Triple Star Research Articles

THE DYNAMICAL STATE AND LONG-TERM STABILITY OF HIP 102589

The dynamical state (component masses and kinematic parameters) of the triple star HIP 102589 is redetermined by fitting the simple double two-body model and the accurate three-body model, respectively, to observational data including those accumulated since the last orbit determination in 1992. Though the precision-weighted sum of squared residuals calculated from our results with both models are significantly smaller than the previous ones, only the result with the three-body model is statistically acceptable according to the goodness-of-fit test. The forward and backward long-term dynamical evolutions are numerically explored on the timescale of an estimated age of the components. It is found that the three-body system remains integrated and its hierarchical configuration keeps unchanged since the formation of the components, despite the fact that the instantaneous double two-body orbits vary significantly. This implies that the triple star may not be formed by a three-body encounter. Also, the possibility that the most massive component is itself a tightly bounded binary is discussed based on the redetermined mass and a stellar empirical mass–luminosity relation.

A first-order dynamical model of hierarchical triple stars and its application

For most hierarchical triple stars, the classical double two-body model of zeroth-order cannot describe the motions of the componentsunder the current observational accuracy. In this paper, Marchal's first-order analytical solution is implemented and a more efficient simplified version is applied to real triple stars. The results show that, for most triple stars, the proposed first-order model is preferable to the zeroth-order model both in fitting observational data and in predicting component positions.

CRITICAL CURVES AND CAUSTICS OF TRIPLE-LENS MODELS

Among the 25 planetary systems detected up to now by gravitational microlensing, there are two cases of a star with two planets, and two cases of a binary star with a planet. Other, yet undetected types of triple lenses include triple stars or stars with a planet with a moon. The analysis and interpretation of such events is hindered by the lack of understanding of essential characteristics of triple lenses, such as their critical curves and caustics. We present here analytical and numerical methods for mapping the critical-curve topology and caustic cusp number in the parameter space of $n$-point-mass lenses. We apply the methods to the analysis of four symmetric triple-lens models, and obtain altogether 9 different critical-curve topologies and 32 caustic structures. While these results include various generic types, they represent just a subset of all possible triple-lens critical curves and caustics. Using the analyzed models, we demonstrate interesting features of triple lenses that do not occur in two-point-mass lenses. We show an example of a lens that cannot be described by the Chang-Refsdal model in the wide limit. In the close limit we demonstrate unusual structures of primary and secondary caustic loops, and explain the conditions for their occurrence. In the planetary limit we find that the presence of a planet may lead to a whole sequence of additional caustic metamorphoses. We show that a pair of planets may change the structure of the primary caustic even when placed far from their resonant position at the Einstein radius.

REVISION OF EARTH-SIZEDKEPLERPLANET CANDIDATE PROPERTIES WITH HIGH-RESOLUTION IMAGING BY THEHUBBLE SPACE TELESCOPE

We present the results of our Hubble Space Telescope program and describe how our analysis methods were used to re-evaluate the habitability of some of the most interesting Kepler planet candidates. Our program observed 22 Kepler Object of Interest (KOI) host stars, several of which were found to be multiple star systems unresolved by Kepler. We use our high-resolution imaging to spatially resolve the stellar multiplicity of Kepler-296, KOI-2626, and KOI-3049, and develop a conversion to the Kepler photometry (Kp) from the F555W and F775W filters on WFC3/UVIS. The binary system Kepler-296 (5 planets) has a projected separation of 0.217" (80AU); KOI-2626 (1 planet candidate) is a triple star system with a projected separation of 0.201" (70AU) between the primary and secondary components and 0.161" (55AU) between the primary and tertiary; and the binary system KOI-3049 (1 planet candidate) has a projected separation of 0.464" (225AU). We use our measured photometry to fit the separated stellar components to the latest Victoria-Regina Stellar Models with synthetic photometry to conclude that the systems are coeval. The components of the three systems range from mid-K dwarf to mid-M dwarf spectral types. We solved for the planetary properties of each system analytically and via an MCMC algorithm using our independent stellar parameters. The planets range from ~1.6R_Earth to ~4.2R_Earth, mostly Super Earths and mini-Neptunes. As a result of the stellar multiplicity, some planets previously in the Habitable Zone are, in fact, not, and other planets may be habitable depending on their assumed stellar host.

MULTIPLICITY OF THE GALACTIC SENIOR CITIZENS: A HIGH-RESOLUTION SEARCH FOR COOL SUBDWARF COMPANIONS

Cool subdwarfs are the oldest members of the low mass stellar population. Mostly present in the galactic halo, subdwarfs are characterized by their low metallicity. Measuring their binary fraction and comparing it to solar metallicity stars could give key insights into the star formation process early in the history of the Milky Way. However, because of their low luminosity and relative rarity in the solar neighborhood, binarity surveys of cool subdwarfs have suffered from small sample sizes and incompleteness. Previous surveys have suggested that the binary fraction of red subdwarfs is much lower than for their main sequence cousins. Using the highly efficient RoboAO system, we present the largest yet high-resolution survey of subdwarfs, sensitive to angular separations, down to 0.15 arcsec, and contrast ratios, up to 6 magnitude difference, invisible in past surveys. Of 344 target cool subdwarfs, 40 are in multiple systems, 16 newly discovered, for a binary fraction of 11.6 percent and 1.8 percent error. We also discovered 6 triple star systems for a triplet fraction of 1.7 percent and 0.7 percent error. Comparisons to similar surveys of solar metallicity dwarf stars gives a 3 sigma disparity in luminosity between companion stars, with subdwarfs displaying a shortage of low contrast companions.

Eclipse timing variation analyses of eccentric binaries with close tertiaries in the Kepler field

We report eclipse timing variation analyses of 26 compact hierarchical triple stars comprised of an eccentric eclipsing (‘inner’) binary and a relatively close tertiary component found in the Kepler field. We simultaneously fit the primary and secondary O − C curves of each system for the light-traveltime effect (LTTE), as well as dynamical perturbations caused by the tertiary on different time-scales. For the first time, we include those contributions of three-body interactions which originate from the eccentric nature of the inner binary. These effects manifest themselves both on the period of the triple system, P2, and on the longer ‘apse-node’ time-scale. We demonstrate that consideration of the dynamically forced rapid apsidal motion yields an efficient and independent tool for the determination of the binary orbit's eccentricity and orientation, as well as the 3D configuration of the triple. Modelling the forced apsidal motion also helps to resolve the degeneracy between the shapes of the LTTE and the dynamical delay terms on the P2 time-scale, due to the strong dependence of the apsidal motion period on the triple's mass ratio. This can lead to the independent determination of the binary and tertiary masses without the need for independent radial velocity measurements. Through the use of our analytic method for fitting O − C curves, we have obtained robust solutions for system parameters for the 10 most ideal triples of our sample, and only somewhat less robust, but yet acceptable, fits for the remaining systems. Finally, we study the results of our 26 system parameter fits via a set of distributions of various physically important parameters, including mutual inclination angle, and mass and period ratios.

Large Monochromatic Triple Stars in Edge Colourings

AbstractFollowing problems posed by Gyárfás 2011, we show that for every r‐edge‐colouring of there is a monochromatic triple star of order at least , improving Ruszinkó's result 2012. An edge colouring of a graph is called a local r‐colouring if every vertex spans edges of at most r distinct colours. We prove the existence of a monochromatic triple star with at least vertices in every local r‐colouring of .

THE MULTIPLICITY OF MASSIVE STARS: A HIGH ANGULAR RESOLUTION SURVEY WITH THEHSTFINE GUIDANCE SENSOR

We present the results of an all-sky survey made with the Fine Guidance Sensor on Hubble Space Telescope to search for angularly resolved binary systems among the massive stars. The sample of 224 stars is comprised mainly of Galactic O- and B-type stars and Luminous Blue Variables, plus a few luminous stars in the Large Magellanic Cloud. The FGS TRANS mode observations are sensitive to detection of companions with an angular separation between 0."01 and 1."0 and brighter than $\triangle m = 5$. The FGS observations resolved 52 binary and 6 triple star systems and detected partially resolved binaries in 7 additional targets (43 of these are new detections). These numbers yield a companion detection frequency of 29% for the FGS survey. We also gathered literature results on the numbers of close spectroscopic binaries and wider astrometric binaries among the sample, and we present estimates of the frequency of multiple systems and the companion frequency for subsets of stars residing in clusters and associations, field stars, and runaway stars. These results confirm the high multiplicity fraction, especially among massive stars in clusters and associations. We show that the period distribution is approximately flat in increments of log P. We identify a number of systems of potential interest for long term orbital determinations, and we note the importance of some of these companions for the interpretation of the radial velocities and light curves of close binaries that have third companions.

KIC 2856960: the impossible triple star

KIC 2856960 is a star in the Kepler field which was observed by Kepler for four years. It shows the primary and secondary eclipses of a close binary of period 0.258 d as well as complex dipping events that last for about 1.5 d at a time and recur on a 204 d period. The dips are thought to result when the close binary passes across the face of a third star. In this paper, we present an attempt to model the dips. Despite the apparent simplicity of the system and strenuous efforts to find a solution, we find that we cannot match the dips with a triple star while satisfying Kepler's laws. The problem is that to match the dips, the separation of the close binary has to be larger than possible relative to the outer orbit given the orbital periods. Quadruple star models can get round this problem but require the addition of a so-far undetected intermediate period of the order of 5–20 d that has been a near-perfect integer divisor of the outer 204 d period. Although we have no good explanation for KIC 2856960, using the full set of Kepler data we are able to update several of its parameters. We also present a spectrum showing that KIC 2856960 is dominated by light from a K3- or K4-type star.

MERGERS AND OBLIQUITIES IN STELLAR TRIPLES

Many close stellar binaries are accompanied by a far-away star. The "eccentric Kozai-Lidov" (EKL) mechanism can cause dramatic inclination and eccentricity fluctuations, resulting in tidal tightening of inner binaries of triple stars. We run a large set of Monte-Carlo simulations including the secular evolution of the orbits, general relativistic precession and tides, and we determine the semimajor axis, eccentricity, inclination and spin-orbit angle distributions of the final configurations. We find that the efficiency of forming tight binaries (<~16 d) when taking the EKL mechanism into account is ~ 21%, and about 4% of all simulated systems ended up in a merger event. These merger events can lead to the formation of blue-stragglers. Furthermore, we find that the spin-orbit angle distribution of the inner binaries carries a signature of the initial setup of the system, thus observations can be used to disentangle close binaries' birth configuration. The resulting inner and outer final orbits' period distributions, and their estimated fraction, suggests secular dynamics may be a significant channel for the formation of close binaries in triples and even blue stragglers.

WASP-12b AND HAT-P-8b ARE MEMBERS OF TRIPLE STAR SYSTEMS

We present high spatial resolution images that demonstrate the hot Jupiters WASP-12b and HAT-P-8b orbit the primary star of hierarchical triple star systems. In each case, two distant companions with colors and brightness consistent with M dwarfs co-orbit the planet host as well as one another. Our adaptive optics images spatially resolve the secondary around WASP-12, previously identified by Bergfors et al. 2011 and Crossfield et al. 2012, into two distinct sources separated by 84.3+/-0.6 mas (21 +/- 3 AU). We find that the secondary to HAT-P-8, also identified by Bergfors et al. 2011, is in fact composed of two stars separated by 65.3+/-0.5 mas (15+/-1 AU). Our follow-up observations demonstrate physical association through common proper-motion. HAT-P-8 C has a particularly low mass, which we estimate to be 0.18+/-0.02Msun using photometry. Due to their hierarchy, WASP-12 BC and HAT-P-8 BC will enable the first dynamical mass determination for hot Jupiter stellar companions. These previously well-studied planet hosts now represent higher-order multi-star systems with potentially complex dynamics, underscoring the importance of diffraction-limited imaging and providing additional context for understanding the migrant population of transiting hot Jupiters.

PHOTOMETRIC PROPERTIES FOR SELECTED ALGOL-TYPE BINARIES. VIII. THE TRIPLE SYSTEMS DI PEG AND AF GEM REVISITED

New extensive photometry for two triple binary stars, DI Peg and AF Gem, was performed from 2012 October to 2013 January, with two small telescopes at Xinglong station (XLs) of NAOC. From new multi-color observations and previously published ones in literature, the photometric models were (re)deduced using the updated Wilson-Devinney code. The results indicated that the low third lights exist in two classic Algol-type binaries, whose fill-out factors for the more massive components are f{sub p} = 78.2(± 0.4)% for DI Peg, and f{sub p} = 69.0(± 0.3)% for AF Gem, respectively. Through analyzing the O–C curves, the orbital periods for two binaries change in the complicated mode. The period of DI Peg possibly appears to show two light-time orbits, whose modulated periods are P {sub 3} = 54.6(± 0.5) yr and P {sub 4} = 23.0(± 0.6) yr, respectively. The inferred minimum masses for the inner and outer sub-stellar companions are M {sub in} = 0.095 M {sub ☉} and M {sub out} = 0.170 M {sub ☉}, respectively. Therefore, DI Peg may be a quadruple star. The orbital period of AF Gem appears to show a continuous period decrease or a cyclic variation; the latter may be preferable.more » The cyclic oscillation, with a period of 120.3(± 2.5) yr, may be attributed to the light-time effect due to the third body. This kind of additional companion may extract angular momentum from the central system, which may play a key role in the evolution of the binary.« less

Bayesian analysis of radial velocity data of GJ667C with correlated noise: evidence for only two planets

GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-years) from Earth. GJ667C has received much attention recently due to the claims that it hosts up to seven planets including three super-Earths inside the habitable zone. We present a Bayesian technique for the analysis of radial velocity (RV) data-sets in the presence of correlated noise component ("red noise"), with unknown parameters. We also introduce hyper-parameters in our model in order to deal statistically with under or over-estimated error bars on measured RVs as well as inconsistencies between different data-sets. By applying this method to the RV data-set of GJ667C, we show that this data-set contains a significant correlated (red) noise component with correlation timescale for HARPS data of order 9 days. Our analysis shows that the data only provides strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19d and 28.13d respectively, with some hints towards the presence of a third signal with period 91d. The planetary nature of this third signal is not clear and additional RV observations are required for its confirmation. Previous claims of the detection of additional planets in this system are due the erroneous assumption of white noise. Using the standard white noise assumption, our method leads to the detection of up to five signals in this system. We also find that with the red noise model, the measurement uncertainties from HARPS for this system are under-estimated at the level of ~50 per cent.

The VAST Survey – III. The multiplicity of A-type stars within 75 pc

With a combination of adaptive optics imaging and a multi-epoch common proper motion search, we have conducted a large volume-limited (D $\le$ 75 pc) multiplicity survey of A-type stars, sensitive to companions beyond 30 au. The sample for the Volume-limited A-STar (VAST) survey consists of 435 A-type stars: 363 stars were observed with adaptive optics, 228 stars were searched for wide common proper motion companions and 156 stars were measured with both techniques. The projected separation coverage of the VAST survey extends from 30 to 45,000 au. A total of 137 stellar companions were resolved, including 64 new detections from the VAST survey, and the companion star fraction, projected separation distribution and mass ratio distribution were measured. The separation distribution forms a log-normal distribution similar to the solar-type binary distribution, but with a peak shifted to a significantly wider value of 387 (+132,-98) au. Integrating the fit to the distribution over the 30 to 10,000 au observed range, the companion star fraction for A-type stars is estimated as 33.8%+-2.6%. The mass ratio distribution of closer (<125 au) binaries is distinct from that of wider systems, with a flat distribution for close systems and a distribution that tends towards smaller mass ratios for wider binaries. Combining this result with previous spectroscopic surveys of A-type stars gives an estimate of the total companion star fraction of 68.9%+-7.0%. The most complete assessment of higher order multiples was estimated from the 156-star subset of the VAST sample with both adaptive optics and common proper motion measurements, combined with a literature search for companions, yielding a lower limit on the frequency of single, binary, triple, quadruple and quintuple A-type star systems of 56.4 (-4.0,+3.8), 32.1 (-3.5,+3.9), 9.0 (-1.8,+2.8), 1.9 (-0.6,+1.8) and 0.6 (-0.2,+1.4) per cent, respectively.

THE AGE AND MASS OF THE α HERCULIS TRIPLE-STAR SYSTEM FROM A MESA GRID OF ROTATING STARS WITH 1.3 ⩽M/M☉⩽ 8.0

\alpha^1 Her is the second closest Asymptotic Giant Branch (AGB) star to the Sun, and the variable luminous M5 Ib-II member of a triple stellar system containing G8 III and A9 IV-V components. However, the mass of this important star was previously uncertain with published values ranging from ~2 - 15 Msun. As shown by this study, its fortuitous membership in a nearby resolved triple star system, makes it possible to determine its fundamental properties including its mass and age. We present over twenty years of VRI photometry of \alpha^1 Her as well as Wing intermediate-band near-IR TiO and NIR continuum photometry. We introduce a new photometry-based calibration technique, and extract the effective temperature and luminosity of \alpha^1 Her, in agreement with recent interferometric measures. We find, Teff=3280 +/- 87 K and log(L/Lsun)=3.92 +/- 0.14. With the MESA code, we calculate a dense grid of evolutionary tracks for Galactic low- to intermediate-mass (1.3 to 8 Msun) rotating stars from the pre-main sequence phase to the advanced AGB phase. We include atomic diffusion and rotation mechanisms to treat the effects of extra elemental mixing. Based on the observed properties of the \alpha Herculis stars, we constrain the age of the system to lie in the range 0.41 to 1.25 Gyr. Thus, the mass of \alpha^1 Her lies in the range 2.175 <= M/Msun <= 3.250. We compare our model-based age inference with recent tracks of the Geneva and STAREVOL codes, and show their agreement. In the prescribed mass range for \alpha^1 Her, the observed 12C/13C and 16O/17O ratios are consistent (within 2\sigma) with the ratios predicted by the MESA, Geneva and STAREVOL codes.

Analysis of the secular problem for triple star systems

The long-term dynamics of the three-body problem is studied. The goal is to study the motion of a planet (m1) around a star (m0) that is perturbed by a third-body (m2) (a planet or a brown dwarf star). The gravitational potential is developed in closed form up to the fourth order. Taking into account the triple system, it is shown here the evolution of some orbital parameters of the planet (m1). A comparison considering models with different orders for the disturbing potential is presented. We show that the behavior of the orbit of the inner planet can flip from prograde to retrograde trajectories. This is due to the third-order term, which strongly affects the eccentricity and inclination. We show that the effect of the fourth order term is to change the times when the phenomenon occurs.

Stars with discrepant v sin i as derived from the Ca II λ3933 Å and Mg II λ4481 Å lines. IV. HD8837—a shell star, HD47964 and HD183986—new binaries

Axial rotation of a star plays an important role in its evolution, physical conditions in its atmosphere, and appearance of its spectrum. We have analyzed CCD spectra of three stars for which their projected rotational velocity remarkably differs when derived from the Ca II λ 3933 A and MgII λ 4481 A lines. We derived effective temperatures and surface gravities using published uvbyβ photometries and computed synthetic spectra. Comparing observed line profiles of the two lines with the computed ones, we estimated values of v sin i. We also derived radial velocities by means of the cross-correlation function. HD8837 is known to be a shell star with pronounced narrow absorption cores in the Balmer lines as well as in the strong metal lines; however, we do not confirm the emission component in the core of Hβ. HD47964 has been discovered by Hipparcos to be a double. However, in our spectra we do not find traces of the other star. Based on the Hipparcos data, we estimated that the other star would be a main sequence A4 star with an extremely high rotational velocity resulting in wiping out any traces of spectral lines of the companion. HD183986 is known to be a triple star. However, we have found a manifestation of a so far not discovered companion of the component HD183986A and estimated it as a main sequence A5 star having v sin i of about 150 km/s.

Binary and multiple magnetic Ap/Bp stars

AbstractWe present the results of speckle interferometric observations of 273 magnetic stars most of which are Ap/Bp type. All observations were made at the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. We resolved 58 binary and 5 triple stars into individual components. Almost half of these stars were astrometrically resolved for the first time. The fraction of speckle interferometric binaries/multiples in the sample of stars with confirmed magnetic fields is 23%. We expect that the total fraction of binaries/multiples in the sample with account for spectroscopic short-period systems and wide common proper motion pairs can be twice higher. The detected speckle components have a prominent peak in the ρ distribution that corresponds to the closest resolved pairs. Full version of present paper is available in electronic form at http://arxiv.org/abs/1308.3168.

Protoplanetary disk evolution and stellar parameters of T Tauri binaries in Chamaeleon I

This study aims to determine the impact of stellar binary companions on the lifetime and evolution of circumstellar disks in the Chamaeleon I (Cha I) star-forming region by measuring the frequency and strength of accretion and circumstellar dust signatures around the individual components of T Tauri binary stars. We used high-angular resolution adaptive optics JHKL'-band photometry and 1.5-2.5mu spectroscopy of 19 visual binary and 7 triple stars in Cha I - including one newly discovered tertiary component - with separations between ~25 and ~1000au. The data allowed us to infer stellar component masses and ages and, from the detection of near-infrared excess emission and the strength of Brackett-gamma emission, the presence of ongoing accretion and hot circumstellar dust of the individual stellar component of each binary. Of all the stellar components in close binaries with separations of 25-100au, 10(+15-5)% show signs of accretion. This is less than half of the accretor fraction found in wider binaries, which itself appears significantly reduced (~44%) compared with previous measurements of single stars in Cha I. Hot dust was found around 50(+30-15)% of the target components, a value that is indistinguishable from that of Cha I single stars. Only the closest binaries (<25au) were inferred to have a significantly reduced fraction (<~25%) of components that harbor hot dust. Accretors were exclusively found in binary systems with unequal component masses M_secondary/M_primary < 0.8, implying that the detected accelerated disk dispersal is a function of mass-ratio. This agrees with the finding that only one accreting secondary star was found, which is also the weakest accretor in the sample. The results imply that disk dispersal is more accelerated the stronger the dynamical disk truncation, i.e., the smaller the inferred radius of the disk. (abridged)

The Lyapunov exponents in the dynamics of triple star systems

The dynamics of weakly heirarchical triple stars with equal masses are considered. Full spectra of the Lyapunov exponents are found via numerical integration of the orbits, for various initial configurations of the systemin the planar problem and with initial conditions in the vicinity of the 2 : 1 resonance (i.e., with the initial ratios of the periods of the outer and inner binaries being close to 2 : 1). Dependences between the Lyapunov time and the disruption time of the systemare constructed for initial conditions near and far from resonance. The character of these relationships is different near and far from resonance, corresponding to two kinds of Hamiltonian intermittency. The trajectories “stick” to the regular component in phase space near resonance, while this effect is not dominant far from resonance. Analysis of the distributions of the disruption times of the triple systems for initial conditions near and far from resonance confirm these conclusions.