Chromaticity of gravitational microlensing events

In this paper, we investigate the colour changes of gravitational microlensing events caused by the two different mechanisms of differential amplification for a limb-darkened extended source and blending. From this investigation, we find that the colour changes of limb-darkened extended source events (colour curves) have dramatically different characteristics depending on whether the lens transits the source star or not. We show that for a source transit event, the lens proper motion can be determined by simply measuring the turning time of the colour curve instead of fitting the overall colour or light curves. We also find that even for a very small fraction of blended light, the colour changes induced by blending are equivalent to those induced by limb darkening, causing serious distortion in the observed colour curve. Therefore, to obtain useful information about the lens and source star from the colour curve of an event, it will be essential to correct for blending. We discuss various methods of blending correction .     

The effect of a binary source companion on the astrometric microlensing behaviour

If gravitational microlensing occurs in a binary source system, both source components are magnified, and the resulting light curve deviates from the standard one of a single source event. However, in most cases only one source component is highly magnified and the other component (the companion) can be treated as a simple blending source: this is a blending approximation. In this paper we show that, unlike the light curves, the astrometric curves, representing the trajectories of the source image centroid, of an important fraction of binary source events will not be sufficiently well-modelled by the blending effect alone. This is because the centroid shift induced by the source companion endures to considerable distances from the lens. Therefore, in determining the lens parameters from astrometric curves to be measured by future high-precision astrometric instruments, it will be important to take the full effect of the source companion into consideration.     

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.     

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.     

On the baseline flux determination of microlensing events detectable with the difference image analysis method

To improve photometric precision by removing the blending effect, a newly developed technique of difference image analysis (DIA) has been adopted by several gravitational microlensing experiment groups. However, the principal problem of the DIA method is that, by its nature, it has difficulties in measuring the baseline flux F ₀ of a source star, causing a degeneracy problem in determining the lensing parameters of an event. Therefore, it is often believed that the DIA method is not as powerful as the classical method based on PSF photometry for determining the Einstein time-scales t _E of events.
In this paper, we demonstrate that the degeneracy problem in microlensing events, detectable from searches using the DIA method, is not as serious as is often thought. This is because a substantial fraction of events will be high amplification events for which the deviations of the amplification curves, constructed with the wrong baseline fluxes from their corresponding best-fit standard amplification curves, will be considerable, even for a small amount of the fractional baseline flux deviation Δ F ₀ F ₀. With a model luminosity function of source stars and under realistic observational conditions, we find that ∼30 per cent of detectable Galactic bulge events are expected to have high amplifications and their baseline fluxes can be determined with uncertainties Δ F ₀ F ₀≤0.5.     

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.     

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.     

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.     

Spectral line profile variations in the γ Doradus variable HD 164615: non-radial pulsations versus star-spots

High-resolution spectral data of the Fe  II 5318 Å line in the γ Doradus star HD 164615 are presented. These show systematic changes in the spectral lineshapes with the photometric period of 0.8133 d which are modelled using either non-radial pulsations or cool star-spots. The non-radial modes that can fit the lineshape changes have m degree of 2–4. However, only the m = 2 mode seems to be consistent with the amplitude of the radial velocity variations measured for this star. The star-spot model, although it can qualitatively fit the lineshape changes, is excluded as a possible hypothesis on the basis of (1) poorer fits to the observed spectral line profiles, (2) an inability to account for the large changes in the spectral linewidth as a function of phase, (3) a predicted radial velocity curve that looks qualitatively different from the observed one, and (4) a predicted photometric curve that is a factor of 5 larger than the observed light curve (and with the wrong qualitative shape). Finally, a 'Doppler image' (assuming cool spots) derived from a sequence of synthetic line profiles having non-radial pulsations results in an image that is almost identical to the Doppler image derived for HD 164615. These results provide strong evidence that non-radial pulsations are indeed the explanation for the variability of HD 164615 as well as the other γ Dor variables.     

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 ∼     .     

临界曲线附近的微引力透镜效应模拟

在光滑物质分布模型下,临界曲线是强引力透镜系统中像平面上一条放大率为无穷的线,而考虑少量离散质量的微透镜效应后,源平面上的放大率分布会出现复杂的结构,为暗物质成分的探测提供了一种有效途径.模拟临界曲线附近微透镜效应存在临界曲线上放大率无穷大和计算量巨大的困难.要达到所需的模拟精度,直接使用传统的光线追踪算法需要巨大的计算资源.为此发展了一个能实现海量计算的Graphics Processing Unit (GPU)并行方法来模拟临界曲线附近的微引力透镜效应.在型号为NVIDIA Tesla V100S PCIe 32 GB的GPU上,对于需要处理13000多个微透镜天体、发射1013量级光线的模拟,耗时在7000 s左右.在GPU并行的基础上,与直接的光线追踪算法相比,插值近似的引入使计算速度提升约两个数量级.利用该方法生成80个放大率分布图,并从中抽取800条光变曲线,进行了微焦散线数密度和峰值放大率的统计.     

A comment on the colour–colour diagrams of low-mass X-ray binaries

Disc-accreting neutron stars come in two distinct varieties, atolls and Z sources, named after their differently shaped tracks on a colour–colour diagram as the source luminosity changes. Here we present analysis of three transient atoll sources showing that there is an additional branch in the colour–colour diagram of atoll sources which appears at very low luminosities. This new branch connects to the top of previously known C-shaped (atoll) path, forming a horizontal track where the average source flux decrease from right to left. This turns the C-shape into a Z. Thus both atolls and Z sources share the same topology on the colour–colour diagram and evolve in similar way, as a function of increasing averaged mass accretion rate. This strongly favours models in which the underlying geometry of these sources changes in similar ways. A possible scenario is one where the truncated disc approaches the neutron star when the accretion rate increases, but in the atolls the disc is truncated by evaporation (similarly to black holes), and in the Z sources it is truncated by the magnetic field.     

Adaptive contouring – an efficient way to calculate microlensing light curves of extended sources

The availability of a robust and efficient routine for calculating light curves of a finite source magnified due to bending of its light by the gravitational field of an intervening binary lens is essential for determining the characteristics of planets in such microlensing events, as well as for modelling stellar lens binaries and resolving the brightness profile of the source star. However, the presence of extended caustics, and the fact that the images of the source star cannot be determined analytically while their number depends on the source position (relative to the lens system), makes such a task difficult in general. Combining the advantages of several earlier approaches, an adaptive contouring algorithm is presented, which only relies on a small number of simple rules and operations on the adaptive search grid. By using the parametric representation of critical curves and caustics found by Erdl & Schneider, seed solutions to the adaptive grid are found, which ensures that no images or holes are missed.     

Zum optischen Langzeitverhalten von AM Herculis I. Das Beobachtungsmaterial,die Langzeitlichtkurve und der bahninduzierte Lichtwechsel

For the variable binary AM Herculis, which is the proto-type of a subgroup of cataclysmic stars, results from the study of long-term behaviour are given. The following part of the publication concerns the observation series, the long-term light curve and the orbital light changes. On the base of 1275 photographic observations in B, V and U, most of B, covering the time interval between the years 1982 and 1991 new statements can be made about the common photometric behaviour of the star, its low and high states and the mutual correlations between them, the individual influences of the orbital light changes superimposed to the total brighhtness and last but not least about the colour behaviour of the star within these individual occurrences and the whole time interval, which is object of the second part of this study.     

Stellar photometry and astrometry with discrete point spread functions

The key features of the matphot algorithm for precise and accurate stellar photometry and astrometry using discrete point spread functions (PSFs) are described. A discrete PSF is a sampled version of a continuous PSF, which describes the two-dimensional probability distribution of photons from a point source (star) just above the detector. The shape information about the photon scattering pattern of a discrete PSF is typically encoded using a numerical table (matrix) or an FITS (Flexible Image Transport System) image file. Discrete PSFs are shifted within an observational model using a 21-pixel-wide damped sinc function, and position-partial derivatives are computed using a five-point numerical differentiation formula. Precise and accurate stellar photometry and astrometry are achieved with undersampled CCD (charge-coupled device) observations by using supersampled discrete PSFs that are sampled two, three or more times more finely than the observational data. The precision and accuracy of the matphot algorithm is demonstrated by using the c -language mpd code to analyse simulated CCD stellar observations; measured performance is compared with a theoretical performance model. Detailed analysis of simulated Next Generation Space Telescope observations demonstrate that millipixel relative astrometry and mmag photometric precision is achievable with complicated space-based discrete PSFs.     

Parameter degeneracies and (un)predictability of gravitational microlensing events

Some of the difficulties in determining the underlying physical properties that are relevant for observed anomalies in microlensing light curves, such as the mass and separation of extrasolar planets orbiting the lens star, or the relative source–lens parallax, are already anchored in factors that limit the amount of information available from ordinary microlensing events and in the way these are being parametrized. Moreover, a real-time detection of deviations from an ordinary light curve while these are still in progress can only be done against a known model of the latter, and such is also required for properly prioritizing ongoing events for monitoring in order to maximize scientific returns. Despite the fact that ordinary microlensing light curves are described by an analytic function that only involves a handful of parameters, modelling these is far less trivial than one might be tempted to think. A well-known degeneracy for small impacts, and another one for the initial rise of an event, makes an interprediction of different phases impossible, while in order to determine a complete set of model parameters, the fundamental characteristics of all these phases need to be properly assessed. While it is found that the wing of the light curve provides valuable information about the time-scale that absorbs the physical properties, the peak flux of the event can be meaningfully predicted only after about a third of the total magnification has been reached. Parametrizations based on observable features not only ease modelling by bringing the covariance matrix close to diagonal form, but also allow good predictions of the measured flux without the need to determine all parameters accurately. Campaigns intending to infer planet populations from observed microlensing events need to invest some fraction of the available time into acquiring data that allow to properly determine the magnification function.     

Objective classification of galaxy spectra using the information bottleneck method

A new method for classification of galaxy spectra is presented, based on a recently introduced information theoretical principle, the information bottleneck . For any desired number of classes, galaxies are classified such that the information content about the spectra is maximally preserved. The result is classes of galaxies with similar spectra, where the similarity is determined via a measure of information. We apply our method to ∼6000 galaxy spectra from the ongoing 2dF redshift survey, and a mock-2dF catalogue produced by a cold dark matter (CDM) based semi-analytic model of galaxy formation. We find a good match between the mean spectra of the classes found in the data and in the models. For the mock catalogue, we find that the classes produced by our algorithm form an intuitively sensible sequence in terms of physical properties such as colour, star formation activity, morphology, and internal velocity dispersion. We also show the correlation of the classes with the projections resulting from a principal component analysis.     

Photometric, spectroscopic and polarimetric variability of the weak-emission T Tauri star HD 288313

Photometric observations over three seasons show HD 288313 to be a light variable with a 2.2636-d period. The observed V amplitudes lie in the range of 0.06–0.15 mag. The star showed appreciable changes in the brightness at maximum and minimum of the light curve from season to season. The (   b − y   ) colour did not show any significant variation during the photometric cycle. The light variation appears to be caused by the rotational modulation of stellar flux by cool starspots distributed asymmetrically across the stellar longitudes. The Hα line strength in HD 288313 varied drastically from completely filled-in emission to almost full absorption, that is typical of a normal star of similar spectral type. The Hα equivalent width is found to show a clear rotational modulation only occasionally. Most of the time, chromospheric active regions are distributed well across the stellar longitudes, thereby suppressing obvious rotational modulations. Broad-band linear polarization measurements show HD 288313 to be a short period, low-amplitude polarization variable. The polarization variation is, apparently, rotationally modulated. Dust grain scattering in a non-spherical circumstellar envelope of a star with inhomogeneities in the surface brightness distribution seems to be the mechanism operating in producing the observed polarization.     

The central region of NGC 3077: ground‐based photometry and age of bright ‘starlike’ objects

We present UBVI_C photometry of starlike objects in the central region of NGC 3077. The colour‐colour and colour‐magnitude diagrams of the objects are discussed. Many of the objects under consideration, starlike from the ground, are probably dense young star clusters (super star clusters, SSC). Ages spreading over ∼4 to ∼150 Myr are estimated for most of these objects. Sakai and Madore (2001) found enhanced star formation ∼30–125 Myr ago also in the halo of this galaxy; thus, high star forming activity has occurred within the entire galaxy (centre and halo) since ∼130…150 Myr. Having ended in the outer regions about 30 Myr ago, it is going on near the centre with full vigour. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Flickering in the Magnetic Cv Star Am Herculis

In this study, we present a photometric study of AM Her, a prototype of a class of magnetic CVs. Optical photometry of AM Her was obtained using the Russian–Turkish 1.5 m telescope at TüBİTAK National Observatory (TUG) in August 2003. The R band light curve of the system shows two maxima and two minima during one orbital cycle. In both observing nights the star showed flickering at a significant level. The measured flickering time scale is about 5 min.