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Galaxies are natural laboratories for testing fundamental physics on the nature of the dark matter. MOdified Newtonian Dynamics (MOND) has been tested for over 20 years on small and large scales. While there are several versions of how MOND extrapolates to the large scales, and these versions are not yet fully successful, the original Bekenstein-Milgrom version of MOND is fully predictive and works very well on galaxy scales. However, little work has been done to explore this theory beyond fitting the rotation curves and Tully-Fisher relation of isolated disc galaxies. So far little is known of MONDian elliptical galaxies accelerating in any galaxy cluster. A defining feature of MOND is that internal dynamics of the galaxy depends on the overall acceleration of the galaxy. The existence of cuspy triaxial equilibria for elliptical galaxies is the minimal requirement to MOND. With the PhD project here, I constructed and then further studied the evolution and stability of gravitationally bound systems resembling like cuspy elliptical galaxies, both in isolation and when embedded in a uniform external field. I also studied the escape speeds from spiral galaxies, in particular by comparing the potentials of the Milky Way Galaxy in the Cold Dark Matter (CDM) and MOND frameworks.

We study the structure and substructure of Lambda-CDM halos using a suite of high-resolution cosmological N-body simulations. Our analysis of the substructure population of dark matter halos focuses on their mass and peak circular velocity functions, as well as their spatial distribution and dynamics. In our analysis, we consider the whole population of subhalos physically associated with the main halo, defined as those that have, at some time, crossed within the virial radius of the main progenitor. We find that this population extends beyond 3 times the virial radius and includes objects on unorthodox orbits, several of which travel at velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups, which results in the ejection of some systems along tidal streams. This process primarily influences low-mass systems leading to clear mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time the more concentrated and kinematically hotter their descendant population. When quantified in terms of present day subhalo mass these trends disappear, presumably due to the increased effect of dynamical friction and tidal stripping on massive systems. We confirm several of these results using the ultra-high resolution Aquarius simulations, which extend the dynamic range of the subhalo mass function by nearly 3 orders of magnitude. Using these simulations we confirm that the substructure mass function follows a power-law, $dN/dM\propto M^{-1.9}$, and exhibits very little halo-to-halo scatter. This implies that the total mass in substructure within a given halo is bounded to a small fraction of the total halo mass, with the smooth component dominating the halo inner regions. Using the Aquarius simulations we study the structure of galaxy-sized Lambda-CDM halos. We find that the spherically averaged density profiles become increasingly shallow toward the halo center, with no sign of converging to an asymptotic power-law; a radial dependence accurately described by the Einasto profile. In our highest resolution run we resolve scales approaching 100 pc, at which point the maximum asymptotic slope is $\approx -0.89$, confidently ruling out recent claims for cusps as steep as $r^{-1.2}$. We find that the spherically averaged density and velocity dispersion profiles are not universal, but rather show subtle but significant deviations from self-similarity. Intriguingly, departures from self-similarity are minimized when cast in terms of the phase-space density profile, $\rho/\sigma^3$, suggesting an intimate scaling between densities and velocity dispersions across the system. The phase-space density profiles follow a power-law with radius, $r^{-1.875}$, identical to that of Bertschinger's similarity solution for self-similar infall onto a point mass in an otherwise unperturbed Einstein-de Sitter universe.

Absorption profiles are found in the observed spectra from quasars, and the most prominent of these are the Damped Lyman-alpha Absorbers (DLAs). They are caused by large collections of neutral hydrogen (HI) gas, which are thought to be housed in galaxies that lie along the line-of-sight to quasars. HI gas associated with DLAs contains most of the HI gas in the Universe during 2 < z < 5, and hence details about DLAs are important for understanding the history of star formation, as well as the formation and evolution of galaxies. Wyithe (2008) proposed a method of determining the characteristic mass of dark matter haloes that host DLAs. This involves generating an analytic power spectrum of the fluctuations in 21cm brightness temperature caused by the HI gas in the Universe. Calculating this analytic 21cm power spectrum requires a formalism for the HI mass weighted clustering bias of DLAs on both large and small scales. We include this DLA clustering bias by firstly generating an analytic galaxy power spectrum using the halo model of Peacock & Smith (2000), as well as including the occupation of haloes by galaxies -- using the Halo Occupation Distribution (HOD) weighting of Peacock (2003). This weighting is then adapted to account for the occupation of haloes by HI gas. / We then fit the analytic 21cm power spectrum generated using this formalism to a simulated 21cm power spectrum, with the characteristic mass of DLA host haloes being used as a fitting parameter. The DLA host halo mass is in turn dependent upon two parameters in our model: the minimum mass of haloes M_{min} included in our formalism, and the HI weighting index alpha_{HI}. The neutral hydrogen fraction is another parameter, which we can choose to be the same as that from our simulation volume. If we also choose a value for alpha_{HI} that is motivated by analysis of the dark matter and HI gas content of the haloes in the simulation, then we are able to fit the 21cm power spectrum at both large and small scales, with an M_{min} that is the same or similar to the lowest mass in the simulation's halo catalogue. This in turn gives a similar value for the DLA host halo mass that is known to be the case in the simulation. This demonstrates the viability of the Wyithe (2008) method for determining the DLA host halo mass using observations of 21cm fluctuations. However, degeneracies in the free parameters of our analytic formalism would hinder an accurate determination of the DLA host halo mass from actual future observations. This is due to the fact that the real space, spherically averaged 21cm power spectrum is used throughout this thesis. However, extending our analytic formalism to the redshift space, angular-dependent 21cm power spectrum should be capable of breaking the degeneracy between DLA host halo mass and neutral hydrogen fraction.

We study the structure and substructure of Lambda-CDM halos using a suite of high-resolution cosmological N-body simulations. Our analysis of the substructure population of dark matter halos focuses on their mass and peak circular velocity functions, as well as their spatial distribution and dynamics. In our analysis, we consider the whole population of subhalos physically associated with the main halo, defined as those that have, at some time, crossed within the virial radius of the main progenitor. We find that this population extends beyond 3 times the virial radius and includes objects on unorthodox orbits, several of which travel at velocities approaching the nominal escape speed from the system. We trace the origin of these unorthodox orbits to the tidal dissociation of bound groups, which results in the ejection of some systems along tidal streams. This process primarily influences low-mass systems leading to clear mass-dependent biases in their spatial distribution and kinematics: the lower the subhalo mass at accretion time the more concentrated and kinematically hotter their descendant population. When quantified in terms of present day subhalo mass these trends disappear, presumably due to the increased effect of dynamical friction and tidal stripping on massive systems. We confirm several of these results using the ultra-high resolution Aquarius simulations, which extend the dynamic range of the subhalo mass function by nearly 3 orders of magnitude. Using these simulations we confirm that the substructure mass function follows a power-law, $dN/dM\propto M^{-1.9}$, and exhibits very little halo-to-halo scatter. This implies that the total mass in substructure within a given halo is bounded to a small fraction of the total halo mass, with the smooth component dominating the halo inner regions. Using the Aquarius simulations we study the structure of galaxy-sized Lambda-CDM halos. We find that the spherically averaged density profiles become increasingly shallow toward the halo center, with no sign of converging to an asymptotic power-law; a radial dependence accurately described by the Einasto profile. In our highest resolution run we resolve scales approaching 100 pc, at which point the maximum asymptotic slope is $\approx -0.89$, confidently ruling out recent claims for cusps as steep as $r^{-1.2}$. We find that the spherically averaged density and velocity dispersion profiles are not universal, but rather show subtle but significant deviations from self-similarity. Intriguingly, departures from self-similarity are minimized when cast in terms of the phase-space density profile, $\rho/\sigma^3$, suggesting an intimate scaling between densities and velocity dispersions across the system. The phase-space density profiles follow a power-law with radius, $r^{-1.875}$, identical to that of Bertschinger's similarity solution for self-similar infall onto a point mass in an otherwise unperturbed Einstein-de Sitter universe.

Title: Study of dark energy and modified gravity and their influence on the cosmological parameters of the universe Author: Michal Vraštil Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: RNDr. Michael Prouza, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Discovery of the accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives due to serious problems connected with the cosmological constant. Numerical predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we found that it is screened away on scales...

We present new N-body, hydrodynamical simulations of the interaction between the starburst galaxy NGC 7714 and its poststarburst companion NGC 7715, focusing on the formation of the collisional features, including (1) the gas-rich star-forming bridge, (2) the large gaseous loop (and stellar tails) to the west of the system, (3) the very extended H I tail to the west and north of NGC 7714, and (4) the partial stellar ring in NGC 7714. Our simulations confirm the results of earlier work that an off-center inclined collision between two disk galaxies is almost certainly responsible for the peculiar morphologies of this system. However, we have explored a wider set of initial galaxy and collisional encounter parameters than previously and have found a relatively narrow range of parameters that reproduce all the major morphologies of this system. The simulations suggest specific mechanisms for the development of several unusual structures. We find that the complex gas bridge has up to four distinct components, with gas contributed from two sides of NGC 7715, as well as from NGC 7714. The observed gas-star offset in this bridge is accounted for in the simulations by the dissipative evolution of the gas. The models suggest that the most recently formed gas bridge component from NGC 7715 is interacting with gas from an older component. This interaction may have stimulated the band of star formation on the north side of the bridge. The models also indicate that the low surface brightness H I tail to the far west of NGC 7714 is the end of the NGC 7715 countertail, curved behind the two galaxies. The sensitivity of the tidal structures to collision parameters is demonstrated by comparisons between models with slightly different parameter values. Comparison of model and observational (H I) kinematics provides an important check that the morphological matches are not merely fortuitous. Line-of-sight velocity and dispersion fields from the model are found to match those of the observations reasonably well at current resolutions. Spectral evolutionary models of the NGC 7714 core by Lançon et al. suggest the possibility of multiple starbursts in the last 300 Myr. Our hydrodynamic models suggest that bursts could be triggered by induced ringlike waves and a postcollision buildup of gas in the core of the galaxy.

Title: Modelling the Orion Nebula Cluster Author: Václav Pavlík Department: Astronomical Institute of the Charles University Supervisor: doc. RNDr. Ladislav Šubr, Ph.D. (Astronomical Institute of the Charles University) Abstract: Young star clusters are widely discussed from the point of view of their evolution and structure. In this work we focused our attention on studying a typical representative of these objects - the Orion Nebula Cluster (ONC, M 42) - based on the observational data, including their confrontation with N- body models from Šubr et al. (2012). These numerical models were inspired by the recently proposed evolutionary scenario, according to which the star clusters begin their evolution from very dense initial conditions. From the analysis of the X-ray sources we revealed that the ONC is likely to be rotationally symmetric in the inner area (� 0.7 pc). Further analysis including also optical and IR observational data led us to the conclusion that the ONC is elongated from the North-East to the South-West on large scales (up to 2 pc). We also compared radial profiles of different mass groups of stars and we discovered a possibly inverse mass segregation between stars with masses in the interval (1 ; 5) M⊙ and the stars less massive than 0.5 M⊙ in the range from 0.5 pc to 1.5 pc. This...

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.

Mapas simpléticos são bem conhecidos por preservarem o volume do espaço de fase em dinâmica Hamiltoniana e são particularmente apropriados para problemas que requerem longos tempos de integração. Nesta tese nós desenvolvemos abordagens baseadas em mapas simpléticos para o acoplamento de multi sub-sistemas/domínios astrofísicos/códigos de simulação, para integração eficiente de sistemas de N-corpos auto-gravitantes com grandes variações nas escalas de tempo características. Nós estabelecemos uma família de 48 novos mapas simpléticos baseados numa separação Hamiltoniana recursiva, que permite que o acoplamento ocorra de uma maneira hierárquica, contemplando assim todas as escalas de tempo das interações envolvidas. Nossa formulação é geral o suficiente para permitir que tal método seja utilizado como receita para combinar diferentes fenômenos físicos, que podem ser modelados independentemente por códigos especializados. Nós introduzimos também uma separação Hamiltoniana baseada em Hamiltonianos de Kepler, para resolver o problema gravitacional geral de N-corpos como uma composição de N2 problemas de 2-corpos. O método resultante é exato para cada problema de 2-corpos individual e produz resultados rápidos e precisos para sistemas de N-corpos quase- Keplerianos, como sistemas planetários ou um aglomerado de estrelas que orbita um buraco-negro supermassivo. O método é também apropriado para integração de sistemas de N-corpos com hierarquias intrínsecas, como um aglomerados de estrelas com binárias compactas. Nós apresentamos a implementação dos algoritmos mencionados e descrevemos o nosso código tupan, que está publicamente disponível na seguinte url: https://github.com/ggf84/tupan. / Symplectic maps are well know for preserving the phase space volume in Hamiltonian dynamics and are particularly suited for problems that require long integration times. In this thesis we develop approaches based on symplectic maps for the coupling of multi sub-systems/astrophysics domains/simulation codes for efficient integration of self-gravitating N-body systems with large variation in characteristic time-scales. We establish a family of 48 new symplectic maps based on a recursive Hamiltonian splitting, which allow the coupling to occur in a hierarchical manner, thus contemplating all time-scales of the involved interactions. Our formulation is general enough to allow that such method be used as a recipe to combine different physical phenomena which can be modeled independently by specialized simulation codes. We also introduce a Keplerian-based Hamiltonian splitting for solving the general gravitational Nbody problem as a composition of N2 2-body problems. The resulting method is precise for each individual 2-body solution and produces quick and accurate results for near-Keplerian N-body systems, like planetary systems or a cluster of stars that orbit a supermassive black-hole. The method is also suitable for integration of N-body systems with intrinsic hierarchies, like a star cluster with compact binaries. We present the implementation of the mentioned algorithms and describe our code tupan, which is publicly available on the following url: https://github.com/ggf84/tupan.