2.6 Cross-section constraints from galaxy clusters

Clusters of galaxies present an interesting environment in which the dark matter density is high and where processes such as collisions present the possibility of distinguishing dark matter from baryonic matter as the two components interact differently. For instance, particulate dark matter and baryonic matter may be temporarily separated during collisions between galaxy clusters, such as 1E 0657-56 [244, 164] and MACS J0025.4-1222 [162]. These ‘bullet clusters’ have provided astrophysical constraints on the interaction cross-section of hypothesized dark matter particles [750], and may ultimately prove the most useful laboratory in which to test for any velocity dependence of the cross-section. Unfortunately, the contribution of individual systems is limited by uncertainties in the collision velocity, impact parameter and angle with respect to the plane of the sky. Current constraints are three orders of magnitude weaker than constraints from the shapes of haloes [361] and, since collisions between two massive progenitors are rare [818, 819], the total observable number of such systems may be inadequate to investigate a physically interesting regime of dark matter properties.

Current constraints from bullet clusters on the cross-section of particulate dark matter are ∼ 18 orders of magnitude larger than that required to distinguish between plausible particle-physics dark matter candidates (for example from supersymmetric extensions to the standard model). In order to investigate a physically interesting régime of dark matter cross-section, and provide smaller error bars, many more individual bullet clusters are required. However collisions between two massive progenitors are rare and ultimately the total observable number of such systems may be inadequate.

2.6.1 Bulleticity

In [643], a method for using every individual infalling substructure in every cluster has been proposed. For each piece of infalling substructure, a local vector from the dark matter peak (identified using weak lensing analysis) and the baryonic mass peak (from X-rays) – dubbed ‘bulleticity’ – can be defined

b = breˆr + btˆet, (2.6.1 )
where the radial b r and azimuthal b t components are defined relative to unit vector towards the cluster center and tangentially and b = |b|. An integrated bulleticity signal of zero would imply an equal cross sections for the dark matter and baryonic matter. By measuring the amplitude of the bulleticity one can empirically measure the ratio between the dark matter and baryonic cross sections.

In Figure 35View Image a result from full hydrodynamical simulations of dark and baryonic matter within clusters in shown. [643] have used these simulations to show that the measurement of a net bulleticity consistent with the cold dark matter used in the simulations is possible.

View Image

Figure 35: Full hydrodynamical simulations of massive clusters at redshift z = 0.6. Total projected mass is shown in blue, while X-ray emission from baryonic gas is in red. The preferential trailing of gas due to pressure from the ICM, and its consequent separation from the non interacting dark matter, is apparent in much of the infalling substructure.

Finally, a Fisher matrix calculation has shown that, under the assumption that systematic effects can be controlled, Euclid could use such a technique to constrain the relative particulate cross-sections to 6 × 10− 27 cm2 GeV −1.

The raw bulleticity measurement would constrain the relative cross-sections of the baryon-baryon interaction and the dark matter-dark matter interaction. However, since we know the baryonic cross-section relatively well, we can infer the dark matter-dark matter cross-section. The dark matter-dark matter interaction probed by Euclid using this technique will be complementary to the interactions constrained by direct detection and accelerator experiments where the primary constraints will be on the dark matter-baryon interaction.


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