Multi-fractal analysis and lacunarity spectrum of the dark matter haloes in the SDSS-DR7. (English) Zbl 1355.85009
Summary: The dark matter halo distribution of the nearby universe is used to study the fractal behaviour in the proximate universe. The data, which is based on four volume-limited galaxy samples was obtained by J. C. Muñoz-Cuartas and V. Mueller [“Galaxy groups and haloes in the seventh data release of the Sloan digital sky survey”, Monthly Notices Royal Astron. Soc. 423, No. 2, 1583–1595 (2012; doi:10.1111/j.1365-2966.2012.20981.x)] from the Seventh Data Release of the Sloan Digital Sky Survey (SDSS-DR7). In order to know the fractal behaviour of the observed universe, from the initial sample which contains 412,468 galaxies and 339,505 dark matter haloes were used as input for the fractal calculations. Using this data we use the sliding-window technique for the dark matter distribution and compute the multi-fractal dimension and the lacunarity spectrum and use it to study its dependence on radial distance in every sample.
The transition to homogeneity is not observed in the dark matter halo distribution obtained from the SDSS-DR7 volume-limited galaxy samples; in its place the dark matter halo distribution exhibits a persistent multi-fractal behaviour where the measured dimension does not arrive at the value of the physical dimension of the space, for all structure parameter values of the analysed set, at least up to radial distances of the ordered from 165 Mpc/h from the available centres of each sample. Our results and their implications are discussed in the context of the formation of large-scale structures in the universe.
The transition to homogeneity is not observed in the dark matter halo distribution obtained from the SDSS-DR7 volume-limited galaxy samples; in its place the dark matter halo distribution exhibits a persistent multi-fractal behaviour where the measured dimension does not arrive at the value of the physical dimension of the space, for all structure parameter values of the analysed set, at least up to radial distances of the ordered from 165 Mpc/h from the available centres of each sample. Our results and their implications are discussed in the context of the formation of large-scale structures in the universe.
References:
| [1] | Abazajian, KN.; Adelman-McCarthy, JK.; Agüeros, MA.; Allam, SS.; Allende Prieto, C.; An, D., The seventh data release of the sloan digital sky survey, Astrophys J Suppl, 182, 543 (2009) |
| [2] | Bagla, JS.; Yadav, J.; Seshadri, TR., Fractal dimensions of a weakly clustered distribution and the scale of homogeneity, MNRAS, 390, 829-838 (2008) |
| [3] | Blanton, MR.; Hogg, DW.; Bahcall, NA.; Brinkmann, J.; Britton, M.; Connolly, AJ., The galaxy luminosity function and luminosity density at redshift \(z = 0.1\), Astrophys J, 592, 819-838 (2003) |
| [4] | Blanton, M. R.; Roweis, S., K-corrections and filter transformations in the ultraviolet, optical, and near-infrared, Astron J, 133, 734-754 (2007) |
| [5] | Blanton, MR.; Schlegel, DJ.; Strauss, MA.; Brinkmann, J.; Finkbeiner, D.; Fukugita, M., New York University value-added galaxy catalog: a galaxy catalog based on new public surveys, Astron J, 129, 2562-2578 (2005) |
| [6] | Blumenfeld, R.; Mandelbrot, BB., Lévy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension, Phys Rev E, 56, 112-118 (1997) |
| [7] | Bondi, H., Spherically symmetrical models in general relativity, MNRAS, 107, 410 (1947) · Zbl 0031.23804 |
| [8] | Borgani, S., The multifractal behaviour of hierarchical density distributions, MNRAS, 260, 537-549 (1993) |
| [9] | Capozziello, S.; Funkhouser, S., Fractal large-scale structure from a stochastic scaling law model, Mod. Phys Lett A, 24, 1743-1748 (2009) · Zbl 1176.85009 |
| [10] | Caruso, F.; Oguri, V., The cosmic microwave background spectrum and an upper limit for fractal space dimensionality, Astrophys J, 694, 151-153 (2009) |
| [11] | Célérier, M.-N., Do we really see a cosmological constant in the supernovae data?, Astron Astrophys, 353, 63-71 (2000) |
| [12] | Chacón-Cardona, CA.; Casas-Miranda, RA., Millennium simulation dark matter haloes: multifractal and lacunarity analysis and the transition to homogeneity, MNRAS, 427, 2613-2624 (2012) |
| [13] | Coleman, PH.; Pietronero, L., The fractal nature of the universe, Phys A Stat Mech Appl, 185, 45-55 (1992) |
| [14] | Durrer, R.; Sylos Labini, F., A fractal galaxy distribution in a homogeneous universe?, Astron Astrophys, 339, L85-L88 (1998) |
| [15] | Enqvist, K., Lemaitre-Tolman-Bondi model and accelerating expansion, Gen Relativ Gravit, 40, 451-466 (2008) · Zbl 1137.83376 |
| [16] | Gabrielli, A.; Sylos; Joyce, M.; Pietronero, L., Statistical physics for cosmic structures (2005), Springer Verlag |
| [17] | Gaite, J., The fractal distribution of haloes, Europhys Lett (EPL), 71, 2, 332 (2005) |
| [18] | Gaite, J., Halos and voids in a multifractal model of cosmic structure, Astrophys J, 658, 11-24 (2007) |
| [19] | Grujić, PV., The concept of a hierarchical cosmos, Publications de l’Observatoire Astronomique de Beograd, 75, 257-262 (2003) |
| [21] | Hamuy, M.; Trager, S. C.; Pinto, P. A.; Phillips, M. M.; Schommer, R. A.; Ivanov, V., A search for environmental effects on type IA supernovae, Astron J, 120, 1479-1486 (2000) |
| [22] | Hausdorff, F., Dimension und ueres ma, Math Ann, 79, 157-179 (1918), 10.1007/BF01457179 · JFM 46.0292.01 |
| [23] | Hogg, D. W.; Eisenstein, D. J.; Blanton, M. R.; Bahcall, N. A.; Brinkmann, J.; Gunn, J. E., Cosmic homogeneity demonstrated with luminous red galaxies, Astrophys J, 624, 54-58 (2005) |
| [24] | Humphreys, N. P.; Matravers, D. R.; Maartens, R., Exact isotropic cosmologies with local fractal number counts, Class Quantum Gravity, 15, 3041-3049 (1998) · Zbl 0942.83074 |
| [25] | Joyce, M.; Sylos Labini, F.; Gabrielli, A.; Montuori, M.; Pietronero, L., Basic properties of galaxy clustering in the light of recent results from the Sloan Digital Sky Survey, Astron Astrophys, 443, 11-16 (2005) |
| [26] | Kobayashi, N.; Yamazaki, Y.; Kuninaka, H.; Katori, M.; Matsushita, M.; Matsushita, S., Fractal structure of isothermal lines and loops on the cosmic microwave background, J Phys Soc Jpn, 80, 7, 074003 (2011) |
| [27] | Komatsu, E.; Dunkley, J.; Nolta, M. R.; Bennett, C. L.; Gold, B.; Hinshaw, G., Five-year Wilkinson microwave anisotropy probe observations: cosmological interpretation, Astrophys J Suppl, 180, 330-376 (2009) |
| [28] | Longair, M., Galaxy formation, Astronomy and astrophysics library (2008), Springer, 9783540734772 |
| [29] | Mandelbrot, B., The fractal geometry of nature (1983), W.H. Freeman, 9780716711865 |
| [30] | Mandelbrot, BB., Galaxy distributions and fractals., Astrophys Lett Commun, 36, 1-5 (1997) |
| [31] | Martínez, V.; Saar, E., Clustering statistics in cosmology, (Starck, J.-L.; Murtagh, F. D., Proceedings of international conference on Society of Photo-Optical Instrumentation Engineers (SPIE) conference series, 4847 (2002)), 86-100 |
| [32] | Martínez, V.; Saar, E., Statistics of the galaxy distribution (2002), Chapman & Hall/CRC, 9781584880844 |
| [33] | Mittal, A.; Lohiya, D., Fractal dust model of the universe based on Mandelbrot’s conditional cosmological principle and general theory of relativity, Fractals, 11, 145-153 (2003) |
| [34] | Muñoz-Cuartas, JC.; Mueller, V., Galaxy groups and haloes in the SDSS-DR7, MNRAS, 423, 1583-1595 (2012) |
| [35] | Nakamichi, A.; Morikawa, M., Is galaxy distribution non-extensive and non-Gaussian?, Phys A Stat Mech Appl, 341, 215-233 (2004) |
| [36] | Peacock, J., Cosmological physics (1999), Cambridge University Press, 9780521422703 · Zbl 0952.83002 |
| [37] | Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, RA.; Nugent, P.; Castro, PG., Measurements of \(Ω\) and \(Λ\) from 42 high-redshift supernovae, Astrophys J, 517, 565-586 (1999) · Zbl 1368.85002 |
| [38] | Provenzale, A.; Spiegel, E. A.; Thieberger, R., Cosmic lacunarity, Chaos, 7, 82-88 (1997) · Zbl 0932.83057 |
| [39] | Ribeiro, MB., On modeling a relativistic hierarchical (fractal) cosmology by Tolman’s spacetime. I. Theory, Astrophys J, 388, 1-8 (1992) |
| [40] | Ribeiro, MB., Cosmological distances and fractal statistics of galaxy distribution, Astron Astrophys, 429, 65-74 (2005) |
| [41] | Riess, AG.; Filippenko, AV.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, PM., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron J, 116, 3, 1009 (1998) |
| [42] | Sarkar, P.; Yadav, J.; Pandey, B.; Bharadwaj, S., The scale of homogeneity of the galaxy distribution in SDSS DR6, MNRAS, 399, L128-L131 (2009) |
| [43] | Scrimgeour, M.; Davis, T.; Blake, C.; James, JB.; Poole, G., The WiggleZ Dark Energy Survey: the transition to large-scale cosmic homogeneity, Mon Not RoyAstron Soc, 425, 116-134 (2012) |
| [44] | Springel, V.; White, SDM.; Jenkins, A.; Frenk, CS.; Yoshida, N.; Gao, L., Simulations of the formation, evolution and clustering of galaxies and quasars, Nature, 435, 629-636 (2005) |
| [45] | Sylos Labini, F.; Vasilyev, NL.; Pietronero, L.; Baryshev, YV., Absence of self-averaging and of homogeneity in the large-scale galaxy distribution, Europhys Lett (EPL), 86, 49001 (2009) |
| [46] | Uchaikin, VV., If the universe were a Levy-Mandelbrot fractal, Gravit Cosmol, 10, 5-24 (2004) · Zbl 1077.83059 |
| [47] | Verevkin, AO.; Bukhmastova, YL.; Baryshev, YV., The non-uniform distribution of galaxies from data of the SDSS DR7 survey, Astron Rep, 55, 324-340 (2011) |
| [48] | Wald, R., General relativity (2010), University of Chicago Press, 9780226870373 |
| [49] | Yadav, JK.; Bagla, JS.; Khandai, N., Fractal dimension as a measure of the scale of homogeneity, MNRAS, 405, 2009-2015 (2010) |
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