Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 02/05

The aim of this thesis is to assess the effect of the metallicity on the Cepheid Period-Luminosity (PL) relation.

The novelty of the approach adopted in this project consists in the homogeneous analysis of a large sample of Cepheids (72) observed in three galaxies (the Milky Way, the Large Magellanic Cloud and the Small Magellanic Cloud), spanning a factor of ten in metallicity. This allows us to explore the effect of the metallicity on the PL relation in a wide range and to study the gas enrichment histories of three different galaxies.

To fulfil this goal, firstly, we have selected a sample of Cepheids for which distances and accurate photometry are available in the literature and we have collected high-resolution, high signal-to-noise spectra of these stars, using the highly advanced facilities of the European Southern Observatory in Chile. Secondly, we have directly measured iron and alpha-elements (O, Na, Mg, Al, Si, Ca, Ti) abundances of our sample from these spectra.

We have compared our iron abundances with studies on Galactic and Magellanic Cepheids and found a good agreement for the average values and for the individual stars in common. We have then made a broader comparison with results for the Magellanic Clouds from the analysis of F and K non-variable supergiants (they have ages and temperatures similar to Cepheid stars) and of B stars, which are progenitors of Cepheids, and found a good agreement. Cepheids do not show any peculiar differences with these two other population of stars, this indicate that, during this evolutionary stage, there are no changes of the original iron content of the gas from which they were formed.

We have then studied the trends of the individual alpha-elements abundance ratios relative to iron as a function of the iron content of our programme star. We can draw some preliminary conclusion considering oxygen, silicon and calcium as the most reliable indicators among the alpha-elements we have analysed. The trends of the abundance ratios of O, Si and Ca are in fairly good agreement with observational studies on Cepheids and on different kinds of stellar populations in the Galaxy and the Magellanic Clouds.

The elemental abundances we have determined were used to investigate the effect of metallicity on the PL relation in the V and K bands, in order to check if there is a change of the effect as wavelength increases.

We note different behaviours in the two bands. The metallicity has an effect in the V band in the sense that metal-rich Cepheids are fainter than metal-poor ones, while it does not have any effects in the K band.

Thus, to safely measure the distances of galaxies, one can use the PL relation in the infrared bands (namely K), so as to minimise the effect of the metallicity. Using the K band has the additional advantage of reducing the effects of the interstellar extinction to the level of other systematic and random errors.

Diese Dissertation beschreibt die Ergebnisse des Wendelstein Calar Alto Pixellensing Project (WeCAPP), welches in Richtung der Andromeda Galaxie (M31) nach Dunkler Materie in Form von "Massiven Kompakten Halo Objekten" (Machos) sucht. Die neuesten wissenschaftlichen Befunde legen ein Universum mit flacher Geometrie nahe, zu dessen Dichteinhalt Dunkle Materie ca. 23% beitraegt. Weitere 4.5% werden baryonischer Materie zugeschrieben, wobei von diesem Anteil bei kleiner Rotverschiebung bisher nur ca. 10% nachgewiesen werden konnten. Die Kandidaten fuer Machos in den Halos von Galaxien umfassen eine baryonische Komponente (vergangene Sterne wie z.B. Weisse Zwerge oder Neutronensterne), sowie eine nicht-baryonische Komponente, zum Beispiel in Form von primordialen Schwarzen Loechern. Da diese Objekte nur sehr schwach leuchten, sind sie dem direkten Nachweis entzogen. Sie koennen jedoch indirekt ueber den Gravitationslinseneffekt nachgewiesen werden, den sie auf das Licht von Sternen im Hintergrund ausueben. Der beobachtbare Helligkeitsanstieg ist charakteristisch fuer solche sogenannten Mikrolinsenereignisse und laesst sich gut von der Helligkeitsaenderung Veraenderlicher Sterne unterscheiden. Die Seltenheit der Gravitationslinsenereignisse machte den Aufbau eines grossen Datensatzes mit entsprechender zeitlicher Ueberdeckung notwendig, was durch simultane Beobachtungen an zwei Standorten (Wendelstein und Calar Alto) erreicht werden konnte. Nach einer kurzen Einfuehrung gibt Kapitel 2 einen Ueberblick ueber das Experiment und die Beobachtungsstrategie und stellt die Teleskope und verwendeten Instrumente vor. Desweiteren behandelt Kapitel 2 die Eigenschaften des Datensatzes (1997 - 2005) und stellt die Algorithmen und Methoden vor, die zum Reduzieren der Daten angewandt wurden. Kapitel 3 praesentiert ein aktualisiertes Modell der Massen- und Lichtverteilung der Andromeda Galaxie, welches gut mit kinematischen Daten, als auch mit Vorhersagen von stellaren Populationsmodellen uebereinstimmt. In Kapitel 4 wird dieses Modell genutzt, um die erwartete Rate von Gravitationslinsenereignissen und deren raeumliche Verteilung fuer das WeCAPP Experiment zu berechnen. Kapitel 5 praesentiert die Kandidaten fuer Mikrolinsenereignisse, die im WeCAPP Datensatz identifiziert werden konnten. Sowohl die Anzahl der Ereignisse als auch ihre raeumliche Verteilung deuten darauf hin, dass sie durch stellare Linsen in M31 selbst verursacht wurden (self-lensing). Der Machoanteil ist demgegenueber als eher gering einzuschaetzen. Der aufgebaute Datensatz ist aufgrund seiner langen zeitlichen Ueberdeckung hervorragend geeignet, intrinsisch Veraenderliche Quellen in M31 zu studieren. In Kapitel 6 wird dieser Katalog von ueber 20 000 Veraenderlichen Quellen praesentiert. Die gemessene Anzahldichte der Quellen weist eine starke Asymmetrie auf, die auf den Einfluss erhoehter Extinktion in den Spiralarmen zurueckzufuehren ist. Die Veraenderlichen lassen sich in 3 Gruppen einteilen, wobei sich in Gruppe 1 die klassischen Cepheiden befinden. Gruppe 2 enthaelt unter anderem Klasse 2 Cepheiden und RV Tauri Veraenderliche, wohingegen sich Gruppe 3 aus Langperiodischen Veraenderlichen zusammensetzt. Die Parameter, die aus der Fourieranalyse der Lichtkurven klassischer Cepheiden extrahiert werden konnten, zeigen den bekannten Verlauf mit der Periode der stellaren Pulsation. Auch fuer die Klasse 2 Cepheiden und die RV Tauri Sterne konnte eine Korrelation bestimmter Phasenparameter gefunden werden, wobei die Relation der RV Tauri Sterne eine Fortfuehrung der Relation der Klasse 2 Cepheiden ist. Dieses Ergebnis unterstuetzt die enge Verbindung zwischen beiden Arten von Veraenderlichen. Neben pulsierenden Veraenderlichen wurden auch ueber 60 klassische Novae identifiziert, deren Helligkeitsverlauf einen eruptiven Charakter aufweist. Der daraus resultierende Novakatalog, der in Kapitel 7 praesentiert wird, ist einer der groessten und homogensten seiner Art. Eine Korrelati

Several lines of evidence suggest that the most active phase of galaxy

evolution, especially in the most massive systems, was largely

completed by $z\sim 1$. This results, e.g., from the observation that

the most massive galaxies at low redshift have very old stellar

populations ($\sim 10$ Gyr) and very little gas to fuel subsequent

star formation. Similarly, active galactic nuclei (AGN) were more

numerous and brighter in the early universe. Ultimately, the direct

observation of high-redshift galaxies will be the only way to

understand which processes shaped the universe we see today, in

spite of the rich ``fossil'' data sets we have of the Milky Way and

neighboring galaxies. Thanks to the new $8-10$ m telescope class and

novel instrumentation, including SPIFFI/SINFONI on the VLT, individual

galaxies at redshifts $z\sim 1-3$ ($2-6$ Gyr after the Big Bang)

are now within the reach of astronomical spectrographs.

Methodologically, this thesis focuses on the analysis of spectrally

and spatially resolved optical emission lines, first of all \ha\ and

[OIII]\lam5007, which are shifted into the near-infrared. {\sc Spiffi

/ Sinfoni}

is very suited to such a programme, because it records the spectra of

a contiguous field of view of up to 8\arcsec$\times$8\arcsec. The

internal kinematic and chemical gradients within a galaxy can thus be

measured in a single observation. Galaxies in the early universe had

particularly high star-formation rates, so that many targets are

bright optical line emitters. Internal kinematics are measured

through the Doppler effect, line profiles and widths indicate the

presence of an AGN, galactic ``superwinds'' and the relationship of

chaotic to ordered motion. Star-formation rates are measured from the

luminosity of the Balmer lines, especially \ha. Characteristic line

ratios indicate the presence of an AGN, chemical composition, and

electron densities in the ISM, and they allow to distinguish shocks

and photoionization.

This thesis is a pilot study: It comprises 9

galaxies that fulfill a variety of selection criteria: they are

either bright UV or submillimeter emitters, or they are radio-loud.

Perhaps the most fundamental result is that gravity (dominated by dark

matter) is the main driver of early galaxy evolution, but it

is not the only important process. Star formation and AGN cause

hydrodynamical feedback processes, which might be a sign of

self-regulated galaxy evolution. It is found that star-formation

related feedback had similar properties at low and high redshift, but

that AGN-driven gas expulsion might have played a major role in the

high-redshift evolution of galaxies, that is without low-redshift

equivalent. Another important result is the rotation curve we find in

the central kiloparsec of a gravitationally lensed UV-selected

galaxy. Velocity gradients of $\sim 100$ \kms\ have been observed in

many high-redshift galaxies, but the interpretation as rotation curves

is generally not unique. Given the relatively coarse spatial

resolution of high-redshift galaxy data, two nearby galaxies, maybe

interacting or undergoing a merger, might blend into one smooth

velocity gradient. Galaxy mergers are an important ingredient of the

``hierarchical model'', the current paradigm of structure formation,

and therefore nearby galaxy pairs were likely more common at high

redshift than they are today. The large similarity of the lensed

rotation curve with those of nearby galaxies might be a first sign

that galaxies evolved inside-out.

During the last ten to fifteen years cosmology has turned from a data-starved to

a data-driven science. Several key parameters of the Universe have now been measured with an accuracy better than 10%. Surprisingly, it has been found that instead of slowing down, the expansion of the Universe proceeds at an ever increasing rate. From this we infer the existence of a negative pressure component -- the so-called Dark Energy (DE) -- that makes up more than two thirds of the total matter-energy content of our Universe. It is generally agreed amongst cosmologists and high energy physicists that understanding the nature of the DE poses one of the biggest challenges for the modern theoretical physics.

Future cosmological datasets, being superior in both quantity and quality to currently existing data, hold the promise for unveiling many of the properties of the mysterious DE component. With ever larger datasets, as the statistical errors decrease, one needs to have a very good control over the possible systematic uncertainties. To make progress, one has to concentrate the observational effort towards the phenomena that are theoretically best understood and also least ``contaminated'' by complex astrophysical processes or several intervening foregrounds. Currently by far the cleanest cosmological information has been obtained through measurements of the angular temperature fluctuations of the Cosmic Microwave Background (CMB). The typical angular size of the CMB temperature fluctuations is determined by the distance the sound waves in the tightly coupled baryon-photon fluid can have traveled since the Big Bang until the epoch of recombination. A similar scale is also expected to be imprinted in the large-scale matter distribution as traced by, for instance, galaxies or galaxy clusters. Measurements of the peaks in the CMB angular power spectrum fix the physical scale of the sound horizon with a high precision. By identifying the corresponding features in the low redshift matter power spectrum one is able to put constraints on several cosmological parameters.

In this thesis we have investigated the prospects for the future wide-field SZ cluster surveys to detect the acoustic scale in the matter power spectrum, specifically concentrating on the possibilities for constraining the properties of the DE. The core part of the thesis is concerned with a power spectrum analysis of the SDSS Luminous Red Galaxy (LRG) sample. We have been able to detect acoustic features in the redshift-space power spectrum of LRGs down to scales of ~ 0.2 hMpc^{-1}, which approximately corresponds to the seventh peak in the CMB angular spectrum. Using this power spectrum measurement along with the measured size of the sound horizon, we have carried out the maximum likelihood cosmological parameter estimation using Markov chain Monte Carlo techniques. The precise measurement of the low redshift sound horizon in combination with the CMB data has enabled us to measure, under some simplifying assumptions, the Hubble constant with a high precision: H_0 = 70.8 {+1.9} {-1.8} km/s/Mpc. Also we have shown that a decelerating expansion of the Universe is ruled out at more than 5-sigma confidence level.

In this thesis gauge-field theories and gravity on noncommutative spaces are studied. We start with an introduction to the concepts underlying the construction of field theories on noncommutative spaces. By a noncommutative space we mean a noncommutative algebra, which replaces the algebra of functions on ordinary space. We construct derivatives and deformed symmetries ("Quantum Group" symmetries) acting on noncommutative spaces. Consistency requires us to change the action on a product of representations ("deformed coproducts"); this gives rise in particular to deformed Leibniz rules. We also show how a noncommutative space and the generators of deformed symmetries acting on it can be represented on the ordinary algebra of functions; the commutative, point-wise product is substituted by a noncommutative one ("star-product").

One possible way to define gauge-field theories on noncommutative spaces is to construct "Seiberg--Witten maps". In this approach it is possible to express all noncommutative quantities in terms of their commutative counterparts. We illustrate this by two examples, the two-dimensional q -deformed Euclidean plane and the \kappa -deformed Minkowski space-time. In addition gauge-field theory on "fuzzy" S^{2}\times S^{2} is discussed as a multi-matrix model. We show that this model reduces in an appropriate limit to gauge-field theory on noncommutative \mathbb{R}^{4} . We also present a new approach to deformed gauge theories, which is based on "twisted" gauge transformations. In this setting new fields occur in addition to the usual gauge fields. Consistent equations of motion and conserved currents are obtained. This is the first time that conservation laws have been derived from a generalized, Quantum Group symmetry.

We discuss in detail how to construct deformed infinitesimal diffeomorphisms by deformations via generic "twists". Then we construct gravity as a theory, which is covariant with respect to these diffeomorphisms. This leads to a deformation of Einstein's equations. For canonically deformed spaces, a deformed Einstein--Hilbert action can be even defined. It reduces to the usual Einstein--Hilbert action in the commutative limit. All relevant quantities are expanded in terms of the usual, commutative fields up to second order in the deformation parameter.

Intracellular transport phenomena, such as kinesins and myosins moving

along cytoskeletal filaments or ribosomes along messenger RNA, can be

modeled by one-dimensional driven lattice gases. Among these, the

Totally Asymmetric Simple Exclusion Process (TASEP), has been

extensively used. It describes a system of particles hopping in a

preferred direction with hard core interaction. The goal of this

thesis is to explore the relevance of some features that are missed by

this simple model, such as the exchange of particles between molecular

track and the cytoplasm, the extended molecular structure of each

motor, and the interaction of motors with imperfections on the track

acting as road blocks for intracellular traffic.

Recent studies have taken into account particle exchange between the

track and bulk solution (Langmuir kinetics). It was found that this

violation of current conservation along the track leads to phase

coexistence regions in the phase diagram not present in the TASEP. We

have extended these studies in two ways. First, motivated by the fact

that many molecular motors are dimers, we study how the stationary

properties of the system (density profile and phase behavior) change

upon replacing monomers with extended particles. Analytical refined

and generalized mean field theory, supported by numerical Monte Carlo

simulations, give a detailed description of the phase diagram. Our

study proves that the extension gives quantitative but not qualitative

changes in the phase diagram, showing that the picture obtained in the

case of monomers is robust upon considering extended particles.

Second, motivated by the presence of structural imperfections of the

track that act as road blocks, we study the influence of an isolated

defect characterized by a reduced hopping rate on the non-equilibrium

steady state. We explore the phase behavior in the full parameter

range and find that the phase diagram changes qualitatively as

compared to the case without defects, showing new phase coexistence

regions. In particular above a certain threshold strength of the

defect, its presence induces a macroscopic change in the density

profile. The regions where the defect is relevant (called bottleneck

phases) are identified and studied.

In the second part of the thesis we investigate the dynamical features

of these models. First we concentrate on the dynamics of the simple

TASEP, for which a complete analysis was missing. We use a technique

borrowed from solid state physics, the Boltzmann-Langevin method, to

give a full description of the correlation function in the whole

parameter space. Finally we study the dynamics of a tracer particle

in a TASEP with on-off kinetics. We observe that it is possible to

reconstruct the density profile from the velocity of the tracer

particle and we propose to perform single molecule experiments with

fluorescently labelled molecular motors to explore the density profile

and ultimately test the phase behavior predicted in this thesis.

Air traffic impacts cirrus cloud cover and consequently the radiation budget of the earth. Additionally air traffic may change the optical properties of already existent cirrus clouds and hence the radiation budget of the atmosphere. For the first time the impact of air traffic was investigated over Europe, North-Atlantic and North-Africa for a period of 11 months of 2004 with a high temporal-resolution satellite sensor. A significant correlation between cirrus cloud cover and air traffic density was shown for the region of interest. The air traffic induced cirrus cloud cover has been estimated with 0.6±0.2% for this region. Global extrapolation yields 0.17± 0.06%. Based on this value an air traffic induced radiative forcing of 34 mW/m2 follows. The direct investigation of the impact of air traffic on outgoing fluxes yields a warming effect of 1.1 W/m2 for the region of interest. This value has been calculated from the difference between outgoing fluxes of air traffic free regions and the whole region. The global extrapolation yields a warming of 290 mW/m2. However this value is very uncertain. Additionally further aspects have been investigated. As a result, a strong dependency of the impact of air traffic on the geographic location and daytime could be shown.

In dieser Arbeit werden Präzisionsrechnungen für die Prozesse gamma gamma -> 4 Fermionen und H -> WW/ZZ -> 4 Fermionen vorgestellt.

An einem gamma-gamma-Collider werden wegen des großen Wirkungsquerschnitts genaue theoretische Vorhersagen für die Prozesse gamma gamma -> WW -> 4f benötigt. Mittels dieser Prozesse lassen sich unter anderem die

Eichboson-Kopplungen gamma-W-W und gamma-gamma-W-W messen. Außerdem wird über virtuelle geladene, massive Teilchen

die Reaktion gamma gamma -> H -> WW/ZZ -> 4f

ermöglicht. Auf diese Weise läßt sich die Kopplung gamma-gamma-H messen, und relativ schwere Higgs-Bosonen könnten erzeugt werden.

Für Massen MH > 135 GeV zerfällt das Higgs-Boson hauptsächlich über W- und Z-Bosonen in vier Fermionen. Bei der kinematischen Rekonstruktion dieser Zerfälle

spielen Quanten-Korrekturen, insbesondere Photon-Bremsstrahlung, eine wichtige Rolle. Die Einbeziehung der Zerfälle der Eichbosonen in Fermionen ist zum einen wichtig, weil unterhalb von MH ≈ 2MW/MZ „off-shell“-Effekte der Eichbosonen berücksichtigt werden müssen. Zum anderen lassen sich mit Hilfe von Winkel- und Energie-Verteilungen der Fermionen der Spin und die CP-Eigenschaften des Higgs-Bosons bestimmen.

Besonders geeignet für den Vergleich theoretischer Vorhersagen mit experimentellen Daten sind Monte-Carlo-Generatoren. Für die Prozesse gamma gamma -> 4f und H -> WW/ZZ -> 4f werden solche Programme konstruiert. Sie liefern zum einen die kompletten Vorhersagen in niedrigster Ordnung der Störungstheorie. Zum anderen enthalten sie Quanten-Korrekturen, die sich unterteilen lassen in reelle Korrekturen, welche durch Photon-Bremsstrahlung gegeben sind, und virtuelle Korrekturen. Während die virtuellen Quanten-Korrekturen zu gamma gamma -> WW -> 4f in der Doppel-Pol-Näherung berechnet werden, in der nur die doppelt resonanten Beiträge berücksichtigt werden, werden zu den Prozessen H -> WW/ZZ -> 4f die kompletten Quantenkorrekturen der Ordnung O(alpha)

berechnet. Für die Behandlung der in den virtuellen und reellen Korrekturen auftretenden infraroten Divergenzen („soft“ und „collinear“) wird wahlweise die Dipol-Subtraktions-Methode oder die Phase-Space-Slicing-Methode verwendet.

Nicht bei allen Observablen müssen sich die bei kollinearer Photon-Abstrahlung auftretenden Massen-Singularitäten gegenseitig aufheben. Um auch solche nicht-kollinear-sichere Observablen untersuchen zu können, wird die Dipol-Subtraktions-Methode diesbezüglich

erweitert.

Die Diskussion der numerischen Ergebnisse umfasst den Einfluss eines realistischen Photon-Spektrums auf die Wirkungsquerschnitte, das Potential eines gamma-gamma-Colliders, Grenzen an anomale

Eichboson-Kopplungen zu setzen, sowie verschiedene Verteilungen in der Invarianten

Masse, in der Energie und in Winkeln, die für eine Rekonstruktion der Eichbosonen und die

Bestimmung der Eigenschaften des Higgs-Bosons genutzt werden können.

Supersymmetry, which is the only non-trivial $Z_{2}$ extension of the Poincar\'e algebra, can be generalized to fractional supersymmetry, when the space time is smaller than 3. Since symmetries play an important role in physics; the principal task of quantum groups consist in extanding these standard symmetries to the deformed ones, which might be used in physics as well. This two aspects will be the main focus of this thesis. In this work, we discuss the matrix formulation of fractional supersymmetry, the q-deformation of KdV hierarchy systems and noncommutative geometry.

In the first part fractional supersymmetry generated by more than one charge operator and those which can be described as a matrix model are studied. Using parafermionic field-theoretical methods, the fundamentals of two-dimensional fractional supersymmetry $Q^{k}=P$ are set up. Known difficulties induced by methods based on the $U_{q}(sl(2))$ quantum group representations and noncommutative geometry are avoided in the parafermionic approach. Moreover, we find that fractional supersymmetric algebras are naturally realized as matrix models. The $k=3$ case is studied in detail.

In the second part we will study the q-deformed algebra and the q-analogues of the generalised KdV hierarchy.

We construct in this part the algebra of q-deformed pseudo-differential operators, shown to be an essential step toward setting up a q-deformed integrability program. In fact, using the results of this q-deformed algebra, we derive the q-analogues of the generalised KdV hierarchy. We focus in particular on the first leading orders of this q-deformed hierarchy, namely the q-KdV and q-Boussinesq integrable systems. We also present the q-generalisation of the conformal transformations of the currents $u_{n}$, $n\geq 2$, and discuss the primary condition of the fields $w_{n}$, $n\geq 2$, by using the Volterra gauge group transformations for the q-covariant Lax operators.

In the last part we will discuss quantum groups and noncommutative space. All studies in this part are based on the idea of replacing the ordinary coordinates with non commuting operators. We will also formulate some aspects of noncommutative geometry mathematically and we will be mainly concerned with quantum algebra and quantum spaces.

Galaxy clusters are the largest gravitationally bound systems in

the universe. Clusters consist of three components: galaxies, gas, and

dark matter. The galaxies themselves contribute the least, at most a

few percent, to the total mass. The remainder consists of diffuse, hot gas (the intracluster medium, or ICM) and an unseen component which is

needed to explain the gravitational stability of clusters (the dark

matter).

The two most obvious means of studying clusters of galaxies are by

observing the optical light emitted from the constituent galaxies or

the X-ray emission from the ICM. Clusters of galaxies, bound ensambles

of hundreds of galaxies, are an ideal environment to study galaxy

evolution and to learn how this is affected by different physical

processes: gravity, starbursts and star formation, interactions with

the intergalactic medium and galaxy-galaxy encounters. Since the very

early works of Hubble in the thirties, it has been recognized that

galaxies in dense environments differ systematically from those in

low-density regions in their morphological types, stellar populations

and gaseous content. When during the history of the Universe and why

such environmental differences were established is currently one of

the subjects of most intensive investigation in the international

astrophysical community.

On the other hand, clusters can teach us a great deal about

cosmology. The distributions of galaxies on the sky shows a net-like

structure in which thin walls and filaments surround large voids. The

galaxy clusters are the nodes of this network. Therefore, they trace

out the Large-Scale Structure (LSS) of the universe and can be used to

study the LSS formation. Moreover, if clusters provide a 'fair sample'

of the universe, then the fraction of their mass in baryons should

equal the universal baryon fraction, known as

$\Omega_b/\Omega_m$. Moreover, the evolution of cluster number density

with redshift can determine the mass density parameter, known as

$\Omega_M$, and possibly determine the equation of state (and nature)

of the dark energy believed to be causing the expansion of the

universe to accelerate.

Thus, galaxy clusters have a twofold importance: first as laboratories

of galaxy formation and evolution, and second as cosmological

tool. The aim of this project is to study galaxy clusters from these

two perspectives. For this purpose we use the largest optical and

X-ray surveys ever realized, the Sloan Digital Sky Survey (SDSS) and

the Rosat All Sky Survey (RASS), respectively, to conduct a

multiwavelenght study of the properties of galaxy clusters. The

project is called RASS-SDSS Galaxy Cluster Survey reflecting the name

of the two big surveys used for this work. All the analyses are

performed on two cluster samples specially created for the survey: the

X-ray selected RASS-SDSS galaxy cluster catalog and a subsample of

optically selected, isolated and spectroscopically confirmed Abell

clusters.

The project consists of two parts. The aim of the first part is to

understand which role play the gravitational processes, galaxy mergers

and collisions and the interaction with ICM in the process of galaxy

formation and evolution. For this purpose, we study the variations of

several properties of the cluster galaxy population such as the

luminosity and spatial distribution, the morphological type mix, the

Star Formation Rate (SFR) and stellar mass as a function of the

environmental conditions and the cluster global properties.

Our detailed analysis of the cluster individual and composite

luminosity functions reveals that the LF clearly shows a bimodal

behavior with an upturn and a evident steepening in the faint

magnitude range in any SDSS band. The LF is well fitted by the sum of

two Schechter functions. The bright end of the LF is found to be

universal in all the clusters. The faint end of the LF is much steeper

and varies significantly from system to system, when calculated within

a fixed metric aperture. The va