Download (765Kb)
Total Page：16
File Type：pdf, Size：1020Kb
Research Paper J. Astron. Space Sci. 31(3), 187-197 (2014) http://dx.doi.org/10.5140/JASS.2014.31.3.187 An Orbital Stability Study of the Proposed Companions of SW Lyncis T. C. Hinse1†, Jonathan Horner2,3, Robert A. Wittenmyer3,4 1Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea 2Computational Engineering and Science Research Centre, University of Southern Queensland, Toowoomba, Queensland 4350, Australia 3Australian Centre for Astrobiology, University of New South Wales, Sydney 2052, Australia 4School of Physics, University of New South Wales, Sydney 2052, Australia We have investigated the dynamical stability of the proposed companions orbiting the Algol type short-period eclipsing binary SW Lyncis (Kim et al. 2010). The two candidate companions are of stellar to substellar nature, and were inferred from timing measurements of the system’s primary and secondary eclipses. We applied well-tested numerical techniques to accurately integrate the orbits of the two companions and to test for chaotic dynamical behavior. We carried out the stability analysis within a systematic parameter survey varying both the geometries and orientation of the orbits of the companions, as well as their masses. In all our numerical integrations we found that the proposed SW Lyn multi-body system is highly unstable on time-scales on the order of 1000 years. Our results cast doubt on the interpretation that the timing variations are caused by two companions. This work demonstrates that a straightforward dynamical analysis can help to test whether a best-fit companion-based model is a physically viable explanation for measured eclipse timing variations. We conclude that dynamical considerations reveal that the proposed SW Lyncis multi-body system most likely does not exist or the companions have significantly different orbital properties from those conjectured in Kim et al. (2010). Keywords: stars: individual (SW Lyncis), stars: binaries, methods: n-body, methods: celestial mechanics 1. INTRODUCTION companions orbiting the eclipsing polar HU Aquarii (hereafter HU Aqr) using the same detection technique. In recent years, a number of multiple star systems Furthermore, Potter et al. (2011) announced a possible have been proposed to orbit a binary pair as a result of detection of two giant extrasolar planets orbiting the photometric follow-up observations of eclipsing binaries. eclipsing polar UZ Fornacis (hereafter UZ For) and Lee The nature of the proposed companions ranges from et al. (2012) found periodic signatures from photometric planetary to sub-stellar objects. Lee et al. (2009) were the measurements of the Algol system SZ Herculis (hereafter first to propose such circumbinary companions to explain SZ Her). Here, the authors associated their detection with eclipse timing variations, suggesting that the short-period the possible existence of two M-type stellar companions pulsating subdwarf binary HW Virginis (hereafter HW with minimum massess of 0.19 M⊙ and 0.22 M⊙. Finally, Vir) was being accompanied by two unseen circumbinary a recent study by Almeida et al. (2013) also proposed the companions of mass 8.5 Mjup and 19.2 Mjup. Following existence of two circumbinary companions orbiting the this announcement, Beuermann et al. (2010) announced post-common envelope binary NSVS 14256825. In addition the detection of two planets with masses of 2 Mjup and 7 to these proposed systems, a number of studies (Kim et al. Mjuporbiting the recently formed post-common envelope (2005)) proposed unseen companions around several other binary NN Serpentis (hereafter NN Ser). Qian et al. (2011) close binaries in the last few years and we refer to Hinse et then also announced the discovery of two circumbinary al. (2014a, and references therein) for further details of these This is an Open Access article distributed under the terms of the Received May 31, 2014 Revised Aug 18, 2014 Accepted Aug 19, 2014 Creative Commons Attribution Non-Commercial License (http:// †Corresponding Author creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, E-mail: [email protected] provided the original work is properly cited. Tel: +82-42-865-3389, Fax: +82 - 42 - 865 - 3272 Copyright © The Korean Space Science Society 187 http://janss.kr plSSN: 2093-5587 elSSN: 2093-1409 J. Astron. Space Sci. 31(3), 187-197 (2014) systems. the secondary eclipses. Parsons et al. (2014) were able to The observational technique which is used for the rule out the possibility of apsidal motion of the orbit of NN discovery of possible circumbinary companions is primarily Ser showing that the secondary eclipse timings followed based on the timing measurements of the primary eclipse the same trend as the primary timing measurements. of the binary star system. Considering the case when the Furthermore, a stable multi-body circumbinary system primary is isolated and positioned at a constant distance was recently detected using Kepler space-telescope data. to Earth, the time of primary eclipses in the future will Orosz et al. (2012) utilized the transit detection technique follow a linear ephemeris relative from some reference to detect two planets transiting a main-sequence primary epoch T0 with binary period P0. However, if an additional star very similar to the Sun accompanied by a cooler M-type massive companion is gravitationally bound to the binary secondary. components, then the binary system will start to follow an In contrast to the stability and feasibility demonstrated orbital trajectory around the total system barycenter. This for the two systems discussed in the previous paragraph, gives rise to the so-called light-travel time effect (LTTE) dynamical studies of the other circumbinary systems (Irwin 1952, Borkovits & Hegedues 1996). As a consequence discussed above have instead revealed a very different of the finite speed of light, the arrival-time of photons will picture. Rather than featuring proposed companions that be delayed (advanced) as a result of the distance between move on dynamically stable orbits, the companions in the binary and the Earth being a maximum (minimum). The those systems have instead been found to move on highly manifestation of this effect is a quasi-periodic change in the unstable orbits (with the exception of NN Ser). Typically, measured timings of the primary eclipses and is also known the companions will either experience close encounters as eclipse timing variations (ETV). The precision with which resulting in the ejection of one or both components or there timing measurements are obtained is mainly governed by will be direct collision events. Several studies have recently the photometric quality of the data, the observing cadence focused on the orbital stability of the proposed circumbinary during the eclipse, and the presence of star-spots. In systems. The first study to test for the orbital longevity of general, timing measurements should be independent of any such post-common eclipsing binary system (HU Aqr) spectral band observations although datasets with mixed was presented in Horner et al. (2011). In their work they timing measurements obtained from various filters could followed the orbits as part of a detailed dynamical analysis result in systematics uncertainties and possibly lead to a and demonstrated that the proposed two-planet system false interpretation of the period variations of an eclipsing would be highly unstable, with break-up time-scales of less binary (Go´zdziewski et al. 2012). than a few thousand years. Two follow-up studies of HU Aqr For nearly all systems with a proposed circumbinary were recently presented (Hinse et al. 2012a, Wittenmyer companion, as mentioned above, there is a fundamental et al. 2012). In the first, where the authors attempted to problem that raises doubts towards the correct determine new best-fit models to the observed timing data interpretation of the measured eclipse timing variations. accompanied with orbital stability requirements. A common denominator for all systems is the three-body In that work, the authors found a new orbital architecture problem: two massive companions orbiting a binary star. for the proposed companions around HU Aqr, but again From a dynamical point of view, such configurations found that architecture to be highly unstable. Long-lived naturally raise the question of orbital stability. The orbits capable of surviving on million-year timescales numerical demonstration of a long-lived stable three-body were found for HU Aqr only when additional orbital system could serve to further support the interpretation stability constraints were imposed on an ensemble of of observed timing variations as being directly caused by best-fit solutions, based on the Hill radii of the proposed the perturbing effects of massive companions. One other companions. The key difference between the stable possibility is that the period variations are indeed caused solutions found in this manner and the unstable ones that by additional companions, but in this case the orbital resulted solely from the observational data was that the architecture must be significantly different than discussed. stable solutions featured near-circular orbits for the two As an example the only multi-body system that seem companions. Two further studies of the HU Aqr system to follow stable orbits around a post-common envelope (Go´zdziewski et al. 2012, Wittenmyer et al. 2012) both (evolved) binary is the NN Ser system (Beuermann et al. suggested