Studies of multiple stellar systems – IV. The triple-lined spectroscopic system Gliese 644

We present a radial velocity study of the triple-lined system Gliese 644 and derive spectroscopic elements for the inner and outer orbits with periods of 2.965 5 and 627 d. We also utilize old visual data, as well as modern speckle and adaptive optics observations, to derive a new astrometric solution for the outer orbit. These two orbits together allow us to derive masses for each of the three components in the system: M _A=0.410±0.028 (6.9 per cent), M _Ba=0.336±0.016 (4.7 per cent), and M _Bb=0.304±0.014 (4.7 per cent) M_⊙. We suggest that the relative inclination of the two orbits is very small. Our individual masses and spectroscopic light ratios for the three M stars in the Gliese 644 system provide three points for the mass–luminosity relation near the bottom of the main sequence, where the relation is poorly determined. These three points agree well with theoretical models for solar metallicity and an age of 5 Gyr. Our radial velocities for Gliese 643 and vB 8, two common proper motion companions of Gliese 644, support the interpretation that all five M stars are moving together in a physically bound group. We discuss possible scenarios for the formation and evolution of this configuration, such as the formation of all five stars in a sequence of fragmentation events leading directly to the hierarchical configuration now observed, versus formation in a small N cluster with subsequent dynamical evolution into the present hierarchical configuration.     

The nearest star of spectral type O3: a component of the multiple system HD 150136

From radial velocities determined in high signal-to-noise digital spectra, we report the discovery that the brightest component of the binary system HD 150136 is of spectral type O3. We also present the first double-lined orbital solution for this binary. Our radial velocities confirm the previously published spectroscopic orbital period of 2.6 d. He  ii absorptions appear double at quadratures, but single lines of N  v and N  iv visible in our spectra define a radial velocity orbit of higher semi-amplitude for the primary component than do the He  ii lines. From our orbital analysis, we obtain minimum masses for the binary components of 27 and  18 M_⊙  . The neutral He absorptions apparently do not follow the orbital motion of any of the binary components, thus they most probably arise in a third star in the system.     

Contribution to the study of F‐G‐K‐M binaries. X. HD 54901, HD 120544 and HD 123280, three nearby F‐type spectroscopic binaries

The orbital elements of HD 54901, HD 120544 and HD 123280, three nearby F‐type spectroscopic binaries, are presented. They are based on observations made between 1982 and 2004 with the CORAVEL instrument of Observatoire de Haute‐Provence. Physical parameters are derived for the two components of HD 54901 (SB2) and for the primaries of HD 120544 and HD 123280. The rotation‐revolution synchronism of the detected components is investigated. Pseudosynchronism is very likely achieved by the F7 V secondary component of HD 54901, whereas the F2/3 IV primary has not yet reached this stage. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-velocity stars from decay of small stellar systems

In this paper we present numerical results on the decay of small stellar systems under different initial conditions (multiplicity 3 ≤  N  ≤ 10, and various mass spectra, initial velocities and initial configurations). The numerical treatment uses the CHAIN1 code (Mikkola &38; Aarseth). Particular attention is paid to the distribution of high-velocity escapers: we define these as stars with velocity above 30 km s⁻¹. These numerical experiments confirm that small N -body systems are dynamically unstable and produce cascades of escapers in the process of their decay. It is shown that the fraction of stars that escape from small dense stellar systems with an escape velocity greater than 30 km s⁻¹ is ∼1 per cent for all systems treated here. This relatively small fraction must be considered in relation to the rate of star formation in the Galaxy in small groups: this could explain some moderately high-velocity stars observed in the Galactic disc and possibly some young stars with relatively high metallicity in the thick disc.     

Application of a probabilistic neural network in radial‐velocity curve analysis of the spectroscopic binary stars HD 152218, HD 143511, HD 27149, and ER Vul

We use an Artificial Neural Network (ANN) to derive the orbital parameters of spectroscopic binary stars. Using measured radial velocity data of four double‐lined spectroscopic binary systems HD 152218, HD 143511, HD 27149, and ER Vul, we find corresponding orbital and spectroscopic elements. Our numerical results are in good agreement with those obtained by others using more traditional methods (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Composite spectra Paper 15: HD 216572, a triple system containing a short-period, double-lined secondary

We analyse 81 optical spectra of the composite-spectrum binary HD 216572, and show that the primary is a cool giant of type G8 III while the secondary is a double-lined binary consisting of two nearly identical B9 dwarfs in a 1.18-d orbit. The inner system undergoes partial eclipses, whose photometry we model to derive the physical parameters of both secondary stars. The outer system does not eclipse. We isolate the combined spectrum of the secondary by spectral subtraction, and from 48 separate radial-velocity measurements of both secondary components we obtain a triple-lined orbit solution from which we determine the individual masses of all three stars and the inclinations of both the inner and the outer orbits. The period of the outer system is 55 d, which is surprisingly short for a giant star, and our detection of small but non-negligible amounts of variable chromospheric emission in the Ca  ii K line is not unlike that detected in other systems with comparably short periods. The secondary components are in a circular orbit and are rotating at about  95 ± 10 km s⁻¹  ; although their surface-to-surface separation is only  4 R_⊙  the stars are not noticeably distorted geometrically by such close proximity. All three stars appear to be in synchronous rotation in their respective orbits. We derive fairly accurate Hertzsprung–Russell diagram positions for all three stars and compare them to evolutionary tracks calculated for the respective stellar masses, but cannot reconcile the age of the cool giant with that of the B stars.     

Degenerate equilibrium states of collisionless stellar systems

We study spherically symmetrical equilibrium states of collisionless stellar systems confined to a spherical box. These equilibrium states correspond to the statistics introduced by Lynden-Bell in his theory of 'violent relaxation', and are described by a Fermi–Dirac distribution function. We compute the corresponding equilibrium diagram and show that a global entropy maximum exists for any accessible control parameter. This equilibrium state shows a pronounced separation between a degenerate core and a halo. We therefore check that degeneracy is able to stop the gravitational collapse (of a collisionless system), and we propose a simple model for the 'core–halo' structure. We also discuss the relevance of our study for real galaxies or other astrophysical systems such as massive neutrinos.     

Optical spectroscopy of X-Mega targets – II. The massive double-lined O-type binary HD 93205

A new high-quality set of orbital parameters for the O-type spectroscopic binary HD 93205 has been obtained combining échelle and coudé CCD observations. The radial velocity orbits derived from the He  ii λ 4686 Å (primary component) and He  i λ 4471 Å (secondary component) absorption lines yield semi-amplitudes of 133±2 and 314±2 km s⁻¹ for each binary component, resulting in minimum masses of 31 and 13 M_⊙ ( q =0.42) . We also confirm for the binary components the spectral classification of O3 V+ O8 V previously assigned. Assuming for the O8 V component a 'normal' mass of 22–25 M_⊙ we would derive for the primary O3 V a mass of 'only' 52–60 M_⊙ and an inclination of about 55° for the orbital plane. We have also determined for the first time a period of apsidal motion for this system, namely 185±16 yr using all available radial velocity data sets of HD 93205 (from 1975 to 1999). Phase-locked variations of the X-ray emission of HD 93205 consisting of a rise of the observed X-ray flux near periastron passage are also discussed.     

The error ellipsoid in phase space of stellar encounters and its evolution in time

We systematically investigate stellar encounters in their six‐dimensional phase space, including also the error ellipsoid and its evolution in time. It allows to give not only a mathematical model of stellar encounters but also an error model for this process. On that occasion we derive fundamental formulae for the positional error in ℝⁿ: the probability of a position X falling into the error ellipsoid, the standard deviation in an arbitrary direction, and we briefly discuss the mean positional error in ℝⁿ. The case of the close encounter of the star GL 710 (HIP 89825) is an illuminating example of applying the derived results. Moreover, we show that the error ellipsoid can also be successfully applied to approximate the confidence region (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contribution to the study of binaries with spectral types F,G, K,and M – XI. Orbital elements of three red‐giant spectroscopic binaries: HR 1304, HR 1908, and HD 126947

The orbital elements of three red‐giant single‐lined spectroscopic binaries, HR 1304, HR 1908 and HD 126947, are presented. They are obtained from observations made with two photoelectric spectrometers of CORAVEL type, the first located at the Observatoire de Haute‐Provence and the second at the Cambridge Observatories. HR 1304 and HR 1908 are known to be chromospherically active stars and to have high spatial velocities; HD 126947 is an intrinsic variable newly detected by Hipparcos. The three systems have long orbital periods: 1.9, 3.2 and 7.7 yr for HR 1304, HR 1908 and HD 126947, respectively. From the orbital elements that we determined and other data available in the literature, we deduce some information about the unseen companions and their separations with respect to the primaries. Finally we discuss the rotation–revolution synchronism and conclude that one star, HR 1908, may have reached the state of pseudo‐synchronism, despite of its long orbital period. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical spectroscopy of XMEGA targets in the Carina Nebula – III. The multiple system Tr 16-104 (≡CPD −59° 2603)

We discuss the orbital elements of the multiple system Tr 16-104 which is usually believed to be a member of the open cluster Trumpler 16 in the Carina complex. We show that Tr 16-104 could be a hierarchical triple system consisting of a short-period (2.15 d) eclipsing O7 V+O9.5 V binary bound to a B0.2 IV star. Our preliminary orbital solution of the third body indicates that the B star most probably describes an eccentric orbit with a period of ∼285 or ∼1341 d around the close binary. Folding photometric data from the literature with our new ephemerides, we find that the light curve of the close binary exhibits rather narrow eclipses indicating that the two O stars must be well inside their Roche lobes. Our analysis of the photometric data yields a lower limit on the inclination of the orbit of the close binary of i ≥77° . The stellar radii and luminosities of the O7 V and O9.5 V stars are significantly smaller than expected for stars of this spectral type. Our results suggest that Tr 16-104 lies at a distance of the order of 2.5 kpc and support a fainter absolute magnitude for zero-age main-sequence O stars than usually adopted. We find that the dynamical configuration of Tr 16-104 corresponds to a hierarchical system that should remain stable provided that it suffers no strong perturbation. Finally, we also report long-term temporal variations of high-velocity interstellar Ca  ii absorptions in the line of sight towards Tr 16-104.     

Observations of structure in the stellar wind of HD 152408

We report on the presence of substantial, low-velocity stellar wind structure in the extreme O supergiant HD 152408, based on optical spectroscopic time-series observations. Systematic variations in the form of migrating optical depth enhancements occur in the absorption trough of the He I 5876 P Cygni profile. These variations start deep in the stellar wind, slowly accelerate bluewards to 0.5v over 1–2 days, and recur at intervals of about 1 day. Sympathetic variations are apparent in the Balmer emission lines. The observations provide constraints on the stability of the low-velocity stellar wind regime, and indicate the presence of large-amplitude perturbations at great depths in the outflow.     

Eccentricity evolution in hierarchical triple systems with eccentric outer binaries

We develop a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular, while the outer one is eccentric. We consider coplanar systems with well-separated components and comparable masses. The derivation of short-period terms is based on an expansion of the rate of change of the Runge–Lenz vector. Then, the short-period terms are combined with secular terms, obtained by means of canonical perturbation theory. The validity of the theoretical equations is tested by numerical integrations of the full equations of motion.