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|Title: ||Using hydrodynamical simulations to combine Sunyaev-Zeldovich and X-ray studies of galaxy clusters|
|Authors: ||Ameglio, Silvia|
|Supervisor/Tutor: ||Borgani, Stefano|
|Issue Date: ||10-Mar-2008|
|Publisher: ||Università degli studi di Trieste|
|Abstract: ||The main focus of the work presented in this Thesis is the study of the potentiality and
possible systematics in combining observations of the thermal Sunyaev-Zeldovich effect (tSZ) and of the X–ray emission in galaxy clusters. The great advantage of the combination of this two types of observations is that they have a different dependence on the properties (density and temperature) of the Intra Cluster Medium (ICM). Also the behavior with redshift is completely different: X–rays provide very bright images of nearby clusters, but decline rapidly with redshift, while the tSZ signal is independent of redshift and is more suitable for observations of distant objects. At present, the X–ray data have far better resolution than the tSZ ones. For this reason, our attention is mainly directed to the present and upcoming generation of tSZ telescopes, which should produce high resolution images. In this perspective, we analyze a sample of galaxy clusters extracted from a set of cosmological hydrodynamical simulations, which have been carried out with the GADGET-2 code. These simulations include the effects of radiative cooling, star formation and supernovae feedback and, as such, they provide a realistic description of the
A widely adopted technique to measure the angular diameter distance of galaxy clusters is based on the combination of X–ray and tSZ observations (e.g. Bonamente et al., 2006). The method is completely independent of any other distance ladder and provides a measure of the Hubble constant out to z ~ 1. We study the systematics of this type of measure through the analysis of simulated clusters. The ICM is usually modelled with an isothermal beta-model. We find that this model does not provide a satisfactory description of our simulated clusters. In order to take into account the presence of temperature gradients, we instead introduce a polytropic equation of state. Our results show that the distance is correctly recovered, with an intrinsic scatter of about 20% which we attribute to cluster asphericities. Finally, we generate a redshift distribution of our clusters in order to test the capabilities of this technique in recovering the cosmological parameters. We first find that the Hubble constant is correctly recovered with an
uncertainty of only 2%. Then, we assume a prior for the Hubble constant and a flat geometry. We find that extending this type of measure out to z ~ 1.5 with future datasets would allow to recover also the density parameter Omega_m with a typical error of about 0.05.
Galaxy clusters are interesting not only as cosmological probes, but also as virialized structures which are the result of a long and complex formation process. Their study has implications on both the thermodynamical processes ongoing in the hot ICM plasma and on the cosmological models of structure formation. Given the poor resolution of past tSZ telescopes, the principal source of information on the structure of the ICM comes from X–ray data, for which both imaging and spectroscopy are available. In the perspective of having new high-resolution tSZ images, we propose a technique aiming at reconstructing gas density and temperature by combining them with the X–ray images, without the need of X–ray spectroscopy which is a potential source of biases in the measure of the ICM temperature. The method is based on a joint deprojection of tSZ and X–ray images and requires the only assumption of spherical symmetry. Gas density (rho) and temperature (T) can be recovered by taking advantage of the different dependence of the two signals on gas properties: tSZ ~ rho*T, while X–ray ~ int rho^2 Lambda(T), where Lambda(T) is the cooling function at X–ray energies. Our technique implements the deprojection by following a Markov Chain Monte Carlo approach, which allows us to deproject both images simultaneously, by the maximization of a joint (tSZ + X–ray) likelihood function. From this method, we obtain at the same time an accurate estimate of the uncertainty on the recovered profiles of density and temperature, along with an analysis of all degeneracies. A typical feature of geometrical deprojection is to introduce spurious fluctuations in the profiles, which are due to the presence of noise. The effect increases rapidly when reducing the width of the bins adopted in the deprojection. Our statistical approach instead allows us to introduce a regularization constraint which has the effect of smoothing out these spurious fluctuations, thus offering a much more stable reconstruction of the gas properties.
We first apply the whole procedure to an ideal model cluster, realized by assuming a polytropic beta–model. We find that density and temperature are recovered unbiased, with errors of < 5% and about 20% respectively. On the simulated clusters we find a general overestimate of density from 5 to 10%, which we attribute to small-scale inhomogeneities and to small unresolved gas clumps which cause a boosting of the X–ray surface brightness. As a consequence the temperature is slightly underestimated. By integrating the density profile one directly obtains the gas mass content of the cluster. Together with an estimate of the total mass, it allows us to measure the gas mass fraction, which is another important constrain on cosmological models. Since the density within each shell depends on the density of all the other shells, it is important to have an estimate of the full covariance matrix, which is naturally provided by the Markov Chain Monte Carlo method. We find that the gas mass is also overestimated by about 5-10%, with a statistical uncertainty of about 5%. A common way to select samples of clusters is to fix a lower limit in their X–ray luminosity. This criterion may slightly favor objects which are elongated along the line of sight. This represents a potential source of bias when these samples are used for a statistical analysis of cluster properties. In fact, we find that cluster elongation along the line of sight causes a systematic underestimate of the gas mass by up to 10%.
Correctly measuring the total cluster mass is of fundamental importance for clusters to be used as tools for precision cosmology. In cluster studies based on the observations of the ICM the mass is obtained by assuming that the gas lies in hydrostatic equilibrium in the cluster gravitational potential. We implemented the solution of the hydrostatic equilibrium equation in the deprojection algorithm, so as to derive profiles of gas density and temperature and total mass simultaneously. In practice, this involves a derivative of gas density and temperature profiles, for which our regularization constraint is quite useful. However, deviations from such equilibrium are expected, due to any non–thermal pressure support (e.g. stochastic velocity fields, turbulence, residual bulk motions). As a consequence, we find the mass to be systematically underestimated by a factor of 10% (in agreement with findings from other authors). In order to better characterize the sources of systematics in the mass measurement, we also compute the hydrostatic mass profile, which is obtained by applying the hydrostatic equilibrium equation to the true gas density and temperature profiles, given by the simulation data. We find that our reconstructed mass profiles are generally close to hydrostatic mass profiles, thus confirming that the main source of systematics is intrinsic (i.e. the non–thermal pressure support), while our
procedure is basically unbiased.
To summarize, in the work presented in this Thesis we use hydrodynamical cosmological simulations to study combined tSZ/X–ray observations, by following two different perspectives. The first makes use of galaxy clusters as distance indicators to probe the geometry of the Universe. We study systematics and future capabilities of this technique, which has been widely adopted with datasets extending out to z ~ 1. The second aims at a detailed characterization of cluster properties, which are relevant to both understand of the ICM physics and calibrate galaxy clusters as precision tools for cosmology. We develope a maximum–likelihood deprojection technique which allows us to recover the three–dimensional profiles of gas density and
temperature and of total mass, which is completely model–independent.
|PhD cycle: ||XX Ciclo|
|PhD programme: ||FISICA|
|Keywords: ||galaxy clusters|
|Main language of document: ||en|
|Type: ||Tesi di dottorato|
|Scientific-educational field: ||FIS/05 ASTRONOMIA E ASTROFISICA|
|Appears in Collections:||Scienze fisiche|
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