Efficiency of ETV diagrams as diagnostic tools for long-term period variations

Abstract

Context. The credibility of an eclipse timing variation (ETV) diagram analysis is investigated for various manifestations of the mass transfer and gravitational radiation processes in binary systems. The monotonicity of the period variations and the morphology of the respective ETV diagrams are thoroughly explored in both the direct impact and the accretion disk mode of mass transfer, accompanied by different types of mass and angular momentum losses (through a hot-spot emission from the gainer and via the L2/L3 points). Aims. Our primary objective concerns the traceability of each physical mechanism by means of an ETV diagram analysis. Also, possible critical mass ratio values are sought for those transfer modes that involve orbital angular momentum losses strong enough to dictate the secular period changes even when highly competitive mechanisms with the opposite direction act simultaneously. Methods. TheJ −Ṗ relation that governs the orbital evolution of a binary system is set to provide the exact solution for the period and the function expected to represent the subsequent eclipse timing variations. The angular momentum transport is parameterized through appropriate empirical relations, which are inferred from semi-analytical ballistic models. Then, we numerically determine the minimum temporal range over which a particular mechanism is rendered measurable, as well as the critical mass ratio values that signify monotonicity inversion in the period modulations. Results. Mass transfer rates comparable to or greater than 10 −8 M yr −1 are measurable for typical noise levels of the ETV diagrams, regardless of whether the process is conservative. However, the presence of a transient disk around the more massive component defines a critical mass ratio (q cr ≈ 0.83) above which the period turns out to decrease when still in the conservative regime, rendering the measurability of the anticipated variations a much more complicated task. The effects of gravitational radiation proved to be rather undetectable, except for systems with physical characteristics that only refer to cataclysmic variables. Conclusions. The monotonicity of the period variations and the curvature of the respective ETV diagrams depend strongly on the accretion mode and the degree of conservatism of the transfer process. Unlike the hot-spot effects, the Lagrangian points L2 and L3 support very efficient routes of strong angular momentum loss. It is further shown that escape of mass via the L3 point -when the donor is the less massive component -safely provides critical mass ratios above which the period is expected to decrease, no matter how intense the process is.

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