Model dependence of transonic properties of accretion flows around black holes

We analytically study how the behaviour of accretion flows changes when the flow model is varied. We study the transonic properties of the conical flow, a flow of constant height and a flow in vertical equilibrium, and show that all these models are basically identical, provided that the polytropic constant is suitably changed from one model to another. We show that this behaviour is extendible even when standing shocks are produced in the flow. The parameter space where shocks are produced remains roughly identical in all these models when the same transformation among the polytropic indices is used. We present applications of these findings.     

Studies of accretion flows around rotating black holes – II. Standing shocks in the pseudo-Kerr geometry

Standing, propagating or oscillating shock waves are common in accretion and winds around compact objects. We study the topology of all possible solutions using the pseudo-Kerr geometry. We present the parameter space spanned by the specific energy and angular momentum and compare it with that obtained from the full general relativity to show that the potential can work satisfactorily in fluid dynamics also, provided the polytropic index is suitably modified. We then divide the parameter space depending on the nature of the solution topology. We specifically study the nature of the standing Rankine–Hugoniot shocks. We also show that as the Kerr parameter is increased, the shock location generally moves closer to the black hole. In future, these solutions can be used as guidelines to test numerical simulations around compact objects.     

Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

Turning points in black holes astrophysics

Black hole astrophysics is expected to have a major breakthrough any day. Theoretical understanding is well advanced, so the breakthrough has to come from observers. Conclusive and direct evidence of event horizons, signatures of tidal deformation of gas clouds (and eventual disappearance of matter behind horizons) could be obtained in matter of months. At this juncture, we wish to summarize how the subject came to this stage and what is the state-of-the-art flow solution around a black hole. We touch upon the most crucial issue of (un)predictability of this subject. We believe that if viscosity is roughly what MRI simulations are pointing to us, we still require very detailed knowledge of properties of the companion, especially time dependent mass transfer from the companion to the black hole.     

Studies of accretion flows around rotating black holes – I. Particle dynamics in a pseudo-Kerr potential

We study the formation of the absorption features, called the cyclotron–annihilation lines, in the γ-spectra of the neutron stars (pulsars), owing to the fundamental quantum-electrodynamic effect of the one–photon pair creation in magnetized vacuum. As a result, we substantiate a new method for the determination of the neutron star magnetic fields B based on measuring the interval between the main annihilation and the first cyclotron–annihilation absorption lines. It is found that these lines may be easily resolved, and, consequently, the method is surely applicable if the following conditions are satisfied. (i) A γ-source has to be compact enough and located near a star, but not close to its magnetic poles. For instance, it may be a disc in the plane of a star magnetic equator with latitudinal angular width less than     and radial extent up to 25 per cent of the star radius. (ii) The source is to produce detectable γ-radiation at large angles ≳60° to the local magnetic field. Being situated in a closed field line region and having a broad radiation pattern, such a source is not what is usually considered in the context of the polar cap and outer gap models of the pulsar γ-emission dealing with open field lines only. (iii) Magnetic field strength must lie in a certain narrow interval with the centre at  ∼(3–4) × 10¹²  G. Its width depends on the star orientation and disc radial extend and in the most favourable case is about 20–30 per cent of its lower boundary. Finally, the influence of the star rotation on this method employment is considered and new possibilities arising from forthcoming polarization observations are briefly discussed.     

A new method of photometric calibration of photographic plats by a doubly refracting crystal filter

A filter composed of a crossed pair of doubly refracting crystals and a polaroid, mounted at the focal plane of the telescope, divides each star image into two images of constant intensity ratio. It is shown that such a filter arrangement is capable of providing reliable photographic calibration for stellar photometry.     

Preliminary assessment of the impacts of deep foundations and land reclamation on groundwater flow in a coastal area in Hong Kong, China

Many coastal areas have been intensively urbanized because people living and working on or near coastlines are increasing. Land reclamation from the sea and high-rise buildings are common approaches to satisfying the growing needs for more housing and other land use. Coastal areas are usually the ultimate discharge zones of groundwater systems. Using a coastal area in Hong Kong as a case study, this paper discusses the change in a groundwater system due to land reclamation and construction of building foundations in a coastal area. The upper part of the study area is in a nearly natural state, whereas the lower part is probably one of the most extensively developed areas in the world. It is evident that the groundwater flow system in this area has been changed over the last century. The piezometers in the transitional zone between the natural slopes and the urbanized areas indicate significant response to rainfall and obvious upward groundwater flow. To understand these piezometric responses to rainfall, a cross section is selected for detailed study using a two-dimensional multilayered numerical model. The parameters and structure of the aquifer system are calibrated by comparing the simulated and observed water levels. To reproduce the observed behavior of the groundwater system, the model has to include two important characteristics: a highly permeable zone at the rockhead and a reduction in hydraulic conductivity of 14–20 times in the urbanized area. The simulation demonstrates that both land reclamation along the coastline and deep foundations have contributed to the modification of the flow system, but the deep foundations have the most profound impact, especially when a high conductivity zone is present at the rockhead.

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Resumen Muchas áreas costeras han sido urbanizadas de manera intensiva, debido a la presión creciente de la gente que quiere vivir y trabajar en estos sitios. Los terrenos arrebatados al mar y los edificios de gran altura, son las respuestas comunes para satisfacer las necesidades de mas vivienda y usos nuevos para el suelo. Las áreas costeras son comúnmente las zonas de descarga final de los sistemas de agua subterránea. A través de un área costera en Hong Kong, tomada como estudio de caso, este artículo discute el cambio causado en un sistema de agua subterránea, debido a la recuperación de terrenos anteriormente cubiertos por el mar y a la construcción de cimientos de edificios en la zona costera. La parte más alta de la área de estudio está casi en su estado natural, mientras que la parte baja es probablemente una de las áreas más extensas en su tipo y más desarrolladas en el mundo. Es evidente que el sistema de flujo del agua subterránea en esta área ha sido cambiado a lo largo del último siglo. Los piezómetros en la zona transicional, entre los taludes naturales y las áreas urbanizadas, muestran una respuesta notable a la lluvia y un flujo evidente hacia arriba del agua subterránea. Para entender estas respuestas piezométricas a la lluvia, se seleccionó una sección vertical para estudio detallado, utilizando un modelo numérico bidimensional multicapa. Los parámetros y estructura del sistema acuífero son calibrados mediante la comparación de los niveles de agua observados y simulados. Para reproducir el comportamiento observado del sistema de agua subterránea, el modelo ha incluido dos características importantes: Una zona altamente permeable en la parte más elevada y una reducción de 14 a 20 veces en la conductividad hidráulica, dentro de la zona urbanizada. La simulación demuestra que tanto los terrenos recuperados del mar, como las cimentaciones profundas a lo largo de la línea de costa, han contribuido a la modificación del sistema de flujo, pero las cimentaciones profundas han causado el mayor impacto, especialmente cuando se presenta una zona de alta conductividad en la parte más elevada del área.

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Résumé La plupart des zones côtières ont été intensivement urbanisé due à la croissance de la population qui travaille et vive sur les zones littorales. La récupération des terrains sur la mer ainsi que la construction des grandes immeubles sont les moyens usuels utilisés pour satisfaire les demandes accrues de logement. Dhabitude les zones côtières représentent lexutoire final des aquifères. En utilisant la zones côtière de Hong Kong comme un étude de cas cet article analyse les changements dans les systèmes aquifères produits par la récupération des terrains et par les fondations des grandes immeubles. Tendis que la partie supérieure de la zone étudiée se trouve presque à létat naturel, la partie inférieure représente une des zones les plus développée du monde. Il est donc évident que la circulation des eaux souterraines a été modifiée pendant le dernière siècle. Les piézomètres remplacés entre les versants et la zone urbanisée montrent une réponse significative aux précipitations ainsi quune hausse générale des niveaux. Pour mieux comprendre la réponse des niveaux aux plues on a modélisé lécoulement dans une coupe vericale en utilisant un modèle numérique multicouches. Les paramètres et la strucure du système aquifère ont été calés en comparant les niveaux calculés et mesurés. Affin de reproduire les niveaux mesurés le modèle doit considérer deux caratéristiques importantes: une zone périglaciaire à grande perméabilité et une diminution jusqu à vingt fois de la perméabilité dans les zone urbanisées. La simulation a mis en évidence que les récupération des terrains au long du littoral aussi bien que les fondations profondes ont modifié lécoulement mais que les dernières ont limpact le plus important surtout lorsquil sagit de la zone périglaciaire à grande perméabilité.