Triple Star Research Articles

Searching for compact hierarchical triple system candidates in astrometric binaries and accelerated solutions

Compact hierarchical triple (CHT) systems, where a tertiary component orbits an inner binary, provide critical insights into stellar formation and evolution. Despite their importance, the detection of such systems, especially compact ones, remains challenging due to the complexity of their orbital dynamics and the limitations of traditional observational methods. This study aims to identify new CHT star systems among \ astrometric binaries and accelerated solutions by analysing the radial velocity (RV) amplitude of these systems, thereby improving our understanding of stellar hierarchies. We selected a sample of bright astrometric binaries and accelerated solutions from the DR3 Non-Single Stars catalogue. The RV peak-to-peak amplitude was used as an estimator, and we applied a new method to detect potential triple systems by comparing the RV-based semi-amplitude with the astrometric semi-amplitude. We used available binary and triple star catalogues to identify and validate candidates, with a subset confirmed through further examination of the RV and astrometric data. Our analysis resulted in the discovery of $956$ CHT candidates among the orbital sources as well as another $3,115$ probable close binary sources in stars with accelerated solutions. Exploring the inclination, orbital period, and eccentricity of the outer companion in these CHT systems provides strong evidence of mutual orbit alignment, as well as a preference towards moderate outer eccentricities. Our novel approach has proven effective in identifying potential triple systems, thereby increasing their number in the catalogues. Our findings emphasise the importance of combined astrometric and RV data analysis in the study of multiple star systems.

Black hole-black hole mergers with and without an electromagnetic counterpart: A model for stable tertiary mass transfer in hierarchical triple systems

Triple stars are prevalent within the population of observed stars. Their evolution compared to binary systems is notably more complex and is influenced by unique dynamical, tidal, and mass transfer processes inherent in higher order multiples. Understanding these phenomena is essential for comprehensive insight into multistar evolution and the formation of energetic transients, including gravitational wave (GW) mergers. Our study aims to probe the evolution of triple star systems when the tertiary component fills its Roche lobe and transfers mass to the inner binary. Specifically, we focus on the impact of tertiary mass transfer on the evolution of the inner orbit and investigate whether it could lead to the formation of GW sources with distinct properties. To achieve this, we developed an analytical model that describes the evolution of the inner and outer orbits of hierarchical triples undergoing stable mass transfer from the tertiary component. We have publicly released this model as a python package on Zenodo. Utilising population synthesis simulations, we investigated triples with a Roche-lobe filling tertiary star and an inner binary black hole (BBH). These systems stem from inner binaries experiencing chemically homogeneous evolution (CHE). Our analysis encompasses two distinct populations with metallicities of $Z=0.005$ and $Z=0.0005$, focusing on primary components in the inner binary with initial masses ranging from 20 to $100\ M odot $ and inner and outer orbital separations of up to $40\ R odot $ and $10^5\ R odot $, respectively, targeting the parameter space where chemically homogeneous evolution is anticipated. Our results indicate that for the systems we studied, the mass transfer phase predominantly leads to orbital shrinkage of the inner binary and evolution towards non-zero eccentricities and is accompanied by an expansion of the outer orbit. In the systems where the inner binary components evolve in a chemically homogeneous manner, 9.5<!PCT!> result in mass transfer from the tertiary onto an inner BBH. Within this subset, we predict a high formation efficiency of GW mergers ranging from 85.1<!PCT!> to 100<!PCT!> at $Z=0.005$ and 100<!PCT!> at $Z=0.0005$ with short delay times, partly attributable to the mass transfer phase. Owing to the rarity of triples with a CHE inner binary in the stellar population, we project local merger rates in the range of 0.69 to 1.74 $ Gpc^ $. Of the prospected BBH mergers that enter the LISA and aLIGO frequency band due to GW emission, a fraction is still accreting gas from the tertiary star. This could produce a strong electromagnetic (EM) counterpart to the GW source and maintain high eccentricities as the system enters the frequency range detectable by GW detectors. The occurrence of EM signals accompanying mergers varies significantly depending on model assumptions, with fractions ranging from less than 0.03<!PCT!> to as high as 46.8<!PCT!> of all mergers if the formation of a circumbinary disc is allowed.

The rotation rate of single- and double-lined southern O stars. Determining what increases the rotation rate in binaries

We determined the projected rotational velocity ($v i$) of 238 southern O stars selected from the Galactic O-star Survey. The sample contains 130 spectroscopic single stars (C) single-lined binaries (SB1), and SB2 systems (including eight triples). We applied the Fourier method to high-resolution spectra taken at Cerro Murphy, Chile, and supplemented by archival spectra. The overall $v i$ statistics peaks at slow rotators (40-100\,km/s) with a tail towards medium (100-200\,km/s) and fast rotators (200-400\,km/s). Binaries, on average, show increased rotation, which differs for close orb < 10$\,d) and wide binaries (10\,d $< orb <$ 3700\,d), and for primaries and secondaries. The spin-up of close binaries is well explained by the superposition of spin-orbit synchronisation and mass transfer via Roche-lobe overflow. The increased rotation of wide binaries, however, needs another explanation. Therefore, we discuss various spin-up mechanisms. Timescale arguments lead us to favour a scenario where wide O binaries are spun-up by a combination of cloud or disk fragmentation, which lays the basis of triple and multiple stars, and the subsequent merging or swallowing of low-mass by higher-mass stars or proto-stars.

Triple trouble with PSR J1618−3921: Mass measurements and orbital dynamics of an eccentric millisecond pulsar

Context. PSR J1618−3921 is one of five known millisecond pulsars (MSPs) in eccentric orbits (eMPSs) located in the Galactic plane, whose formation is poorly understood. Earlier studies of these objects revealed significant discrepancies between observations and predictions from standard binary evolution scenarios of pulsar-helium white dwarf (HeWD) binaries, especially in the case of PSR J0955−6150, for which mass measurements ruled out most eMSP formation models. Aims. We aim to measure the masses of the pulsar and its companion, and constrain the orbital configuration of PSR J1618−3921. This facilitates understanding similarities among eMSPs and could offer hints as to their formation mechanism. Methods. We conducted observations with the L-band receiver of the MeerKAT radio telescope and the UWL receiver of the Parkes Murriyang radio telescope between 2019 and 2021. These data were added to archival Parkes and Nançay observations. We performed a full analysis on this joint data set with a timing baseline of 23 years. We also used the data from recent observations to give a brief account of the emission properties of J1618−3921, including a rotating vector model (RVM) fit of the linear polarisation position angle of the pulsar. Results. From the timing analysis, we measure a small but significant proper motion of the pulsar. The long timing baseline allowed for a highly significant measurement of the rate of advance of periastron of ω̇ = (0.00145±0.00010)°yr−1. Despite the tenfold improvement in timing precision from MeerKAT observations, we can only report a low-significance detection of the orthometric Shapiro delay parameters, h3 = 2.70−1.47+2.07 μs and ς = 0.68−0.09+0.13. Under the assumption of the validity of general relativity (GR), the self-consistent combination of these three parameters leads to mass estimates of the total and individual masses in the binary of Mtot = 1.42−0.19+0.20 M⊙, Mc = 0.20−0.03+0.11 M⊙, and Mp = 1.20−0.20+0.19 M⊙. We detect an unexpected change in the orbital period of Ṗb = −2.26−0.33+0.35 × 10−12, that is an order of magnitude larger and carries an opposite sign to what is expected from the Galactic acceleration and the Shklovskii effect, which are a priori the only non-negligible contributions expected for Ṗb. We also detect a significant second derivative of the spin frequency, f̈. The RVM fit reveals a viewing angle of ζ = (111 ± 1)°. Furthermore, we report an unexpected, abrupt change in the mean pulse profile in June 2021 of unknown origin. Conclusions. We propose that the anomalous Ṗb and f̈ we measure for J1618−3921 indicate an additional varying acceleration due to a nearby mass. The J1618−3921 binary system is likely part of a hierarchical triple, but with the third component much farther away than the outer component of the MSP in a triple star system, PSR J0337+1715. This finding suggests that at least some eMSPs might have formed in triple star systems. Although the uncertainties are large, the binary companion mass is consistent with the Pb − MWD relation, which has been verified for circular HeWD binaries and also for the two HeWDs in the PSR J0337+1715 system. Future regular observations with the MeerKAT telescope will, due to the further extension of the timing baseline, improve the measurement of Ṗb and f̈. This will help us further understand the nature of this system, and perhaps improve our understanding of eMSPs in general.

On Radio k – Chromatic Number for Mycielski of Some Graphs

Objectives: In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. Methods : This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proximity to one another. For a graph , with node set , edge set and an integer , a radio k - coloring of is a function satisfying the condition for any two nodes and , where is the distance between and in . The radio k - coloring of , is the maximum color assigned to any node of and it is denoted by . The radio k -chromatic number of is the minimum value of taken over all radio k - coloring of and it is denoted by . Findings: This study obtained the radio k-chromatic number for Mycielski of some graphs for and 3 Novelty: To solve the channel assignment problem in radio transmitters, the interference graph is developed, and the channel assignment has been converted into a graph coloring. Reducing the interference by a radio k - coloring problem will motivate many researchers to find the radio k - coloring in various graphs. Keywords: Radio k – Coloring, Mycielski graph, Double Star graph, Triple Star graph, Sunlet graph, Helm graph and Closed Helm graph

On Total Coloring of Triple Star and Lobster Graphs

On Total Coloring of Triple Star and Lobster Graphs

Eclipse-timing study of new hierarchical triple star candidates in the northern continuous viewing zone of TESS (Corrigendum)

Eclipse-timing study of new hierarchical triple star candidates in the northern continuous viewing zone of TESS (<i>Corrigendum</i>)

Control and Performance Analysis of an Indirect Matrix Converter Fed Triple Star Induction Motor

Efficient operation is a recommended factor in most of industrial applications. In this paper, an indirect matrix converter (IMC) topology is developed and proposed to substitute the classical (AC/DC/AC) three phase converter topologies; where the control strategy is frequently performed with a voltage source inverter (VSI). Large electrolytic capacitors are viewed as hazardous due to their short lifetime compared to ordinary capacitors and power switches, as well as their contribution to the total bulk and weight of the converter. Matrix converters may be the answer to getting rid of the capacitor, shrinking the converter, and improving its efficiency (MC). These advantages are offset by the fact that the (MC) calls for a tricky switching technique based on pulse width modulation, which is prone to commutation failure. The direct frequency conversion using the indirect matrix converter (IMC) with many advantages has appeared as an alternative to these conventional voltage inverters. This study investigates a field-oriented control (FOC) scheme for indirect matrix converter fed triple star induction motor (TSIM). After building the proposed IMC converter topology, an adequate field-oriented control strategy-based space vector modulation (SVM) is proposed and adapted for the control of the triple star induction motor. The FOC technique guarantees flux and torque decoupling while ensuring good operation performance as required in many industrial applications. The obtained numerical simulation results show and confirm the effectiveness of this control scheme.

Seven new triply eclipsing triple star systems

Aims. We have identified nearly a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. These systems are noteworthy in that we can potentially determine their dynamical and astrophysical parameters with a high precision. In the present paper, we report the comprehensive study of seven new compact triply eclipsing triple star systems taken from this larger sample: TICs 133771812, 176713425, 185615681, 287756035, 321978218, 323486857, and 650024463. Methods. Most of the data for this study come from TESS observations, but two of them have Gaia measurements of their outer orbits, and we obtained supplemental radial velocity (RV) measurements for three of the systems. The eclipse timing variation curves extracted from the TESS data, the photometric light curves, the RV points, and the spectral energy distribution (SED) are combined in a complex photodynamical analysis to yield the stellar and orbital parameters of all seven systems. Results. Four of the systems are quite compact with outer periods in the range of 41–56 days. All of the systems are substantially flat, with mutual inclination angles of ≲2°. Including the systems reported in this work, we have now studied in considerable detail some 30 triply eclipsing triples with TESS, and are accumulating a meaningful census of these systems.

Eclipse-timing study of new hierarchical triple star candidates in the northern continuous viewing zone of TESS

Aims. We compiled a list of more than 3500 eclipsing binaries located in and near the northern continuous viewing zone (NCVZ) of the TESS space telescope that have sufficient TESS photometry to search for additional hidden components in these systems. In addition to discovering their hierarchical nature, we also determined their orbital parameters and analyzed their distributions. Methods. We obtained the TESS light curves of all targets in an automated way by applying convolution-aided differential photometry on the TESS full-frame images from all available sectors up to sector 60. Using a new self-developed Python GUI, we visually confirmed all of these light curves, determined the eclipsing periods of the objects, and calculated their eclipse-timing variations (ETVs). The ETV curves were used in order to search for nonlinear variations that could be attributed to a light travel-time effect (LTTE) or dynamical perturbations caused by additional components in these systems. We preselected 351 such candidates and modeled their ETVs with the analytic formulae of pure LTTE or with a combination of LTTE and dynamical perturbations. Results. We were able to fit a model solution for the ETVs of 135 hierarchical triple candidates, 10 systems of which were known from the literature, and the remaining 125 systems are new discoveries. These systems include some more noteworthy ones, such as five tight triples that are very close to their dynamical stability limit with a period ratio lower than 20, and three newly discovered triply eclipsing triples. We point out that dynamical perturbations occur in GZ Dra, which we found to be a triple, and that the system is one of the most strongly inclined systems known in the literature, with im = 58° ±7°. We also compared the distributions of some orbital parameters from our solutions with those from a previous Kepler sample. Finally, we verified the correlations between the available parameters for systems that have Gaia non-single star orbital solutions with those from our ETV solutions.

Search for Stellar Companions of Exoplanet Host Stars with AstraLux/CAHA 2.2 m

ABSTRACT Stellar multiplicity is a key aspect of exoplanet diversity, as the presence of more than one star in a planetary system can have both devastating and positive effects on its formation and evolution. In this paper, we present the results of a Lucky Imaging survey of 212 exoplanet host stars performed with AstraLux at the 2.2 m telescope of the Centro Astronómico Hispano en Andalucía. The survey includes data from seven observing epochs between August 2015 and September 2020, and data for individual targets from four earlier observing epochs. The targets of this survey are nearby, bright, solar-like stars with high proper motions. In total, we detected 46 co-moving companions of 43 exoplanet host stars. Accordingly, this survey shows that the minimum multiplicity rate of exoplanet host stars is $20 \pm 3~{\rm per\ cent}$. In total, 33 binary and 10 hierarchical triple star systems with exoplanets have been identified. All companions were found to have a common proper motion with the observed exoplanet host stars, and with our astrometry we even find evidence of orbital motion for 28 companions. For all targets, we determine the detection limit and explore the detection space for possible additional companions of these stars. Based on the reached detection limit, additional co-moving companions beyond the detected ones can be excluded around all observed exoplanet host stars. The increasing number of exoplanets discovered in multiple stellar systems suggests that the formation of planets in such systems is by no means rare, but common. Therefore, our study highlights the need to consider stellar multiplicity in future studies of exoplanet habitability.

JWST observations of the Ring Nebula (NGC 6720): I. Imaging of the rings, globules, and arcs

ABSTRACT We present JWST images of the well-known planetary nebula NGC 6720 (the Ring Nebula), covering wavelengths from 1.6 to 25 $\, \mu$m. The bright shell is strongly fragmented with some 20 000 dense globules, bright in H2, with a characteristic diameter of 0.2 arcsec and density nH ∼ 105–106 cm−3. The shell contains a narrow ring of polycyclic aromatic hydrocarbon (PAH) emission. H2 is found throughout the shell and also in the halo. H2 in the halo may be located on the swept-up walls of a biconal polar flow. The central cavity is filled with high-ionization gas and shows two linear structures which we suggest are the edges of a biconal flow, seen in projection against the cavity. The central star is located 2 arcsec from the emission centroid of the cavity and shell. Linear features (‘spikes’) extend outward from the ring, pointing away from the central star. Hydrodynamical simulations reproduce the clumping and possibly the spikes. Around 10 low-contrast, regularly spaced concentric arc-like features are present; they suggest orbital modulation by a low-mass companion with a period of about 280 yr. A previously known much wider companion is located at a projected separation of about 15 000 au; we show that it is an M2–M4 dwarf. NGC 6720 is therefore a triple star system. These features, including the multiplicity, are similar to those seen in the Southern Ring Nebula (NGC 3132) and may be a common aspect of such nebulae.

Observational Detection of Higher-Order Secular Perturbations in Tight Hierarchical Triple Stars

In this work, we search for observational evidence of higher-order secular perturbations in three eclipsing binaries. These are slightly eccentric binaries, and they form the inner pairs of tight, compact, hierarchical triple star systems. Simultaneously, we analyze the high-precision satellite (Kepler and TESS) light curves; eclipse timing variations; combined spectral energy distributions (through catalog passband magnitudes); and, where available, radial velocities of KICs 9714358, 5771589, and TIC 219885468. Besides the determination of the robust astrophysical and dynamical properties of the three systems, we find evidence that the observed unusual eclipse timing variations of KIC 9714358 are a direct consequence of the octupole-order secular eccentricity perturbations forced by unusual, resonant behavior between the lines of the apsides of the inner and outer orbital ellipses. We also show that, despite its evident cyclic eclipse depth variations, KIC 5771589 is an almost perfectly coplanar system (to within 0.3∘), and we explain the rapid eclipse depth variations with the grazing nature of the eclipses. Finally, we find that the inner pair of TIC 219885468 consists of two twin stars; hence, in this triple there are no octupole-order three-body perturbations. Moreover, we show that this triple is also coplanar on the same level as the former one, but due to its deep eclipses, it does not exhibit eclipse depth variations. We intend to follow this work up with further analyses and a quantitative comparison of the theoretical and the observed perturbations.

Astrophysical investigation on the virtual planet pandora in Avatar film

The story of AVATAR happened in an imaginary planet Pandora. It is in the nearest stellar system from us, which is a triple star system located in the constellation Centauri. Currently, only one Earth-size planet has been detected around Proxima Centauri in 2016 by radial velocity technique, and any Jupiter-size planet has been ruled out around all the three stars. The result is in conflict with the scenario in AVATAR film, where Pandora is an Earth-size moon of Polyphemus, a Jupiter-size planet around Centauri B. Earth-size planets in habitable zones around Centauri A and Centauri B are still possible but have not been detected in the precision of current observations. Considering the dynamical complexity of planets in triple star system, which may induce extreme climate change in the possible habitable planets to prohibit development of civilization, we take long-term orbital revolution simulation to explore the stability of Earth-size planet in habitable zones around stars. We focus on habitable planets around Centauri A and Centauri B, as they are close, the average distance between them is small than the size of Solar system. We found that habitable planets with orbits aligned with the binary orbit are long-term stable. However, the orbital eccentricity and inclination changes a lot, if the planetary orbits significantly are tilted with the binary orbit. In comparison with the Milankovitch cycles observed in paleoclimate, we conclude that the titled planets in habitable zone around Centauri A and Centauri B cannot support development of intelligent life.

Compact binary formation in open star clusters – I. High formation efficiency of Gaia BHs and their multiplicities

ABSTRACT Gaia BHs, black hole (BH) binaries discovered from data base of an astrometric telescope Gaia, pose a question to the standard binary evolution model. We have assessed whether Gaia BHs can be formed through dynamical capture in open clusters rather than through isolated binary evolution. We have performed gravitational N-body simulations of 100 open clusters with $10^5 \, \mathrm{M}_\odot$ in total for each metallicity Z = 0.02, 0.01, and 0.005. We have discovered one Gaia BH-like binary escaping from an open cluster, and found that the formation efficiency of Gaia BHs in open clusters ($\sim 10^{-5} \, \mathrm{M}_\odot ^{-1}$) is larger than in isolated binaries ($\sim 10^{-8} \, \mathrm{M}_\odot ^{-1}$) by 3 orders of magnitude. The Gaia BH-like binary is the inner binary of a triple star system. Gaia BHs can have tertiary stars frequently, if they are formed in open clusters. Combining additional N-body simulations with 8000 open clusters with $8 \times 10^6 \, \mathrm{M}_\odot$, we have estimated the number of Gaia BHs in the Milky Way disc to 104–105 (depending on the definitions of Gaia BHs), large enough for the number of Gaia BHs discovered so far. Our results indicate that the discoveries of Gaia BHs do not request the reconstruction of the standard binary evolution model, and that Gaia BHs are a probe for the dynamics of open clusters already evaporated.

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.

Four new compact triply eclipsing triples found with Gaia and TESS

ABSTRACT This paper presents a comprehensive analysis of four triply eclipsing triple star systems, namely TIC 88206187, TIC 14839347, TIC 298714297, and TIC 66893949. The four systems with third-body eclipses were found in the TESS light curves from among a sample of ∼400 matches between known eclipsing binaries and the Gaia DR3 Non-Single Star solution data base. We combined photometric light curves, eclipse timing variations, archival spectral energy distributions, and theoretical evolution tracks in a robust photodynamical analysis to determine the orbital and system parameters. The triples have outer periods of 52.9 d, 85.5 d, 117 d, and 471 d, respectively. All dozen stars have masses ≲ 2.6 M⊙. The systems are quite flat with mutual inclination angles between the inner and outer orbital planes that are all ≲ 4°. The outer mass ratios (q ≡ M3/Mbin) range from 0.39 to 0.76, consistent with our earlier collection of compact triply eclipsing triples. TIC 88206187 exhibits a fractional radius of the outer tertiary component (rB ≡ RB/aout) exceeding 0.1 (only the third such system known), and we consider its future evolution. Finally, we compare our photodynamical analysis results and the orbital parameters given in the Gaia DR3 NSS solutions, indicating decent agreement, but with the photodynamical results being more accurate.

Stability of hierarchical triples – II. The inclination ι = 140° resonance in the stability surface

ABSTRACT The stability of a hierarchical triple star may be decided by a simple criterion, which was derived in Paper I. However, there is a region in the phase space where the stability limit Qmax is raised by a factor of two in a small region of the phase space with respect to the surrounding phase space. The phase space is defined by the inner and outer eccentricities ein and eout, respectively, as well as by the inclination ιtot between the inner and outer orbits. Additional parameters of the phase space are the masses of the three bodies. We study by numerical integration the orbits of over 100 000 triple systems in the resonance region. We find that the instability that causes the high value of Qmax arises from the octupole Kozai–Lidov resonance. This resonance region has rather equal contributions from the quadrupole and octupole terms and leads to secular evolution with an amplitude larger than either of the two oscillations in isolation. The conditions for this situation are best satisfied near the relative inclination ι = 140°. Additionally, the relative orientation of the two orbits plays a decisive role: the resonance is found only at certain values of the orbit’s node line longitude Ω. An analytical approximation of the energy change in a single close encounter between the inner and outer systems suggests a cos 2Ω dependence of Qmax on Ω, which seems to be qualitatively valid. We model Qmax as a function of cos ι and ein by a Gaussian function.

Detection of incipient faults in nine-phase machines: Impact of the star winding configuration

Two approaches are commonly used for modelling and control of nine-phase (triple star) fault-tolerant machines with symmetrical and asymmetrical star winding configurations: The Vector Space Decomposition (VSD) and the decentralized d-q modelling. In this paper, it will be shown how the VSD approach used for machines with an Asymmetrical Star Winding Configuration (ASWC), unlike the decentralized d-q one used for machines with a Symmetrical Star Winding Configuration (SSWC), can be helpful for non-intrusive Fault Detection and Diagnosis (FDD) purposes. Supporting MATLAB/Simulink simulations are discussed.

A crystallizing white dwarf in a sirius-like quadruple system

ABSTRACT The observational signature of core crystallization of white dwarfs has recently been discovered. However, the magnitude of the crystallization-powered cooling delay required to match observed white dwarfs is larger than predicted by conventional models, requiring additional mechanisms of energy release in white dwarf interiors. The most ideal benchmarks for understanding this discrepancy would be bright and nearby crystallizing white dwarfs with total ages that can be externally constrained. In this work, we report that a recently discovered white dwarf is a bound companion to the triple star HD 190412, forming a new Sirius-like system in the solar neighbourhood. The location of HD 190412 C on the Teff − mass diagram implies it is undergoing crystallization, making this the first confirmed crystallizing white dwarf whose total age can be externally constrained. Motivated by the possibility that a cooling delay caused by crystallization can be directly detected for this white dwarf we employ a variety of methods to constrain the age of the system; however, our empirical age anomaly of +3.1 ± 1.9 Gyr is ultimately too imprecise to reach statistical significance, preventing us from making strong constraints to models of white dwarf crystallization. Our results are none the less compatible with the recent hypothesis that 22Ne phase separation is responsible for the excess cooling delay of crystallizing white dwarfs. The discovery of this system at only 32 parsecs suggests that similar benchmark systems are likely to be common; future discoveries may therefore provide powerful tests for models of white dwarf crystallization.