Galaxy distributions as fractal systems

Abstract

Abstract This paper discusses if large scale galaxy distribution samples containing almost one million objects can be characterized as fractal systems. The analysis performed by Teles et al. (Phys Lett B 813:136034, 2021) on the UltraVISTA DR1 survey is extended here to the SPLASH and COSMOS2015 catalogs, hence adding 750k new galaxies with measured redshifts to the studied samples. The standard $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM cosmology having $$H_0=(70\pm 5)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>70</mml:mn> <mml:mo>±</mml:mo> <mml:mn>5</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> km/s/Mpc and number density tools required for describing these galaxy distributions as single fractal systems with dimension D are adopted. We use the luminosity distance $$d_{\scriptscriptstyle L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mstyle> <mml:mi>L</mml:mi> </mml:mstyle> </mml:msub> </mml:math> , redshift distance $$d_z$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mi>z</mml:mi> </mml:msub> </mml:math> and galaxy area distance (transverse comoving distance) $$d_{\scriptscriptstyle G}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>d</mml:mi> <mml:mstyle> <mml:mi>G</mml:mi> </mml:mstyle> </mml:msub> </mml:math> as relativistic distance definitions to derive galaxy number densities in the redshift interval $$0.1\le z\le 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>z</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> at volume limited subsamples defined by absolute magnitudes in the K-band. Similar to the findings of Teles et al. (2021), the results show two consecutive redshift scales where galaxy distribution data behave as single fractal structures. For $$z&lt;1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> we found $$D=1.00\pm 0.12$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1.00</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:math> for the SPLASH galaxies, and $$D=1,39\pm 0.19$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>39</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.19</mml:mn> </mml:mrow> </mml:math> for the COSMOS2015. For $$1\le z\le 4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:mi>z</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> we respectively found $$D=0.83^{+0.36}_{-0.37}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>83</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.37</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.36</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> and $$D=0.54^{+0.27}_{-0.26}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>54</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.26</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> . These results were verified to be robust under the assumed Hubble constant uncertainty. Calculations considering blue and red galaxies subsamples in both surveys showed that the fractal dimensions of blue galaxies as basically unchanged, but the ones for the red galaxies changed mostly to smaller values, meaning that D may be seen as a more intrinsic property of the distribution of objects in the Universe, therefore allowing for the fractal dimension to be used as a tool to study different populations of galaxies. All results confirm the decades old theoretical prediction of a decrease in the fractal dimension for $$z&gt;1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> .

Topics & Concepts