Binary Orbital Motion Research Articles

Measurement of neutron star parameters: A review of methods for low-mass X-ray binaries

Measurement of at least three independent parameters, for example, mass, radius and spin frequency, of a neutron star is probably the only way to understand the nature of its supranuclear core matter. Such a measurement is extremely difficult because of various systematic uncertainties. The lack of knowledge of several system parameter values gives rise to such systematics. Low-mass X-ray binaries, which contain neutron stars, provide a number of methods to constrain the stellar parameters. Joint application of these methods has a great potential to significantly reduce the systematic uncertainties, and hence to measure three independent neutron star parameters accurately. Here we review the methods based on (1) thermonuclear X-ray bursts; (2) accretion-powered millisecond-period pulsations; (3) kilohertz quasi-periodic oscillations; (4) broad relativistic iron lines; (5) quiescent emissions; and (6) binary orbital motions.

How do binaries affect the derived dynamical mass of a star cluster?

The dynamical mass of a star cluster can be derived from the virial theorem, using the measured half-mass radius and line-of-sight velocity dispersion of the cluster. However, this dynamical mass may be a significant overestimation of the cluster mass if the contribution of the binary orbital motion is not taken into account. Here, we describe the mass overestimation as a function of cluster properties and binary population properties, and briefly touch on the issue of selection effects. We find that for clusters with a measured velocity dispersion of σ los≳10 km s−1 the presence of binaries does not affect the dynamical mass significantly. For clusters with σ los≲1 km s−1 (i.e., low-density clusters), the contribution of binaries to σ los is significant, and may result in a major dynamical mass overestimation. The presence of binaries may introduce a downward shift of Δlog (L V /M dyn)=0.05–0.4 (in solar units) in the log (L V /M dyn) versus age diagram.

GEMINI/GMOS SEARCH FOR MASSIVE BINARIES IN THE IONIZING CLUSTER OF 30 DOR

If binaries are common among massive stars, it will have important consequences for the derivation of fundamental properties such as the cluster age, initial mass function, and dynamical mass. Making use of the multiplexing facilities of the Gemini Multi-Object Spectrograph, we were able to investigate the presence of binary stars within the ionizing cluster of 30 Doradus. From a seven-epoch observing campaign at Gemini South we detect a binary candidate rate of about 50%, which is consistent with an intrinsic 100% binary rate among massive stars. We find that single-epoch determinations of the velocity dispersion give values around 30 km s−1. After correcting the global velocity dispersion for the binary orbital motions, the "true" cluster velocity dispersion is 8.3 km s−1. This value implies a virial mass of about 4.5 × 105 M☉ or 8% of the mass calculated using the single-epoch value. The binary corrected virial mass estimate is consistent with photometric mass determinations, thus suggesting that NGC 2070 is a firm candidate for a future globular cluster.

Gemini/GMOS detection of stellar velocity variations in the ionising cluster of 30 Dor

AbstractWe have analysed spectra obtained with the Gemini Multi Object Spectrograph (GMOS) for more than 50 stars in the ionising cluster of 30 Doradus during a seven epochs observing campaign at Gemini South. We derive a binary candidate rate of about 50%, which is however consistent with an intrinsic 100% binary rate among massive stars. After decontaminating the sample from the stars that show binary orbital motions, we were able to calculate the “true” cluster velocity dispersion and found it to be about 8 km s−1. This value implies a virial mass of about 4.5 × 105 M⊙ which is consistent with previous photometric mass determinations therefore suggesting that NGC 2070 is a firm candidate for a future globular cluster.

The effect of binaries on the dynamical mass determination of star clusters

The total mass of distant star clusters is often derived from the virial theorem, using line-of-sight velocity dispersion measurements and half-light radii. Although most stars form in binary systems, this is mostly ignored when interpreting the observations. The components of binary stars exhibit orbital motion, which may increase the measured velocity dispersion, and may therefore result in a dynamical mass overestimation. In this paper we quantify the effect of neglecting the binary population on the derivation of the dynamical mass of a star cluster. We simulate star clusters numerically, and study the dependence of the derived dynamical mass on the properties of the binary population. We find that the presence of binaries plays a crucial role for very sparse clusters with a stellar density comparable to that of the field star population (~0.1 stars/pc3), as the velocity dispersion is fully dominated by the binary orbital motion. For such clusters, the dynamical mass may overestimate the true mass by up to an order of magnitude. For very dense clusters (>10^7 stars/pc3), binaries do not affect the dynamical mass estimation significantly. For clusters of intermediate density (0.1-10^7 stars/pc3), the dynamical mass can be overestimated by 10-100%, depending on the properties of the binary population.

LINE BROADENING IN FIELD METAL-POOR RED GIANT AND RED HORIZONTAL BRANCH STARS

We report 349 radial velocities for 45 metal-poor field red giant and red horizontal branch stars. We have have identified one new spectroscopic binary, HD 4306, and one possible such system, HD 184711. We also report 57 radial velocities for 11 of the 91 stars reported on previously by Carney et al. (2003). As was found in the previous study, radial velocity jitter is present in many of the most luminous stars. Excluding stars showing spectroscopic binary orbital motion, all 7 of the red giants with M(V) <= -2.0 display jitter, as well as 3 of the 14 stars with -2.0 <= M(V) <= -1.4. We have also measured line broadening in all of the new spectra, using synthetic spectra as templates. The most luminous red giants show significant line broadening, as do many of the red horizontal branch stars, and we discuss briefly possible causes.

TEMPO2, a new pulsar timing package - II. The timing model and precision estimates

Tempo2 is a new software package for the analysis of pulsar pulse times of arrival. In this paper we describe in detail the timing model used by tempo2, and discuss limitations on the attainable precision. In addition to the intrinsic slow-down behaviour of the pulsar, tempo2 accounts for the effects of a binary orbital motion, the secular motion of the pulsar or binary system, interstellar, Solar system and ionospheric dispersion, observatory motion (including Earth rotation, precession, nutation, polar motion and orbital motion), tropospheric propagation delay, and gravitational time dilation due to binary companions and Solar system bodies. We believe the timing model is accurate in its description of predictable systematic timing effects to better than one nanosecond, except in the case of relativistic binary systems where further theoretical development is needed. The largest remaining sources of potential error are measurement error, interstellar scattering, Solar system ephemeris errors, atomic clock instability and gravitational waves.

A Planetesimal Accretion Zone in a Circumbinary Disk

We investigate the conditions for planetesimal accretion in a circumbinary disk. Until recently, it had been believed that only single solar-type stars might harbor planetary systems. On the other hand, circumbinary disks have been detected by infrared or radio observation. Planets may be formed in such disks. Binary systems give stronger gravitational perturbation against planetesimals orbiting nearer to the binary. Therefore, the relative velocities between planetesimals will be larger and when they exceed the escape velocity it is impossible for the planetesimals to accumulate into planets. We performed long-term numerical integrations of binary and planetesimal orbital motions in the framework of the coplanar elliptic restricted three-body problem and have found the upper limit of the orbital radius inside of which the relative velocity between the planetesimals exceeds the escape velocity. One of our results is that planetesimal accretion cannot occur in a zone within 13 AU from the barycenter of the binary system when the binary semimajor axis is 1 AU, the binary eccentricity 0.1, the total mass m1 + m2 = 1 M☉, and the mass ratio m2/(m1 + m2) = 0.2. In regions farther out than 13 AU, planetesimals can accrete. We also derive analytic expressions of the eccentricity of a planetesimal pumped up by the gravitational perturbation of the binary and the inner boundary radius of the planetesimal accretion zone according to the secular perturbation theory.

Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order

An equation of motion for relativistic compact binaries is derived through the third post-Newtonian (3 PN) approximation of general relativity. The strong field point particle limit and multipole expansion of the stars are used to solve iteratively the harmonically relaxed Einstein equations. We take into account the Lorentz contraction on the multipole moments defined in our previous works. We then derive a 3 PN acceleration of the binary orbital motion of the two spherical compact stars based on a surface integral approach which is a direct consequence of local energy momentum conservation. Our resulting equation of motion admits a conserved energy (neglecting the 2.5 PN radiation reaction effect), is Lorentz invariant and is unambiguous: there exist no undetermined parameter reported in the previous works. We shall show that our 3 PN equation of motion agrees physically with the Blanchet and Faye 3 PN equation of motion if $\lambda = - 1987/3080$, where $\lambda$ is the parameter which is undetermined within their framework. This value of $\lambda$ is consistent with the result of Damour, Jaranowski, and Sch\"afer who first completed a 3 PN iteration of the ADM Hamiltonian in the ADMTT gauge using the dimensional regularization.

On the equation of motion of compact binaries in the post-Newtonian approximation

A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle limit enables us to incorporate a notion of a self-gravitating regular star into general relativity. The resulting 3 PN equation of motion is Lorentz invariant, unambiguous, and conserves the energy of the binary orbital motion.

New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity

A third post-Newtonian (3 PN) equation of motion for an inspiralling binary consisting of two spherical compact stars with strong internal gravity is derived under harmonic coordinate condition using the strong field point particle limit. The equation of motion is complete in a sense that it is Lorentz invariant in the post-Newtonian perturbative sense, admits conserved energy of the orbital motion, and is unambiguous, that is, with no undetermined coefficient. In this paper, we show explicit expressions of the 3 PN equation of motion and an energy of the binary orbital motion in case of the circular orbit (neglecting the 2.5 PN radiation reaction effect) and in the center of the mass frame. It is argued that the 3 PN equation of motion we obtained is physically unambiguous. Full details will be reported elsewhere.

INTEGRAL observations of SS433, a supercritically accreting microquasar with hard spectrum

Observations of SS433 by INTEGRAL carried out in March-May 2003 are presented. SS433 is evidently detected on the INTEGRAL images of the corresponding sky region in the energy bands 25-50 and 50-100 keV. The precessional variability of the hard X-ray flux is clearly seen. The X-ray eclipse caused by the binary orbital motion is also detected. A possible origin of the hard continuum is briefly discussed.

Stability of a Planet in a Binary System: MACHO 97-BLG-41

An extrasolar planet was detected in a binary system by gravitational microlensing. This is considered to be the first one detected orbiting both components of a binary star system. The event is now known as MACHO 97-BLG-41. Whether such a planetary system can last on a large timescale is a major concern to celestial mechanics. We investigate the stability of the planetary orbits with the observed mass ratios of the three bodies by taking the binary and planetary eccentricities as parameters. The eccentricities could hardly be determined by gravitational microlensing but may be estimated by long-term numerical integrations of the binary and planetary orbital motions. We performed such long-term numerical integrations of the coplanar elliptic restricted three-body problem with various initial conditions in order to see what initial conditions produce stable planetary orbits during the integration for 106 binary periods (2.8 × 106 yr). The results of our numerical integrations permit us to estimate the upper limit of binary eccentricity, which ensures stable planetary orbital motion to be about 0.5 in the cases of circular initial orbits of the planet. In the cases of elliptic initial orbits of the planet, the planetary orbital motion is found to be less stable; hence, the upper limit of the binary eccentricity is estimated to be smaller than that in the cases of circular initial orbits of the planet. The upper limit of the initial planetary eccentricity is estimated to be about 0.4 for stable planetary orbital motion. The results of similar integrations for retrograde orbits indicate that the planetary retrograde orbits are more stable than the prograde ones.

Polarization variability in the interacting Be binary CX Draconis

We present new UBVRIpolarization measurements of the interacting Be binary CX Dra. On time scale of several weeks polarization variations clearly correlate with the binary orbital motion. Long term changes in polarization are seen in the course of several months. Analysis of the periodic component of polarization gives orbital inclination i � 73 ◦ which is substantially higher than values previously reported in the literature (55 ◦ ). Our two datasets obtained about 9 months apart reveal significant changes in the distribution of the scattering material of the circumbinary envelope.

Formation of Double Rings around Evolved Stars

I propose a scenario for the formation of double-ring systems, as observed in some planetary nebulae and in the outer rings of SN 1987A. In this scenario, two jets, one jet on each side of the equatorial plane, expand into a thin, dense shell. Such a flow is expected in binary systems in which the mass-losing primary undergoes an impulsive mass-loss episode that forms a thin, dense shell. I assume that a small fraction of that mass is accreted onto a companion that blows the jets. Each jet accelerates the shell's material that it hits sideways, forming a higher density ring. Using several simplifying assumptions, I derive an expression for the radius of the ring, which depends relatively weakly on the jets and impulsive mass-loss episode properties. This shows that such a scenario is feasible. If there are several such impulsive mass-loss episodes, more double rings will be formed. Because of the binary interaction and orbital motion, the double-ring system is displaced from the symmetry axis of the main nebula, as observed.

Spherical cocoon models for the flat infrared spectrum of the T Tauri phenomenon

Numerical radiative transfer models are used to discuss the observed flat infrared spectrum of T Tauri stars showing moderate dust obscuration. The models consist of a central young star surrounded by a static cocoon of gas and dust, but with no equatorial accretion disc. Here the cocoon is treated as a spherical dust shell undergoing no systematic inflow or outflow motion. The static cocoon is supported against the gravity of the central star by a large-scale magnetic field system that anchors in the star and threads the cocoon material. Using an approximation in which magnetic force densities inside the cocoon are averaged over all polar and azimuthal angles, the cocoon may be treated as a spherical-like configuration for the purpose of numerical radiative transfer calculations. It is shown that the model infrared spectral energy distributions of a spherical static cocoon produce both the Lada spectral types and the flat infrared spectrum of T Tauri stars as well as do models based upon discs or infalling clouds with a bipolar cavity. The static dust cocoon model is applied to the young T Tau binary system. The cocoon is illuminated by radiation emitted from the optical primary (T Tau N), which is a classical T Tauri star. The infrared secondary (T Tau S) is identified as a magnetic brown dwarf in binary orbital motion outside the cocoon, but still embedded in a large nebula of cold gas and dust distributed around the binary system. Both T Tau N and T Tau S are magnetically linked to each other. The radiative transfer model for the cocoon infrared energy distribution is compared with observational flux data for T Tau N. The model appears in good agreement with the data from the optical to submillimetre wavebands. The model shows an almost flat infrared spectrum for T Tau N, except for the strong 10-μm silicate band in emission as observed. It is suggested that the magnetic brown dwarf (T Tau S) undergoes episodic and luminous non-thermal infrared and radio outburst emissions. Such a possibility is well in accord with a non-thermal origin for the circular polarized radio emission observed from the T Tau system. Nevertheless, if future high-resolution observations prove that the blue continuum emission from T Tauri stars originates from stellar chromospheric activity or boundary-layer emission from an equatorial disc, then a spherical cocoon model for the T Tauri phenomenon is wrong.

First Microlens Mass Measurement: PLANET Photometry of EROS BLG‐2000‐5

We analyze PLANET photometric observations of the caustic-crossing binary lens microlensing event, EROS BLG-2000-5, and find that modeling the observed light curve requires incorporation of the microlens parallax and the binary orbital motion. The projected Einstein radius (E = 3.61 ± 0.11 AU) is derived from the measurement of the microlens parallax, and we are also able to infer the angular Einstein radius (θE = 1.38 ± 0.12 mas) from the finite source effect on the light curve, combined with an estimate of the angular size of the source given by the source position in a color-magnitude diagram. The lens mass, M = 0.612 ± 0.057 M☉, is found by combining these two quantities. This is the first time that parallax effects are detected for a caustic-crossing event and also the first time that the lens mass degeneracy has been completely broken through photometric monitoring alone. The combination of E and θE also allows us to conclude that the lens lies in the near side of the disk, within 2.6 kpc of the Sun, while the radial velocity measurement indicates that the source is a Galactic bulge giant.

The planet search program at the ESO Coudé Echelle spectrometer

In this article we present the results of the planet search program carried out at the ESO Coude Echelle Spectrometer (CES) for components A and B of the α Centauri system. Since November 1992 we have obtained high precision differential radial velocities (RV s) for both stars. We demonstrate that, after subtraction of the binary orbital motion, no additional residual RV signal is present within our detection limits, which could have been attributed to giant planets orbiting either of the two stars. We performed numerical simulations to determine the detection threshold of the CES survey for planets around both stars. In combination with known dynamical limitations for stable planetary orbits (Wiegert & Holman [CITE]) we can now set strong constraints on the existence of Jupiter-mass-type planets in the α Centauri system.

Evolutionary self-energy-loss effects in compact binary systems

The spin-down of a millisecond pulsar in a compact binary system leads to self-energy losses, that cause the binary's orbital period to increase (the effect being of first post-Newtonian (1PN) order). If the pulsar's period-derivative is not exceedingly small, this effect can become measurable in long-term high-precision timing measurements of the binary's orbital motion. We use rotating compressible spheroids to obtain an approximate, explicit expression for the orbital period derivative, due to spin-down, valid to 1PN order. This expression can be used to observationally constrain the pulsar's moment of inertia, and, combined with other observations, the high-density equation of state of compact stars. We apply our expression to representative models of millisecond pulsars in binary systems and demonstrate the importance of including higher-order rotational effects as well as the importance of the choice of equation of state, which both have been neglected, so far, in the literature. The computed increase in orbital period is larger, by as much as 32% , when the higher-order rotational effects are included, while it can change by more than a factor of two between different plausible equations of state.

Critical Complements: Progress on the Orbit of T Mon

AbstractA preliminary orbit has been derived for the high luminosity, 27-d classical Cepheid T Mon. Velocities for the hot companion have been measured from an HST GHRS spectrum and 3 IUE spectra. The companion velocities are inconsistent with binary orbital motion and it is likely that the companion is itself a short period binary. The HST spectrum also shows that the companion is a chemically peculiar star, probably magnetic.