International Astronomy and Astrophysics Research Journal

Study of f(T) Mass Function of Nearby Galaxy Clusters: Determining σ8

Mohammad Shafi Khan *

Government Degree College Sumbal, University of Kashmir, Srinagar, 193501, J&K, India.

*Author to whom correspondence should be addressed.

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Abstract

This paper presents a new analytical method to determine amplitude of density fluctuations of 152 nearby clusters (z ≤ 0.15). We investigate the rms linear fluctuation in the mass distribution on scales of 8h−1M pc i.e. σ8 , by using Press-Shechter mass function. The mass function is estimated for masses larger than Mlim = 4 ×1014h−1M⊙. We find rms density fluctuation equal to 0.52 for the critical density universe. The results found are consistent with those, obtained with alternative models for the high density universe. The results agree with the previous papers obtained from different models and considerations. This takes us to introduce a new approach to estimate the cosmological parameters. For critical density , the slight variation in results may be due to the fact that there are observational uncertainties in estimates of cluster masses, which are in general not neglegible.

Keywords: Galaxies, clusters, general - cosmological parameters theory, large-scale structure of the universe

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References

Vikhlinin A, et.al. Chandra cluster cosmology project III: cosmological parameter constraints. ApJ. 2009;692:1060.

b102 Khan MS, Malik MA. Critical phenomena in the cosmological many body problem. Monthly Notices of the Royal Astronomical Society. 2012;421:2629.

Khan MS, Malik MA. Lee yang theory for cosmological many body problem, Astrophs. Space Sci. 2013;348:211.

Hasselfield M. et.al. The atacama cosmology telescope: Sunyaev-Zel’dovich selected galaxy clusters at 148 GHz from three seasons of data. J. Cosmol. Astropart. Phys. 2013;07:008.

Khan MS, Abdullah HM, Ali GB, A comparison between observed and analytical velocity dispersion profiles of 20 nearby galaxy clusters, Astrophs. Space Sci. 2014;351:289.

Jenkins A. et.al. The mass function of dark matter haloes. Monthly Notices of the Royal Astronomical Society. 2001;321:372.

Tinker et. al. Toward a halo mass function for precision cosmology: the limits of universality. ApJ. 2008;688:709.

Watson WA. et. al. The halo mass function through the cosmic ages. Monthly Notices of the Royal Astronomical Society. 2013;433:1230.

Press WH, Shecter P. Formation of galaxies and clusters of galaxies by self-similar gravitational condensation. ApJ, 1974; 187: 425.

Mandelbaum R. et. al. Cosmological parameter constraints from galaxygalaxy lensing and galaxy clustering with the SDSS DR7. Monthly Notices of the Royal Astronomical Society. 2013;432:1544-1575.

Girardi M, Borgani S, Giuricin G. et.al. The observational mass function of nearby galaxy clusters. ApJ. 1998;506:45.

Cusworth SJ, et.al. Impact of baryons on the cluster mass function and cosmological parameter determination. Monthly Notices of the Royal Astronomical Society. 2014;439:2485-2493.

Lacey C, Cole S. Merger rates in hierarchical models of galaxy formation - Part Two - comparison with N-Body simulations. Monthly Notices of the Royal Astronomical Society. 1994;271:676.

Viana P.P., and Liddle A.R., The cluster abundance in flat and open cosmologies, Monthly Notices of the Royal Astronomical Society, 1996; 281: 323.

Eke VR, Cole S, Frenk C. Cluster evolution as a diagnostic for Ω, Monthly Notices of the Royal Astronomical Society. 1996;282:263.

Markevitch M. The LX-T relation and temperature function for nearby clusters revisited. ApJ. 1998;504(1):27-34.

Henry JP, Arnaud KA. A Measurement of the mass fluctuation spectrum from the cluster X-Ray temperature function. ApJ. 1991;372:410.

White SDM, Efstathiou G, Frenk CS. The amplitude of mass fluctuations in the Universe. Monthly Notices of the Royal Astronomical Society. 1993;262:1023.

Edge AC, et.al. An X-ray flux-limited sample of clusters of galaxies: evidence for evolution of the luminosity function. Monthly Notices of the Royal Astronomical Society. 1990;245:559.

Oukbir J, et.al. X-Ray galaxy clusters: constraints on models of galaxy formation. Astronomy and Astrophysics. 1997;320:365.

Borgani S, et.al. Cosmological constraints from the clustering properties of the X ray Brightest Abell-type Cluster sample. Monthly Notices of the Royal Astronomical Society. 1999;305:4:866-874.

Hudson MJ, Turnbull SJ. The growth rate of cosmic structure from peculiar velocities at low and high redshifts. The Astrophysical Journal Letters. 2012;751:2-5.

Aghanim et. al., Planck 2018 results VI. Cosmological parameters. Astronomy and Astrophysics. 2020;641(A6):67.

Aghanim et. al., Planck 2018 results I. overview and the cosmological legacy of planck. Astronomy and Astrophysics. 2020;641:A1.

Sheth RK, Tormen G. An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier. Monthly Notices of the Royal Astronomical Society. 2002;329:61.