Моделирование полей излучения плоского анизотропно рассеивающего однородного слоя произвольной оптической толщины

Modeling of radiation fields of an arbitrary optical thickness uniform slab in the case of a weak absorption and strongly elongated phase functions has been carried. The simple modification of classical Ambarzumian’s — Chandrasekhar’s invariance principle indispensable for the receiving of new non-linear integral equations connected with azimuthal Fourier harmonics of generalized unified photometric function and photometric invariants has been used. These values join upgoing and downgoing radiation fields intensities making use of simple linear manner at arbitrary optical levels in mirror vision directions including fixed azimuthal angles and solar zenith distance. Parametrizations of obtained non-linear integral equations have demonstrated in the absence of reflecting underlying surfaces, placed at the lowest level of considered uniform slab, the possibility to express angular-spatial properties of unified photometrical function and appropriate photometrical invariants taking into account the phase functions strongly elongation near small scattering angles and small slab’s absorption with the help of primary scattered radiation field intensities and adaptive fitting multipliers. These functional adaptive corrections have been stipulated by uniform slab’s multiple light scattering and possess the clear physical interpretation. The use of mirror reflection (symmetry) principle, elaborated by the author, and conception of unified photometric function allows one to estimate the above-mentioned peculiarities of real environment’s phase functions in the framework of photometric invariants numerical modeling. An analysis of appropriate radiative modeling results has shown a dominating influence of primary light scattering in the formation of anisotropically scattered radiation fields of an arbitrary optical thickness uniform slab in the case of weak radiation absorption and strongly elongated phase functions.Проведено моделирование полей излучения плоского однородного слоя произвольной оптической толщины при сильно вытянутых индикатрисах рассеяния. Для реализации этой задачи использовалась модификация классического принципа инвариантности Амбарцумяна — Чандрасекара, позволившая получить новые нелинейные интегральные уравнения для азимутальных Фурье-гармоник обобщенной единой фотометрической функции излучения и фотометрических инвариантов, которые объединяют интенсивности восходящего и нисходящего излучения на произвольных зеркально-симметричных оптических уровнях в зеркальных направлениях визирования при фиксированных азимутах и зенитных расстояниях Солнца. Параметризация полученных нелинейных интегральных уравнений показала, что при отсутствии отражающей подстилающей поверхности на уровне нижней границы слоя пространственно-угловые свойства фотометрических инвариантов и единой фотометрической функции в случае сильно вытянутых индикатрис рассеяния с максимальными значениями вблизи малых углов рассеяния при малом истинном поглощении излучения в среде позволяют приближенно представить общее поле излучения в виде интенсивностей однократно рассеянного излучения с адаптивными поправочными множителями. Эти функциональные поправки обусловлены многократным рассеянием излучения и имеют четкое физическое обоснование. Использование принципа зеркального отображения (симметрии) позволило учесть указанные особенности реальных индикатрис рассеяния при численном моделировании фотометрических инвариантов и единой фотометрической функции. Проведенный анализ показал доминирующую роль однократного рассеяния при формировании полей излучения анизотропно рассеивающего однородного слоя в случае слабого поглощения излучения при сильно вытянутых индикатрисах рассеяния

Statistical Description of a Magnetized Corona above a Turbulent Accretion Disk

We present a physics-based statistical theory of a force-free magnetic field in the corona above a turbulent accretion disk. The field is represented by a statistical ensemble of loops tied to the disk. Each loop evolves under several physical processes: Keplerian shear, turbulent random walk of the disk footpoints, and reconnection with other loops. To build a statistical description, we introduce the distribution function of loops over their sizes and construct a kinetic equation that governs its evolution. This loop kinetic equation is formally analogous to Boltzmann's kinetic equation, with loop-loop reconnection described by a binary collision integral. A dimensionless parameter is introduced to scale the (unknown) overall rate of reconnection relative to Keplerian shear. After solving for the loop distribution function numerically, we calculate self-consistently the distribution of the mean magnetic pressure and dissipation rate with height, and the equilibrium shapes of loops of different sizes. We also compute the energy and torque associated with a given loop, as well as the total magnetic energy and torque in the corona. We explore the dependence of these quantities on the reconnection parameter and find that they can be greatly enhanced if reconnection between loops is suppressed.Comment: 22 pages, 15 figures. Submitted to the Astrophysical Journa

Gravitating discs around black holes

Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole--disc system by analytical solutions of stationary, axially symmetric Einstein's equations. Then, more detailed considerations are focused to middle and outer parts of extended disc-like configurations where relativistic effects are small and the Newtonian description is adequate. Within general relativity, only a static case has been analysed in detail. Results are often very inspiring, however, simplifying assumptions must be imposed: ad hoc profiles of the disc density are commonly assumed and the effects of frame-dragging and completely lacking. Astrophysical discs (e.g. accretion discs in active galactic nuclei) typically extend far beyond the relativistic domain and are fairly diluted. However, self-gravity is still essential for their structure and evolution, as well as for their radiation emission and the impact on the environment around. For example, a nuclear star cluster in a galactic centre may bear various imprints of mutual star--disc interactions, which can be recognised in observational properties, such as the relation between the central mass and stellar velocity dispersion.Comment: Accepted for publication in CQG; high-resolution figures will be available from http://www.iop.org/EJ/journal/CQ

Численное моделирование коэффициентов яркости плоского однородного слоя на основе принципа зеркального отображения и решений линейных сингулярных интегральных уравнений

Based on the mirror reflection principle and solutions of modified linear singular integral equations, the numerical modeling of the unified exit function of the outside radiation field and photometrical invariants of brightness coefficients for a uniform slab of finite optical thickness has been carried out. The efficacy of applying the angular discretization method for problems of numerical modeling of outer radiation fields in the «atmosphere — underlying surface» system has been proved. This new approach allows generalizing the basic results in the particular case of a semi-infinite uniform slab. In this connection the main mathematical aspects and computational peculiarity of the numerical realization of the angular discretization method have been considered. Due to linearity of the used basic integral equations, the conducted analysis can be generalized to the case of scalar and polarized inner radiation fields taking into account the multiple anisotropic scattering of photons and their reflection from an arbitrary horizontally uniform underlying surface.На основе принципа зеркального отображения и соответствующих решений модифицированных линейных сингулярных интегральных уравнений проведено численное моделирование единой функции внешнего поля излучения и фотометрических инвариантов коэффициентов яркости плоского однородного слоя конечной оптической толщины на его внешних границах. Показана эффективность этих уравнений при использовании метода угловой дискретизации в задачах численного моделирования полей излучения системы «атмосфера — подстилающая поверхность». Указанный новый подход позволяет обобщить основные результаты численного радиационного моделирования в частном случае полубесконечного однородного слоя. В этой связи рассмотрены основные математические аспекты и вычислительные особенности численной реализации метода угловой дискретизации. Вследствие линейности используемых базовых интегральных уравнений проведенный анализ можно обобщить на случай скалярных и поляризованных полей излучения при учете многократного анизотропного рассеяния излучения и его отражения от произвольной горизонтально-однородной подстилающей поверхности

Large Deployable Reflector Science and Technology Workshop. Volume 3: Systems and Technology Assessment

The results of five technology panels which convened to discuss the Large Deployable Reflector (LDR) are presented. The proposed LDR is a large, ambient-temperature, far infrared/submillimeter telescope designed for space. Panel topics included optics, materials and structures, sensing and control, science instruments, and systems and missions. The telescope requirements, the estimated technology levels, and the areas in which the generic technology work has to be augmented are enumerated

Polarized thermal emission from X-ray Dim Isolated Neutron Stars: the case of RX J1856.5-3754

The observed polarization properties of thermal radiation from isolated, cooling neutron stars depend on both the emission processes at the surface and the effects of the magnetized vacuum which surrounds the star. Here we investigate the polarized thermal emission from X-ray Dim Isolated Neutron Stars, taking RX J1856.5-3754 as a representative case. The physical conditions of the star outermost layers in these sources is still debated, and so we consider emission from a magnetized atmosphere and a condensed surface, accounting for the effects of vacuum polarization as the radiation propagates in the star magnetosphere. We have found that, for a significant range of viewing geometries, measurement of the phase-averaged polarization fraction and phase-averaged polarization angle at both optical and X-ray wavelengths allow us to determine whether this neutron star has an atmosphere or a condensed surface. Our results may therefore be relevant in view of future developments of soft X-ray polarimeters.Comment: 12 pages, 12 figures, accepted for publication in MNRA

Imaging light transport at the femtosecond scale

Paper, milk, clouds and white paint share a common property: they are opaque disordered media through which light scatters randomly rather than propagating in a straight path. For very thick and turbid media, indeed, light eventually propagates in a ‘diffusive’ way, i.e. similarly to how tea infuses through hot water. Frequently though, a material is neither perfectly opaque nor transparent and the simple diffusion model does not hold. In this work, we developed a novel optical-gating setup that allowed us to observe light transport in scattering media with sub-ps time resolution. An array of unexplored aspects of light propagation emerged from this spatio-temporal description, unveiling transport regimes that were previously inaccessibile due to the extreme time scales involved and the lack of analytical models