Are there sextuplet and octuplet image systems
Are there sextuplet and octuplet image systems
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DOI：
10.1046/j.1365-8711.2001.04826.x
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发表时间：
2001-08
影响因子：
4.8
通讯作者：
N. Evans;H. Witt
中科院分区：
文献类型：
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作者：
N. Evans;H. Witt
我们研究了具有平坦旋转曲线的无标度星系族的引力透镜效应。这些模型是由形状函数定义的，它规定了同径体的半径作为与长轴的位置角度的函数。临界曲线是解析曲线，而焦散网络可简化为简单的正交。顶点总是位于形状函数的转折点上。我们表明，具有完全椭圆同卵体的模型从不承认蝴蝶或燕尾的尖端，因此最多有四个（或五个）图像。高阶成像是由同长石与纯椭圆的偏差引起的，如嵌盘引起的指向性或最近合并引起的方框性。六元和八元成像的起始标准可以根据椭圆率e和四阶傅立叶系数（a4和b4）进行解析计算，观测者用来参数化异构形状。这六张或八张图像大致排列成一个圆圈，如果分辨率不充分，就会出现一个不完整的爱因斯坦环。利用椭圆星系的形状和合并残留物的数据，我们估计所有多重成像的类星体中有1%可能是六联体系统或更高的系统。即将发射的卫星，如全球天体物理测量干涉仪（GAIA）将提供约4000个多重成像系统的数据集，因此约40个将显示六倍或更高的成像。
We study gravitational lensing by the family of scale-free galaxies with flat rotation curves. The models are defined by a shape function, which prescribes the radius of the isophote as a function of the position angle from the major axis. The critical curves are analytic, while the caustic network is reducible to a simple quadrature. The cusps are always located at the turning points of the shape function. We show that the models with exactly elliptic isophotes never admit butterfly or swallowtail cusps and so have at most four (or five) images. Higher order imaging is brought about by deviations of the isophotes from pure ellipses, such as pointedness caused by embedded discs or boxiness caused by recent merging. The criteria for the onset of sextuple and octuple imaging can be calculated analytically in terms of the ellipticity e and the fourth-order Fourier coefficients (a4 and b4) used by observers to parametrize the isophote shapes. The six or eight images are arranged roughly in a circle, which appears as an incomplete Einstein ring if inadequately resolved. Using data on the shapes of elliptical galaxies and merger remnants, we estimate that ∼1 per cent of all multiply imaged quasars may be sextuplet systems or higher. Forthcoming satellites such as the Global Astrometric Interferometer for Astrophysics (GAIA) will provide data sets of ∼4000 multiply imaged systems, and so ∼40 will show sextuple imaging or higher.