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arXiv 1409.5409astro-ph.COgr-qc
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红移0.45 < z < 5.0范围内星系分布的分形分析

Fractal analysis of the galaxy distribution in the redshift range 0.45 < z < 5.0

G. Conde-Saavedra, A. Iribarrem, Marcelo B. Ribeiro

备注：
LaTex, 15 pages, 28 figures, 4 tables. To appear in "Physica A"
发表信息：
Physica A 417 (2015) 332-344
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摘要：

证据表明，星系分布可以描述为一个分形系统的红移范围内的FDF星系巡天。在空间均匀的标准宇宙学模型$Ω_{m_0}=0.3$、$Ω_{Λ_0}=0.7$和$H_0=70 \; \mbox{km} \; {\mbox{s}}^{-1} \; {\mbox{Mpc}}^{-1}$中，利用FDF星系体数密度导出了分维$D$.从红色和蓝色FDF星系获得的微分和积分数密度$γ$和$γ^\ast$之间的比率提供了一个直接的方法来估计$D$，这意味着$γ$和$γ^\ast$随宇宙学距离呈幂律变化。将光度距离$d_{\scriptscriptstyle L}$、星系面积距离$d_{\scriptscriptstyle G}$和红移距离$d_z$与各自的数密度作图，通过线性拟合计算出$D$。结果表明，FDF星系的分布在连续的距离范围内具有两个单一的分形维数。两条直线拟合数据，其斜率根据所选的宇宙学距离在$z \approx 1.3$或$z \approx 1.9$处变化。使用$γ^\ast$计算的平均分维变化从$\langle D \rangle=1.4^{\scriptscriptstyle +0.7}_{\scriptscriptstyle -0.6}$到$\langle D \rangle=0.5^{\scriptscriptstyle +1.2}_{\scriptscriptstyle -0.4}$的所有星系，和$D$减少$z$增加。在高$z$下，$D$的值较小，意味着过去星系的分布要稀疏得多，大尺度星系结构可能由空洞主导。还提到了Iribarrem等人（2014，arXiv：1401.6572）的结果，其表明在$1.5 \lesssim z \lesssim 3.2$的Herschel/PACS进化探针（PEP）的远红外源中具有与$\langle D \rangle =0.6 \pm 0.1$相似的分形特征。

英文摘要：

Evidence is presented that the galaxy distribution can be described as a fractal system in the redshift range of the FDF galaxy survey. The fractal dimension $D$ was derived using the FDF galaxy volume number densities in the spatially homogeneous standard cosmological model with $Ω_{m_0}=0.3$, $Ω_{Λ_0}=0.7$ and $H_0=70 \; \mbox{km} \; {\mbox{s}}^{-1} \; {\mbox{Mpc}}^{-1}$. The ratio between the differential and integral number densities $γ$ and $γ^\ast$ obtained from the red and blue FDF galaxies provides a direct method to estimate $D$, implying that $γ$ and $γ^\ast$ vary as power-laws with the cosmological distances. The luminosity distance $d_{\scriptscriptstyle L}$, galaxy area distance $d_{\scriptscriptstyle G}$ and redshift distance $d_z$ were plotted against their respective number densities to calculate $D$ by linear fitting. It was found that the FDF galaxy distribution is characterized by two single fractal dimensions at successive distance ranges. Two straight lines were fitted to the data, whose slopes change at $z \approx 1.3$ or $z \approx 1.9$ depending on the chosen cosmological distance. The average fractal dimension calculated using $γ^\ast$ changes from $\langle D \rangle=1.4^{\scriptscriptstyle +0.7}_{\scriptscriptstyle -0.6}$ to $\langle D \rangle=0.5^{\scriptscriptstyle +1.2}_{\scriptscriptstyle -0.4}$ for all galaxies, and $D$ decreases as $z$ increases. Small values of $D$ at high $z$ mean that in the past galaxies were distributed much more sparsely and the large-scale galaxy structure was then possibly dominated by voids. Results of Iribarrem et al. (2014, arXiv:1401.6572) indicating similar fractal features with $\langle D \rangle =0.6 \pm 0.1$ in the far-infrared sources of the Herschel/PACS evolutionary probe (PEP) at $1.5 \lesssim z \lesssim 3.2$ are also mentioned.

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