Hierarchical Triple System Research Articles

Verification of Gaia Data Release 3 Single-lined Spectroscopic Binary Solutions With Three Transiting Low-mass Secondaries

While secondary mass inferences based on single-lined spectroscopic binary (SB1) solutions are subject to degeneracies, this degeneracy can be lifted through the observations of eclipses. We combine the subset of Gaia Data Release 3 SB1 solutions consistent with brown dwarf-mass secondaries with the Transiting Exoplanet Survey Satellite (TESS) Object of Interest (TOI) list to identify three candidate transiting brown dwarf systems. Ground-based precision radial velocity follow-up observations confirm that TOI-2533.01 is a transiting brown dwarf with orbiting TYC 2010-124-1 and that TOI-5427.01 is a transiting very low-mass star with orbiting UCAC4 515-012898. We validate TOI-1712.01 as a very low-mass star with transiting the primary in the hierarchical triple system BD+45 1593. Even after accounting for third light, TOI-1712.01 has a radius nearly a factor of 2 larger than predicted for isolated stars with similar properties. We propose that the intense instellation experienced by TOI-1712.01 diminishes the temperature gradient near its surface, suppresses convection, and leads to its inflated radius. Our analyses verify Gaia DR3 SB1 solutions in the low Doppler semiamplitude limit, thereby providing the foundation for future joint analyses of Gaia radial velocities and Kepler, K2, TESS, and PLAnetary Transits and Oscillations light curves for the characterization of transiting massive brown dwarfs and very low-mass stars.

Mass Ratio Distribution of Hierarchical Triple Systems from the LAMOST-MRS Survey

Hierarchical triple-star systems consists of three components organized into an inner binary (M 1, M 2) and a more distant outer tertiary (M 3) star. The LAMOST Medium-Resolution Spectroscopic Survey has offered a great sample for the study of triple-system populations. We used the peak amplitude ratio method to obtain the mass ratio (q in, q out) of a triple system from its normalized spectrum. By calculating the cross-correlation function, we determined the correlation between the mass ratio q out (M 3/(M 1 + M 2)) and the amplitude ratio (A 3/(A 1 + A 2)). We derived a q in of 0.5–1.0 and a q out between 0.2 and 0.8. By fitting a power-law function of the corrected q in distribution, γ in is estimated to be −0.654 ± 2.915, 4.304 ± 1.125, and 11.371 ± 1.309 for A-, F-, and G-type stars. The derived γ in values increase as the mass decreases, indicating that less massive stars are more likely to have companion stars with similar masses. By fitting a power-law function of the corrected q out distribution, γ out is estimated to be −2.016 ± 0.172, −1.962 ± 0.853, and −1.238 ± 0.141 for G-, F-, and A-type stars, respectively. The γ out values show a trend of growth toward lower primary star masses.

Solaris photometric survey: Search for circumbinary companions using eclipse timing variations

ABSTRACT Eclipse timing variations (ETVs) have been a successful tool for detecting circumbinary companions to eclipsing binaries (EBs). While TESS and Kepler have been prolific for ETV searches, they sometimes can be limited by time and sky coverage, a limitation that can be addressed by specialized ground-based ETV surveys. We present the initial results from the Solaris photometric survey, which uses four 0.5-m robotic telescopes in the Southern hemisphere to look for circumbinary companions. We present the method of light-curve extraction, detrending, and EB modelling using observations from the Solaris network. Using these light curves, we extract precise eclipse timings for seven EBs and look for companions using a Lomb–Scargle periodogram search. We find two possible periodic signals for the target GSC 08814–01026. With the system having strong activity, we check for the feasibility of orbital solutions at these two periods. We find that the 245 ± 1 d period is due to an M dwarf-mass companion. This makes GSC 08814–01026 a candidate compact hierarchical triple system. The other periodic signal at 146 ± 1 d is an artefact of stellar activity.

The main evolutionary pathways of massive hierarchical triple stars

Context. So far, stellar population studies have mainly focused on the evolution of single and binary stars. Recent observations show that triple and higher order multiple star systems are ubiquitous in the local population, especially among massive stars. Introducing three-body dynamical effects can influence the evolution of an individual stellar system and can therefore affect the predicted rates of astrophysical sources that are a product of stellar evolution. Therefore, predictions of triple star evolution are necessary for a more complete understanding of the evolutionary behaviour of stellar populations and their end products. Aims. We aim to constrain the main evolutionary pathways of massive hierarchical triple star systems and to quantify the effect of the third star on the evolution of the system. Methods. We model the massive triple star population by performing simulations of triple star evolution with the TRES code, which combines stellar evolution with secular evolution of triple systems, and explore how robust the predictions of these simulations are under variations of uncertain initial conditions. We focus on coeval, hierarchical stellar triples in pre-mass-transfer phases. Results. Interactions are common among massive triple stars. The majority of systems (65%–77%) experience a phase of mass transfer in the inner binary, often with a main sequence donor star. This differs significantly from isolated binary evolution, where mass transfer is less frequent (52.3% instead of 67% for our fiducial model) and the donors are typically post-main sequence stars. Initial constraints for dynamical stability as well as eccentricity oscillations driven by the third body facilitate the occurrence of interactions, such as mass transfer. The requirement of dynamical stability at formation places quite stringent constraints on allowed orbital properties, reducing uncertainties in triple evolution that resort from these initial conditions. Ignoring three-body dynamics during evolution of non-interacting triples leads to triple compact-object systems with stronger eccentricity oscillations and thereby likely over-predicts the merger rate of compact objects in such systems.

Dynamics of supermassive black hole triples in the ROMULUS25 cosmological simulation

For a pair of supermassive black holes (SMBHs) in the remnant of a dual galaxy merger, well-known models exist to describe their dynamical evolution until the final coalescence accompanied by the emission of a low-frequency gravitational wave signal. In this article, we investigate the dynamical evolution of three SMBH triple systems recovered from the ROMULUS25 cosmological simulation to explore common dynamical evolution patterns and assess typical coalescence times. For this purpose, we construct initial conditions from the ROMULUS25 data and perform high-resolution gravitodynamical N-body simulations. We track the orbital evolution from the galactic inspiral to the formation of hard binaries at sub-parsec separation and use the observed hardening rates to project the time of coalescence. In all cases, the two heaviest black holes form an efficiently hardening binary that merges within fractions of the Hubble time. The lightest SMBH either gets ejected, forms a stable hierarchical triple system with the heavier binary, forms a hardening binary with the previously merged binary’s remnant, or remains on a wide galactic orbit. The coalescence times of the lighter black holes are thus significantly longer than for the heavier binary, as they experience lower dynamical friction and stellar hardening rates. We observe the formation of hierarchical triples when the density profile of the galactic nucleus is sufficiently steep.

NY Bootes: An Active Deep and Low-mass-ratio Contact Binary with a Cool Companion in a Hierarchical Triple System

The first detailed photometric and spectroscopic study of G-type short-period binary NY Boo is presented. The radial velocity curve was obtained by the cross-correlation function (CCF) method based on LAMOST and SDSS spectra, which derived its mass ratio as q = 0.139(1/7.2). The CCF profiles of the SDSS spectra clearly show the existence of a cool third component, which is supported by the results of the orbital period investigation. The period study based on the O-C analysis indicates that besides a long-term decrease, the orbital period has a periodic oscillation due to the light-travel time effect caused by a third body. When the third light contribution is consistent with the CCF results, the orbit of the third body and the inner pair are non-coplanar with m 3 = 0.31 M ⊙. Combining with the TESS light curves, it is found that the target is a deep and low-mass-ratio contact binary (DLMRCB) with a fill-out factor of f = 73%. The notable asymmetry in light curves was detected and explained by the spot model very well. The spectroscopic profiles, the cyclic variation in the O-C diagram, and the radial velocity curve and light-curve solutions all suggest that NY Boo is a hierarchical triple system with a cool tertiary component orbiting around an active DLMRCB. With the orbital period shrinking, the binary may eventually merge. The period of NY Boo decreases faster than other shrinking DLMRCB, together with active inner pair and non-coplanar tertiary component, making NY Boo an important target for studying the late evolution of binaries.

Discovery of two rotational modulation periods from a young hierarchical triple system

Discovery of two rotational modulation periods from a young hierarchical triple system

G 68-34: A Double-lined M-dwarf Eclipsing Binary in a Hierarchical Triple System

Using high-resolution spectra from the Tillinghast Reflector Echelle Spectrograph and photometry from sector 56 of the Transiting Exoplanet Survey Satellite, we report that the nearby M dwarf G 68-34 is a double-lined eclipsing binary. The pair is spin–orbit synchronized with a period of 0.655 days. The light curve shows significant spot modulation with a larger photometric amplitude than that of the grazing eclipses. We perform a joint fit to the spectroscopic and photometric data, obtaining masses of 0.3280 ± 0.0034M ⊙ and 0.3207 ± 0.0036M ⊙ and radii of 0.345 ± 0.014R ⊙ and 0.342 ± 0.014R ⊙ after marginalizing over unknowns in the starspot distribution. This system adds to the small but growing population of fully convective M dwarfs with precisely measured masses and radii that can be used to test models of stellar structure. The pair also has a white-dwarf primary at 9″ separation, with the system known to be older than 5 Gyr from the white-dwarf cooling age. The binarity of G 68–34 confirms our hypothesis from Pass et al.: in that work, we noted that G 68-34 was both rapidly rotating and old, highly unusual given our understanding of the spin-down of M dwarfs, and that a close binary companion may be responsible.

Effect of Orbital Characteristic of Inclined Third-body on Motion of Secondary-body for a Hierarchical Triple Systems

The influence of a third-body’s orbital elements on the second-body’s motion in a hierarchical triple system is a crucial problem in astrophysics. Most prolonged evaluation studies have focused on a distant zero-inclined third-body. This study presents a new perspective on second-body motion equations that addresses a perturbing-body in an elliptic orbit derived with consideration of the axial-tilt (obliquity) of the primary. The proposed model is compared by the dual-averaged method and the N-body problem algorithm. After validation, a generalized three-body model is derived to investigate the effects of the third-body’s orbital elements on secondary-body motion behavior. The proposed model considers short-time oscillations that affect secular evaluation and applies to exoplanets with all the primary and third body eccentricities, inclinations, and mass ratios. It is shown that the obliquity of the primary (or third-body’s inclination) must be considered for precise long-term assessment, even in highly-hierarchical systems.

Hidden Companions to Nearby Intermediate-mass Stars. I. Discovery of a 0.82M ⊙, 15 au Companion to the Resolved 0.4 au Spectroscopic Binary in HIP 67199* *Based on observations collected at the European Southern Observatory, Chile, Program ID 102.D-0817(C)

Further discoveries and detailed studies of close binaries of intermediate-mass stars in hierarchical triple systems are needed in order to understand their formation. Here we report the discovery of a 0.82M ⊙ companion to the intermediate mass spectroscopic binary HIP 67199 at a projected separation of 150 mas ↔ 15 au based on a VLTI/GRAVITY observation. In addition, the spectroscopic binary was spatially resolved with a projected separation 1.70 mas ↔ 0.18 au and inferred masses 1.84M ⊙ + 1.72M ⊙. Further observations can determine the amplitude of eccentricity oscillations in the inner system induced by the third star. HIP 67199 is a potential progenitor for a double white dwarf hiding within the glow of a main-sequence companion.

Discovery of a 0.58M ⊙, 0.9 au Companion to HIP 42313 = δ Hya* *Based on observations collected at the European Southern Observatory, Chile, Program ID 110.241W.002.

In spite of them being the main progenitors of white dwarfs, the multiplicity of intermediate mass stars is relatively less explored when compared to solar-type and O-type stars. Here we report the discovery of a new companion to the nearby 2.43M ⊙ A1V star HIP 42313 = δ Hya with a K band flux ratio of 1.3% based on a VLTI/GRAVITY interferometric observation. This new 0.58M ⊙ companion at a projected separation 16.7 mas ↔ 0.90 au explains both the Hipparcos-GaiaDR2 as well as the GaiaDR2-GaiaDR3 proper motion changes of δ Hya. Together with the previously known 0.44M ⊙ companion at ρ = 2.″7 ↔ 147 au, this makes δ Hya a hierarchical triple system.

The Hamiltonian for von Zeipel–Lidov–Kozai oscillations

ABSTRACTThe Hamiltonian used in classical analyses of von Zeipel–Lidov–Kozai or ZLK oscillations in hierarchical triple systems is based on the quadrupole potential from a distant body on a fixed orbit, averaged over the orbits of both the inner and the outer bodies (‘double averaging’). This approximation can be misleading, because the corresponding Hamiltonian conserves the component of angular momentum of the inner binary normal to the orbit of the outer binary, thereby restricting the volume of phase space that the system can access. This defect is usually remedied by including the effects of the octopole potential, or by allowing the outer orbit to respond to variations in the inner orbit. However, in a wide variety of astrophysical systems, non-linear perturbations are comparable to or greater than these effects. The long-term effects of non-linear perturbations are described by an additional Hamiltonian, which we call Brown’s Hamiltonian. At least three different forms of Brown’s Hamiltonian are found in the literature; we show that all three are related by a gauge freedom, although one is much simpler than the others. We argue that investigations of ZLK oscillations in triple systems should include Brown’s Hamiltonian.

Tidal deformations of a binary system induced by an external Kerr black hole

The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this work, for the Kerr black hole, we derive the electric and magnetic tidal moments at quadrupole order, where the latter are computed for the first time in full generality. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extreme-mass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. Our treatment includes strong gravitational effects beyond the post-Newtonian approximation both for the binary system and for the tidal forces since the binary system is allowed to be close to the event horizon of the Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gauge invariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. Our results are relevant for the astrophysical situation in which the binary system is in the vicinity of a supermassive black hole.

Observable tertiary tides in TIC242132789

ABSTRACT Many stars live in hierarchical triple systems, but the physics of such systems are still poorly understood. One understudied physical aspect of these systems is tertiary tides, wherein the tidal deformation of a tertiary in a hierarchical triple drains energy from the inner binary, causing the inner binary’s orbital separation to decrease. This tidal process is difficult to observe directly, since such an observation requires a very compact hierarchical triple, the tertiary of which must be almost large enough to fill its Roche lobe at the epoch of observation. Concurrently, the recently discovered stellar system TIC242132789 is the fourth most compact observed hierarchical triple, and the most compact in which the tertiary is a giant. In this paper, we demonstrate that TIC242132789 provides a rare opportunity to place constraints on the model parameters for tertiary tides, and can even be a rare opportunity to directly observe tertiary-tides-induced orbital shrinkage of the inner binary. We calculate our expectations of how fast the inner orbit will shrink, and demonstrate that our estimates of this rate of shrinkage should be observable using current techniques. We conclude with a call for relevant observations of this system to commence.

Wide Binaries from GAIA EDR3: preference for GR over MOND?

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt to emulate dark matter. These systems should be entirely Newtonian according to standard dark-matter theories, while the predictions for MOND-like theories are distinctly different, if the various observational issues can be overcome. Here we provide an updated version of our 2019 study using the recent GAIA EDR3 data release: we select a large sample of 73 159 candidate wide binary stars with distance <300 parsec and magnitudes G<17 from GAIA EDR3, and estimate component masses using a main-sequence mass-luminosity relation. We then examine the frequency distribution of pairwise relative projected velocity (relative to circular-orbit value) as a function of projected separation, compared to simulations; as before, these distributions show a clear peak at a value close to Newtonian expectations, along with a long 'tail' which extends to much larger velocity ratios and may well be caused by hierarchical triple systems with an unresolved or unseen third star. We then fit these observed distributions with a simulated mixture of binary, triple and flyby populations, for GR or MOND orbits, and find that standard gravity is somewhat preferred over one specific implementation of MOND; though we have not yet explored the full parameter space of triple population models and MOND versions. Improved data from future GAIA releases, and followup of a subset of systems to better characterise the triple population, should allow wide binaries to become a decisive test of GR vs MOND in the future.

Tidal perturbations and eclipse mapping in the pulsations in the hierarchical triple system U Gru

Context. Unambiguous examples of the influence of tides on self-excited, free stellar pulsations have recently been observationally detected in space-based photometric data. Aims. We aim to investigate U Gru and contextualise it within the growing class of tidally influenced pulsators. An initial analysis of U Gru revealed frequencies spaced by the orbital frequency that are difficult to explain by currently proposed tidal mechanisms. Methods. We reinvestigate the TESS photometry for U Gru alongside new UVES spectroscopy. We analyse the UVES spectroscopy with least-squares deconvolution and spectral disentangling techniques, and perform an atmospheric analysis. We remove the binary signature from the light curve using an effective model in order to investigate the pulsation signal in the residuals. We track the amplitudes and phases of the residual pulsations as a function of the orbital period to reveal their tidal influence. Results. We establish that U Gru is likely a hierarchical triple system. We identify a single p-mode oscillation that exhibits amplitude and phase variation over the binary orbit. We propose a toy model to demonstrate that the series of frequencies separated by the orbital frequency can be reproduced by eclipse mapping. We find no evidence of modulation to the other independent oscillation modes. Conclusions. We demonstrate that U Gru hosts at least one tidally perturbed pulsation. Additionally, we argue that eclipse mapping of the dominant, tidally perturbed mode can produce the series of frequencies separated by the observed orbital frequency. Our simulations show that the effects of eclipse mapping are mode dependent, and are not expected to produce an observable signature for all pulsation modes in an eclipsing binary.

The Binary and the Disk: The Beauty is Found within NGC3132 with JWST

The planetary nebula (PN) NGC 3132 is a striking example of the dramatic but poorly understood mass-loss phenomena that (1–8) M ⊙ stars undergo during their death throes as they evolve into white dwarfs (WDs). From an analysis of JWST multiwavelength (0.9–18 μm) imaging of NGC 3132, we report the discovery of an extended dust cloud around the WD central star (CS) of NGC 3132, seen most prominently in the 18 μm image, with a surface-brightness-limited radial extent of ≳2″. We show that the A2V star located 1.″7 to CS’s northeast (and 0.75 kpc from Earth) is gravitationally bound to the latter, as evidenced by the detection of relative orbital angular motion of 0.°24 ± 0.°045 between these stars over ∼20 yr. Using aperture photometry of the CS extracted from the JWST images, together with published optical photometry and an archival UV spectrum, we have constructed the spectral energy distribution (SED) of the CS and its extended emission over the UV to mid-IR (0.091–18 μm) range. We find that fitting the SED of the CS and the radial intensity distributions at 7.7, 12.8, and 18 μm with thermal emission from dust requires a cloud that extends to a radius of ≳1785 au, with a dust mass of ∼1.3 × 10−2 M ⊕ and grains that are 70% silicate and 30% amorphous carbon. We propose plausible origins of the dust cloud and an evolutionary scenario in which a system of three stars—the CS, a close low-mass companion, and a more distant A2V star—forms a stable hierarchical triple system on the main sequence but becomes dynamically unstable later, resulting in the spectacular mass ejections that form the current, multipolar PN.

Lagrange versus Lyapunov Stability of Hierarchical Triple Systems: Dependence on the Mutual Inclination between Inner and Outer Orbits

While there have been many studies examining the stability of hierarchical triple systems, the meaning of “stability” is somewhat vague and has been interpreted differently in previous literatures. The present paper focuses on “Lagrange stability,” which roughly refers to the stability against the escape of a body from the system, or “disruption” of the triple system, in contrast to “Lyapunov-like stability,” which is related to the chaotic nature of the system dynamics. We compute the evolution of triple systems using direct N-body simulations up to 107 P out, which is significantly longer than previous studies (with P out being the initial orbital period of the outer body). We obtain the resulting disruption timescale T d as a function of the triple orbital parameters with particular attention to the dependence on the mutual inclination between the inner and outer orbits, i mut. By doing so, we have clarified explicitly the difference between Lagrange and Lyapunov stabilities in astronomical triples. Furthermore, we find that the von Zeipel–Kozai–Lidov oscillations significantly destabilize inclined triples (roughly with 60° < i mut < 150°) relative to those with i mut = 0°. On the other hand, retrograde triples with i mut > 160° become strongly stabilized with much longer disruption timescales. We show the sensitivity of the normalized disruption timescale T d/P out to the orbital parameters of triple system. The resulting T d/P out distribution is practically more useful in a broad range of astronomical applications than the stability criterion based on the Lyapunov divergence.

Parameter distributions of binary black hole mergers near supermassive black holes as seen by advanced gravitational wave detectors

ABSTRACT The environment surrounding supermassive black holes (SMBHs) in galactic nuclei (GNs) is expected to harbour stellar-mass binary black hole (BBH) populations. These binaries were suggested to form a hierarchical triple system with the SMBH, and gravitational perturbations from the SMBH can enhance the mergers of BBHs through Lidov–Kozai (LK) oscillations. Previous studies determined the expected binary parameter distribution for this merger channel in single GNs. Here, we account for the different spatial distribution and mass distribution models of BBHs around SMBHs and perform direct high-precision regularized N-body simulations, including Post-Newtonian (PN) terms up to order PN2.5, to model merging BBH populations in single GNs. We use a full inspiral-merger-ringdown waveform model of BBHs with non-zero eccentricities and take into account the observational selection effect to determine the parameter distributions of LK-induced BBHs detected with a single advanced gravitational-wave (GW) detector from all GNs in the Universe. We find that the detected mergers’ total binary mass distribution is tilted towards lower masses, and the mass ratio distribution is roughly uniform. The redshift distribution peaks between ∼0.15 and 0.55, and the vast majority of binaries merge within redshift ∼1.1. The fraction of binaries entering the LIGO/Virgo/KAGRA band with residual eccentricities &amp;gt;0.1 is below $\sim 10 {{\ \rm per\ cent}}$. We identify a negative correlation between residual eccentricity and mass parameters and a negative correlation between residual eccentricity and source distance. Our results for the parameter distributions and correlations among binary parameters may make it possible to disentangle this merger channel from other BBH merger channels statistically.

KIC 7955301: A hierarchical triple system with eclipse timing variations and an oscillating red giant

KIC 7955301 is a hierarchical triple system with clear eclipse timing and depth variations that was discovered by the Kepler satellite during its original mission. It is composed of a non-eclipsing primary star at the bottom of the red giant branch (RGB) on a 209-day orbit with a K/G-type main-sequence (MS) inner eclipsing binary (EB), orbiting in 15.3 days. This system was noted for the large amplitude of its eclipse timing variations (ETVs, over 4 h), and the detection of clear solar-like oscillations of the red-giant (RG) component, including p-modes of degree up to l = 3 and mixed l = 1 modes. The system is a single-lined spectroscopic triple, meaning that only spectral lines from the RG are detected. We performed a dynamical model by combining the 4-year-long Kepler photometric data, ETVs, and radial-velocity data obtained with the high-resolution spectrometers ARCES, of the 3.5 m ARC telescope at Apache Point observatory, and SOPHIE, of the 1.93 m telescope at Haute-Provence Observatory. The “dynamical” mass of the RG component was determined with a 2% precision at 1.30−0.02+0.03 M⊙. We performed asteroseismic modeling based on the global seismic parameters and on the individual frequencies. Both methods provide an estimate of the mass of the RG that matches the dynamical mass within the uncertainties. Asteroseismology also revealed the rotation rate of the core (≈15 days), the envelope (∼150 days), and the inclination (∼75°) of the RG. Three different approaches led to an estimation of the age between 3.3 and 5.8 Gyr, which highlights the difficulty of determining stellar ages despite the exceptional wealth of information available for this system. On short timescales, the inner binary exhibits eclipses with varying depths during a 7.3-year long interval, and no eclipses during the consecutive 11.9 years. This is why Kepler could detect its eclipses but TESS cannot, and the future ESA PLATO mission should detect these. In the long term, the system appears to be stable and owes its evolution to the evolution of its individual components. This triple system could end its current smooth evolution by merging by the end of the RGB of the primary star because the periastron distance is ≈142 R⊙, which is close to the expected radius of the RG at the tip of the RGB.