Top PDF A unified model for AGN feedback in cosmological simulations of structure formation

A unified model for AGN feedback in cosmological simulations of structure formation

A unified model for AGN feedback in cosmological simulations of structure formation

We here analyse how AGN feedback affects the intracluster medium and the stellar properties of the cluster galaxies. In Figure 9, we show radial profiles of gas density, temperature and entropy of the g676 cluster at three different epochs, both without (continuous blue lines) and with AGN heating (dashed red lines). Additionally, we have explored a model in which the BHAR was not limited to the Eddington rate, which is drawn with a dotted green line. It can be seen that at all redshifts considered, the central gas density is reduced significantly as a result of AGN feedback. We also observe that the gas temperature in the central regions is fluctuating around the “isothermal” value, sometimes for short time in- tervals increasing towards the centre, but most of the time being roughly constant or decreasing. These trends in gas temperature are due to the periodic nature of the bubble feedback. If a very energetic bubble is injected in the in- nermost cluster regions, the gas temperature increases for a short time, and reduces the BHAR considerably. After some time has elapsed, the gas will begin to cool again such that the central gas temperature will gradually start to decrease towards the centre. When enough gas has cooled off from the hot cluster atmosphere and has become available for accretion onto the supermassive BH, a new bubble will be triggered, establishing a self-regulated loop for the growth of the BH and the heating of the ICM. In some sense, this feedback loop acts as a thermometer for the ICM, preventing it to develop strong cooling flows.
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A model for cosmological simulations of galaxy formation physics

A model for cosmological simulations of galaxy formation physics

any feedback does not reproduce the Tully-Fisher relation. (vi) Mass-metallicity relation: Among all the relations that we examined in this paper, the mass–metallicity relation shows the largest tension between observations and our simulations. Although we find a positive correlation between stellar mass and [O/H], the overall amplitude of this relation is not fully correctly reproduced. But given the observational uncertainties we do not consider this a very severe problem at this point. The main issue is that the simulations overpredict the metallicity of higher mass systems. Here our simulations do not predict the turnover in the mass–metallicity relation correctly, and therefore lead to too many metals in massive galaxies. For lower to intermediate mass systems we can only achieve a reasonable agreement with the observations through our novel wind metal loading scheme, which decouples the actual mass loading from the metal loading of winds. Without such a scheme, low mass galaxies particularly would lose far too many metals owing to the high mass loadings of our energy-driven wind scalings. However, such high mass loadings are required to reduce star formation sufficiently in these low mass systems. (vii) Luminosity function: We used stellar population synthesis models to derive SDSS-band luminosity functions (g-, r-, i-, z-bands). Our highest resolution simulations produce luminosity functions at z = 0 which are in reasonable agreement with observations. Especially the faint end slope and the exponen- tial drop towards brighter systems are well reproduced. Our highest resolution simulation has a slightly too high faint-end normalisation compared to the observations. Also the exponential drop happens at slightly too high halo masses. Interestingly, this effect is strongest for the g-band luminosity function, whereas the agreement with the other bands is typically better. Feedback models with faster winds strongly disagree with the observations. Weakening the radio-mode AGN feedback leads to a significant overshoot of the luminosity function at the bright end while weak winds cause an overproduction of faint galaxies.
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Stellar Feedback, AGN Feedback and Fluid Microphysics in Galaxy Evolution

Stellar Feedback, AGN Feedback and Fluid Microphysics in Galaxy Evolution

In this paper, we have attempted a systematic exploration of different qualitative physical mechanisms by which energy can be injected into massive haloes to quench galaxies and suppress cooling flows. We specifically considered models with radial momentum injection (e.g., “wind” or “radiation pressure” or “isotropic kinetic” models), thermal heating (e.g., “shocked wind” or “isotropic sound wave” or “photo/Compton-heating” or “blastwave” models), turbulent “stirring” (e.g., “con- vective/buoyant bubble” or “precessing jet” or “jet/bubble instability-driven” or “subhalo/merger/satellite wind-driven” models), and cosmic ray injection (e.g., CRs from compact or extended radio jets/lobes, shocked disk winds, or inflated bubbles). We vary the associated energetics and/or momentum fluxes, spatial coupling/driving scales, and halo mass scale from ∼ 10 12 − 10 14 M . These were studied in fully global but non-cosmological simulations including radiative heating and cooling, self-gravity, star formation, and stellar feedback from supernovae, stellar mass-loss, and radiation, enabling a truly “live” response of star formation and the multi-phase ISM to cooling flows; we used a hierarchical super-Lagrangian refinement scheme to reach ∼ 10 4 M mass resolution, much higher than many previous global studies. Of the cases surveyed, only turbulent stirring within a radius of order the halo scale radius, or cosmic ray injection (with appropriate energetics) were able to maintain a stable, cool-core, low-SFR halo for extended periods of time, across all halo masses surveyed, without obviously violating observational constraints on halo
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Wang, Jie
  

(2008):


	Simulating structure formation with N-Body and semi-analytic models.


Dissertation, LMU München: Fakultät für Physik

Wang, Jie (2008): Simulating structure formation with N-Body and semi-analytic models. Dissertation, LMU München: Fakultät für Physik

We combine N -body simulations of structure growth with physical modelling of galaxy evolution to investigate whether the shift in cosmological parameters between the 1- year and 3-year results from the Wilkinson Microwave Anisotropy Probe affects pre- dictions for the galaxy population. Structure formation is significantly delayed in the WMAP3 cosmology, because the initial matter fluctuation amplitude is lower on the relevant scales. The decrease in dark matter clustering strength is, however, almost entirely offset by an increase in halo bias, so predictions for galaxy clustering are barely altered. In both cosmologies several combinations of physical parameters can repro- duce observed, low-redshift galaxy properties; the star formation, supernova feedback and AGN feedback efficiencies can be played off against each other to give similar results. Models which fit observed luminosity functions predict projected 2-point cor- relation functions which scatter by about 10-20 per cent on large scale and by larger factors on small scale, depending both on cosmology and on details of galaxy formation. Measurements of the pairwise velocity distribution prefer the WMAP1 cosmology, but careful treatment of the systematics is needed. Given current modelling uncertainties, it is not easy to distinguish the WMAP1 and WMAP3 cosmologies on the basis of low-redshift galaxy properties. Model predictions diverge more dramatically at high redshift. Better observational data at z > 2 will better constrain galaxy formation and perhaps also cosmological parameters.
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A model for cosmological simulations of galaxy formation physics: multi-epoch validation

A model for cosmological simulations of galaxy formation physics: multi-epoch validation

et al. (2011b) used SPH simulations to investigate the im- pact and importance of stellar winds. They found that stellar winds are able to reproduce the faint-end of the z = 0 galaxy stellar mass function, while also leading to appropriate levels of enrichment in the inter galactic medium (Oppenheimer & Dav´ e 2008; Oppenheimer et al. 2009). Even more recently, it was shown (Kannan et al. 2013) that large-scale hydrody- namical simulations are capable of producing galaxy stellar mass functions and stellar mass to halo mass relations that are consistent with observations by enforcing strong (Stinson et al. 2006) and early (Stinson et al. 2013) stellar feedback. In the “GIMIC” project (Crain et al. 2009), roughly spherical volumes of size L ∼ 20h −1 Mpc drawn from re- gions of various over-densities in the Millennium simula- tion were re-simulated at high resolution. This work has been used to study systematic variations in galaxy formation that scales with large scale environment (Crain et al. 2009), the formation (Font et al. 2011) and structure (McCarthy et al. 2012a) of galactic stellar haloes, and the characteris- tics (McCarthy et al. 2012b) and origin (Sales et al. 2012) of disk galaxies. The “Mare-Nostrum Horizon” (Ocvirk et al. 2008) is perhaps the largest, high-resolution, full-volume cos- mological simulation run and it was performed using the Adaptive Mesh Refinement (AMR) simulation code RAM- SES (Teyssier 2002). This simulation was used to study the mode of gas accretion into galaxies (Ocvirk et al. 2008) and the angular momentum evolution of high redshift galax- ies (Danovich et al. 2012). Other simulations aimed at study- ing galaxy formation in large volumes have been carried out using RAMSES by Hahn et al. (2010) and Few et al. (2012). Recently, a moving-mesh hydro solver was developed and incorporated into the hydrodynamical simulation code AREPO (Springel 2010). This method combines advantages of traditional Lagrangian hydro solvers (e.g., continuous res- olution enhancement, adaptive geometry, Galilean invari- ance) with the strengths of Eulerian hydro solvers (e.g., in- stability handling, shock capturing, phase boundary resolu- tion). It has been demonstrated that the hydro solver used in AREPO can lead to systematic changes in the properties of galaxies formed in cosmological simulations. In particu- lar, the hot-haloes of galaxies are found to contain less hot gas (Vogelsberger et al. 2012) because it is able to cool effi- ciently onto the central gas disk (Sijacki et al. 2012; Kereˇ s et al. 2012). This leads to an increase in hot-mode gas ac- cretion rates (Nelson et al. 2013) and the creation of large, gas disks (Torrey et al. 2012). However, the first cosmologi- cal simulations published with this code lacked strong feed- back, and therefore formed stars far too efficiently compared to actual galaxies.
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Schmidt, Andreas Stefan
  

(2018):


	Measuring the tidal response of structure formation using anisotropic expanding cosmological simulations.


Dissertation, LMU München: Fakultät für Physik

Schmidt, Andreas Stefan (2018): Measuring the tidal response of structure formation using anisotropic expanding cosmological simulations. Dissertation, LMU München: Fakultät für Physik

subgrid models have to be used to represent physical processes, that cannot be resolved, since the range of scales involved is enormous, spanning multiple orders of magnitude. To simulate from first principles one would start at least on the atomic level (∼ 10 −10 m) while the length scale of interest in the simulations can be of the order of hundreds of Megaparsecs (Mpc ≈ 3.1 · 10 22 m) in cosmological runs or a few hundred kiloparsecs (kpc ≈ 3.1 · 10 19 m) in isolated galaxy simulations. This is with the current codes and technology, not feasible even with the largest supercomputers to date. To circumvent this, most processes below a certain scale are approximated by empirical or physically motivated models that are valid at and above (to a certain extent) the resolution limit. One of the prominent examples for this is star formation, which is mostly stochastic and depends on the mean density and temperature of the resolution element. This effectively mirrors the observed Schmidt relation (Schmidt, 1959). The mass of the star is then drawn according to the mass function. Stellar feedback is also modeled as heating the surroundings depending on the mass of the star but for the bulk of models only contains supernova explosions. Another energy source in galaxies is the central black hole which is modeled as a sink particle that accretes surrounding gas and grows while also heating the medium (e.g. Springel et al., 2005a). In the recent years the models have grown more complicated to incorporate different physical processes like shielding through dust, kinematic feedback from black holes, metal enrichment and so on.
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A Model Of Critical Peer Feedback To Facilitate Business English Writing Using Qzone Weblogs Among Chinese Undergraduates

A Model Of Critical Peer Feedback To Facilitate Business English Writing Using Qzone Weblogs Among Chinese Undergraduates

Peer feedback holds the four theoretical frameworks including social constructivism, sociocultural theory, Vygotsgy’s Zone of Proximal Development, and interaction in second language acquisition (Hyland & Hyland, 2006; Lai, 2016). These theories emphasize the role of “peer” in different perspectives. For the perception of peer feedback, peer feedback is identified as a valuable approach in higher education (Lai, 2016). Some researchers believed that peer feedback can promote in-depth learning, the development of professional practice and self-praise skills (Hyland & Hyland, 2006; Lai, 2016; Morris, 2001). However, some pointed out the drawbacks such as the high cost of organizing and supervising the peer feedback process, students’ lack of trust in peer feedback, low efficiency and time-consuming (Hovardas et al., 2014; Llado et al., 2014; McGarr & Clifford, 2013). Recent studies indicated that peer feedback can be associated with a larger degree of student autonomy (Yang et al., 2006). The self-efficacy of students and knowledge foundation is the basis of peer feedback.
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Campisi, Maria Angela
  

(2009):


	Gamma-ray Bursts and their Host Galaxies from Cosmological Simulation.


Dissertation, LMU München: Fakultät für Physik

Campisi, Maria Angela (2009): Gamma-ray Bursts and their Host Galaxies from Cosmological Simulation. Dissertation, LMU München: Fakultät für Physik

The current interpretation of the energy release in GRBs is that a large amount of gravitational energy (roughly a fraction of a solar mass) is released on short time-scales (seconds or less) in a very small region (tens of kilometers or so) by a catastrophic stellar event, i.e. the collapse of the core of a massive star, or the merger of two remnant compact cores for long and short bursts, respectively. Most of the available energy would escape in the form of thermal neutrinos and a substantial fraction may be emitted as gravitational waves. Only a small fraction of the available energy will lead to the formation of a very high temperature fireball expanding at highly relativistic speeds, which undergoes internal dissipation (Rees and Meszaros, 1992) events leading to gamma-ray prompt emission and it would later develop into a blast wave (Meszaros and Rees, 1993) as it decelerates against the external medium, producing an afterglow which gets progressively weaker.
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The Role of Stellar Feedback in Star Cluster Formation

The Role of Stellar Feedback in Star Cluster Formation

In general, scenarios requiring more than a few Myr can be ruled out, as good Elson et al. (1987) fits appear to have been achieved for quite young star clusters. Indeed, Ryon et al. (2015) found no correlation of γ with cluster age in M83, suggesting that any secular evolutionary processes occurring within these YMCs typically takes longer than ∼ 100 Myr to have an appreciable systematic effect on the outer structure. Such young cluster have not existed long enough to experience any significant number of dynamical relaxation times or orbits around the host galaxy during which they may be tidally stripped. Thus, we will explore explanations in which γ is established over a relatively short cluster formation timescale and then evolves only slowly. The most promising of these is the other physical explanation proposed by Elson et al. (1987): dissipationless relaxation following a rapid star formation event. It was noted that simulations of the collisionless relaxation of galaxies from a clumpy, non-equlibrium state (van Albada, 1982; McGlynn, 1984a) could reproduce the range of profile slopes observed in star clusters. We will revisit this scenario in the context of modern star formation theory.
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How a Minimum Time Step and Formation of Initial Causal Structure in Space Time Is Linked to an Enormous Initial Cosmological Constant

How a Minimum Time Step and Formation of Initial Causal Structure in Space Time Is Linked to an Enormous Initial Cosmological Constant

This is on the order of the Cosmological constant, as computed by [12] and Peskins, in [13] so that the Pre-Planckian Cosmological constant would have an enormous value on par with the Quantum field theory estimate of the Plancks constant, in Pre-Planckian space-time [12] [13].

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How a Minimum Time Step and Formation of Initial Causal Structure in Space Time Is Linked to an Enormous Initial Cosmological Constant

How a Minimum Time Step and Formation of Initial Causal Structure in Space Time Is Linked to an Enormous Initial Cosmological Constant

DOI: 10.4236/jhepgc.2018.43032 547 Journal of High Energy Physics, Gravitation and Cosmology This is on the order of the Cosmological constant, as computed by [12] and Peskins, in [13] so that the Pre Planckian Cosmological constant would have an enormous value on par with the Quantum field theory estimate of the Plancks constant, in Pre Planckian space-time [12] [13].

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Shao, Li
  

(2013):


	The nature of AGN-host co-evolution.


Dissertation, LMU München: Fakultät für Physik

Shao, Li (2013): The nature of AGN-host co-evolution. Dissertation, LMU München: Fakultät für Physik

At higher redshift, Swift BAT is no longer suitable for searching AGNs. The detection rate is too low at redshift ∼1 for such shallow survey. Instead we use deep X-ray survey in GOODS-N, which is included in the Chandra Deep Field North (CDFN). The CDFN 2Ms Chandra X-ray catalog [2] provides 503 X-ray sources at sensitivity level of ∼2.5 × 10 −17 erg cm −2 s −1 . 328 of them are located within the Herschel PACS image coverage, which will be used to measure rest-frame 60 µm luminosities. At this sensitivity level, the X-ray detections may include a large number of star forming galaxies. In order to remove these objects, we use an updated version of the criterion suggested by F. Bauer et al. [17] to separate star formation dominated objects from AGNs, based on the X-ray luminosity, obscuring gas column density or X-ray hardness ratio, optical spectroscopic classifications and X-ray-to-optical flux ratio. There are totally 224 X-ray selected AGNs in the final sample. Different from local Universe where usually the redshift is available by matching to a nearby NGC galaxy, at higher redshift it is more difficult to get spectroscopic redshifts for a large number of galaxies. Thanks to intensive follow-up observation coverage, 57% of our X-ray AGNs have spectroscopic redshifts (spec-z) [15]. For the other objects, the redshifts are estimated by F. Bauer, using photometric data (phot-z) based on the method suggested by A. Barger et al. [13] (see Figure 4.1). F. Bauer also kindly provides the intrinsic X-ray luminosities L 2–10 keV and the obscuring column density N H by performing model fitting
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The Development of a Model for the Process and Structure of a Control System for an Induction Hardening Cell

The Development of a Model for the Process and Structure of a Control System for an Induction Hardening Cell

The initial distribution of heat sources rep- resents the input variable for the computation of the nonstationary temperature field and the interacting phase transformation during heating. The changeable physical properties of the material which depend on temperature are included in the model via correspond- ing spline temperature dependent functions, derived from experiments or literature sources. The depen- dence of properties on temperature produces nonlin- ear data in the magneto-thermal procedure, thus ne- cessitating iterative calculations of the dissipated power using numerical methods (i.e. Finite Element method, Boundary Element Method etc.) ([3] to [7]). Preglednica 1. Velièine, ki vplivajo na obliko zakaljenega sloja, globino kaljenja in potek trdot po zakaljenem sloju in jih popisujejo vhodni parametri simulacijsko optimizacijskega modela
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Kiloparsec-scale simulations of star formation in disk galaxies. I. the unmagnetized and zero-feedback limit

Kiloparsec-scale simulations of star formation in disk galaxies. I. the unmagnetized and zero-feedback limit

We present hydrodynamic simulations of the evolution of self-gravitating dense gas on scales of 1 kpc down to parsec in a galactic disk, designed to study dense clump formation from giant molecular clouds (GMCs). These structures are expected to be the precursors to star clusters and this process may be the rate limiting step controlling star formation rates in galactic systems as described by the Kennicutt–Schmidt relation. We follow the thermal evolution of the gas down to ∼5 K using extinction-dependent heating and cooling functions. We do not yet include magnetic fields or localized stellar feedback, so the evolution of the GMCs and clumps is determined solely by self-gravity balanced by thermal and turbulent pressure support and the large-scale galactic shear. While cloud structures and densities change significantly during the simulation, GMC virial parameters remain mostly above unity for timescales exceeding the free-fall time of GMCs indicating that energy from galactic shear and large-scale cloud motions continuously cascades down to and within the GMCs. We implement star formation at a slow, inefficient rate of 2% per local free-fall time, but even this yields global star formation rates that are about two orders of magnitude larger than the observed Kennicutt–Schmidt relation due to overproduction of dense gas clumps. We expect a combination of magnetic support and localized stellar feedback is required to inhibit dense clump formation to ∼ 1% of the rate that results from the nonmagnetic, zero-feedback limit.
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Decelerating Non Static Plane Symmetric cosmological Model with Varying

Decelerating Non Static Plane Symmetric cosmological Model with Varying

of Einstein field equation of VI 0 space time in stiff fluid has been investigated by Ellis and McCollum [21]. The class of Bianchi type VI 0 perfect fluid cosmological model associated with electromagnetic field has been obtained by Dunn and Tupper [22]. Some Bianchi type cosmological model in Biometric theory of gravitation presented by Reddy and Rao [23]. An algorithm for generating exact perfect fluid solution Einstein field equation, not satisfying the equation of state, for spatially homogeneous cosmological model of Bianchi type VI 0 has been presented by Shri Ram [24]. The solution of string cosmological models with magnetic field in general relativity have been obtained by Singh and Singh [25].Solution of Bianchi string cosmological model with Bulk viscosity and magnetic field have been obtained Xing-Xiang [26-28]. Bianchi type III for cloud string cosmological model described by Tikekar and Patel [29]. Tikekar and Patel [30] obtained Some exact solutions. Bianchi type I and Bianchi type III discussed by Bali et al. [31-34] Recently, Bali and Poonia [35] investigated Bianchi type VI 0 Inflationary Cosmological Model in General Relativity. Tyagi et. al [36-38] obtained Bianchi Type
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Structure formation by fifth force : power spectrum from N body simulations

Structure formation by fifth force : power spectrum from N body simulations

This Letter is organized as follows: in Section 2, we shall briefly review the general equations of motion for the coupled scalar field model introduced in Li & Zhao (2009), and present our specific choices of the coupling function and the scalar field potential. In Section 3, we describe the formulae and the algorithm of the N-body simulation, analyze the results of our coupled scalar field N-body simulations, compare it with that of the standard ΛCDM model, and explain the physical origin of the new features. Finally, we conclude and discuss observational implications in Section 4.
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Maio, Umberto
  

(2008):


	Switching on the first light in the Universe.


Dissertation, LMU München: Fakultät für Physik

Maio, Umberto (2008): Switching on the first light in the Universe. Dissertation, LMU München: Fakultät für Physik

of stars. Nevertheless, efforts are being made in this direction (Abel et al., 2000, 2002; Bromm and Larson, 2004; Yoshida et al., 2007; Whalen et al., 2008, for example). For this reason, more practical, even if sometimes coarse, approximations are adopted. In brief, star formation relies on semi-empirical and numerical recipes based on chosen criteria to convert gas into stars and obtain the star formation rate, carefully normalized to fit observational data at the present day. The standard method used is to assume that once the gas has reached a given density threshold it automatically forms stars (e.g. Katz et al., 1996), regardless of the time between the moment when the threshold is reached and the effective run-away collapse which typically takes place at densities ∼ 10 2 cm −3 − 10 4 cm −3 .
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A remarkably flat relationship between the average star formation rate and AGN luminosity for distant X-ray AGN

A remarkably flat relationship between the average star formation rate and AGN luminosity for distant X-ray AGN

Here, we explore whether X-ray AGN have SFRs that are consistent with being selected from the overall star-forming galaxy population. We compare the average SFRs of the AGN to the observed rela- tionship between SFR, redshift, and stellar mass (M ∗ ) of normal star-forming galaxies, which is defined as the ‘main sequence’ of star-forming galaxies (e.g. Noeske et al. 2007; Elbaz et al. 2011; Speagle et al. 2014; Schreiber et al. 2015). To make this compari- son, we require stellar masses for the AGN in our sample. We use the stellar masses from Ilbert et al. (2013) for the sources in the C-COSMOS area. Since their analysis did not take into account of a possible AGN component to the rest-frame UV to near-IR SEDs, we applied a colour cut to exclude sources for which there is likely to be significant AGN contamination to the SED. We only include AGN with rest-frame colours U − V > 1 and V − J > 1 based on the analyses of Mullaney et al. (2012b). This results in a subsample of primarily moderate luminosity AGN ( L 2 − 8 keV 10 44 erg s −1 )
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Kiloparsec-scale Simulations of Star Formation in Disk Galaxies. IV. Regulation of Galactic Star Formation Rates by Stellar Feedback

Kiloparsec-scale Simulations of Star Formation in Disk Galaxies. IV. Regulation of Galactic Star Formation Rates by Stellar Feedback

simulations of galaxies with up to subparsec resolution in which stars form when n H, * > 1000 cm - 3 and including momentum feedback representing stellar winds, radiation pressure and supernovae, and an approximate Strömgren-type model for ionization feedback. However, the SPH method has been criticized for being very diffusive and for having dif fi culties in accurately modeling the multiphase ISM that is expected in regions affected by strong feedback ( Agertz et al. 2007 ) . Agertz & Kratsov ( 2015 ) have simulated a global disk galaxy with a cosmological zoom-in grid-based adaptive mesh re fi nement ( AMR ) simulation that includes energy and momentum feedback from winds, radiation pressure, and supernova feedback, but with a resolution of only 75 pc. The treatment of radiative transfer in the above simulations has generally been very approximate in comparison to the moment-based method we utilize here. Rosdahl et al. ( 2015 ) have presented global galaxy simulations including photo- ionization, radiation pressure, and supernova feedback, but with minimum resolutions of about 20 pc, which is still too small to resolve GMCs. Photodissociation feedback with a moment-based method of radiative transfer has not been included in any of the above simulations.
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Jasche, Jens
  

(2010):


	Bayesian Methods for Analyzing the Large Scale Structure of the Universe.


Dissertation, LMU München: Fakultät für Physik

Jasche, Jens (2010): Bayesian Methods for Analyzing the Large Scale Structure of the Universe. Dissertation, LMU München: Fakultät für Physik

Today, it is widely known that ordinary baryonic matter alone cannot explain the formation of the currently observed structures in the Universe via gravitational interaction. In the process of gravitational clustering, matter flows away from regions where the density is below average and aggregates in places with higher densities. In general, this gravitational clustering is a slow process. Thus, in order to explain the presently observed cosmic structures by a purely baryonic matter component, the fluctuations in the cosmic microwave backround would be expected to be at least two orders of magnitude larger in amplitude than actually measured by modern cosmic microwave background experiments (Einasto 2009). Cosmologists resolved this mass discrepancy by introducing a hypothetical material component of the Universe, which does not interact via electromagnetic or strong forces, but possibly by weak nuclear interactions. Observational indications for such a "dark matter" component have been found already very early. Zwicky (1933) studied the radial velocities of galaxies in the Coma cluster, and found that in order to explain the observed orbital velocities the cluster must contain huge amounts of invisible matter. Further dynamical evidence for dark matter was obtained in the 1970’s by measuring rotation curves of galaxies (Rubin & Ford 1970). A peculiarity in this measurements was that rotation curves do not exhibit the expected Keplerian fall but tend to be flat at radii larger than a few kpc from the center. These observations, are consistent with extended massive haloes, containing about ten times more mass than the galactic mass observed optically (Del Popolo 2007). However, as noted in the beginning most stringent evidence for dark matter comes from measurements of the cosmic microwave background temperature fluctuations, such as carried out by the COBE or the WMAP satellites. Also weak lensing or discrepancies in the estimated mass of clusters of galaxies via the virial theorem give strong indications for the existence of a dark matter component. A very impressive evidence for dark matter was provided by the Chandra X-ray observatory which observed the bullet cluster of galaxies and a joint analysis of its lensing properties. This analysis revealed that the gravitational centers do not coincide with the visible luminous matter.
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