Partial frequency redistribution of polarized radiation

Resonance polarization, which is created by the scattering of an anisotropic radiation field in regions of zero or weak magnetic fields, is strongly dependent on the frequency redistribution taking place during the scatterings. Here we discuss the frequency redistribution matrix relevant to resonance lines, concentrating on linear polarization. First we analyze in detail the redistribution matrix in a zero magnetic field given by the theory of Omont, Smith and Cooper (1972), revisited by Domke and Hubeny (1988). We explain that the linear polarization maxima which may appear in the wings of the Stokes Q profiles of strong resonances lines such as the Ca I 4227 Å line are coherent frequency redistribution effects. Various approximate forms of the frequency redistribution matrix are also examined. For resonance polarization in a weak magnetic field, we suggest a new expression for the redistribution matrix which can be used at all line frequencies, and is consistent with the condition that the Hanle effect acts only in the line core.     

Comoving frame calculations of spectral lines formed in rapidly expanding media with the partial frequency redistribution function for zero natural line width

Comoving frame calculations have been used to compute the spectral lines formed in rapidly expanding spherical media. We have employed the angle-averaged partial frequency redistribution functionR _I with a two-level atom model in non-LTE atom approximation. A linear velocity law increasing with radius has been employed with maximum velocity at Τ=0 being set equal to 30 mean thermal units. It is found that one obtains almost symmetric emission line profiles at large velocities similar to those found in quasars.     

Effects of redistribution with dipole scattering on line source functions

The partial frequency redistribution function for zero natural line width with dipole scattering (R_I) has been considered in obtaining the simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of the expanding gas. We have considered a non-LTE two level atom in an expanding spherical medium whose outer radii are 3, 10 and 20 times the stellar radius with a total optical depthT ≃ 2 × 10³. In all the cases, we have calculated the population ratio of the two levels N₂/N₁ and compared these results with those obtained by using different expansion velocities and geometrical extensions. Initially, the upper level population (N₂) is set equal to zero. The converged simultaneous solution shows that the upper level population is enhanced considerably from the initial value. Variation in velocity gradients seem to have little effect on the ratio N₂/N₁ when the geometrical thickness of the medium is 3 or 10 times the stellar radius. However, when the thickness is increased to 20 times the central radius, the velocity gradients change the ratio N₂/N₁ considerably in the region where log T ≤ 2. The effect of variation of geometrical thickness is to reduce the N₂/N₁ ratio atτ = 0.     

The two-body problem with drag and radiation pressure

The Kepler problem including radiation pressure and drag is treated. The equation of the orbit is derived and the scalar and vector integrals of motion are obtained by direct operation on the vector form of the equation of motion.     

Gamma ray signatures of ultra high energy cosmic ray accelerators: electromagnetic cascade versus synchrotron radiation of secondary electrons

We discuss the possibility of observing ultra high energy cosmic ray sources in high energy gamma rays. Protons propagating away from their accelerators produce secondary electrons during interactions with cosmic microwave background photons. These electrons start an electromagnetic cascade that results in a broad band gamma ray emission. We show that in a magnetized Universe (B≳10⁻¹² G) such emission is likely to be too extended to be detected above the diffuse background. A more promising possibility comes from the detection of synchrotron photons from the extremely energetic secondary electrons. Although this emission is produced in a rather extended region of size ∼10 Mpc, it is expected to be point-like and detectable at GeV energies if the intergalactic magnetic field is at the nanogauss level.      

The motion and radiation of electrons in a neutral sheet

The motion and radiation of an electron in the neighbourhood of a neutral sheet are discussed. Formulae for the synchrotron and cyclotron radiation of an electron in an inhomogeneous field are obtained. The results are compared with radiation in a homogeneous field. It is predicted that the momentum of charged particles flying from a neutral sheet may take discrete eigenvalues.     

原子模型对散射偏振理论轮廓的影响

太阳磁场的诊断是太阳物理研究中非常重要的一部分.斯托克斯参量I、Q、U和V可以用来完整描述偏振光的信息,对观测得到的斯托克斯光谱进行反演可以诊断太阳磁场的信息.近几十年来,塞曼效应成为磁场诊断的主要手段,利用塞曼效应使谱线产生的分裂可以诊断强度达到几百高斯的强磁场,但是在太阳宁静区中存在大量强度小于100 Gs的弱磁场,对于弱磁场可以利用汉勒效应来诊断,应用汉勒效应诊断弱磁场一直是磁场诊断的主要内容之一,需要对偏振的产生机制有更完整的理解.文章的主要内容是研究在采用不同原子模型的假设下,由散射产生的谱线轮廓的区别,以及在存在磁场时,不同原子模型谱线的汉勒效应的区别.以中性镁为研究对象,选取了7能级、4能级和2能级原子模型,分别研究了这几个原子模型对散射偏振和汉勒效应的影响.发现2能级原子模型和多能级(7能级和4能级)原子模型产生的谱线的偏振度有很大的区别,并且在2能级原子模型假设下b_4线不存在下能级的汉勒效应,但是在多能级的原子模型下b_4线仍存在下能级的汉勒效应.对比7能级原子模型和4能级原子模型,谱线的偏振度只有很小的变化,汉勒效应的表现也基本相同.主要结论如下:在利用中性镁b 3线的线偏振轮廓Q/I反演磁场时,至少需要采用4个能级的原子模型.这主要依赖于谱线形成区域的原子的能级分布,原子能级占有数多的能级在研究中是必须考虑的.     

Light Scattering by Dust Under Microgravity Conditions

Most of our knowledge on heterogeneous media in the Universe comes from the light they scatter. This light is mainly linearly polarized, and the polarization phase curves contain information about the properties of the scattering dust. In the solar system, the dust seems to be made of irregular aggregates with a size greater than a few microns and a fractal structure. Many constraints appear in the scattering computations, due to the trickiness of the mathematical calculations, and to our ignorance of the precise structure of the dust. This leads to the necessity to perform light scattering measurements on characteristic aggregates, built under low velocity ballistic collisions. Microgravity is a sensible way to achieve such measurements on a cloud of levitating and aggregating dust particles. A first step has been the PROGRA² experiment, which operates during parabolic flights on an aircraft. The instrument is a polar nephelometer measuring successively the light scattered by a dust sample at various angles; it is fully operational, and will provide a data base of polarization phase curves. A second step is the CODAG-SR experiment, which uses the duration of a rocket flight to build up dust aggregates. The instrument measures simultaneously the light scattered at numerous phase angles; it is now space qualified, and should provide in a near future a monitoring of the intensity and polarization phase curves while the aggregation processes are taking place. This revised version was published online in July 2006 with corrections to the Cover Date.     

The spectra of radiation and relativistic electrons formed by Compton scattering at non-zero particle fluxes

The formation of steady-state spectra of radiation or particles by Compton scattering is discussed for the case when the flux from the source is present. Power-law distributions, or those characterized by a power-law asymptotic behaviour, can appear under these conditions.The power indices and normalizations have been found as well as the flux directions for the electron and photon distributions in two cases. The first case is that of differential energy transfer over the electron spectrum (interaction with soft radiation). For the case of integrated transfer, relations have been found between the indices.The possibility of a power-law electron spectrum (with an index =2) has been shown for scattering by equilibrium radiation (the black-body background included).     

强磁场中的逆Compton散射与γ射线爆能谱

本文认为强磁场中的逆Compton散射可能是γ射线爆的主要辐射机制.其能谱是由源区质子产生的低频光子经强磁场中非热电子的Compton散射形成的.我们利用非相对论情形(B/B_(cr)≤1,hv_i/m_ec~2≤1)下强磁场中的Compton散射微分截面,导出了上述Compton散射的辐射谱公式,由此很好地拟合了典型γ射线爆GB811016的观测能谱.     

The effect of angle-dependent non-coherent electron scattering and partial redistribution on the polarization of resonance lines

The polarized radiative transfer equation is solved when angle-dependent partial redistribution and non-coherent electron scattering are included as line-scattering mechanisms. A static atmosphere with plane parallel symmetry is assumed. Test calculations are used to illustrate the effects of the electron-scattering coefficient, the thermalization parameter and the continuous absorption coefficient on the line polarization. Results of angle-averaged and angle-dependent redistribution functions are compared and it is shown that angle-dependent functions should be used to model the wing polarization of optically thin lines. The lower the continuous absorption compared with the electron scattering, the higher the wing polarization.     

Effects of partial frequency redistribution functions RII,RIII and RV on source functions

The effects of partial frequency redistribution on the formation of spectral lines have been studied. We considered the angle-averaged R_II, R_III andR _v types of redistribution with isotropic phase function, Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S_L (R _v) lies below S_L (R_III) but above S_L(R _III) in the line wings.     

Distribution of free electrons in the galactic plane

A method is proposed for constructing a map of the electron density distribution in the galactic plane. Data on the dispersion measures DM of more than 1500 pulsars and their distances, found by an independent method, are used. The independent distances of the pulsars are estimated using an empirical relation of the form L=γP ^α Ṗ ^β W ^δ between the radio luminosity L of the pulsars and their periods P, the rate of change Ṗ. of their periods, and the half width W of their pulses. A map of the electron density distribution in the galactic plane within a ±400 pc layer is provided. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 277–287 (May 2006).