Another channel to detect close-in binary companions via gravitational microlensing

Gaudi & Gould showed that close companions of remote binary systems can be efficiently detected by using gravitational microlensing via the deviations in the lensing light curves induced by the existence of the lens companions. In this paper, we introduce another channel to detect faint close-in binary companions by using microlensing. This method utilizes a caustic-crossing binary lens event with a source also composed of binary stars, where the companion is a faint star. Detection of the companion is possible because the flux of the companion can be highly amplified when it crosses the lens caustic. The detection is facilitated since the companion is more amplified than the primary because it, in general, has a smaller size than the primary, and thus experiences less finite source effect. The method is an extension of the previous one suggested to detect close-in giant planets by Graff & Gaudi and Lewis & Ibata and further developed by Ashton & Lewis. From the simulations of realistic Galactic bulge events, we find that companions of K-type main-sequence or brighter stars can be efficiently detected from the current type of microlensing follow-up observations by using the proposed method. We also find that compared with the method of detecting lens companions for which the efficiency drops significantly for binaries with separations ≲0.2 of the angular Einstein ring radius, θ _E, the proposed method has an important advantage of being able to detect companions with substantially smaller separations down to ∼     .     

exofit: orbital parameters of extrasolar planets from radial velocities

Retrieval of orbital parameters of extrasolar planets poses considerable statistical challenges. Due to sparse sampling, measurement errors, parameters degeneracy and modelling limitations, there are no unique values of basic parameters, such as period and eccentricity. Here, we estimate the orbital parameters from radial velocity data in a Bayesian framework by utilizing Markov Chain Monte Carlo (MCMC) simulations with the Metropolis–Hastings algorithm. We follow a methodology recently proposed by Gregory and Ford. Our implementation of MCMC is based on the object-oriented approach outlined by Graves. We make our resulting code, exofit , publicly available with this paper. It can search for either one or two planets as illustrated on mock data. As an example we re-analysed the orbital solution of companions to HD 187085 and HD 159868 from the published radial velocity data. We confirm the degeneracy reported for orbital parameters of the companion to HD 187085, and show that a low-eccentricity orbit is more probable for this planet. For HD 159868, we obtained slightly different orbital solution and a relatively high 'noise' factor indicating the presence of an unaccounted signal in the radial velocity data. exofit is designed in such a way that it can be extended for a variety of probability models, including different Bayesian priors.     

A warped m= 2 water maser disc in V778 Cyg?

The silicate carbon star V778 Cyg is a source of 22-GHz water maser emission which was recently resolved by MERLIN. Observations revealed an elongated     -like structure along which the velocities of the maser features show a linear dependence on the impact parameter. This is consistent with a doubly warped   m = 2  disc observed edge-on. Water masers and silicate dust emission (detected by the Infrared Astronomical Satellite and Infrared Space Observatory ) have a common origin in O-rich material and are likely to be co-located in the disc. We propose a detailed self-consistent model of a masing gas–dust disc around a companion to the carbon star in a binary system, which allows us to estimate the companion mass of  1.7 ± 0.1 M_⊙  , the disc radius of  40 ± 3  au and the distance between companions of ∼80 au. Using a dust–gas coupling model for water masing, we calculate the maser power self-consistently, accounting for both the gas and the dust energy balances. Comparing the simulation results with the observational data, we deduce the main physical parameters of the masing disc, such as the gas and dust temperatures and their densities. We also present an analysis of the stability of the disc.     

Constraints on Jupiters from observations of Galactic bulge microlensing events during 2000

We present observations of eight Galactic bulge microlensing events taken with the 1.0-m Jacobus Kapteyn Telescope (JKT) on La Palma during 2000 June and July. The JKT observing schedule was optimized using a prioritizing algorithm to automatically update the target list. For most of these events we have sampled the light curves at times where no information was available from the OGLE alert team. We assume a point-source point-lens (PSPL) model and perform a maximum likelihood fit to both our data and the OGLE data to constrain the event parameters of the fit. We then refit the data assuming a binary lens and proceed to calculate the probability of detecting planets with mass ratio   q = 10⁻³  . We have seen no clear signatures of planetary deviations on any of the eight events and we quantify constraints on the presence of planetary companions to the lensing stars. For two well-observed events, 2000BUL31 and 2000BUL33, our detection probabilities peak at ∼30 and ∼20 per cent respectively for   q = 10⁻³  and   a ∼ R _E  for a  Δχ²  threshold value of 60.     

Analytic relations between the observed gravitational microlensing parameters with and without the effect of blending

When a microlensing light curve is contaminated by blended light from unresolved stars near the line of sight to the lensed star, the light curve shape and corresponding parametrization for the event will differ from the values expected when the event is not affected by blending. As a result, blending makes it difficult to identify the major lens population and to estimate the amount of lensing matter. In order to estimate the effect of blending on the result of lensing experiments, it is, therefore, essential to know how the observed lensing parameters change depending on the fraction of blended light. Previously, the changed lensing parameters were obtained with a statistical method that not only required a large amount of computation time but also was prone to uncertainty. In this paper, we derive analytic relations between the lensing parameters with and without the effect of blending. By using these relations, we investigate the dependence of the observed lensing parameters on the amount of blended light, the impact parameter and the threshold amplification for event detection.     

Where are the binary source gravitational microlensing events? II

Despite the same multiplicity of lenses and sources, the frequency of detection of binary source events is relatively very low compared with that of binary lens events. Dominik pointed out that the rarity of binary source events is caused mainly by the large difference in amplification between the component stars. In this paper, we determine that the fraction of events with similar source star amplifications is as large as ∼8 per cent, and thus show that the very low detection rate for binary source events cannot be explained by this effect alone. By carrying out realistic simulations of binary source events, we find that a significant number of binary source events are additionally missed from detection for various other reasons. First, if the flux ratio between the component stars is very large, the light curve of the bright star is hardly affected by the light from the faint star. Secondly, if the separation is too small, the binary source stars behave like a single star, making it difficult to separate the binary source event from a single source event. Finally, although the probability of detecting binary source events increases as the source separation increases, some fraction of binary source events will still be missed because the light curves of these events will mimic those of single source events with longer time-scales and larger values of the impact parameter.     

A genetic algorithm for the non-parametric inversion of strong lensing systems

We present a non-parametric technique to infer the projected mass distribution of a gravitational lens system with multiple strong-lensed images. The technique involves a dynamic grid in the lens plane on which the mass distribution of the lens is approximated by a sum of basis functions, one per grid cell. We used the projected mass densities of Plummer spheres as basis functions. A genetic algorithm then determines the mass distribution of the lens by forcing images of a single source, projected back on to the source plane, to coincide as well as possible. Averaging several tens of solutions removes the random fluctuations that are introduced by the reproduction process of genomes in the genetic algorithm and highlights those features common to all solutions. Given the positions of the images and the redshifts of the sources and the lens, we show that the mass of a gravitational lens can be retrieved with an accuracy of a few percent and that, if the sources sufficiently cover the caustics, the mass distribution of the gravitational lens can also be reliably retrieved. A major advantage of the algorithm is that it makes full use of the information contained in the radial images, unlike methods that minimize the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

On the intrinsic bias in detecting caustic crossings between Galactic halo and self-lensing events in the Magellanic Clouds

In this paper, we investigate the intrinsic bias in detecting caustic crossings between the Galactic halo and self-lensing gravitational microlensing events in the Magellanic Clouds. For this, we determine the region for optimal caustic-crossing detection in the parameter space of the physical binary separations, ℓ, and the total binary lens mass, M , and find that the optimal regions for both populations of events are similar to each other. In particular, if the Galactic halo is composed of lenses with the claimed average mass of 〈 M 〉∼0.5 M_⊙, the optimal binary separation range of Galactic halo events of 3.5 au≲ℓ≲14 au matches well with that of a Magellanic Cloud self-lensing event caused by a binary lens with a total mass of M ∼1 M_⊙; well within the mass range of the most probable lens population of stars in the Magellanic Clouds. Therefore, our computation implies that if the binary fractions and the distributions of binary separations of the two populations of lenses are not significantly different from each other, there is no strong detection bias against Galactic halo caustic-crossing events.     

An Inventory of Gravitational Microlenses Toward the Galactic Bulge

Although microlensing experiments toward the Galactic bulge were originally initiated to check the feasibility of the experiments, they have now become an important tool which allows one to investigate Galactic matter composition. However, previous determination of the lens mass function was not based on the actual number of lenses even for the well-determined population of stellar lenses, but rather on arbitrarily assumed functional forms such as power laws, and thus the derived mass functions were subject to large uncertainties. In this paper, we take a different approach in which we first estimate the event rate distribution expected from observationally well-constrained populations of lenses, and then test other possible lens populations. By comparing the determined event rate distribution Γ( t _E) for various mass function models of lens populations with the observed distribution, we find that stars and white dwarfs explain just ∼ 50 per cent of the total observed events even including very faint stars just above the hydrogen-burning limit. Additionally, the expected time-scale distribution of events caused by these known populations of lenses deviates significantly from the observed distribution, especially in the short time-scale region. However, if the rest of the dynamical mass of the bulge (∼ 2.1 × 10¹⁰ M) is composed of brown dwarfs, the expected event rate distribution matches the observation well.     

Identification of bright lenses from the astrometric observations of gravitational microlensing events

When a source star is gravitationally microlensed by a dark lens, the centroid of the source star image is displaced relative to the position of the unlensed source star, with an elliptical trajectory. Recently, routine astrometric follow-up measurements of these source star image centroid shifts by using high-precision interferometers have been proposed to measure the lens proper motion, which can resolve the lens parameter degeneracy in the photometrically determined Einstein time-scale. When an event is caused by a bright lens, on the other hand, the astrometric shift is affected by the light from the lens, but one cannot identify the existence of the bright lens from the observed trajectory because the resulting trajectory of the bright lens event is also an ellipse. As results, lensing parameters determined from the trajectory differ from those of a dark lens event, causing an incorrect identification of the lens population. In this paper, we show that although the shape and size of the astrometric centroid shift trajectory are changed because of the bright lens, the angular speed of centroid shifts around the apparent position of the unlensed source star is not affected by the lens brightness. Therefore, one can identify the existence of a bright lens and determine its brightness by comparing the lens parameters determined from the 'angular speed curve' with those determined from the trajectory of observed centroid shifts. Once the lens brightness is determined, one can correct for the lens proper motion. As the proposed method provides information about both the lens brightness (dark or bright) and the corrected values of the physical parameters of the lens, one can constrain the nature of massive compact halo objects (MACHOs) significantly better.     

Substellar companions and isolated planetary-mass objects from protostellar disc fragmentation

Self-gravitating protostellar discs are unstable to fragmentation if the gas can cool on a time-scale that is short compared with the orbital period. We use a combination of hydrodynamic simulations and N -body orbit integrations to study the long-term evolution of a fragmenting disc with an initial mass ratio to the star of   M _disc/ M _*= 0.1  . For a disc that is initially unstable across a range of radii, a combination of collapse and subsequent accretion yields substellar objects with a spectrum of masses extending (for a Solar-mass star) up to  ≈0.01 M_⊙  . Subsequent gravitational evolution ejects most of the lower mass objects within a few million years, leaving a small number of very massive planets or brown dwarfs in eccentric orbits at moderately small radii. Based on these results, systems such as HD 168443 – in which the companions are close to or beyond the deuterium burning limit – appear to be the best candidates to have formed via gravitational instability. If massive substellar companions originate from disc fragmentation, while lower-mass planetary companions originate from core accretion, the metallicity distribution of stars which host massive substellar companions at radii of ∼1 au should differ from that of stars with lower mass planetary companions.     

Pixel lensing as a way to detect extrasolar planets in M31

We study the possibility to detect extrasolar planets in M31 through pixel-lensing observations. Using a Monte Carlo approach, we select the physical parameters of the binary lens system, a star hosting a planet, and we calculate the pixel-lensing light curve taking into account the finite source effects. Indeed, their inclusion is crucial since the sources in M31 microlensing events are mainly giant stars. Light curves with detectable planetary features are selected by looking for significant deviations from the corresponding Paczyński shapes. We find that the time-scale of planetary deviations in light curves increase (up to 3–4 d) as the source size increases. This means that only few exposures per day, depending also on the required accuracy, may be sufficient to reveal in the light curve a planetary companion. Although the mean planet mass for the selected events is about     , even small mass planets  ( M _P < 20 M_⊕)  can cause significant deviations, at least in the observations with large telescopes. However, even in the former case, the probability to find detectable planetary features in pixel-lensing light curves is at most a few per cent of the detectable events, and therefore many events have to be collected in order to detect an extrasolar planet in M31. Our analysis also supports the claim that the anomaly found in the candidate event PA-99-N2 towards M31 can be explained by a companion object orbiting the lens star.     

Degeneracy of semi-analytic solution for axially symmetric lens equations

We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when   r /ξ₀≪ 1  and ξ₀ is the scalelength of the density profile. At the strong lensing regime, which is mostly constrained by the inner part of the mass density profile, we assume ρ∝ r ^α.
A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c ₁ and the total mass M . We apply our semi-analytical model to show how the solutions of the axially symmetric lens equations are degenerated in respect to the parameters α and c ₁.
In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed.
Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter  α=[−2.0, −1.0]  .     

Kinematical studies of the low-mass X-ray binary GR Mus (XB 1254–690)

We present simultaneous high-resolution optical spectroscopy and X-ray data of the X-ray binary system GR Mus (XB 1254–690), obtained over a full range of orbital phases. The X-ray observations are used to re-establish the orbital ephemeris for this source. The optical data include the first spectroscopic detection of the donor star in this system through the use of the Doppler Tomography technique on the Bowen fluorescence blend (∼4630–4650 Å). In combination with an estimate for the orbital parameters of the compact object using the wings of the He  ii λ4686 emission line, dynamical mass constraints of  1.20 ≤ M _X /M_⊙≤ 2.64  for the neutron star and  0.45 ≤ M ₂/M_⊙≤ 0.85  for the companion are derived.     

Astrometric microlensing: a channel to detect multiple lens systems

If a source star is gravitationally microlensed by a multiple lens system, the resulting light curve can have significant deviations from the standard form of a single lens event. The chance of producing significant deviations becomes important when the separations between the component lenses are equivalent to the combined angular Einstein ring radius of the system. For multiple lens systems composed of more than two lenses, however, this condition is difficult to meet because the orbits of such systems are unstable. Even if events are caused by a multiple lens system with stable orbits where a pair of lenses are closely located and the other component (a third body) has a wide separation from the pair, identifying the lens multiplicity photometrically will be difficult because the event will be identified by either a binary lens event caused by the close pair of lenses or a single lens event caused by the third body. In this paper, we show that if a seemingly binary lens event is followed up astrometrically using future high-precision interferometers, the existence of an additional third body can be identified via a repeating event. We show that the signatures of third bodies can be unambiguously identified from the characteristic distortions they make in the centroid shift trajectories. We also show that owing to the long-range astrometric effect of third bodies, the detection efficiency will be considerable even for third bodies with large separations from their close lens pairs.     

A dimensional study of disc galaxies

We present a highly simplified model of the dynamical structure of a disc galaxy where only two parameters fully determine the solution, mass and angular momentum. We show through simple physical scalings that once the mass has been fixed, the angular momentum parameter λ is expected to regulate such critical galactic disc properties as colour, thickness of the disc and bulge-to-disc ratio. It is, hence, expected to be the determinant physical ingredient resulting in a given Hubble type. A simple analytic estimate of λ for an observed system is provided. An explicit comparison of the distribution of several galactic parameters against both Hubble type and λ is performed using observed galaxies. Both such distributions exhibit highly similar characteristics for all galactic properties studied, suggesting λ as a physically motivated classification parameter for disc galaxies.     

A systematic fitting scheme for caustic-crossing microlensing events

We outline a method for fitting binary-lens caustic-crossing microlensing events based on the alternative model parametrization proposed and detailed by Cassan. As an illustration of our methodology, we present an analysis of OGLE-2007-BLG-472, a double-peaked Galactic microlensing event with a source crossing the whole caustic structure in less than three days. In order to identify all possible models we conduct an extensive search of the parameter space, followed by a refinement of the parameters with a Markov Chain Monte Carlo algorithm. We find a number of low-  χ²  regions in the parameter space, which lead to several distinct competitive best models. We examine the parameters for each of them, and estimate their physical properties. We find that our fitting strategy locates several minima that are difficult to find with other modelling strategies and is therefore a more appropriate method to fit this type of event.     

Rotation, planets, and the 'second parameter' of the horizontal branch

We analyse the angular momentum evolution from the red giant branch (RGB) to the horizontal branch (HB) and along the HB. Using rotation velocities for stars in the globular cluster M13, we find that the required angular momentum for the fast rotators is up to 1–3 orders of magnitude (depending on some assumptions) larger than that of the Sun. Planets of masses up to 5 times Jupiter's mass and up to an initial orbital separation of ~2 au are sufficient to spin-up the RGB progenitors of most of these fast rotators. Other stars have been spun-up by brown dwarfs or low-mass main-sequence stars. Our results show that the fast rotating HB stars have been probably spun-up by planets, brown dwarfs or low-mass main-sequence stars while they evolved on the RGB. We argue that the angular momentum considerations presented in this paper further support the 'planet second parameter' model. In this model, the 'second parameter' process, which determines the distribution of stars on the HB, is interaction with low-mass companions, in most cases with gas-giant planets, and in a minority of cases with brown dwarfs or low-mass main-sequence stars. The masses and initial orbital separations of the planets (or brown dwarfs or low-mass main-sequence stars) form a rich spectrum of different physical parameters, which manifests itself in the rich varieties of HB morphologies observed in the different globular clusters.