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Centro de Astrofísica da Universidade do Porto

CAUP Researchers: António C. da Silva
Team at CAUP: Galaxies and Observational Cosmology
Other Researchers: Andrea Catalano (FR), Ludovic Montier (FR), Etienne Pointecouteau (FR), Joseph Lanoux (FR), Martin Giard (FR)

The impact of dust on the scaling properties of galaxy clusters,
Monthly Notices of the Royal Astronomical Society, Volume 396, pp. 849 (2009)

We investigate the effect of dust on the scaling properties of galaxy clusters based on hydrodynamic N-body simulations of structure formation. We have simulated five dust models plus radiative cooling and adiabatic models using the same initial conditions for all runs. The numerical implementation of dust was based on the analytical computations of Montier & Giard. We set up dust simulations to cover different combinations of dust parameters that make evident the effects of size and abundance of dust grains. Comparing our radiative plus dust cooling runs with a purely radiative cooling simulation, we find that dust has an impact on cluster scaling relations. It mainly affects the normalization of the scalings (and their evolution), whereas it introduces no significant differences in their slopes. The strength of the effect critically depends on the dust abundance and grain size parameters as well as on the cluster scaling. Indeed, cooling due to dust is effective in the cluster regime and has a stronger effect on the 'baryon driven' statistical properties of clusters such as LX-M, Y-M, S-M scaling relations. Major differences, relative to the radiative cooling model, are as high as 25 per cent for the LX-M normalization, and about 10 per cent for the Y-M and S-M normalizations at redshift zero. On the other hand, we find that dust has almost no impact on the 'dark matter driven' Tmw-M scaling relation. The effects are found to be dependent in equal parts on both dust abundances and grain size distributions for the scalings investigated in this paper. Higher dust abundances and smaller grain sizes cause larger departures from the radiative cooling (i.e. with no dust) model.

Figure 1 | Cluster scalings at redshift zero for Tmw-M (left panel) and S-M, (right panel). Displayed quantities are computed within R200, the radius where the mean cluster density is 200 times larger than the critical density. Blue colour and triangles stand for the cooling (C) run, cyan and diamonds are for the D4 run, yellow and filled circles are for clusters in the D2 run, and red and crosses are for the D1 run. The lines in the embedded plots are the best-fitting lines to the cluster distributions and the shaded areas are the fit rms dispersions for the C model, for each scaling.

The baryonic component of the Universe is ruled, together with gravity, by non-gravitational processes since the first stages of stellar formation. Therefore, the study of gravitational processes is vital to our understanding of the formation and evolution of the large-scale structure of the Universe. We now know that the intragalactic medium (IGM) and the intracluster medium (ICM) are constantly enriched in metal, gas, stars and dust by several processes, including active galactic nuclei (AGN) feedback, supernova-driven galactic winds, ram-pressure striping and by interaction between the ICM and IGM taking place during merger events. Some studies have already been done regarding the effects of these components of the IGM and ICM, but the role played by dust is less well known. Nevertheless, it has already been shown that dust can be an important cooling/heating vector and, thus, its contribution to the formation and evolution of the large scale structures of the Universe must not be overlooked. In order to address the issue of the impact of dust on the statistical properties of structures such as clusters of galaxies, we ran the first N-body numerical simulations of hierarchical structure formation implementing the cooling effect of dust according to the dust nature and abundance. The first results of this work, focusing in the scaling properties of galaxy clusters, were presented in this paper.

The implementation of the physical effects of the dust model was based on the computations by Montier and Giard (2004) of the dust heating/cooling function. However, the heating by dust grains is mainly effective at temperatures below ~105 K and in the presence of strong UV fields, which happens only at a local scale and not at the clusters' typical scales. Therefore, we have chosen to implement only the dust cooling effect, which results from re-radiation in the infrared of the collisional energy deposited on grains by impinging free electrons of the ICM/IGM. As this is a first step in the computation of dust effects on the large scale structures' evolution, we did not yet account for mechanisms of dust creation and destruction. The cooling effect of dust depends on the electronic temperature and density of the medium and also on the dust temperature and grain sizes, with smaller grains presenting higher cooling power. The distribution of dust, which is a vital parameter for our simulations, is linked to the star formation rate (SFR) but, as we don't compute the SFR in our hydrodynamic simulations, we assumed the distribution of dust particles mimics that of metals, with these distributions being related by a constant, ƒd.

Besides an adiabatic and a radiative run (both with no dust), we tested a total of five dust models, with three different grain sizes: a=0.5 μm ("big" grains), a=10-3 μm ("small" grains) and a distribution as the one found by Mathis, Rumpl & Nordsieck (N(a) ∝ a-3.5, for a within the range 0.001-0.5 μm, hereafter referenced as "MRN"). We also tested three different values (0.001, 0.01 and 0.1) for ƒd, which cover the current theoretical and observational range for dust abundances in the ICM/IGM (table 1). In the simulations including dust effects, the total cooling rates are given by the added effect of cooling due to dust and radiative gas cooling.

RunPhysicsƒdGrain size
AAdiabatic (no dust)--
CCooling (no dust)--
D1Cooling with dust0.100Small
D2Cooling with dust0.100MRN
D3Cooling with dust0.100Big
D4Cooling with dust0.010MRN
D5Cooling with dust0.001MRN
Table 1 | Simulation parameters for the different models tested.

Simulations were carried out with the public code package HYDRA, modified to accommodate the effects of dust cooling. Cluster catalogues were then extracted from the simulations and all galaxy groups with masses below Mlim = 5×1013 h-1 M were excluded; our catalogues at z = 0 have at least 60 clusters with masses above Mlim. Cluster properties investigated in this paper are the mass, M, mass-weighted temperature and entropy, Tmw and S, integrated Compton parameter, Y (i.e. the SZ signal times the square of the angular diameter distance to the cluster), and core excised (50 h-1 kpc) X-ray bolometric luminosity, LX. These were computed in the cluster catalogues according to their usual definitions.

In this paper, we investigated the scaling of Tmw, S, Y and LX with M, in the form

yƒ(z) = y0(z) (M/M0)α,

where y is a cluster property (e.g., Tmw), y0(z) = A(1 + z)β and the quantities A, α and β are the scaling normalization at z = 0, the power on the independent variable, and the departures from the expected self-similar evolution with redshift.

The results obtained for z = 0 (Fig. 1) show that the scaling relations studied are sensitive to the underlying dust model, which is particularly obvious in the S-M and LX-M relations. Generally, the inclusion of dust tends to increase temperature and entropy because the additional cooling increases the formation of collisionless (star-forming) material, leaving the remaining particles in the gas phase with higher mean temperatures and entropies. The decrease of Y and LX reflects the effect of lowering the hot-gas fraction and density due to dust cooling. These effects dominate over the effect of increasing the temperature.

Regarding the evolution of the scaling relations with redshift, we concluded that the slopes of our scalings are fairly insensitive to dust cooling; the scatter at high redshift is caused by the decrease of the number of clusters with mass over Mlim, the sample selection used for all fits. The main effect of cooling by dust is reflected in the changes it produces in the normalizations of the cluster scaling laws. For the Tmw-M scaling, we see a systematic variation with the dust model, but differences between models are within the errors and dispersions of each other. For the evolution of the normalizations of the S-M, Y-M and LX-M scalings (Fig. 2), we conclude that the inclusion of dust cooling causes significant departures from the standard radiative cooling model, depending on the dust model parameters.

Figure 2 | Evolution of the slope (top panels), normalization (middle panels) and normalization best-fitting lines (bottom panels) of the Y-M (left panels) and LX-M (right panels) cluster scaling relations for the C (triangles, solid line), D4 (diamonds, triple-dot-dashed line), D3 (squares, short-dashed line), D2 (circles, dashed line) and D1 (crosses, dot-dashed line) simulation models. Colour bands are best fitting errors to the cluster distributions at each redshift. The shaded area in the bottom panel is the rms dispersion of the normalization fit for the cooling model.

Thus, with this work, we conclude that the cooling due to dust is effective in the cluster regime and has a significant effect on the 'baryon driven' statistical properties of clusters such as LX-M, Y-M and S-M scaling relations. As an added non-gravitational cooling process, dust changes the normalization of these laws by a factor up to 25% for the LX-M relation, and up to 10% for the Y-M and S-M relations. In contrast, dust has almost no effect on a 'dark matter driven' scaling relation such as the Tmw-M relation. Through the implementation of our different dust models, we have demonstrated that the dust cooling effect at the scale of clusters depends strongly on the dust abundance in the ICM, but also to a similar extent on the size distribution of the dust grains. Therefore, the dust efficiency is strongly dependent on the nature of the stripped and ejected galactic material, as well as the history of these injection and destruction processes along the cluster history. Indeed, the early enrichment of dust might provide an already modified thermodynamical setup for the 'to-be-accreted' gas at lower redshifts. The setup of our simulations and the limitation of our dust implementation can be considered a 'zero-order' test with which we demonstrated the active effect of dust on structure formation and especially at cluster scales.

A significant part of the work developed for this paper was performed by CAUP members. This includes the complete implementation of dust cooling in the cosmological simulations - some of which were run at CAUP - and the computation and analysis of the relevant physical quantities. In addition, the discussion of the results also had a major contribution from the CAUP author.

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