Confronting dark energy models using galaxy cluster number counts

The mass function of cluster-size halos and their redshift distribution are computed for 12 distinct accelerating cosmological scenarios and confronted to the predictions of the conventional flat Lambda CDM model. The comparison with Lambda CDM is performed by a two-step process. First, we determine the free parameters of all models through a joint analysis involving the latest cosmological data, using supernovae type Ia, the cosmic microwave background shift parameter, and baryon acoustic oscillations. Apart from a braneworld inspired cosmology, it is found that the derived Hubble relation of the remaining models reproduces the Lambda CDM results approximately with the same degree of statistical confidence. Second, in order to attempt to distinguish the different dark energy models from the expectations of Lambda CDM, we analyze the predicted cluster-size halo redshift distribution on the basis of two future cluster surveys: (i) an X-ray survey based on the eROSITA satellite, and (ii) a Sunayev-Zeldovich survey based on the South Pole Telescope. As a result, we find that the predictions of 8 out of 12 dark energy models can be clearly distinguished from the Lambda CDM cosmology, while the predictions of 4 models are statistically equivalent to those of the Lambda CDM model, as far as the expected cluster mass function and redshift distribution are concerned. The present analysis suggests that such a technique appears to be very competitive to independent tests probing the late time evolution of the Universe and the associated dark energy effects.

Cosmology from probe combination: synergies between the number counts of galaxy clusters and cosmic voids

This Thesis work concerns the complementary study of the abundance of galaxy clusters and cosmic voids identified in cosmological simulations, at different redshifts. In particular, we focus our analyses on the combination of the cosmological constraints derived from these probes, which can be considered statistically independent, given the different aspects of Universe density field they map. Indeed, we aim at showing the orthogonality of the derived cosmological constraints and the resulting impressive power of the combination of these probes. To perform this combination we apply three newly implemented algorithms that allow us to combine independent probes. These algorithms represent a flexible and user-friendly tool to perform different techniques for probe combination and are implemented within the environment provided by the large set of free software C++/Python CosmoBolognaLib. All the new implemented codes provide simple and flexible tools that will be soon applied to the data coming from currently available and next-generation wide-field surveys to perform powerful combined cosmological analyses.

Modelling the Halo mass number counts in modified gravity cosmological scenarios

In this Thesis work we investigate some of different cosmological background scenarios using one of the main probes used in cosmology: the halo mass function. The observed abundance of galaxy clusters (or similarly DM haloes) can indeed be compared to its theoretical predictions to derive fundamental constrains on the cosmological scenario assumed. Given the importance of exploring and constraining models degenerate with the ΛCDM one, we test the applicability of some notable halo mass function models to these scenarios. To this purpose, we made use of the DUSTGRAIN-pathfinder N-body simulations, which assume cosmological scenarios that include modified gravity in the form of f(R) models and massive neutrinos. We carried on the analysis of 3 simulation snapshots at different redshifts, z = 0, 0.5, 1, building multiple samples of dark matter haloes by applying different overdensity thresholds during the procedure of halo identification. We started our analysis by considering the halo mass function model introduced by Despali et al. (2016), who proposed a parametrization that encapsulates the effect of the different halo mass definitions and the relative evolution with the redshift. We calibrated the main parameters of this relation by using the ΛCDM halo catalogues extracted from the DUSTGRAIN-pathfinder simulations, fitting the measured halo abundances at all redshifts and density thresholds. Afterwards we tested the same model parametrization with halo catalogues extracted from the simulations implementing both modified gravity and massive neutrinos. We repeated therefore the calibration procedure on these data to search for discrepancies with respect to the ΛCDM model. Finally we focused the analysis on the cosmological models implementing modified gravity only. We took our ΛCDM calibrated halo mass function and we modified it with the additional f (R) gravity form proposed by Gupta et al. (2022).

DECISION TREE CLASSIFIERS FOR STAR/GALAXY SEPARATION

We study the star/galaxy classification efficiency of 13 different decision tree algorithms applied to photometric objects in the Sloan Digital Sky Survey Data Release Seven (SDSS-DR7). Each algorithm is defined by a set of parameters which, when varied, produce different final classification trees. We extensively explore the parameter space of each algorithm, using the set of 884,126 SDSS objects with spectroscopic data as the training set. The efficiency of star-galaxy separation is measured using the completeness function. We find that the Functional Tree algorithm (FT) yields the best results as measured by the mean completeness in two magnitude intervals: 14 <= r <= 21 (85.2%) and r >= 19 (82.1%). We compare the performance of the tree generated with the optimal FT configuration to the classifications provided by the SDSS parametric classifier, 2DPHOT, and Ball et al. We find that our FT classifier is comparable to or better in completeness over the full magnitude range 15 <= r <= 21, with much lower contamination than all but the Ball et al. classifier. At the faintest magnitudes (r > 19), our classifier is the only one that maintains high completeness (> 80%) while simultaneously achieving low contamination (similar to 2.5%). We also examine the SDSS parametric classifier (psfMag - modelMag) to see if the dividing line between stars and galaxies can be adjusted to improve the classifier. We find that currently stars in close pairs are often misclassified as galaxies, and suggest a new cut to improve the classifier. Finally, we apply our FT classifier to separate stars from galaxies in the full set of 69,545,326 SDSS photometric objects in the magnitude range 14 <= r <= 21.

Physical approximations for the nonlinear evolution of perturbations in inhomogeneous dark energy scenarios

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

Dynamical mutation of dark energy

We discuss the intriguing possibility that dark energy may change its equation of state in situations where large dark energy fluctuations are present. We show indications of this dynamical mutation in some generic models of dark energy.

Quasars from a complete spectroscopic survey

With the advent of multi-fibre spectrographs such as the 'Two-Degree Field' (2dF) instrument at the Angle-Australian Telescope, quasar surveys that are free of any preselection of candidates and any biases this implies have become possible for the first time. The first of these is that which is being undertaken as part of the Fornax Spectroscopic Survey, a survey of the area around the Fornax Cluster of galaxies, and aims to obtain the spectra of all objects in the magnitude range 16.5 < b(j) < 19.7. To date, 3679 objects in the central pi -deg(2) area have been successfully identified from their spectral characteristics. Of these, 71 are found to be quasars, 61 with redshifts 0.3 < z < 2.2 and 10 with redshifts z > 2.2. Using this complete quasar sample, a new determination of quasar number counts is made, enabling an independent check of existing quasars surveys. Cumulative counts per square degree at a magnitude limit of b(j) < 19.5 are found to be 11.5 +/- 2.2 for 0.3 < z < 2.2, 2.22 +/- 0.93 for z > 2.2 and 13.7 +/- 3.1 for z > 0.3. Given the likely detection of extra quasars in the Fornax survey, we make a more detailed examination of existing quasar selection techniques. First, looking at the use of a stellar criterion, four of the 71 quasars are 'non-stellar' on the basis of the automated plate measuring facility (APM) b(j) classification, however inspection shows all are consistent with stellar, but misclassified due to image confusion. Examining the ultraviolet excess and multicolour selection techniques, for the selection criteria investigated, ultraviolet excess would find 69 +/- 6 per cent of our 0.3 < z < 2.2 quasars and only 50(-18)(+14), per cent of our z > 2.2 quasars, while the completeness level for multicolour selection is found to be 90(-4)(+3) per cent for 0.3 < z < 2.2 quasars and 80(-12)(+14) per cent for z > 2.2 quasars. The extra quasars detected by our all-object survey thus have unusually red star-like colours, and this appears to be a result of the continuum shape rather than any emission features. An intrinsic dust extinction model may, at least partly, account for the red colours.

THE VORONOI TESSELLATION CLUSTER FINDER IN 2+1 DIMENSIONS

We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10(13.5) solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ACDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity > 80% for the redshift range up to similar to 1 and mass range down to similar to 10(13.5) solar masses.

The imprint of the interaction between dark sectors in galaxy clusters

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibrium when they are in interaction. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with dark matter. When dark energy does not trace dark matter, we present a new treatment on studying the structure formation in the spherical collapsing system. Furthermore we examine the cluster number counts dependence on the interaction between dark sectors and analyze how dark energy inhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction and dark energy inhomogeneities.

The signature of dark energy perturbations in galaxy cluster surveys

Models of dynamical dark energy unavoidably possess fluctuations in the energy density and pressure of that new component. In this paper we estimate the impact of dark energy fluctuations on the number of galaxy clusters in the Universe using a generalization of the spherical collapse model and the Press-Schechter formalism. The observations we consider are several hypothetical Sunyaev-Zel`dovich and weak lensing (shear maps) cluster surveys, with limiting masses similar to ongoing (SPT, DES) as well as future (LSST, Euclid) surveys. Our statistical analysis is performed in a 7-dimensional cosmological parameter space using the Fisher matrix method. We find that, in some scenarios, the impact of these fluctuations is large enough that their effect could already be detected by existing instruments such as the South Pole Telescope, when priors from other standard cosmological probes are included. We also show how dark energy fluctuations can be a nuisance for constraining cosmological parameters with cluster counts, and point to a degeneracy between the parameter that describes dark energy pressure on small scales (the effective sound speed) and the parameters describing its equation of state.

Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations. In order to compute the rate of formation of massive objects we employ the spherical collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift (number counts).

Physical approximations for the nonlinear evolution of perturbations in inhomogeneous dark energy scenarios

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

Bactérias coliformes totais e coliformes de origem fecal em águas usadas na dessedentação de animais

Foram colhidas 105 amostras de água sendo 44 de mananciais e de 61 bebedouros, a partir das quais foram realizadas as determinações dos NMP (Número Mais Provável) de bactérias coliformes totais e fecais. de acordo com a Portaria GM/0013 de 15 de janeiro de 1976, da Secretaria Especial do Meio Ambiente do Ministério do Interior, os 44 mananciais revelaram-se dentro dos parâmetros estabelecidos. Embora não haja referência com relação a bebedouros, aplicando-se os valores estabelecidos para mananciais, das 61 amostras estudadas, somente 6 (9,8%) não poderiam ser usadas para a dessedentação de animais. Das 105 amostras analisadas, verificou-se que as condições sanitárias revelaram-se não satisfatórias em 6 (5,7%) amostras de bebedouros quanto a coliformes fecais, sendo 3 (2,8%) também com relação a coliformes totais.

Dark energy parametrizations and their effect on dark halos

There are a plethora of dark energy parametrizations that can fit current supernovae Ia data. However, these data are only sensitive to redshifts up to order one. In fact, many of these parametrizations break down at higher redshifts. In this paper we study the effect of dark energy models on the formation of dark halos. We select a couple of dark energy parametrizations which are sensible at high redshifts and compute their effect on the evolution of density perturbations in the linear and non-linear regimes. Using the Press-Schechter formalism we show that they produce distinguishable signatures in the number counts of dark halos. Therefore, future observations of galaxy clusters can provide complementary constraints on the behaviour of dark energy.

Statistical properties of Radio Halos and the re-acceleration model

Galaxy clusters occupy a special position in the cosmic hierarchy as they are the largest bound structures in the Universe. There is now general agreement on a hierarchical picture for the formation of cosmic structures, in which galaxy clusters are supposed to form by accretion of matter and merging between smaller units. During merger events, shocks are driven by the gravity of the dark matter in the diffuse barionic component, which is heated up to the observed temperature. Radio and hard-X ray observations have discovered non-thermal components mixed with the thermal Intra Cluster Medium (ICM) and this is of great importance as it calls for a “revision” of the physics of the ICM. The bulk of present information comes from the radio observations which discovered an increasing number of Mpcsized emissions from the ICM, Radio Halos (at the cluster center) and Radio Relics (at the cluster periphery). These sources are due to synchrotron emission from ultra relativistic electrons diffusing through µG turbulent magnetic fields. Radio Halos are the most spectacular evidence of non-thermal components in the ICM and understanding the origin and evolution of these sources represents one of the most challenging goal of the theory of the ICM. Cluster mergers are the most energetic events in the Universe and a fraction of the energy dissipated during these mergers could be channelled into the amplification of the magnetic fields and into the acceleration of high energy particles via shocks and turbulence driven by these mergers. Present observations of Radio Halos (and possibly of hard X-rays) can be best interpreted in terms of the reacceleration scenario in which MHD turbulence injected during these cluster mergers re-accelerates high energy particles in the ICM. The physics involved in this scenario is very complex and model details are difficult to test, however this model clearly predicts some simple properties of Radio Halos (and resulting IC emission in the hard X-ray band) which are almost independent of the details of the adopted physics. In particular in the re-acceleration scenario MHD turbulence is injected and dissipated during cluster mergers and thus Radio Halos (and also the resulting hard X-ray IC emission) should be transient phenomena (with a typical lifetime <» 1 Gyr) associated with dynamically disturbed clusters. The physics of the re-acceleration scenario should produce an unavoidable cut-off in the spectrum of the re-accelerated electrons, which is due to the balance between turbulent acceleration and radiative losses. The energy at which this cut-off occurs, and thus the maximum frequency at which synchrotron radiation is produced, depends essentially on the efficiency of the acceleration mechanism so that observations at high frequencies are expected to catch only the most efficient phenomena while, in principle, low frequency radio surveys may found these phenomena much common in the Universe. These basic properties should leave an important imprint in the statistical properties of Radio Halos (and of non-thermal phenomena in general) which, however, have not been addressed yet by present modellings. The main focus of this PhD thesis is to calculate, for the first time, the expected statistics of Radio Halos in the context of the re-acceleration scenario. In particular, we shall address the following main questions: • Is it possible to model “self-consistently” the evolution of these sources together with that of the parent clusters? • How the occurrence of Radio Halos is expected to change with cluster mass and to evolve with redshift? How the efficiency to catch Radio Halos in galaxy clusters changes with the observing radio frequency? • How many Radio Halos are expected to form in the Universe? At which redshift is expected the bulk of these sources? • Is it possible to reproduce in the re-acceleration scenario the observed occurrence and number of Radio Halos in the Universe and the observed correlations between thermal and non-thermal properties of galaxy clusters? • Is it possible to constrain the magnetic field intensity and profile in galaxy clusters and the energetic of turbulence in the ICM from the comparison between model expectations and observations? Several astrophysical ingredients are necessary to model the evolution and statistical properties of Radio Halos in the context of re-acceleration model and to address the points given above. For these reason we deserve some space in this PhD thesis to review the important aspects of the physics of the ICM which are of interest to catch our goals. In Chapt. 1 we discuss the physics of galaxy clusters, and in particular, the clusters formation process; in Chapt. 2 we review the main observational properties of non-thermal components in the ICM; and in Chapt. 3 we focus on the physics of magnetic field and of particle acceleration in galaxy clusters. As a relevant application, the theory of Alfv´enic particle acceleration is applied in Chapt. 4 where we report the most important results from calculations we have done in the framework of the re-acceleration scenario. In this Chapter we show that a fraction of the energy of fluid turbulence driven in the ICM by the cluster mergers can be channelled into the injection of Alfv´en waves at small scales and that these waves can efficiently re-accelerate particles and trigger Radio Halos and hard X-ray emission. The main part of this PhD work, the calculation of the statistical properties of Radio Halos and non-thermal phenomena as expected in the context of the re-acceleration model and their comparison with observations, is presented in Chapts.5, 6, 7 and 8. In Chapt.5 we present a first approach to semi-analytical calculations of statistical properties of giant Radio Halos. The main goal of this Chapter is to model cluster formation, the injection of turbulence in the ICM and the resulting particle acceleration process. We adopt the semi–analytic extended Press & Schechter (PS) theory to follow the formation of a large synthetic population of galaxy clusters and assume that during a merger a fraction of the PdV work done by the infalling subclusters in passing through the most massive one is injected in the form of magnetosonic waves. Then the processes of stochastic acceleration of the relativistic electrons by these waves and the properties of the ensuing synchrotron (Radio Halos) and inverse Compton (IC, hard X-ray) emission of merging clusters are computed under the assumption of a constant rms average magnetic field strength in emitting volume. The main finding of these calculations is that giant Radio Halos are naturally expected only in the more massive clusters, and that the expected fraction of clusters with Radio Halos is consistent with the observed one. In Chapt. 6 we extend the previous calculations by including a scaling of the magnetic field strength with cluster mass. The inclusion of this scaling allows us to derive the expected correlations between the synchrotron radio power of Radio Halos and the X-ray properties (T, LX) and mass of the hosting clusters. For the first time, we show that these correlations, calculated in the context of the re-acceleration model, are consistent with the observed ones for typical µG strengths of the average B intensity in massive clusters. The calculations presented in this Chapter allow us to derive the evolution of the probability to form Radio Halos as a function of the cluster mass and redshift. The most relevant finding presented in this Chapter is that the luminosity functions of giant Radio Halos at 1.4 GHz are expected to peak around a radio power » 1024 W/Hz and to flatten (or cut-off) at lower radio powers because of the decrease of the electron re-acceleration efficiency in smaller galaxy clusters. In Chapt. 6 we also derive the expected number counts of Radio Halos and compare them with available observations: we claim that » 100 Radio Halos in the Universe can be observed at 1.4 GHz with deep surveys, while more than 1000 Radio Halos are expected to be discovered in the next future by LOFAR at 150 MHz. This is the first (and so far unique) model expectation for the number counts of Radio Halos at lower frequency and allows to design future radio surveys. Based on the results of Chapt. 6, in Chapt.7 we present a work in progress on a “revision” of the occurrence of Radio Halos. We combine past results from the NVSS radio survey (z » 0.05 − 0.2) with our ongoing GMRT Radio Halos Pointed Observations of 50 X-ray luminous galaxy clusters (at z » 0.2−0.4) and discuss the possibility to test our model expectations with the number counts of Radio Halos at z » 0.05 − 0.4. The most relevant limitation in the calculations presented in Chapt. 5 and 6 is the assumption of an “averaged” size of Radio Halos independently of their radio luminosity and of the mass of the parent clusters. This assumption cannot be released in the context of the PS formalism used to describe the formation process of clusters, while a more detailed analysis of the physics of cluster mergers and of the injection process of turbulence in the ICM would require an approach based on numerical (possible MHD) simulations of a very large volume of the Universe which is however well beyond the aim of this PhD thesis. On the other hand, in Chapt.8 we report our discovery of novel correlations between the size (RH) of Radio Halos and their radio power and between RH and the cluster mass within the Radio Halo region, MH. In particular this last “geometrical” MH − RH correlation allows us to “observationally” overcome the limitation of the “average” size of Radio Halos. Thus in this Chapter, by making use of this “geometrical” correlation and of a simplified form of the re-acceleration model based on the results of Chapt. 5 and 6 we are able to discuss expected correlations between the synchrotron power and the thermal cluster quantities relative to the radio emitting region. This is a new powerful tool of investigation and we show that all the observed correlations (PR − RH, PR − MH, PR − T, PR − LX, . . . ) now become well understood in the context of the re-acceleration model. In addition, we find that observationally the size of Radio Halos scales non-linearly with the virial radius of the parent cluster, and this immediately means that the fraction of the cluster volume which is radio emitting increases with cluster mass and thus that the non-thermal component in clusters is not self-similar.