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.     

Optical spectroscopy of two overlapping, flux-density-limited samples of radio sources in the North Ecliptic Cap, selected at 38 and 151 MHz

We present the results of optical spectroscopy of two flux-density-limited samples of radio sources selected at frequencies of 38 and 151 MHz in the same region around the North Ecliptic Cap, the 8C-NEC and 7C- iii samples respectively. Both samples are selected at flux density levels ≈20 times fainter than samples based on the 3C catalogue. They are amongst the first low-frequency selected samples with no spectral or angular size selection for which almost complete redshift information has been obtained, and contain many of the lowest-luminosity z >2 radio galaxies so far discovered. They will therefore provide a valuable resource for understanding the cosmic evolution of radio sources and their hosts and environments. The 151-MHz 7C- iii sample is selected to have S ₁₅₁≥0.5 Jy and is the more spectroscopically complete; out of 54 radio sources fairly reliable redshifts have been obtained for 44 objects. The 8C sample has a flux limit of S ₃₈≥1.3 Jy and contains 58 sources of which 46 have fairly reliable redshifts. We discuss possible biases in the observed redshift distribution, and some interesting individual objects, including a number of cases of probable gravitational lensing. Using the 8C-NEC and 7C- iii samples in conjunction, we form the first sample selected on low-frequency flux in the rest-frame of the source, rather than the usual selection on flux density in the observed frame. This allows us to remove the bias associated with an increasing rest-frame selection frequency with redshift. We investigate the difference this selection makes to correlations of radio source properties with redshift and luminosity by comparing the results from traditional flux-density selection with our new method. We show in particular that flux-density-based selection leads to an overestimate of the steepness of the correlation of radio source size with redshift.     

Measuring the three-dimensional shear from simulation data, with applications to weak gravitational lensing

We have developed a new three-dimensional algorithm, based on the standard P³M method, for computing deflections resulting from weak gravitational lensing. We compare the results of this method with those of the two-dimensional planar approach, and rigorously outline the conditions under which the two approaches are equivalent. Our new algorithm uses a Fast Fourier Transform convolution method for speed, and has a variable softening feature to provide a realistic interpretation of the large-scale structure in a simulation. The output values of the code are compared with those from the Ewald summation method, which we describe and develop in detail. With an optimal choice of the high-frequency filtering in the Fourier convolution, the maximum errors, when using only a single particle, are about 7 per cent, with an rms error less than 2 per cent. For ensembles of particles, used in typical N -body simulations, the rms errors are typically 0.3 per cent. We describe how the output from the algorithm can be used to generate distributions of magnification, source ellipticity, shear and convergence for large-scale structure.     

Generation of block and ash flows during the 1990–1995 eruption of Unzen Volcano, Japan

Processes generating block and ash flows by gravitational dome collapse (Merapi-type pyroclastic flow) were observed in detail during the 1990–1995 eruption of Unzen volcano, Japan. Two different types were identified by analysis of video records and observations during helicopter flights. Most of the block and ash flows erupted during the 1991–1993 exogenous dome growth stage initially involved crack propagation due to cooling and flowage of the dome lava lobes. The mass around the crack became unstable, locally decreasing in tensile strength. Finally, a slab separated from the lobe front, fragmented progressively from the base to the top within a few seconds, and became a block and ash flow. Rock falls immediately followed, in response to local instability of the lobe front. Clasts in these rock falls fragmented and merged with the preceding flow. In contrast, block and ash flows during the endogenous dome growth stage in 1994 were generated due to local bulge of the dome. Unstable lava blocks collapsed and subsequently fragmented to produce block and ash flows.     

The onset of extension during lithospheric shortening:a two-dimensional thermomechanical model for lithospheric unrooting

We model the evolution of the lithosphere during its shortening and consequent gravitational collapse with special emphasis on the induced variations in the surface stress regime and dynamic topography. In particular, we analyse the conditions leading, immediately after lithospheric failure, to local extension, eventually coeval with compression. Different crustal rheologies and kinematic conditions as well as thermally imposed mechanical rupture are considered. Numerical calculations have been performed by using a 2-D finite element code that couples the thermal and mechanical equations for a Newtonian rheology with a temperature-dependent viscosity. The results show that, after the failure of a gravitationally unstable lithospheric root, the replacement of lithospheric mantle by warmer asthenospheric material induces a considerable variation in the dynamic topography and in the surface stress regime. The occurrence of local extension, its intensity and its spatial distribution depend mainly on whether convergence continues throughout the process or ceases after or before the lithospheric failure. Similarly, uplift/subsidence and topographic inversion are controlled by kinematic conditions and crustal rheology. Mechanical rupture produces drastic changes in the surface stress regime and dynamic topography but only for a short time period, after which the system tends to evolve like a continuous model.     

板块汇聚带的造山和重力垮塌作用及其力学成因:以雅鲁藏布江-喜马拉雅山汇聚带为例

从大洋底部磁异常条带的宽度变化可以看出,大洋的扩张速率是时常变化的,这种变化与板块俯冲角度的变化一样,对板块汇聚带的应力和应变场有重要的控制作用。中国存在众多不同特征、不同年代的板块汇聚带,根据其中发生的构造作用可以反演汇聚带在板块扩张速率和俯冲角度控制下的演化。有着巨大高差的喜马拉雅山构造带和雅鲁藏布江缝合带在喜马拉雅山东、西构造结逐渐交汇在一起,其平均海拔高度随之增大而宽度不断变小。喜马拉雅山中段的推覆发生在中新世早期,在推覆的过程中,其北缘沿藏南拆离系还发生了大规模的南北向伸展。这表明在中新世前,在雅鲁藏布江缝合带和喜马拉雅山之间可能存在一个规模很大的造山带,在这里称之为喜马拉雅山—雅鲁藏布江造山带,它在中新世初发生了垮塌。作为这个造山带的前缘,喜马拉雅山中段发生向南的推覆,这就是喜马拉雅山中段的推覆时间要远远滞后于印度和欧亚大陆的碰撞时间的原因。造山带的垮塌可能是印度与欧亚大陆间水平汇聚速率的突然减小造成的。发生在古近纪的日本海和中国的松辽盆地的弧后扩张与喜马拉雅山—雅鲁藏布江造山带的重力垮塌作用可以对比,可能是太平洋和欧亚大陆汇聚速率的突然减小造成的。在白垩纪,太平洋和欧亚大陆汇聚速率很大,所以,欧亚大陆东缘,包括日本海和中国的松辽盆地,在当时可能是规模很大的造山带。位于秦岭南侧,上覆在四川盆地之上的大巴山推覆带的形成机制与喜马拉雅山在中新世的推覆成因类似,与晚白垩世—古近纪秦岭的垮塌有成因关联。秦岭的垮塌可能是华南—华北汇聚速率减小造成的,在此之前秦岭要比现今高得多。     

Long-term Circulation and Eutrophication Model for Tolo Harbour,Hong Kong

Since the early 1980s excessive discharges of organic waste into Tolo Harbour have created serious problems through nutrient enrichment. A number of eutrophication related problems have been reported which incurred financial losses of billions of dollars and serious ecological imbalance. This work addresses the development, verification and application of a water quality model to synthesize the available large database of water quality and to study water quality management issues of Tolo Harbour. Since detrimental water quality problems usually occur during summer when there is stratification and the water temperature is high, the tidally-averaged hydrodynamics and the relative contribution of gravitational circulation and tidal exchanges in Tolo Harbour have been studied. Gravitational circulation is found to be the dominant mixing process for most of the year, accounting for 70 percent of the mixing. A simple and tractable predictive two-layer mass transport and diagenetic dynamic eutrophication model has been developed. The model computes daily variation of key water quality variables in the water column: algal biomass, dissolved oxygen, organic-nitrogen, ammonium-nitrogen, nitrate-nitrogen, and carboneous oxygen demand. In addition, to study the response and impact of the seabed to the overall eutrophication process a sediment sub-model is developed. The diagenetic sediment sub-model computes explicitly the amount of nutrient recycled and the sediment oxygen demand exerted on the water column. The calibrated model has been validated against a 20 year water quality data base under a wide range of hydro-meteorological and environmental conditions. Both spatial and seasonal variation of observed water quality variables are reproduced. The verified model shows that a significant reduction of total nitrogen loading would be required to meet the water quality objectives, with a recovery time of three months for water column and more than two years for sediment.     

A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius ( ₀), but consistent with that expected for thermal accretion discs . However, other studies have shown that models having sources as large as 5 ₀ can reproduce the observed variation . In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (0.81.5 mag) between image brightnesses over a period of 700 d or 15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2 ₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025 ₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass m in Q2237+0305 is The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.     

Probing the gravity-induced bias with weak lensing: test of analytical results against simulations

Future weak lensing surveys will directly probe the density fluctuation in the Universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field, we show that the bias associated with the convergence field can be directly related to the bias associated with the statistics of underlying overdense objects. This will provide us with a direct method to study the gravity-induced bias in galaxy clustering. Based on our analytical results, which use the hierarchical Ansatz for non-linear clustering, we study how such a bias depends on the smoothing angle and the source redshift. We compare our analytical results with ray-tracing experiments through N -body simulations of four different realistic cosmological scenarios, and find a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity-induced bias in galaxy clustering.     

A strategy for finding gravitationally lensed distant supernovae

Distant Type Ia and II supernovae (SNe) can serve as valuable probes of the history of the cosmic expansion and star formation, and provide important information on their progenitor models. At present, however, there are few observational constraints on the abundance of SNe at high redshifts. A major science driver for the Next Generation Space Telescope is the study of such very distant SNe. In this paper we discuss strategies for finding and counting distant SNe by using repeat imaging of supercritical intermediate redshift clusters whose mass distributions are well constrained via modelling of strongly lensed features. For a variety of different models for the star formation history and supernova progenitors, we estimate the likelihood of detecting lensed SNe as a function of their redshift. In the case of a survey conducted with Hubble Space Telescope ( HST ), we predict a high probability of seeing a supernova in a single return visit with either Wide Field Planetary Camera 2 or Advanced Camera for Surveys, and a much higher probability of detecting examples with     in the lensed case. Most events would represent magnified SNe II at     and a fraction will be more distant examples. We discuss various ways to classify such events using ground-based infrared photometry. We demonstrate an application of the method using the HST archival data and discuss the case of a possible event found in the rich cluster AC 114     .