Abstract
Apsidal motion is the precession of the line of apsides in the orbit of a binary star due to perturbations from General Relativity (GR), tides, or third-body interactions. The rate of ...precession due to tidal effects depends on the interior structures of the stars, and as a result, binaries in which this precession occurs are of great interest. Apsidal motion is observed through the analysis of eclipse times, which reveal small changes in the average interval between successive primary and secondary eclipses, taking all available observed times of eclipse and yielding an estimate of the apsidal rate. Given that this is a single observed quantity, various degeneracies are unavoidably present. Ideally, one would have a model that predicts eclipse times given the orbital and stellar parameters. These parameters for a given binary could then be computed using least squares, provided a suitably large number of eclipse times. Here we use the eclipsing light curve (ELC) program as such a model. The Newtonian equations of motion with additional force terms accounting for GR contributions and tidal distortions are integrated, yielding precise sky positions as a function of time. Times of mid-eclipse and instantaneous orbital elements are computed as a function of time. In this paper, we outline the method and compare numerically computed apsidal rates with standard formulae using a set of 15 binaries based on real systems. For our simulated systems, the derived apsidal rates agree with the standard formula.
We present the first optical spectroscopy of five confirmed (or strong candidate) redback millisecond pulsar binaries, obtaining complete radial velocity curves for each companion star. The ...properties of these millisecond pulsar binaries with low-mass, hydrogen-rich companions are discussed in the context of the 14 confirmed and 10 candidate field redbacks. We find that the neutron stars in redbacks have a median mass of 1.78 0.09 M with a dispersion of = 0.21 0.09. Neutron stars with masses in excess of 2 M are consistent with, but not firmly demanded by, current observations. Redback companions have median masses of 0.36 0.04 M with a scatter of = 0.15 0.04 M , and a tail possibly extending up to 0.7-0.9 M . Candidate redbacks tend to have higher companion masses than confirmed redbacks, suggesting a possible selection bias against the detection of radio pulsations in these more massive candidate systems. The distribution of companion masses between redbacks and the less massive black widows continues to be strongly bimodal, which is an important constraint on evolutionary models for these systems. Among redbacks, the median efficiency of converting the pulsar spin-down energy to γ-ray luminosity is ∼10%.
We present photodynamical models of four eclipsing binary systems that show strong evidence of being members of higher-order multiple systems via their strong eclipse timing variations and/or via the ...presence of extra eclipse events. Three of these systems are from the main Kepler mission, and the other is from the K2 mission. We provide some ground-based radial velocities measurements for the three Kepler systems and make use of recent light curves from the TESS mission. Our sample consists of two 2 + 1 systems and two 2 + 2 systems. The first 2 + 1 system, KIC 7668648, consists of an eclipsing binary (Pbin = 27.8 days) with late-type stars (M1=0.8403±0.0090M⊙, R1=1.0066±0.0036R⊙ and M2=0.8000±0.0085M⊙, R2=0.8779±0.0032R⊙) with a low-mass star (M3=0.2750±0.0029M⊙, R3=0.2874±0.0010R⊙) on a roughly coplanar outer orbit (P3=208 days). There are several eclipse events involving the third star that allow for the precise determination of the system parameters. The second 2 + 1 system, KIC 10319590, consists of a binary (Pbin=21.3 days) with late-type stars (M1=1.108±0.043M⊙, R1=1.590±0.019R⊙ and M2=0.743±0.023M⊙, R2=0.7180±0.0086R⊙) that stopped eclipsing about a third of the way into the nominal Kepler mission. We show here that the third star in this system is a Sun-like star (M3=1.049±0.038M⊙, R3=1.39±0.11R⊙) on an inclined outer orbit (P3=456 days). In this case, there are no extra eclipse events. We present the first comprehensive solution for KIC 5255552 and demonstrate that it is a 2 + 2 system consisting of an eclipsing binary (Pbin,1=32.5 days) with late-type stars (M1=0.950±0.018M⊙, R1=0.9284±0.0063R⊙ and M2=0.745±0.014M⊙, R2=0.6891±0.0051R⊙) paired with a non-eclipsing binary (Pbin,2=33.7 days) with somewhat lower-mass stars (M3=0.483±0.010M⊙, R3=0.4640±0.0036R⊙ and M4=0.507±0.010M⊙, R4=0.4749±0.0031R⊙). The two binaries, which have nearly coplanar orbits, orbit their common barycenter on a roughly aligned outer orbit (Pout=878 days). There are extra eclipse events involving the component stars of the non-eclipsing binary, which leads to relatively small uncertainties in the system parameters. The second 2 + 2 system, EPIC 220204960, consists of a pair of eclipsing binaries (Pbin,2=13.3 days, Pbin,2=14.4 days) that both consist of two low-mass stars (M1=0.54M⊙, R1=0.46R⊙, M2=0.46M⊙, R2=0.37R⊙ and M3=0.38M⊙, R3=0.40R⊙, M4=0.38M⊙, R4=0.37R⊙) that orbit their common barycenter on a poorly determined outer orbit. Because of the relatively short time span of the observations (≈80 days for the photometry and ≈70 days for the radial velocity measurements), the masses and radii of the four stars in EPIC 220204960 can only be determined with accuracies of ≈10% and ≈5%, respectively. We show that the most likely period of the outer orbit is 957 days, with a 1σ range of 595 to 1674 days. We can only place weak constraints on the mutual inclinations of the orbital planes, and additional radial velocity measurements and/or additional eclipse observations would allow for much tighter constraints on the properties of the outer orbit.
Measuring the spins of accreting black holes McClintock, Jeffrey E; Narayan, Ramesh; Davis, Shane W ...
Classical and quantum gravity,
06/2011, Volume:
28, Issue:
11
Journal Article, Conference Proceeding
Peer reviewed
Open access
A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black ...holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the x-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit, whose radius depends only on the mass and spin of the black hole. In the Fe Kalpha method, which applies to both classes of black holes, one models the profile of the relativistically broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting (CF) method, which has so far only been applied to stellar-mass black holes, one models the thermal x-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the CF method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.
The Mass of the Black Hole in Cygnus X-1 Orosz, Jerome A; McClintock, Jeffrey E; Aufdenberg, Jason P ...
The Astrophysical journal,
12/2011, Volume:
742, Issue:
2
Journal Article
Peer reviewed
Open access
Cygnus X-1 is a binary star system that is comprised of a black hole and a massive giant companion star in a tight orbit. Building on our accurate distance measurement reported in the preceding ...paper, we first determine the radius of the companion star, thereby constraining the scale of the binary system. To obtain a full dynamical model of the binary, we use an extensive collection of optical photometric and spectroscopic data taken from the literature. By using all of the available observational constraints, we show that the orbit is slightly eccentric (both the radial velocity and photometric data independently confirm this result) and that the companion star rotates roughly 1.4 times its pseudosynchronous value. We find a black hole mass of M = 14.8 ? 1.0 M , a companion mass of M opt = 19.2 ? 1.9 M , and the angle of inclination of the orbital plane to our line of sight of i = 27.1 ? 0.8 deg.
We report the discovery and confirmation of a transiting circumbinary planet (PH1b) around KIC 4862625, an eclipsing binary in the Kepler field. The planet was discovered by volunteers searching the ...first six Quarters of publicly available Kepler data as part of the Planet Hunters citizen science project. Transits of the planet across the larger and brighter of the eclipsing stars are detectable by visual inspection every ~ 137 days, with seven transits identified in Quarters 1-11. The physical and orbital parameters of both the host stars and planet were obtained via a photometric-dynamical model, simultaneously fitting both the measured radial velocities and the Kepler light curve of KIC 4862625. The 6.18 + or - 0.17 R sub(+ in circle) planet orbits outside the 20 day orbit of an eclipsing binary consisting of an F dwarf (1.734 + or - 0.044 R sub(middot in circle), 1.528 + or - 0.087 M sub(middot in circle)) and M dwarf (0.378 + or - 0.023 R sub(middot in circle), 0.408 + or - 0.024 M sub(middot in circle)). For the planet, we find an upper mass limit of 169 M sub(+ in circle) (0.531 Jupiter masses) at the 99.7% confidence level. With a radius and mass less than that of Jupiter, PH1b is well within the planetary regime. Outside the planet's orbit, at ~ 1000 AU, a previously unknown visual binary has been identified that is likely bound to the planetary system, making this the first known case of a quadruple star system with a transiting planet.
Abstract Identifying sources exhibiting ellipsoidal variability in large photometric surveys is becoming a promising method to search for candidate detached black holes (BHs) in binaries. This ...technique aims to exploit the orbital-phase-dependent modulation in optical photometry caused by the BH distorting the shape of the luminous star to constrain the mass ratio of the binary. Without understanding if, or how much, contamination is present in the candidate BH samples produced by this new technique it is hard to leverage them for BH discovery. Here, we follow up one of the best candidates identified from Gaia Data Release 3, Gaia DR3 4042390512917208960, with a radial velocity (RV) campaign. Combined photometric and RV modeling, along with spectral disentangling, suggests that the true mass ratio (the mass of the unseen object divided by the mass of the luminous star) is an order of magnitude smaller than that inferred assuming the modulations arise from ellipsoidal variability. We therefore infer that this system is likely a contact binary, or on the boundary of both stars nearly filling their Roche lobes; however, further observations are required to confidently detect the secondary. We find that the well-known problem of discriminating between ellipsoidal and contact binary light curves results in a larger contamination from contact binaries than previously suggested. Until ellipsoidal variables can be reliably distinguished from contact binaries, samples of BH candidates selected based on ellipsoidal variability are likely to be highly contaminated by contact binaries or similar systems.
We measure the spin of XTE J1550−564 using the two leading methods: (i) modelling the thermal continuum spectrum of the accretion disc; and (ii) modelling the broad red wing of the reflection ...fluorescence Fe Kα line. We find that these two independent measurements of spin are in agreement. For the continuum-fitting analysis, we use a data sample consisting of several dozen Rossi X-ray Timing Explorer spectra, and for the Fe Kα analysis, we use a pair of ASCA spectra from a single epoch. Our spin estimate for the black hole primary using the continuum-fitting method is −0.11 < a
* < 0.71 (90 per cent confidence), with a most likely spin of a
*= 0.34. In obtaining this result, we have thoroughly explored the dependence of the spin value on a wide range of model-dependent systematic errors and observational errors; our precision is limited by uncertainties in the distance and orbital inclination of the system. For the Fe-line method, our estimate of spin is a
*= 0.55+0.15
− 0.22. Combining these results, we conclude that the spin of this black hole is moderate, a
*= 0.49+0.13
− 0.20, which suggests that the jet activity of this microquasar is powered largely by its accretion disc rather than by the spin energy of the black hole.
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BFBNIB, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK
The TESS light curve of AI Phoenicis Maxted, P F L; Gaulme, Patrick; Graczyk, D ...
Monthly notices of the Royal Astronomical Society,
10/2020, Volume:
498, Issue:
1
Journal Article
Peer reviewed
Open access
ABSTRACT
Accurate masses and radii for normal stars derived from observations of detached eclipsing binary stars are of fundamental importance for testing stellar models and may be useful for ...calibrating free parameters in these model if the masses and radii are sufficiently precise and accurate. We aim to measure precise masses and radii for the stars in the bright eclipsing binary AI Phe, and to quantify the level of systematic error in these estimates. We use several different methods to model the Transiting Exoplanet Survey Satellite (TESS) light curve of AI Phe combined with spectroscopic orbits from multiple sources to estimate precisely the stellar masses and radii together with robust error estimates. We find that the agreement between different methods for the light-curve analysis is very good but some methods underestimate the errors on the model parameters. The semi-amplitudes of the spectroscopic orbits derived from spectra obtained with modern échelle spectrographs are consistent to within 0.1 per cent. The masses of the stars in AI Phe are $M_1 = 1.1938 \pm 0.0008\, \rm M_{\odot }$ and $M_2 = 1.2438 \pm 0.0008\, \rm M_{\odot }$, and the radii are $R_1 = 1.8050 \pm 0.0022\, \rm R_{\odot }$ and $R_2 = 2.9332 \pm 0.0023\, \rm R_{\odot }$. We conclude that it is possible to measure accurate masses and radii for stars in bright eclipsing binary stars to a precision of 0.2 per cent or better using photometry from TESS and spectroscopy obtained with modern échelle spectrographs. We provide recommendations for publishing masses and radii of eclipsing binary stars at this level of precision.
We report the discovery of a Neptune-sized ( ) transiting circumbinary planet, Kepler-1661 b, found in the Kepler photometry. The planet has a period of ∼175 days and its orbit precesses with a ...period of only 35 yr. The precession causes the alignment of the orbital planes to vary, and the planet is in a transiting configuration only ∼7% of the time as seen from Earth. As with several other Kepler circumbinary planets, Kepler-1661 b orbits close to the stability radius, and is near the (hot) edge of the habitable zone. The planet orbits a single-lined, grazing eclipsing binary, containing a 0.84 and 0.26 pair of stars in a mildly eccentric (e = 0.11), 28.2 day orbit. The system is fairly young, with an estimated age of ∼1-3 Gyr, and exhibits significant starspot modulations. The grazing eclipse configuration means the system is very sensitive to changes in the binary inclination, which manifests itself as a change in the eclipse depth. The starspots contaminate the eclipse photometry, but not in the usual way of inducing spurious eclipse timing variations. Rather, the starspots alter the normalization of the light curve, and hence the eclipse depths. This can lead to spurious eclipse depth variations, which are then incorrectly ascribed to binary orbital precession.
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