Clustering statistics in cosmology

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 4847, Issue , 2002, Pages 86-100

  Martínez, Vicent J ^a   Saar, Enn ^b  

^a UNIVERSITY OF VALENCIA   (Spain)

^b TARTU OBSERVATORY   (Estonia)

Author keywords

Galaxies: statistics; Large scale structure of universe; Methods: data analysis; Methods: statistical; Surveys

Indexed keywords

DATA REDUCTION; FUNCTIONS; GALAXIES; STATISTICAL METHODS;

COSMOLOGY;

ASTRONOMY;

EID: 0038301338     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.461972     Document Type: Conference Paper

References (63)

1. V. J. Martínez and E. Saar, Statistics of the Galaxy Distribution, Chapman and Hall/CRC Press, Boca Raton, 2002.
2. W. L. Freedman, B. F. Madore, B. K. Gibson, L. Ferrarese, D. D. Kelson, S. Sakai, J. R. Mould, R. C. Kennicutt, H. C. Ford, J. A. Graham, J. P. Huchra, S. M. G. Hughes, G. D. Illingworth, L. M. Macri, and P. B. Stetson, "Final results from the Hubble Space Telescope Key Project to measure the Hubble constant," Astrophys. J. 553, pp. 47-72, 2001.
3. A. J. S. Hamilton, "Linear redshift distortions: A review," in The Evolving Universe, Astrophysics and Space Science Library 231, pp. 185-275, Kluwer Academic Publishers, (Dordrecht), 1998.
4. L. Guzzo, "Large-scale structure from galaxy and cluster surveys," in DARK2002, 4th Heidelberg Int. Conference on Dark Matter in Astro- and Particle Physics, H.-V. Klapdor-Kleingrothaus and R. Viollier, eds., Springer-Verlag, 2002. In press, astro-ph/0207285.
5. V. de Lapparent, M. J. Geller, and J. P. Huchra, "A slice of the universe," Astrophys. J. Lett. 302, pp. L1-L5, 1986.
6. S. A. Shectman, S. D. Landy, A. Oemler, D. L. Tucker, H. Lin, R. P. Kirshner, and P. L. Schechter, "The Las Campanas Redshift Survey," Astrophys. J. 470, p. 172, 1996.
7. V. J. Martínez, "Is the universe fractal?," Science 284, pp. 445-446, 1999.
8. R. P. Kirshner, "Galaxy redshift surveys," in Dark Matter in the Universe, S. Bonometto, J. R. Primack, and A. Provenzale, eds., pp. 36-48, IOS Press, (Amsterdam), 1996.
9. V. J. Martínez, "Non-fractality on large scales," in New Cosmological Data and the Values of the Fundamental Parameters, IAU Symposium, A. N. Lasenby and A. Wilkinson, eds., 201, Astronomical Society of the Pacific, San Francisco, 2002. In press.
10. J. A. Peacock, S. Cole, P. Norberg, C. M. Baugh, J. Bland-Hawthorn, T. Bridges, R. D. Cannon, M. Colless, C. Collins, W. Couch, G. Dalton, K. Deeley, R. D. Propris, S. P. Driver, G. Efstathiou, R. S. Ellis, C. S. Frenk, K. Glazebrook, C. Jackson, O. Lahav, I. Lewis, S. Lumsden, S. Maddox, W. J. Percival, B. A. Peterson, I. Price, W. Sutherland, and K. Taylor, "A measurement of the cosmological mass density from clustering in the 2dF galaxy redshift survey," Nature 410, pp. 169-173, 2001.
11. J. Loveday, "The Sloan Digital Sky Survey," Contemporary Physics, 2002. In press, astro-ph/0207189.
12. P. Schechter, "An analytic expression for the luminosity function for galaxies.," Astrophys. J. 203, pp. 297-306, 1976.
13. D. J. Schlegel, D. P. Finkbeiner, and M. Davis, "Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds," Astrophys. J. 500, pp. 525-553, 1998.
14. P. J. E. Peebles, The Large-Scale Structure of the Universe, Princeton University Press, Princeton, 1980.
15. H. Totsuji and T. Kihara, "The correlation function for the distribution of galaxies," Publ. Astron. Soc. Japan 21, p. 221, 1969.
16. M.-J. Pons-Bordería, V. J. Martínez, D. Stoyan, H. Stoyan, and E. Saar, "Comparing estimators of the galaxy correlation function," Astrophys. J. 523, pp. 480-491, 1999.
17. M. Kerscher, I. Szapudi, and A. S. Szalay, "A comparison of estimators for the two-point correlation function," Astrophys. J. 535, pp. L13-L16, 2000.
18. A. J. S. Hamilton, "Toward better ways to measure the galaxy correlation function," Astrophys. J. 417, pp. 19-35, 1993.
19. S. D. Landy and A. S. Szalay, "Bias and variance of angular correlation functions," Astrophys. J. 412, pp. 64-71, 1993.
20. D. Stoyan, W. Kendall, and J. Mecke, Stochastic Geometry and its Applications, John Wiley & Sons, Chichester, 1995.
21. M. Snethlage, V. J. Martínez, D. Stoyan, and E. Saar, "Point field models for the galaxy point pattern. Modelling the singularity of the two-point correlation function," Astron. Astrophys. 388, pp. 758-765, 2002.
22. V. J. Martínez, M. Portilla, B. J. T. Jones, and S. Paredes, "The galaxy clustering correlation length," Astron. Astrophys. 280, pp. 5-19, 1993.
23. D. L. Tucker, A. Oemler, R. P. Kirshner, H. Lin, S. A. Shectman, S. D. Landy, P. L. Schechter, V. Muller, S. Gottlober, and J. Einasto, "The Las Campanas Redshift Survey galaxy-galaxy autocorrelation function," Mon. Not. R. Astr. Soc. 285, pp. L5-L9, 1997.
24. I. Zehavi, M. R. Blanton, J. A. Frieman, D. H. Weinberg, H. J. Mo, M. A. Strauss, S. F. Anderson, J. Annis, N. A. Bahcall, M. Bernardi, J. W. Briggs, J. Brinkmann, S. Burles, L. Carey, F. J. Castander, A. J. Connolly, I. Csabai, J. J. Dalcanton, S. Dodelson, M. Doi, D. Eisenstein, M. L. Evans, D. P. Finkbeiner, S. Friedman, M. Fukugita, J. E. Gunn, G. S. Hennessy, R. B. Hindsley, Ž. Ivezić, S. Kent, G. R. Knapp, R. Kron, P. Kunszt, D. Q. Lamb, R. F. Leger, D. C. Long, J. Loveday, R. H. Lupton, T. McKay, A. Meiksin, A. Merrelli, J. A. Munn, V. Narayanan, M. Newcomb, R. C. Nichol, R. Owen, J. Peoples, A. Pope, C. M. Rockosi, D. Schlegel, D. P. Schneider, R. Scoccimarro, R. K. Sheth, W. Siegmund, S. Smee, Y. Snir, A. Stebbins, C. Stoughton, M. SubbaRao, A. S. Szalay, I. Szapudi, M. Tegmark, D. L. Tucker, A. Uomoto, D. Vanden Berk, M. S. Vogeley, P. Waddell, B. Yanny, and D. G. York, "Galaxy clustering in early Sloan Digital Sky Survey redshift data," Astrophys. J. 571, pp. 172-190, 2002.
25. C. M. Baugh, "The real space correlation function measured from the APM galaxy survey," Mon. Not. R. Astr. Soc. 280, pp. 267-275, 1996.
26. L. Pietronero, M. Montuori, and F. Sylos-Labini, "On the fractal structure of the visible universe," in Critical Dialogues in Cosmology, N. Turok, ed., pp. 24-49, 1997.
27. M. Davis, "Is the universe homogeneous on large scales?," in Critical Dialogues in Cosmology, N. Turok, ed., pp. 13-23, 1997.
28. L. Guzzo, "Is the universe homogeneous? (on large scales)," New Astronomy 2, pp. 517-532, 1997.
29. V. J. Martínez, M. Pons-Bordería, R. A. Moyeed, and M. J. Graham, "Searching for the scale of homogeneity," Mon. Not. R. Astr. Soc. 298, pp. 1212-1222, 1998.
30. A. Cappi, C. Benoist, L. N. da Costa, and S. Maurogordato, "Is the Universe a fractal? Results from the Southern Sky Redshift Survey 2," Astron. Astrophys. 335, pp. 779-788, 1998.
31. K. K. S. Wu, O. Lahav, and M. J. Rees, "The large-scale smoothness of the universe," Nature 397, pp. 225-235, 1999.
32. R. Scaramella, L. Guzzo, G. Zamorani, E. Zucca, C. Balkowski, A. Blanchard, A. Cappi, V. Cayatte, G. Chincarini, C. Collins, A. Fiorani, D. Maccagni, H. MacGillivray, S. Maurogordato, R. Merighi, M. Mignoli, D. Proust, M. Ramella, G. M. Stirpe, and G. Vettolani, "The ESO Slice Project [ESP] galaxy redshift survey: V. Evidence for a D=3 sample dimensionality," Astr. Astrophys. 334, pp. 404-408, 1998.
33. S. Hatton, "Approaching a homogeneous galaxy distribution: Results from the Stromlo-APM redshift survey," Mon. Not. R. Astr. Soc. 310, pp. 1128-1136, 1999.
34. L. Amendola and E. Palladino, "The scale of homogeneity in the Las Campanas redshift survey," Astrophys. J. Lett. 514, pp. L1-L4, 1999.
35. J. Pan and P. Coles, "Large-scale cosmic homogeneity from a multifractal analysis of the PSCz catalogue," Mon. Not. R. Astr. Soc. 318, pp. L51-L54, 2000.
36. T. Kurokawa, M. Morikawa, and H. Mouri, "Scaling analysis of galaxy distribution in the Las Campanas Redshift Survey data," Astron. Astrophys. 370, pp. 358-364, 2001.
37. M. Colless, G. Dalton, S. Maddox, W. Sutherland, P. Norberg, S. Cole, J. Bland-Hawthorn, T. Bridges, R. Cannon, C. Collins, W. Couch, N. Cross, K. Deeley, R. De Propris, S. P. Driver, G. Efstathiou, R. S. Ellis, C. S. Frenk, K. Glazebrook, C. Jackson, O. Lahav, I. Lewis, S. Lumsden, D. Madgwick, J. A. Peacock, B. A. Peterson, I. Price, M. Seaborne, and K. Taylor, "The 2dF Galaxy Redshift Survey: spectra and redshifts," Mon. Not. R. Astr. Soc. 328, pp. 1039-1063, 2001.
38. M. Davis, A. Meiksin, M. A. Strauss, L. N. da Costa, and A. Yahil, "On the universality of the two-point galaxy correlation function," Astrophys. J. Lett. 333, pp. L9-LL12, 1988.
39. V. J. Martínez, B. López-Martí, and M.-J. Pons-Bordería, "Does the galaxy correlation length increase with the sample depth?," Astrophys. J. 554, pp. L5-L8, 2001.
40. C. Allain and M. Cloitre, "Characterizing the lacunarity of random and deterministic fractal sets," Phys. Rev. A 44, pp. 3552-3558, 1991.
41. R. E. Plotnick, R. H. Gardner, W. W. Hargrove, K. Prestegaard, and M. Perlmutter, "Lacunarity analysis: A general technique for the analysis of spatial patterns," Phys. Rev. E 53, pp. 5461-5468, 1996.
42. J. Gaite and S. C. Manrubia, "Scaling of voids and fractality in the galaxy distribution," Mon. Not. R. Astr. Soc. 335, pp. 977-983, 2002.
43. R. Blumenfeld and B. Mandelbrot, "Lévy dusts, Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension," Phys. Rev. E 56, pp. 112-118, 1997.
44. B. B. Mandelbrot, "Sur un modèle décomposable d'Univers hiérarchisé: déduction des corrélations galactiques sur la spheère céleste," C.R. Acad. Sci. (Paris) A 280, pp. 1551-1554, 1975.
45. R. M. Soneira and P. J. E. Peebles, "A computer model universe - Simulation of the nature of the galaxy distribution in the Lick catalog," Astronom. J. 83, pp. 845-849, 1978.
46. V. J. Martínez, B. J. T. Jones, R. Domínguez-Tenreiro, and R. van de Weygaert, "Clustering paradigms and multifractal measures," Astrophys. J. 357, pp. 50-61, 1990.
47. H. A. Feldman, N. Kaiser, and J. A. Peacock, "Power-spectrum analysis of three-dimensional redshift surveys," Astrophys. J. 426, pp. 23-37, 1994.
48. M. Tegmark, A. J. S. Hamilton, M. A. Strauss, M. S. Vogeley, and A. S. Szalay, "Measuring the galaxy power spectrum with future redshift surveys," Astrophys. J. 499, pp. 555-576, 1998.
49. W. J. Percival, C. M. Baugh, J. Bland-Hawthorn, T. Bridges, R. Cannon, S. Cole, M. Colless, C. Collins, W. Couch, G. Dalton, R. De Propris, S. P. Driver, G. Efstathiou, R. S. Ellis, C. S. Frenk, K. Glazebrook, C. Jackson, O. Lahav, I. Lewis, S. Lumsden, S. Maddox, S. Moody, P. Norberg, J. A. Peacock, B. A. Peterson, W. Sutherland, and K. Taylor, "The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe," Mon. Not. R. Astr. Soc. 327, pp. 1297-1306, 2001.
50. M. Tegmark, A. J. S. Hamilton, and Y. Xu, "The power spectrum of galaxies in the 2dF 100k redshift survey," Man. Not. R. Astr. Soc. 335, pp. 887-908, 2002.
51. P. Schuecker, H. Böhringer, L. Guzzo, C. A. Collins, D. M. Neumann, S. Schindler, W. Voges, S. De Grandi, G. Chincarini, R. Cruddace, V. Müller, T. H. Reiprich, J. Retzlaff, and P. Shaver, "The ROSAT-ESO Flux-Limited X-Ray (REFLEX) galaxy cluster survey. III. The power spectrum," Astron. Astrophys. 368, pp. 86-106, 2001.
52. E. Gaztañaga, "N-point correlation functions in the CfA and SSRS redshift distribution of galaxies," Astrophys. J. Lett. 398, pp. L17-L20, 1992.
53. P. J. E. Peebles, "The galaxy and mass N-point correlation functions: a blast from the past," in ASP Conf. Ser. 252: Historical Development of Modern Cosmology, V. J. Martínez, V. Trimble, and M. J. Pons-Bordería, eds., pp. 201-218, Astronomical Society of the Pacific, San Francisco, 2001.
54. I. Gott, J. R., M. Dickinson, and A. L. Melott, "The sponge-like topology of large-scale structure in the universe," Astrophys. J. 306, pp. 341-357, 1986.
55. R. J. Adler, The Geometry of Random Fields, John Wiley & Sons, New York, 1981.
56. K. R. Mecke, T. Buchert, and H. Wagner, "Robust morphological measures for large-scale structure in the universe," Astron. Astrophys. 288, pp. 697-704, 1994.
57. M. Kerscher, J. Schmalzing, J. Retzlaff, S. Borgani, T. Buchert, S. Gottlober, V. Muller, M. Plionis, and H. Wagner, "Minkowski functionals of Abell/ACO clusters," Mon. Not. R. Astr. Soc. 284, pp. 73-84,1997.
58. S. Maurogordato and M. Lachieze-Rey, "Void probabilities in the galaxy distribution - scaling and luminosity segregation," Astrophys. J. 320, pp. 13-25, 1987.
59. M. Kerscher, M. Pons-Bordería, J. Schmalzing, R. Trasarti-Battistoni, T. Buchert, V. J. Martínez, and R. Valdarnini, "A global descriptor of spatial pattern interaction in the galaxy distribution," Astrophys. J. 513, pp. 543-548, 1999.
60. J. D. Barrow, D. H. Sonoda, and S. P. Bhavsar, "Minimal spanning trees, filaments and galaxy clustering," Mon. Not. R. Astr. Soc. 216, pp. 17-35, 1985.
61. A. G. Doroshkevich, V. Müller, J. Retzlaff, and V. Turchaninov, "Superlarge-scale structure in N-body simulations," Mon. Not. R. Astr. Soc. 306, pp. 575-591, 1999.
62. P. Querre, J.-L. Starck, and V. J. Martínez, "Analysis of the galaxy distribution using multiscale methods," in SPIE conference on Astronomical Telescopes and Instrumentation: Astronomical Data Analysis II, J.-L. Stark and F. Murtagh, eds., SPIE, 2002.
63. D. L. Donoho, O. Levi, J.-L. Starck, and V. J. Martínez, "Multiscale geometric analysis for 3-D catalogs," in SPIE conference on Astronomical Telescopes and Instrumentation: Astronomical Data Analysis II, J.-L. Stark and F. Murtagh, eds., SPIE, 2002.