Accreting matter around clusters of galaxies: one-dimensional considerations

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Abstract
During the formation of large-scale structure in the Universe, matter accretes on to high-density peaks. Accreting collisionless dark matter (DM) forms caustics around them, while accreting collisional baryonic matter (BM) forms accretion shocks. The properties of the accreting matter depend upon the power spectrum of the initial perturbations on a given scale as well as the background expansion in a given cosmological model. In this paper, we have calculated the accretion of DM particles in one-dimensional spherical geometry under various cosmological models including the Einstein-de Sitter universe, the open universe with Ω0 < 1, and the flat universe with ΩΛ= 1Ω0 — Ω0. A density parameter in the range 0.1 ≤ Ω0 ≤ 1 has been considered. The initial perturbation characterized by a point mass at the origin has been considered. Since the accretion shock of BM is expected to form close to the first caustic of DM, the properties of the accreting BM are common with those of the DM. Hence, the accretion calculations with DM particles have been used to find the position and velocity of the accretion shock and the cluster mass inside it. The average temperature of BM has been estimated by adopting simplifying assumptions. The velocity of the accreting BM around clusters of a given temperature is lower in a universe with lower Ω0 but only by up to ∼ 24 per cent in the models with 0.1≤Ω0≤l. Thus, it would be difficult to use that quantity to discriminate among the cosmological models. However, the accretion velocity around clusters of a given mass or a given radius depends more sensitively on the cosmological models. It is lower in a universe with lower Ω0 by up to ∼ 41 and ∼ 65 per cent, respectively. So, it can provide a better signature of the background expansion for different cosmological models. Although the existence of the caustics and the accretion shocks may not be confirmed by direct X-ray observations, the infalling warm gas of 104−105 K upstream of the shocks may be observed as the absorption systems of quasar emission lines. According to this study, the suggestion made by Kang, Ryu & Jones that the large-scale accretion shocks around clusters of galaxies can serve as possible acceleration sites of ultrahigh-energy cosmic rays above 1018 eV remains plausible in all viable cosmological models.
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