XITAU :: An advanced N-body model for interacting multiple stellar systems

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ABSTRACT: We construct an advanced model for interacting multiple stellar systems in which we compute all trajectories with a numerical N-body integrator, namely the Bulirsch-Stoer from the SWIFT package. We can then derive various observables: astrometric positions, radial velocities, minima timings (TTVs), eclipse durations, interferometric visibilities, closure phases, synthetic spectra, spectral-energy distribution, and even complete light curves. We use a modified version of the Wilson-Devinney code for the latter, in which the instantaneous true phase and inclination of the eclipsing binary are governed by the N-body integration.

If one has all kinds of observations at disposal, a joint A χ2 ($\chi^2$) metric and an optimisation algorithm (a simplex or simulated annealing) allows to search for a global minimum and construct very robust models of stellar systems. At the same time, our N-body model is free from artefacts which may arise if mutual gravitational interactions among all components are not self-consistently accounted for.

Finally, we present a number of examples showing dynamical effects that can be studied with our code and we discuss how systematic errors may affect the results (and how to prevent this from happening).

The model description was published in Broz (2017), ApJS 230, 19. Moreover, an unoffcial Appendix C briefly describes dynamical effects that can be expected in N-body simulations. Yet another useful reference is Nemravova et al. (2016), A&A 594, A55.

  1. xitau_chi2_simplex_GAMMA_*.tar.gz ... the N-body code actually used in Nemravova et al. (2016) paper;

  2. xitau_chi2_simplex_CLOSUREPHASE_*.tar.gz ... an improved version which also fits interferometric visibilities and closure phases;

  3. xitau_chi2_simplex_PERIOD_*.tar.gz ... a new advanced N-body model (Broz 2017) capable to fit also light curves and user-supplied synthetic spectra; moreover, it includes tides, oblateness and PPN terms; can call Pyterpol (Nemravova et al. 2016) to generate synthetic spectra for various Teff, log g, vrot; use absolute synthetic spectra instead of the Planck approximation, compute limb-darkened visibilities with linear coefficients (of Van Hamme 1993), and fit the spectral-energy distribution (SED) in standard UBVRIJHK bands.

  4. xitau_chi2_simplex_HEC88_*.tar.gz ... additional improvements related to V746 Cas problem (described in Harmanec et al. 2017).

  5. swift_bs_fp_*.tar.gz ... a modified Bulirsch-Stoer integrator with digital filters to study long-term evolution and stability.



Figure 1: A χ2 ($\chi^2$) vs the number of iterations, showing a smooth convergence of simplex to a local minimum. We can distinguish individual contributions to χ2, namely astrometry (SKY), radial velocities (RV), minima timings (TTV), eclipse durations (ECL), squared visibilities (VIS), closure phases (CLO), triple product amplitude (T3), light curve (LC), synthetic spectra (SYN), spectral-energy distribution (SED), and additional mass constraints (MASS; actually not visible).

Miroslav Broz (miroslav.broz@email.cz), Aug 4th 2017