观测洞在星系巡天掩模分形分析中的作用
Effect of observational holes in fractal analysis of galaxy survey masks
摘要：
观测结果表明，宇宙有一个层次的星系集群过渡到均匀的大尺度根据$Λ$ CDM模型。另一方面，一些观测估计表明，星系团的多重分形行为是基于相关维的泛化。研究了否决区域对星系巡天掩模分形测量的影响。我们调查这些洞是否可以产生分形行为或修改宇宙均匀性的尺度。从BOSS-DR 12的足迹，我们建立了一个均匀的样本以下的径向选择功能的73,412点限于红移范围$0.002<z<0.2$。在样本的RA和DEC中累积产生了不同百分比的观察孔。对于合成的样品和一个真实的星系样品，我们确定了分形维数$D_q(r)$的范围$2\leq q\leq6$使用滑动窗口技术来表征空间点分布。我们的研究结果表明，广义维数随尺度而变化，对于低尺度有一个分形行为与波动的所有孔的百分比研究和大于113 Mpc/h的尺度的统计均匀性与其他分析一致。我们发现，观测孔引起的均匀性尺度$r_H$的移位，特别是对于合成样品的孔的百分比在0-10%之间的均匀性尺度达到$(83\pm1)$ Mpc/h，而分形维数变化为$2.83^{\pm0.09}\leq D_q\leq2.855^{\pm0.09}$。对于孔百分比大于10%的合成样品，我们发现$r_H$的值成比例地增加。因此，如果否决掩模的大小是显着的，那么基于分形分析的关于均匀性尺度的未来结果必须通过观测孔和星系目录几何中的不完整区域来校正。
英文摘要：
Observations reveal that the Universe has a hierarchy of galaxy clustering with transition to homogeneity on large scales according to the $Λ$CDM model. On the other hand some observational estimates suggest a multifractal behavior where galactic clustering is based on generalization of the correlation dimension. We study the influence of veto areas on fractal measurements in masks of galaxy surveys. We investigate if these holes can produce fractal behaviors or modify the scale of cosmic homogeneity. From the footprint of BOSS-DR12, we build a homogeneous sample following the radial selection function for 73,412 points limited to the redshift range $0.002<z<0.2$. Different percentages of observational holes were created cumulatively in RA and dec on the sample. For the synthetic sample and for a real sample of galaxies we determined the fractal dimension $D_q(r)$ in the range $2\leq q\leq6$ using the sliding window technique to characterize the spatial point distribution. Our results show that generalized dimension varies with the scale, for low scales there are a fractal behavior with fluctuations for all hole percentages studied and for larger scales than 113 Mpc/h the statistical homogeneity is achieved in concordance with other analysis. We find that observational holes cause a shift in the homogeneity scale $r_H$, in particular for synthetic samples with percentages of holes between 0-10% the homogeneity scale is reached at $(83\pm1)$Mpc/h while the fractal dimension changes as $2.83^{\pm0.09}\leq D_q\leq2.855^{\pm0.09}$. For synthetic samples with percentages of holes greater than 10%, we find that the value of $r_H$ increases proportionally. Consequently future results about homogeneity scale based in fractal analyses must be corrected by observational holes and regions of incompleteness in the geometry of the galaxy catalogue if the size of the veto mask is significant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
