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arXiv 1701.03533astro-ph.CO
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NVSS射电目录对数N -对数S斜率的各向同性检验

Testing the isotropy of the log N - log S slope for the NVSS radio catalogue

Shamik Ghosh, Pankaj Jain

摘要:

已知高于阈值的源的累积数量计数$N$近似遵循幂律行为$N\propto S^{-x}$。我们研究了光谱指数$x$在天空中的变化,以寻找可能的违反各向同性的信号。我们开发了一个严格的似然最大化算法,以准确地适合的光谱指数。我们将天空分为上半球和下半球的$z$轴的特定选择,并确定两个半球之间的光谱指数的最佳拟合值之间的差异$Δx$。通过在$z$轴上变化而获得的这种差异的最大值为我们提供了偏离各向同性的度量。我们发现,数据支持各向同性的光谱指数。最大差值为$x$全天空最佳拟合值的1.3%。发现仅在2 $σ$水平上的偏离是显著的,这表明与各向同性的弱偏离。我们还执行偶极拟合的光谱指数作为角坐标的函数。结果表明,该结果与各向同性相一致。

英文摘要:

The cumulative number count $N$, of sources above a threshold is known to approximately follow a power law behaviour $N\propto S^{-x}$. We study the variation of spectral index $x$ across the sky in order to look for possible signals of violation of isotropy. We develop a rigorous algorithm of likelihood maximisation to accurately fit for the spectral index. We divide the sky into upper and lower hemispheres for a particular choice of $z$-axis and determine the difference $Δx$ between the best fit values of the spectral indices between the two hemispheres. The maximum value of this difference obtained by varying over the $z$-axis provides us with a measure of departure from isotropy. We find that the data support isotropy of the spectral index. The maximum difference is found to be 1.3\% of the full sky best fit value of $x$. The deviation is found to be significant only at 2$σ$ level which indicates a weak departure from isotropy. We also perform a dipole fit to the spectral index as a function of the angular coordinates. The result is found to be consistent with isotropy.

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