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Large-Scale Structure Formation: From the First Non-linear Objects to Massive Galaxy Clusters

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Abstract

The large-scale structure of the Universe formed from initially small perturbations in the cosmic density field, leading to galaxy clusters with up to 1015 M⊙ at the present day. Here, we review the formation of structures in the Universe, considering the first primordial galaxies and the most massive galaxy clusters as extreme cases of structure formation where fundamental processes such as gravity, turbulence, cooling and feedback are particularly relevant. The first non-linear objects in the Universe formed in dark matter halos with 105–108 M⊙ at redshifts 10–30, leading to the first stars and massive black holes. At later stages, larger scales became non-linear, leading to the formation of galaxy clusters, the most massive objects in the Universe. We describe here their formation via gravitational processes, including the self-similar scaling relations, as well as the observed deviations from such self-similarity and the related non-gravitational physics (cooling, stellar feedback, AGN). While on intermediate cluster scales the self-similar model is in good agreement with the observations, deviations from such self-similarity are apparent in the core regions, where numerical simulations do not reproduce the current observational results. The latter indicates that the interaction of different feedback processes may not be correctly accounted for in current simulations. Both in the most massive clusters of galaxies as well as during the formation of the first objects in the Universe, turbulent structures and shock waves appear to be common, suggesting them to be ubiquitous in the non-linear regime.

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Notes

  1. The Jeans length, the characteristic length scale for the self-gravity of the gas, is defined as \(\lambda_{J}=\sqrt{\frac{15k_{\mathrm{B}} T}{4\pi G\mu\rho_{\it gas}}}\), with k B the Boltzmann constant, T the gas temperature, G the Newton’s constant, μ the mean molecular weight and \(\rho_{\it gas}\) the mass density of the gas.

  2. The functional form of the window function, which depends on the particular choice of filter, provides the connection between mass and smoothing scale. Two common filter functions are W R (k)=3[sin(kR)−kRcos(kR)]/(kR)3 and W R (k)=exp(−(kR)2/2) corresponding to the top-hat and the Gaussian windows, respectively. For each of these filters, the correspondent relation between mass and smoothing scale is given by \(M=(4\pi/3)R^{3}\bar{\rho}\) and \(M=(2\pi R^{2})^{3/2}\bar{\rho}\).

  3. Early redshift surveys showed that σ∼1 for spheres of R=8 h−1 Mpc (e.g. Davis and Peebles 1983).

  4. On the contrary, the linear-theory extrapolation to t ta yields a smaller value: δ +(t ta )≃1.07.

  5. While the FoF algorithm identifies DM halos with groups of DM particles separated by a distance shorter than a given linking length parameter, the SO algorithm is based on the mean overdensity criterion.

  6. In the general case, however, this overdensity depends weakly on redshift and cosmology (for example, δ c ≃1.675 in a ΛCDM model at z=0).

  7. The fit obtained for the HMF based on the FoF halos takes the form: \(f(\sigma)=A [ (\frac{\beta}{\sigma} )^{\alpha}+1 ]e^{-\gamma /\sigma^{2}}\), with A=0.282, α=2.163, β=1.406, and γ=1.210. This fit holds for −0.55≤lnσ −1<1.31, corresponding to masses within [1.8×1012,7.0×1015] h−1 M⊙ at z=0.

  8. http://kromepackage.org/.

  9. Based on the Forrey (2013) calculation, the chemical uncertainties are thus strongly reduced.

  10. The Mach number, which characterizes the strength of a shock, is given by \(\mathcal{M}=v_{s}/c_{s}\), where v s is the shock speed and c s is the sound speed ahead of the shock.

  11. It is important to point out that the Bondi approach is the simplest model of gas accretion. A number of studies (e.g. Hobbs et al. 2012; Gaspari et al. 2013) have already highlighted the main drawbacks of this approach and the necessity of adopting alternative and more realistic schemes.

  12. An alternative formation scenario for the star SDSS J1029151+172927 has been recently proposed by MacDonald et al. (2013), who suggest that it may have been a subgiant formed with significantly higher metallicity in the vicinity of a SN-Ia.

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Acknowledgements

We would like to thank the ISSI staff for their hospitality and for providing an inspiring atmosphere at the International Space Science Institute Workshop in Bern in 2013. We also would like to thank the anonymous referee for his/her constructive comments. S. Planelles acknowledges support by the PRIN-INAF09 project “Towards an Italian Network for Computational Cosmology” and by the PRIN-MIUR09 “Tracing the growth of structures in the Universe”. D.R.G. Schleicher thanks for funding from the German Science Foundation (DFG) in the DFG priority program SPP 1573 “Physics of the Interstellar Medium” under grant SCHL 1964/1-1, and via the collaborative research center (CRC) 963/1 “Astrophysical flow instabilities and turbulence” (project A12). A.M. Bykov was supported in part by RAS Presidium and OFN 15 and 17 programs. We further thank for stimulating discussions with Stefano Borgani, Stefano Bovino, Muhammad Latif, Wolfram Schmidt, Jens Niemeyer and Barbara Sartoris.

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Authors and Affiliations

  1. Department of Astronomy, University of Trieste, via Tiepolo 11, 34143, Trieste, Italy

    S. Planelles

  2. INAF—National Institute for Astrophysics, Trieste, Italy

    S. Planelles

  3. Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    D. R. G. Schleicher

  4. A.F. Ioffe Institute for Physics and Technology, 194021, St. Petersburg, Russia

    A. M. Bykov

  5. St. Petersburg State Politechnical University, St. Petersburg, Russia

    A. M. Bykov

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  1. S. Planelles
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  2. D. R. G. Schleicher
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  3. A. M. Bykov
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Correspondence to S. Planelles.

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Planelles, S., Schleicher, D.R.G. & Bykov, A.M. Large-Scale Structure Formation: From the First Non-linear Objects to Massive Galaxy Clusters. Space Sci Rev 188, 93–139 (2015). https://doi.org/10.1007/s11214-014-0045-7

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