Fractal dimension of the cosmic web with different galaxy types

TL;DR

The study addresses how galaxy color populations trace the cosmic web by using a single fractal dimension, $D$, derived from the Pietronero-Wertz relation applied to a COSMOS2020 subsample. It analyzes cumulative counts with relativistic distance measures $d_L$ and $d_G$, obtaining $D$ for blue, green, and red galaxies in two redshift bins ($z<1$ and $1<z\le4$). The main findings reveal two distinct fractal-dimension gradients: for $z<1$, $D_{ ext{blue}} > D_{ ext{red}} > D_{ ext{green}}$, and for $1<z\le4$, $D_{ ext{blue}} > D_{ ext{green}} > D_{ ext{red}}$, with overall $D$ values decreasing at higher redshift due to sparser samples. This demonstrates that fractal dimension is a sensitive, color-dependent observational diagnostic for mapping large-scale structure, while acknowledging limitations and suggesting future multifractal extensions to capture more nuanced clustering.

Abstract

The fractal dimension $D$ is used to map the large-scale galaxy distribution in the Universe by color types: blue, green and red. Using a $NUVrK$-complete COSMOS2020 subsample of 618,952 galaxies observed up to $z=4$, number densities were derived and plotted against two cosmological distance measures, the luminosity and comoving (galaxy area) distances, in order to estimate $D$ for each galaxy color type in two redshift intervals: $z\gtrless1$. We found a general gradient $D_{\mathrm{blue}}> D_{\mathrm{red}}>D_{\mathrm{green}}$ with $D=1.40-2.03$ for $z<1$. For $1<z\leq4$, the gradient changes to $D_{\mathrm{blue}}>D_{\mathrm{green}}D_{\mathrm{red}}$, and the fractal dimension values are lower, $D=0.03-0.44$. These results suggest that the fractal dimension is a sensitive diagnostic for how galaxy populations trace the evolving cosmic web, and confirm the fractal dimension as a useful tool for observational mapping of large-scale structure by galaxy color.

Figures (4)

• Figure 1: Absolute magnitude in the $i$-band as a function of redshift for the initial sample of COSMOS2020. Black circles indicate galaxies that lie above the red solid line, which represents the limiting threshold $M_\mathrm{lim}$ defined by Eq. \ref{['eq6:eq6']}, while grey circles mark those that fall below it and were discarded in this study.
• Figure 2: $NUV-r$ vs. $r-K$ color-color diagrams for 6 equally lengthened redshift intervals. Solid lines correspond to the criterion defined by Ref. REF26, which separates galaxies into three classes: red (above the superior solid line), blue (below the inferior solid line), and green (in between the solid lines). The colorbar represents the sSFR.
• Figure 3: Histogram of the redshift distribution of blue (top left), green valley (top right) and red galaxy types (bottom). After discarding galaxies having $z>4$ we ended up with a final subsample containing 618,952 objects, constituted by 532,190 blue galaxies, 50,383 red ones, and 36,379 objects being classified as galaxies belonging to the green-valley.
• Figure 4: Galaxy number densities $\gamma_{{ { \rm obs}}}^\ast$ obtained as counts per cumulative volume with steps of 200 Mpc in terms of the luminosity distance $d_{ L}$ and galaxy area distance $d_{ G}$ribeiro2005 for three color type populations: blue, red and green. The shaded gray region represents the 1$\sigma$ uncertainty range derived from the upper and lower bounds of the photometric redshifts (lpzPDFu68, lpzPDFl68). The vertical dashed line marks the fractal dimension transition at $z = 1$.