Effects of microlensing on parameters of the images seen near the critical curves of gravitational lens galaxies

We investigate the effect of microlensing on parameters of the images of distant sources seen near the critical curves of complex gravitational lenses, which are represented as a sum of compact structures—microlenses (stars, star-like or planet-like bodies) and diffusely distributed matter (dust and gas clouds etc.). The observation of merging, cross-shaped, annular, or arc-shaped source images is an indication that the images are close to the critical curves of gravitational lenses. Our analysis and numerical solution have allowed us to determine the structures of the critical curves and caustics formed by macro-and microlenses, as well as to estimate the characteristic perturbations introduced by microlenses at their various positions relative to the critical curve of a regular gravitational lens. We show that, the closer are the microlenses to the critical curve, the larger is the discrepancy between our results and those obtained previously with standard (linearized) allowance for the effect of a regular gravitational lens.     

Background-field effects in astrometric microlensing

We consider the motion of the image of a distant radiation source microlensed by one and many point masses in the presence of an external background field, which produces a shear in the lens equation. The trajectories of the image brightness centroid (BC) in a Chang-Refsdal lens are very sensitive to the magnitude of the shear and to the direction of motion of the microlenses, allowing these parameters to be unambiguously determined from the BC motion. Stochastic motions of the BC for an extended source are simulated in a problem with a large number of randomly arranged microlenses. We derive dependences of the root-mean-square variations in BC velocity on microlense density, on external shear, and on the continuous component of the mass density, which may be related to dark matter in extragalactic lenses.     

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.     

Amplification and variability of the AGN X‐ray emission due to microlensing

We consider the contribution of microlensing to the AGN Fe Kα line and X‐ray continuum amplification and variation. To investigate the variability of the line and X‐ray continuum, we studied the effects of microlensing on quasar X‐ray spectra produced by crossing of a microlensing pattern across a standard relativistic accretion disk. To describe the disk emission we used a ray tracing method considering both metrics, Schwarzschild and Kerr. We found that the Fe Kα and continuum may experience significant amplification by a microlensing event (even for microlenses of very small mass). Also, we investigate a contribution of microlensing to the X‐ray variability of high‐redshifted QSOs, finding that cosmologically distributed deflector may contribute significantly to the X‐ray variability of high‐redshifted QSOs (z > 2). (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The microlensing rate and mass function versus dynamics of the Galactic bar

With the steady increase of the sample size of observed microlenses towards the central regions of the Galaxy, the main source of the uncertainty in the lens mass will shift from the simple Poisson noise to the intrinsic non-uniqueness of our dynamical models of the inner Galaxy, particularly the Galactic bar. We use a set of simple self-consistent bar models to investigate how the microlensing event rate varies as a function of axis ratio, bar angle and velocity distribution. The non-uniqueness of the velocity distribution of the bar model adds a significant uncertainty (by about a factor of 1.5) to any prediction of the lens mass. Kinematic data and self-consistent models are critical to lift the non-uniqueness. We discuss the implications of these results for the interpretation of microlensing observations of the Galactic bulge. In particular we show that Freeman bar models scaled to the mass of the Galactic bulge/bar imply a typical lens mass of around 0.8 M⊙, a factor of 3–5 times larger than the value from other models.     

The use of gravitational microlensing to scan the structure of BAL QSOs

Approximately 10% of the QSOs show broad absorption lines (BAL) in their spectra which, if interpreted in terms of Doppler velocities, reveal the presence of high velocity gas outflows. One of these BAL QSOs is known to be gravitationally lensed. It therefore constitutes a good candidate to search for microlensing effects, i.e. the selective amplification of different line forming regions. Considering current models for the BAL region, we have investigated the effects of moving microlenses on the line profiles, and we conclude that these effects strongly depend on the adopted model. A regular spectroscopic monitoring of lensed BAL QSOs would therefore be highly valuable to distinguish between the various models proposed so far to interpret the origin of broad absorption lines.Also, Maître de Recherches au FNRS     

The distribution of microlensed light-curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light-curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.     

Search for exotic matter from gravitational microlensing observations of stars

We consider small-scale spheroidal clusters of weakly interacting massive particles in our Galaxy as non-compact gravitational microlenses and predict the appearance of caustics in the plane of a lensed source. The crossing of these caustics by a lensed star can produce a large variety of light curves, including some observed in actual microlensing events that have been interpreted as manifestations of binary gravitational lenses. We consider also observable effects during the gravitational microlensing of stars of non-zero angular size with a given brightness distribution across their disks by such an exotic objects as natural wormholes and objects whose space-time environment is described with the NUT metric. We demonstrate that, under certain conditions, the microlensing light curves, chromatic and polarizational effects due to the properties of the lens and the star disk brightness distributions can differ considerably from those observed for a Schwarzschild gravitational lens, so that their analysis can facilitate the identification of such objects.     

Studies of a sample of CPM stars

Summary A sample of CPM stars selected from the AGK2/3 is used to investigate the following points: (a) What is the distribution of mass ratios of binaries with wide separations?, and (b) what is the proportion of wide binaries among stars. The distribution previously derived from the visual binaries of theBright Star Catalogue seem to be an acceptable solution to question (a). On the basis of this, the proportion of stars that have a companion with a separation between 300 and 10000 AU is found to be about 13%. Another possibility is that the distribution of mass ratios is similar to the initial mass function derived by Miller and Scalo (1979) for stars lighter than the Sun. The proportion of wide binaries with mass ratios greater than 0.16 should then be around 17%.     

High surface brightness dwarf galaxies in the Fornax cluster

We report the discovery, in an Extreme Ultraviolet Explorer ( EUVE ) short-wavelength spectrum, of an unresolved hot white dwarf companion to the 5th magnitude B5Vp star HR 2875. This is the first time that a non-interacting white dwarf+B star binary has been discovered: previously, the earliest type of star known with a white dwarf companion was Sirius (A1V). As the white dwarf must have evolved from a main-sequence progenitor with a mass greater than that of a B5V star (≯6.0 M⊙), this places a lower limit on the maximum mass for white dwarf progenitors, with important implications for our knowledge of the initial–final mass relation. Assuming a pure-hydrogen atmospheric composition, we constrain the temperature of the white dwarf to be between 39 000 and 49 000 K. We also argue that this degenerate star is likely to have a mass significantly greater than the mean mass for white dwarf stars (≈0.55 M⊙). Finally, we suggest that other bright B stars (e.g. θ Hya) detected in the extreme ultraviolet surveys of the ROSAT Wide Field Camera and EUVE may also be hiding hot white dwarf companions.     

The V-band Empirical Mass-luminosity Relation for Main Sequence Stars

Stellar mass is an indispensable parameter in the studies of stellar physics and stellar dynamics. On the one hand, the most reliable way to determine the stellar dynamical mass is via orbital determinations of binaries. On the other hand, however, most stellar masses have to be estimated by using the mass luminosity relation (MLR). Therefore, it is important to obtain the empirical MLR through fitting the data of stellar dynamical mass and luminosity. The effect of metallicity can make this relation disperse in the V-band, but studies show that this is mainly limited to the case when the stellar mass is less than 0.6M_⊙ Recently, many relevant data have been accumulated for main sequence stars with larger masses, which make it possible to significantly improve the corresponding MLR. Using a fitting method which can reasonably assign weights to the observational data including two quantities with different dimensions, we obtain a V-band MLR based on the dynamical masses and luminosities of 203 main sequence stars. In comparison with the previous work, the improved MLR is statistically significant, and the relative error of mass estimation reaches about 5%. Therefore, our MLR is useful not only in the studies of statistical nature, but also in the studies of concrete stellar systems, such as the long-term dynamical study and the short-term positioning study of a specific multiple star system.     

主序星的Ⅴ波段经验质光关系

恒星质量是恒星物理以及恒星系统动力学研究中一个不可或缺的参量.双星轨道拟合是获取恒星(动力学)质量的最可靠途径,而绝大部分恒星的质量仍然需要通过恒星质光关系来估计,因此,通过拟合恒星动力学质量和光度数据得到经验质光关系的工作具有重要意义.尽管主序星的Ⅴ波段质光关系由于金属丰度的影响而具有一定的弥散性,但有研究表明这种影响主要限于恒星质量小于 0.6M_⊙的情况.对于较大质量的主序星,近年来的观测拟合研究积累了比较充分的动力学质量和Ⅴ波段光度数据,从而为显著改进上述质光关系提供了可能.利用一个能合理分配两个不同量纲观测量权重的拟合方法,根据 203 颗恒星的动力学质量和光度数据给出了主序星的Ⅴ波段经验质光关系,该结果对此前结果的改进不仅具有统计显著性,而且其对恒星质量估计的相对误差已达到约 5%.因此,该结果不仅可以用于开展有关恒星物理或恒星系统动力学方面的统计性研究,而且对具体实际多星系统的长期动力学研究和短期定位研究等也有应用价值.     

The Occurrences of Coronal Mass Ejection at Solar Minimum and their Association with Surface Activity

We have developed a non-subjective technique for recording the occurrences of coronal mass ejection (CME) in data recorded by the Large Angle Spectrometric Coronagraph experiment (LASCO) aboard the Solar and Heliospheric Observatory spacecraft (SOHO). We have found evidence for, and quantified, an asymmetry in the apparent longitudes at which mass ejections occurred during the first year of LASCO synoptic observations and coinciding with the 1996–1997 solar minimum. Throughout this period the solar surface could loosely be characterized as having both an active and a quiet hemisphere and the observed mass ejection asymmetry is seen to relate closely with the longitudes of most persistent disc activity. However, our best estimate for the centroid of the CME distribution is 45 deg to the west of the brightest regions visible in Fe 195 Å emission on the disc and in an area of reduced coronal emission. This corresponds to the location of a trans-equatorial extension of the northern coronal hole which persisted to some degree throughout the year and was directly associated with the most active region on the disc. We suggest that this indicates magnetic reconnection, which is necessary at the boundaries of coronal holes to maintain their quasi-rigid rotation above the differentially rotating photosphere, could play an important role in triggering the destabilization of nearby structures and result in the observed prevalence of mass ejections. We estimate that the events included in the study could contribute around 8% to the total solar mass loss through the solar wind (which is around 10¹⁴ kg day^–1) and find a scale of asymmetry indicating that close to 70% of this mass is ejected from within a single hemisphere.     

Impact of magnetic field on the gas mass fraction of galaxy clusters

Magnetic fields have been observed in galaxy clusters with strengths of the order of  ~ μG. The non-thermal pressure exerted by magnetic fields also contributes to the total pressure in galaxy clusters and can in turn affect the estimates of the gas mass fraction, f_gas. In this paper, we have considered a central magnetic field strength of 5μG, motivated by observations and simulations of galaxy clusters. The profile of the magnetic field has also been taken from the results obtained from simulations and observations. The role of magnetic field has been taken into account in inferring the gas density distribution through the hydrostatic equilibrium condition (HSE) by including the magnetic pressure. We have found that the resultant gas mass fraction is smaller with magnetic field as compared to that without magnetic field. However, this decrease is dependent on the strength and the profile of the magnetic field. We have also determined the total mass using the NFW profile to check for the dependency of f_gas estimates on total mass estimators. From our analysis, we conclude that for the magnetic field strength that galaxy clusters seem to possess, the non-thermal pressure from magnetic fields has an impact of  ≈ 1 % on the gas mass fraction of galaxy clusters. However, with upcoming facilities like Square Kilometre Array (SKA), it can be further expected to improve with more precise observations of the magnetic field strength and profile in galaxy clusters, particularly in the interior region.     

Laboratory investigations of marine impact events: Factors influencing crater formation and projectile survivability

Abstract— Given that the Earth's surface is covered in around two‐thirds water, the majority of impact events should have occurred in marine environments. However, with the presence of a water layer, crater formation may be prohibited. Indeed, formation is greatly controlled by the water depth to projectile diameter ratio, as discussed in this paper. Previous work has shown that the underlying target material also influences crater formation (e.g., Gault and Sonett 1982; Baldwin et al. 2007). In addition to the above parameters we also show the influence of impact angle, impact velocity and projectile density for a variety of water depths on crater formation and projectile survivability. The limiting ratio of water depth to projectile diameter on cratering represents the point at which the projectile is significantly slowed by transit through the water layer to reduce the impact energy to that which prohibits cratering. We therefore study the velocity decay produced by a water layer using laboratory, analytical and numerical modelling techniques, and determine the peak pressures endured by the projectile. For an impact into a water depth five times the projectile diameter, the velocity of the projectile is found to be reduced to 26–32% its original value. For deep water impacts we find that up to 60% of the original mass of the projectile survives in an oblique impact, where survivability is defined as the solid or melted mass fraction of the projectile that could be collected after impact.     

Origin of Coronal Shocks without Mass Ejections

We present an analysis of all the events (around 400) of coronal shocks for which the shock-associated metric type IIs were observed by many spectrographs during the period April 1997– December 2000. The main objective of this analysis is to give evidence for the type IIs related to only flare-blast waves, and thus to find out whether there are any type II-associated coronal shocks without mass ejections. By carefully analyzing the data from multi-wavelength observations (Radio, GOES X-ray, Hα, SOHO/LASCO and SOHO/EIT-EUV data), we have identified only 30 events for which there were actually no reports of CMEs. Then from the analysis of the LASCO and EIT running difference images, we found that there are some shocks (nearly 40%, 12/30) which might be associated with weak and narrow mass ejections. These weak and narrow ejections were not reported earlier. For the remaining 60% events (18/30), there are no mass ejections seen in SOHO/LASCO. But all of them are associated with flares and EIT brightenings. Pre-assuming that these type IIs are related to the flares, and from those flare locations of these 18 cases, 16 events are found to occur within the central region of the solar disk (longitude ≤45^∘). In this case, the weak CMEs originating from this region are unlikely to be detected by SOHO/LASCO due to low scattering. The remaining two events occurred beyond this longitudinal limit for which any mass ejections would have been detected if they were present. For both these events, though there are weak eruption features (EIT dimming and loop displacement) in the EIT images, no mass ejection was seen in LASCO for one event, and a CME appeared very late for the other event. While these two cases may imply that the coronal shocks can be produced without any mass ejections, we cannot deny the strong relationship between type IIs and CMEs.     

The porosities of ordinary chondrites: Models and interpretation

Abstract— Densities and porosities for 285 ordinary chondrites have been assembled and analyzed. Measured chondrite porosities are bimodal; finds have an average porosity of <3%, whereas fall porosities average 7% but range from zero to >30%. We conclude that mild degrees of weathering fill pore spaces, lowering grain densities and porosities without significantly changing the bulk size or mass of the sample. By assuming an original pristine grain density (as a function of the meteorite's mineralogy—determined by its class), we can derive model pristine porosities. These model porosities cluster around an average value of 10% for all classes of ordinary chondrites. Ordinary chondrites do not show any correlation of porosity (model or measured) with petrographic grade or sample size (over a range from 0.2 g to 2 kg). However, we do see a correlation between shock state and porosity. Shock-blackened meteorites are less porous than other meteorites. Furthermore, less severely shocked meteorites show a much broader range of porosities, with the maximum porosity seen among meteorites of a given shock class falling linearly as a function of that shock class. This is consistent with the idea that shock compresses and closes pore space. Analysis of meteorite porosity provides a lower bound to the fine-scale porosity of asteroids. Our densities, even with 10% primordial porosity, are significantly higher than inferred densities of possible asteroid parent bodies. These asteroids are probably loose piles of rubble.     

Mass-injection rate from Io into the Io plasma torus

Theoretical arguments have been presented to the effect that both plasma and energy are supplied to the Jovian magnetosphere primarily from internal sources. If we assume that Io is the source of plasma for the Jovian magnetosphere and that outward flow of plasma from the torus is the means of drawing from the kinetic energy of rotation of Jupiter to drive magnetospheric phenomena, we can obtain a new, independent estimate of the rate of mass injection from Io into the Io plasma torus. We explicitly assume the solar wind supplies neither plasma nor energy to the Jovian magnetosphere in significant amounts. The power expended by the Jovian magnetosphere is supplied by torus plasma falling outward through the corotational-centrifugal-potential field. A lower limit to the rate of mass injection into the torus, which on the average must equal the rate of mass loss from the torus, is therefore derivable if we adopt a value for the power expended to drive the various magnetospheric phenomena. This method yields an injection rate of at least 10³ kg/sec, a value in agreement with the results obtained by two other independent methods of estimating mass injection rate. If this injection rate from Io and extraction of energy from Jupiter's kinetic energy of rotation has been maintained over geologic time, then approximately 0.1% of Io's mass (principally in the form of sulfur and oxygen) has been lost to the Jovian magnetosphere, and Jupiter's spin rate has been reduced by less than 0.1%.     

Local missing mass

Assuming that local missing mass exists, we consider its total amount, its nature, and its spatial distribution, emphasizing brown dwarfs and less massive objects. We show that under these assumptions the problem of local missing mass is essentially the problem of determining the lower limit of the masses of stars in the process of formation.We propose in addition one other possible source of local missing mass: photometrically unresovable double systems. We show that under certain conditions they can make a significant contribution to the visible matter in the solar neighborhood.Translated fromAstrofizika, Vol. 37, No. 3, 1994.In this paper we have also shown that under certain conditions photometrically unresolved double systems may make an important contribution to the amount of visible matter in the solar neighborhood.In the present paper we have attempted to explain only local missing mass. However, it may be that the nature of missing mass is the same on the whole range of scales of astronomical systems.The author is grateful to A. G. Masevich for a number of useful observations. This work was supported by the Russian Fund for Basic Research (RFFI 93-02-2942).     

Weighing the black holes in ultraluminous X-ray sources through timing

We describe a new method to estimate the mass of black holes in Ultraluminous X-ray Sources (ULXs). The method is based on the recently discovered 'variability plane', populated by Galactic stellar-mass black-hole candidates (BHCs) and supermassive active galactic nuclei (AGNs), in the parameter space defined by the black-hole mass, accretion rate and characteristic frequency. We apply this method to the two ULXs from which low-frequency quasi-periodic oscillations have been discovered, M82 X-1 and NGC 5408 X-1. For both sources we obtain a black-hole mass in the range  100–1300 M_⊙  , thus providing evidence for these two sources to host an intermediate-mass black hole.