New analysis of the light time effect in TU Ursae Majoris

Abstract

Context. Recent statistical studies prove that the percentage of RR Lyrae pulsators that are located in binaries or multiple stellar systems is considerably lower than might be expected. This can be better understood from an in-depth analysis of individual candidates. We investigate in detail the light time effect of the most probable binary candidate TU UMa. This is complicated because the pulsation period shows secular variation. Aims. We model possible light time effect of TU UMa using a new code applied on previously available and newly determined maxima timings to confirm binarity and refine parameters of the orbit of the RRab component in the binary system. The binary hypothesis is also tested using radial velocity measurements. Methods. We used new approach to determine brightness maxima timings based on template fitting. This can also be used on sparse or scattered data. This approach was successfully applied on measurements from different sources. To determine the orbital parameters of the double star TU UMa, we developed a new code to analyse light time effect that also includes secular variation in the pulsation period. Its usability was successfully tested on CL Aur, an eclipsing binary with mass-transfer in a triple system that shows similar changes in the O-C diagram. Since orbital motion would cause systematic shifts in mean radial velocities (dominated by pulsations), we computed and compared our model with centre-of-mass velocities. They were determined using high-quality templates of radial velocity curves of RRab stars. Results. Maxima timings adopted from the GEOS database (168) together with those newly determined from sky surveys and new measurements (85) were used to construct an O-C diagram spanning almost five proposed orbital cycles. This data set is three times larger than data sets used by previous authors. Modelling of the O-C dependence resulted in 23.3-yr orbital period, which translates into a minimum mass of the second component of about 0.33 M . Secular changes in the pulsation period of TU UMa over the whole O-C diagram were satisfactorily approximated by a parabolic trend with a rate of −2.2 ms yr −1 . To confirm binarity, we used radial velocity measurements from nine independent sources. Although our results are convincing, additional long-term monitoring is necessary to unambiguously confirm the binarity of TU UMa.

Candidates for RR Lyrae in binary systems from the OGLE Galactic bulge survey

“…2 from Irwin (1952a): In this relation, ν is the true anomaly, ω is the argument of periastron, e is the numerical eccentricity, and A is the shift in radial position in light days. We refer the interested reader to the appendix A in Liška et al (2016b) for a thorough description of the individual parameters. For stars with O − C diagrams that can be described by Eq.…”

Phenomenological modelling of eclipsing system light curves

“…Similarly, we can establish other arbitrarily complex period models of ϑ(t) determined by a set of free parameters, including cyclic period modulation of the light time effect (LiTE) caused by another body in the system (Mikulášek et al 2011c;Liška et al 2015) or the apsidal motion. The real shape of the phase curve can also be approximated using so-called O-C time shifts of the observed phase curves versus the predicted LC derived by the period model with fixed parameters (typically P 0 , M 0 ) expressed in time units (usually in days).…”

“…Qian, M. Vaňko, R. E. Wilson, and 9 The detailed study about the triple star AR Aur is in preparation. For formulae see Liška et al (2015).…”

RR Lyrae binary systems in the Galactic bulge

“…Previously only one RR Lyrae star was known to be in a binary system with high confidence ( [5,10]). This has changed when we announced 20 candidate binary systems, using OGLE observations of RR Lyrae stars towards the bulge ( [1]).…”