note that $\rho^2$ is dimensionless; its absolute value depends on the internal normalization of the template and is meaningful only relative to its empirical noise distribution.
• Figure 5: a) Top: discrete noiseless observations in the phase-domain representation; bottom: the discrete time series, with the $\pm 0.5$ km/s. b) Top: the matched filter statistic $\rho^2$ for the noisy discrete observed signal in the phase-domain representation; bottom: in the time-domain representation, with the running mean overlaid. As in Fig. \ref{['fig:filtering_res']}$\rho^2$ is dimensionless and interpretable only in comparison to its empirical noise distribution.