Triple Stellar Systems Research Articles

Planetary Nebulae that Cannot Be Explained by Binary Systems

Abstract We examine the images of hundreds of planetary nebulae (PNe) and find that for about one in six PNe the morphology is too “messy” to be accounted for by models of stellar binary interaction. We speculate that interacting triple stellar systems shaped these PNe. In this preliminary study, we qualitatively classify PNe by one of four categories. (1) PNe that show no need for a tertiary star to account for their morphology. (2) PNe whose structure possesses a pronounced departure from axial-symmetry and/or mirror-symmetry. We classify these, according to our speculation, as “having a triple stellar progenitor.” (3) PNe whose morphology possesses departure from axial-symmetry and/or mirror-symmetry, but not as pronounced as in the previous class, and are classified as “likely shaped by triple stellar system.” (4) PNe with minor departure from axial-symmetry and/or mirror-symmetry that could have been also caused by an eccentric binary system or the interstellar medium. These are classified as “maybe shaped by a triple stellar system.” Given a weight η t = 1, η l = 0.67, and η m = 0.33 to classes 2, 3, and 4, respectively, we find that according to our assumption about 13%–21% of PNe have been shaped by triple stellar systems. Although in some evolutionary scenarios not all three stars survive the evolution, we encourage the search for a triple stellar systems at the center of some PNe.

Eccentricity and spin-orbit misalignment in short-period stellar binaries as a signpost of hidden tertiary companions

Eclipsing binaries are observed to have a range of eccentricities and spin-orbit misalignments (stellar obliquities). Whether such properties are primordial, or arise from post-formation dynamical interactions remains uncertain. This paper considers the scenario in which the binary is the inner component of a hierarchical triple stellar system, and derives the requirements that the tertiary companion must satisfy in order to raise the eccentricity and obliquity of the inner binary. Through numerical integrations of the secular octupole-order equations of motion of stellar triples, coupled with the spin precession of the oblate primary star due to the torque from the secondary, we obtain a simple, robust condition for producing spin-orbit misalignment in the inner binary: In order to excite appreciable obliquity, the precession rate of the stellar spin axis must be smaller than the orbital precession rate due to the tertiary companion. This yields quantitative requirements on the mass and orbit of the tertiary. We also present new analytic expressions for the maximum eccentricity and range of inclinations allowing eccentricity excitation (Lidov-Kozai window), for stellar triples with arbitrary masses and including the non-Keplerian potentials introduced by general relativity, stellar tides and rotational bulges. The results of this paper can be used to place constraints on unobserved tertiary companions in binaries that exhibit high eccentricity and/or spin-orbit misalignment, and will be helpful in guiding efforts to detect external companions around stellar binaries. As an application, we consider the eclipsing binary DI Herculis, and identify the requirements that a tertiary companion must satisfy to produce the observed spin-orbit misalignment.

B fields in OB stars (BOB): The magnetic triple stellar system HD 164492C in the Trifid nebula.

HD 164492C is a spectroscopic triple stellar system that has been recently detected to possess a strong magnetic field. We have obtained high-resolution spectroscopic and spectropolarimetric observations over a timespan of two years and derived physical, chemical, and magnetic properties for this object. The system is formed by an eccentric close spectroscopic binary (Ca1-Ca2) with a period of 12.5 days, and a massive tertiary Cb. We calculated the orbital parameters of the close pair, reconstructed the spectra of the three components, and determined atmospheric parameters and chemical abundances by spectral synthesis. From spectropolarimetric observations, multi-epoch measurements of the longitudinal magnetic fields were obtained. The magnetic field is strongly variable on timescales of a few days, with a most probable period in the range of 1.4-1.6 days. Star Cb with Teff~25000 K is the apparently fastest rotator and the most massive star of this triple system and has anomalous chemical abundances with a marked overabundance of helium, 0.35+/-0.04 by number. We identified this star as being responsible for the observed magnetic field, although the presence of magnetic fields in the components of the Ca pair cannot be excluded. Star Ca1 with a temperature of about 24000 K presents a normal chemical pattern, while the least massive star Ca2 is a mid-B type star (Teff~15000 K) with an overabundance of silicon. The obtained stellar parameters of the system components suggest a distance of 1.5 kpc and an age of 10-15 Myr.

On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples

Hot Jupiters (HJs) are Jupiter-like planets orbiting their host star in tight orbits of a few days. They are commonly believed not to have formed in situ, requiring inwards migration towards the host star. One of the proposed migration scenarios is secular high-eccentricity or high-$e$ migration, in which the orbit of the planet is perturbed to high eccentricity by secular processes, triggering strong tidal evolution and orbital migration. Previous theoretical studies have considered secular excitation in stellar binaries. Recently, a number of HJs have been observed in stellar triple systems. In the latter, the secular dynamics are much richer compared to stellar binaries, and HJs could potentially be formed more efficiently. Here, we investigate this possibility by modeling the secular dynamical and tidal evolution of planets in two hierarchical configurations in stellar triple systems. We find that the HJ formation efficiency is higher compared to stellar binaries, but only by at most a few tens of per cent. The orbital properties of the HJs formed in the simulations are very similar to HJs formed in stellar binaries, and similarly to studies of the latter we find no significant number of warm Jupiters. HJs are only formed in our simulations for triples with specific orbital configurations, and our constraints are approximately consistent with current observations. In future, this allows to rule out high-$e$ migration in stellar triples if a HJ is detected in a triple grossly violating these constraints.

FORMATION AND EVOLUTION OF BLUE STRAGGLERS IN 47 TUCANAE

ABSTRACT Blue stragglers (BSS) are stars whose position in the color–magnitude diagram (CMD) places them above the main sequence (MS) turn-off (TO) point of a star cluster. Using data from the core of 47 Tuc in the ultraviolet (UV), we have identified various stellar populations in the CMD, and used their radial distributions to study the evolution and origin of BSS, and obtain a dynamical estimate of the mass of BSS systems. When we separate the BSS into two samples by their magnitude, we find that the bright BSS show a much more centrally concentrated radial distribution and thus higher mass estimate (over twice the TO mass for these BSS systems), suggesting an origin involving triple or multiple stellar systems. In contrast, the faint BSS are less concentrated, with a radial distribution similar to the MS binaries, pointing to the MS binaries as the likely progenitors of these BSS. Putting our data together with available photometric data in the visible and using MESA evolutionary models, we calculate the expected number of stars in each evolutionary stage for the normal evolution of stars and the number of stars coming from the evolution of BSS. The results indicate that BSS have a post-MS evolution comparable to that of a normal star of the same mass and a MS BSS lifetime of about 200–300 Myr. We also find that the excess population of asymptotic giant branch stars in 47 Tuc is due to evolved BSS.

The way to a double degenerate: ∼15–20 per cent of 1 M⊙ ≤ M ≤ 8 M⊙ stars have an M > 1 M⊙ companion

Abstract We find that ∼15–20 per cent of A-type stars or red giants are bound with a massive companion (Msecondary > 1 M⊙) in an intermediate wide orbit (0.5 < P < 5000 yr). These massive binaries are expected to form wide-orbit, double-degenerate systems (WODDs) within ≲10 Gyr implying that ∼10 per cent of white dwarfs (WDs) are expected to be part of a WODD with a lighter WD companion. These findings are based on an analysis of previous adaptive optics observations of A-type stars and radial velocity measurements of red giants and shed light on the connection between multiplicity function of stars and detected double degenerates. We expect that Gaia will find ∼10 new WODDs within 20 pc from the sun. These results put a stringent constraint on the collision model of Type Ia supernovae in which triple stellar systems that include a WODD as the inner binary are required to be abundant.

Shaping planetary nebulae with jets in inclined triple stellar systems

AbstractWe conduct three-dimensional hydrodynamical simulations of two opposite jets launched obliquely to the orbital plane around an asymptotic giant branch (AGB) star and within its dense wind, and demonstrate the formation of a ‘messy’ planetary nebula (PN), namely, a PN lacking any type of symmetry (highly irregular). In building the initial conditions we assume that a tight binary system orbits the AGB star, and that the orbital plane of the tight binary system is inclined to the orbital plane of binary system and the AGB star. We further assume that the accreted mass onto the tight binary system forms an accretion disk around one of the stars, and that the plane of the disk is in between the two orbital planes. The highly asymmetrical lobes that we obtain support the notion that messy PNe might be shaped by triple stellar systems.

The International Deep Planet Survey

Radial velocity and transit methods are effective for the study of short orbital period exoplanets but they hardly probe objects at large separations for which direct imaging can be used. We carried out the international deep planet survey of 292 young nearby stars to search for giant exoplanets and determine their frequency. We developed a pipeline for a uniform processing of all the data that we have recorded with NIRC2/Keck II, NIRI/Gemini North, NICI/Gemini South, and NACO/VLT for 14 years. The pipeline first applies cosmetic corrections and then reduces the speckle intensity to enhance the contrast in the images. The main result of the international deep planet survey is the discovery of the HR 8799 exoplanets. We also detected 59 visual multiple systems including 16 new binary stars and 2 new triple stellar systems, as well as 2,279 point-like sources. We used Monte Carlo simulations and the Bayesian theorem to determine that 1.05[+2.80-0.70]% of stars harbor at least one giant planet between 0.5 and 14M_J and between 20 and 300 AU. This result is obtained assuming uniform distributions of planet masses and semi-major axes. If we consider power law distributions as measured for close-in planets instead, the derived frequency is 2.30[+5.95-1.55]%, recalling the strong impact of assumptions on Monte Carlo output distributions. We also find no evidence that the derived frequency depends on the mass of the hosting star, whereas it does for close-in planets. The international deep planet survey provides a database of confirmed background sources that may be useful for other exoplanet direct imaging surveys. It also puts new constraints on the number of stars with at least one giant planet reducing by a factor of two the frequencies derived by almost all previous works.

Secular and tidal evolution of circumbinary systems

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin-orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star-planet-satellite systems and triple stellar systems.

Testing the strong equivalence principle with the triple pulsar PSRJ0337+1715

Three conceptually different masses appear in equations of motion for objects under gravity, namely, the inertial mass, $m_{\cal I}$, the passive gravitational mass, $m_{\cal P}$, and the active gravitational mass, $m_{\cal A}$. It is assumed that, for any objects, $m_{\cal I} = m_{\cal P} = m_{\cal A}$ in the Newtonian gravity, and $m_{\cal I} = m_{\cal P}$ in the Einsteinian gravity, oblivious to objects' sophisticated internal structure. Empirical examination of the equivalence probes deep into gravity theories. We study the possibility of carrying out new tests based on pulsar timing of the stellar triple system, PSR J0337+1715. Various machine-precision three-body simulations are performed, from which, the equivalence-violating parameters are extracted with Markov chain Monte Carlo sampling that takes full correlations into account. We show that the difference in masses could be probed to $3\times10^{-8}$, improving the current constraints from lunar laser ranging on the post-Newtonian parameters that govern violations of $m_{\cal P}=m_{\cal I}$ and $m_{\cal A}=m_{\cal P}$ by thousands and millions, respectively. The test of $m_{\cal P}=m_{\cal A}$ would represent the first test of Newton's third law with compact objects.

KELT-4Ab: AN INFLATED HOT JUPITER TRANSITING THE BRIGHT (V∼ 10) COMPONENT OF A HIERARCHICAL TRIPLE

We report the discovery of KELT-4Ab, an inflated, transiting Hot Jupiter orbiting the brightest component of a hierarchical triple stellar system. The host star is an F star with $T_{\rm eff}=6206\pm75$ K, $\log g=4.108\pm0.014$, $\left[{\rm Fe}/{\rm H}\right]=-0.116_{-0.069}^{+0.065}$, ${\rm M_*}=1.201_{-0.061}^{+0.067} \ {\rm M}_{\odot}$, and ${\rm R_*}=1.610_{-0.068}^{+0.078} \ {\rm R}_{\odot}$. The best-fit linear ephemeris is $\rm {BJD_{TDB}} = 2456193.29157 \pm 0.00021 + E\left(2.9895936 \pm 0.0000048\right)$. With a magnitude of $V\sim10$, a planetary radius of $1.699_{-0.045}^{+0.046} \ {\rm R_J}$, and a mass of $0.902_{-0.059}^{+0.060} \ {\rm M_J}$, it is the brightest host among the population of inflated Hot Jupiters ($R_P > 1.5R_J$), making it a valuable discovery for probing the nature of inflated planets. In addition, its existence within a hierarchical triple and its proximity to Earth ($210$ pc) provides a unique opportunity for dynamical studies with continued monitoring with high resolution imaging and precision radial velocities. In particular, the motion of the binary stars around each other and of both stars around the primary star relative to the measured epoch in this work should be detectable when it rises in October 2015.

Planetary nebula progenitors that swallow binary systems

I propose that some irregular `messy' planetary nebulae owe their morphologies to triple-stellar evolution where tight binary systems evolve inside and/or on the outskirts the envelope of asymptotic giant branch (AGB) stars. In some cases the tight binary system can survive, in other it is destroyed. The tight binary system might breakup with one star leaving the system. In an alternative evolution, one of the stars of the brook-up tight binary system falls toward the AGB envelope with low specific angular momentum, and drowns in the envelope. In a different type of destruction process the drag inside the AGB envelope causes the tight binary system to merge. This releases gravitational energy within the AGB envelope, leading to a very asymmetrical envelope ejection, with an irregular and `messy' planetary nebula as a descendant. The evolution of the triple-stellar system can be in a full common envelope evolution (CEE) or in a grazing envelope evolution (GEE). Both before and after destruction (if take place) the system might lunch pairs of opposite jets. One pronounced signature of triple-stellar evolution might be a large departure from axisymmetrical morphology of the descendant planetary nebula. I estimate that about one in eight non-spherical PNe is shaped by one of these triple-stellar evolutionary routes.

NEARBY STARS AS GRAVITATIONAL WAVE DETECTORS

Sun-like stellar oscillations are excited by turbulent convection and have been discovered in some 500 main sequence and sub-giant stars and in more than 12,000 red giant stars. When such stars are near gravitational wave sources, low-order quadrupole acoustic modes are also excited above the experimental threshold of detectability, and they can be observed, in principle, in the acoustic spectra of these stars. Such stars form a set of natural detectors to search for gravitational waves over a large spectral frequency range, from $10^{-7}$ Hz to $10^{-2}$ Hz. In particular, these stars can probe the $10^{-6}$ Hz -- $10^{-4}$ Hz spectral window which cannot be probed by current conventional gravitational wave detectors, such as SKA and eLISA. The PLATO stellar seismic mission will achieve photospheric velocity amplitude accuracy of $~ {\rm cm/s}$. For a gravitational wave search, we will need to achieve accuracies of the order of $10^{-2}{\rm cm/s}$, i.e., at least one generation beyond PLATO. However, we have found that multi-body stellar systems have the ideal setup for this type of gravitational wave search. This is the case for triple stellar systems formed by a compact binary and an oscillating star. Continuous monitoring of the oscillation spectra of these stars to a distance of up to a kpc could lead to the discovery of gravitational waves originating in our galaxy or even elsewhere in the universe. Moreover, unlike experimental detectors, this observational network of stars will allow us to study the progression of gravitational waves throughout space.

High-contrast imaging search for stellar and substellar companions of exoplanet host stars

We present the results of our high-contrast imaging survey of close stellar and substellar companions of exoplanet host stars, carried out with the adaptive optics imager NACO at the ESO Paranal observatory, in Chile. In total, 33 exoplanet host stars were observed with NACO in the Ks-band. New comoving companions could be identified close to the stars HD 9578, HD 96167, and HD 142245. The newly detected companions exhibit masses between 0.21 and 0.56 M⊙ and are located at projected separations from their primaries between about 190 and 510 au. In the case of HD 142245, we found evidence that the detected companion is actually a close binary itself with a projected separation of only about 4 au, i.e. HD 142245 might be a hierarchical triple stellar system, which hosts an exoplanet, a new member in the short list of such systems, presently known. In our imaging campaign, a limiting magnitude of Ks = 18.5 mag is reached in average in the background noise limited region around our targets at projected separations beyond about 100 au, which allows the detection of substellar companions with masses down to about 60 MJup. With our NACO observations we can rule out additional stellar companions at projected separations between about 30 and 370 au around the observed exoplanet host stars.

Secular motion in a hierarchic triple stellar system

A system of equations is derived for the secular motion of a hierarchic triple stellar system. Mean anomalies of the inner binary system and of the outer star orbit are eliminated up to order 9 in the ratio of their Delaunay momenta. Thanks to the use of vectorial elements (angular momenta and Laplace vectors) the equations are non-singular, compact, and independent on the choice of the reference frame axes directions. In the limit of circular outer orbit, the secular Hamiltonian agrees with the forgotten solution by Brown. Being more complete, yet simpler, the present model differs from that of Krymolowski & Mazeh, except for the circular outer orbit limit. A simple extension of the secular equations of motion describing tidal friction is also provided.

Planet formation in a triple stellar system: implications of the third star's orbital inclination

AbstractPlanets have been revealed both in binary and triple stellar systems. Although there have been several studies of the late stages of planet formation in binary stars this process does not appear to have been studied in triple stellar systems. To understand how the late stage of planetary accretion is affected by a third companion, in this work we have numerically investigated the formation of planets in a hypothetical triple stellar system. The system is composed by an inner binary formed by two half-solar-mass components orbited by a solar-mass star. In our experiments, lunar and Mars-sized planetary embryos are distributed around the centre of mass of the inner binary system. Our main goal is to analyse how the formation of planets evolves depending on the orbital configuration of the massive distant companion. We have performed an extensive number of numerical simulations considering different orbital configurations for the third star. All simulations were numerically integrated for at least 107 years. The results show that when the protoplanetary disc and the stars are initially on coplanar orbits, one or two planets are quickly formed between 6 and 8 AU. In general such planets have also small eccentricities with values about 10−2. On the other hand, when the third star is considered initially on inclined orbits (even tiny values), there tends to occur a significant increase in the inclination of bodies of protoplanetary disc, which prevents the collisions between these objects and their growth. As a result, in this latter case we do not evidence the formation of planets during the timescale of our integrations but note the existence of several leftover objects that can survive for longer than 10 Myr, moving in orbits with semi-major axes ranging between ~6 and 8 AU. Thus, our results do not rule out the planet formation in this kind of stellar arrangements at all, but they indicate that, if planetary bodies keep stable orbits, the late stage of planet formation in systems with a highly inclined third star can be a very long process and many of these triple hierarchical systems might not have had time to form planets and planetary systems. They could be harbouring only debris discs, fragments or planetesimals.

Dynamical detection of three triple stellar systems in open clusters

We present a kinematic analysis of three triple stellar systems belonging to two open clusters: CPD-60{\deg}961 and HD66137 in NGC2516, and HD315031 in NGC6530. All three systems are hierarchical triples with a close binary bound to a third body in a wider orbit, whose presence is detected through velocity variations of the close binary barycentre. Orbital parameters are derived from radial velocity curves. Absolute parameters for all stars are estimated assuming cluster membership. Some dynamical and evolutionary aspects of these systems are discussed, particularly the possible influence of Kozai cycles. The two systems of NGC2516 have similar orbital configurations with inner periods of 11.23 d and 8.70 d and outer periods of 9.79 yr and 9.24 yr. We report also radial velocity measurements of the components of the visual binary CPD-60{\deg}944 in NGC2516. Including results from previous works, this cluster would harbor 5 hierarchical triples. The young system HD315031 has an inner binary with a period of 1.37 d and a very eccentric (e=0.85) outer orbit with a period of 483 d. Possible dynamical evolutionary scenarios are discussed. Long-term radial velocity monitoring is highlighted as strategy for the detection of subsystems with intermediate separations, which are hard to cover with normal spectroscopic studies or visual techniques.

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.

Doppler Tomographic Observations of Kepler-13b

AbstractWe present Doppler tomographic observations of the transiting planet Kepler-13b (aka KOI-13b), a highly inflated hot Jupiter orbiting the Teff=8500 K primary of a hierarchical triple stellar system. As the planet transits the rapidly rotating host star, it successively blocks regions of the stellar disk with different radial velocities, causing a “bump” in the stellar spectral line shape, which we resolve spectroscopically. The manner in which this perturbation moves across the stellar line during the transit gives information on the relative alignment between the stellar spin and planetary orbital angular momentum vectors. This is a powerful statistical probe of planetary migration processes, as the expected spin-orbit misalignment distributions from dynamically cold migration (disk interactions) and dynamically hot migration (planet-planet scattering, Kozai cycles) are significantly different: the former will lead to primarily aligned orbits; the latter to a wide distribution. Doppler tomography also promises to be a powerful technique for confirming transiting planet candidates around rapidly rotating stars like Kepler-13A, which are not amenable to radial velocity follow-up and thus are currently a poorly sampled region of parameter space.

Mean motion resonances and the stability of a circumbinary disk in a triple stellar system

We numerically investigated the orbital stability of a circumbinary disk in a 3-D triple stellar system. We verified that there is a stable region (protected region) in which highly eccentric and/or inclined orbits can remain stable. In this paper we identify two-body mean motion resonances as a powerful mechanism to increase the eccentricity of the particle on short time-scales (10 kyr or less) and produce a longer-lived high-eccentricity population. These resonances are of high order and have not been previously considered in triple stellar systems. We show that this powerful mechanism can lead to regions containing instabilities and gaps. This process also produces a number of highly eccentric particles whose orbits remain stable. We show that there are limit values of eccentricity and semi-major axis for an orbit to be within the stability region. These quantities represent the dynamical effects of the inner binary and third star companion on a circumbinary disk. The value of this limit depends on the system parameters and should be considered in estimates of the stability, formation, and survival of bodies in triple systems.