Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 03/05

This thesis reports on the measurement of the masses of supermassive black holes in the centres of four galaxies using stellar dynamics. It is based on observations in the near-infrared (1.9-2.5\mum) with the integral-field spectrograph SINFONI at the Very Large Telescope (VLT). These data were used to determine the motions of stars in the very centre of the galaxies, which then were modelled to derive the mass of the central black hole using the Schwarzschild method. Such measurements were until now restricted to massive and dust-free galaxies, observed with the Hubble Space Telescope in the optical wavelength range. With SINFONI and the technique of adaptive optics it is now possible to measure the mass of supermassive black holes also in dusty, low-mass and faint galaxies. This is essential in order to understand the correlations between the evolution of galaxies and the growth of central black holes.

The faint elliptical galaxy NGC4486a contains a nuclear disc of dust and stars. With a velocity dispersion of 110km/s it belongs to the class of low-mass galaxies. The mass of the central black hole is M_BH=1.26x10^7 M_sun. Fornax A, a radio galaxy located in the outskirts of the Fornax galaxy cluster, experienced a recent major merger. A mass of M_BH=1.5x10^8 M_sun was derived for the central supermassive black hole. NGC3368 and NGC3489 are both galaxies which host a composite pseudobulge, i.e. a central disclike component grown via secular evolution and an additional small classical bulge. The derived masses of the central black holes are M_BH=7.5x10^6 M_sun for NGC3368 and

M_BH=6.00x10^6 M_sun for NGC3489. The tight correlation between M_BH and the velocity dispersion of the galaxy bulge, which is mainly based on elliptical galaxies, seems to be also a good indicator of the black hole mass for other galaxy types. All black hole masses derived here are in agreement with this relation. The correlation between M_BH and bulge mass, however, only seems to be valid for old classical bulges. It predicts several times larger black hole masses for the merger remnant Fornax A and for the two pseudobulge galaxies. The masses of the small classical bulge components in NGC3368 and NGC3489 seem to be a much better indicator of M_BH.

Hybridmethoden, welche eine quantenmechanische

Beschreibung eines Moleküls im Rahmen der Dichtefunktionaltheorie (DFT)

mit einer molekülmechanischen (MM) Modellierung seiner Umgebung kombinieren, eröffnen einen Zugang zur Berechnung von Lösungsmitteleffekten in molekularen Schwingungsspektren.

In der vorliegenden Arbeit wird eine solche DFT/MM-Hybridmethode

exemplarisch zur Analyse der Schwingungsspektren von Biomolekülen

eingesetzt. Durch Vergleich mit spektroskopischen Daten werden die

erzielbare Genauigkeit und der dazu nötige Rechenaufwand ausgelotet.

Bei den untersuchten Systemen handelt es sich um den

Retinalchromophor der lichtgetriebenen Protonenpumpe Bakteriorhdopsin (BR) und um ein in Methanol gelöstes, lichtschaltbares beta-Hairpinpeptid.

Die inhomogen verbreiterten Schwingungsspektren werden mit DFT/MM unter Verwendung

der „instantanen Normalmodenanalyse (INMA)“ beschrieben. Dabei wird durch eine MM Molekulardynamik-(MD-)Simulation ein Raumtemperatur-Ensemble von Strukturen des Moleküls in seiner jeweiligen Umgebung generiert und für jeden solchen Strukturschnappschuss das Infrarot-(IR-) Spektrum durch DFT/MM Normalmodenanalyse berechnet. Das inhomogen verbreiterte Raumtemperaturspektrum ergibt sich durch Überlagerung dieser Linienspektren.

Für BR ist die Erzeugung eines solchen Ensembles schwierig,

da die BR Struktur bei Verwendung der üblichen nicht-polarisierbaren

MM-Kraftfelder unter MD „zerfällt“. Einen Ausweg bietet ein

mit DFT/MM Methoden berechnetes polarisiertes BR-Kraftfeld, das die

BR-Struktur auch bei Langzeit-MD-Simulationen (50 ns) erhält.

Mit einem speziell entwickelten Hamiltonschen Replika-Austauschverfahren lässt sich anschließend zeigen, dass die bei den tiefen Temperaturen der Kristallstrukturanalyse homogene BR Struktur bei Raumtemperatur heterogen wird, was eine Vielzahl experimenteller Befunde erklärt. Die INMA Berechnung der Schwingungspektren des BR-Chromophors bei Raumtemperatur in situ, eine systematische Analyse diverser Einflussparameter und Vergleiche mit experimentellen Daten beantworten schließlich die Frage, mit welcher Qualität

solche Spektren bei sorgfältiger Modellierung und unter Einsatz der gewgenwärtig verfügbaren DFT/MM Methoden berechnet werden können.

Weiterhin werden DFT/MM-Hybridrechnungen dazu eingesetzt, um den strukturellen Gehalt von ps-zeitaufgelöste IR Daten zur Entfaltungsdynamik eines lichtschaltbaren beta-Hairpinpeptids zu dekodieren. Der lichtinduzierte Entfaltungsprozess wird

mit MM/MD simuliert. DFT/MM Berechnungen der durch den Entfaltungsprozess ausgelösten Bandenverschiebungen im Amid-I Bereich zeigen dann, dass die spektrospopischen Beobachtungen das sukzessive Aufreissen der ursprünglich geordneten H-Brückenstruktur des Peptids

anzeigen.

Holographic models, i.e. theories describing higher-dimensional gravitational physics in terms of lower-dimensional models without gravitation and vice versa, come in two guises in string theory: The AdS/CFT-Correspondence reformulates strongly coupled nonabelian field theories in terms of weakly coupled gravity theories on Anti-de Sitter space-times, thus allowing studies of strongly coupled gauge theory dynamics. On the other hand, eleven-dimensional quantum gravity (M-theory) can be reformulated in terms of matrix models, field theories of matrix-valued degrees of freedom in 0+1 dimensions. This thesis is concerned with both aspects of holography in string theory: In chapter 3, a way of holographically introducing constant electric and magnetic background fields in the D3-D7 model of holographic quarks is laid out. Magnetic background fields are found to induce spontaneous chiral symmetry breaking, while electric fields induce a vacuum instability which can be interpreted in terms of Schwinger pair production of quark-antiquark pairs. Chapter 4 of this thesis is concerned with the introduction of holographic Fayet-Iliopoulos terms in the D3-D7 model, which lead to spontaneous breaking of supersymmetry and gauge symmetry. The holographic dual of the N=2 Fayet-Iliopoulos term, a particular mode of the Kalb-Ramond field, is identified. Chapter 5 of this thesis is concerned with matrix models in the Friedmann-Robertson-Walker universe: A bosonic matrix model in this particular background is derived for a general scale factor, and the emergence of space-time away from cosmological singularities is shown by a semiclassical argument. An in-depth introduction into string theory, holography, and the AdS/CFT correspondence can be found in chapter 2, while chapter 1 and 6 respectively contain a general introduction and a discussion of the results of this thesis.

In this dissertation we use the gauge/gravity duality to investigate various properties of strongly coupled gauge theories, which we interpret as models for the quark-gluon plasma (QGP). In particular, we use variants of the D3/D7 setup as an implementation of the top-down approach of connecting string theory with phenomenologically relevant gauge theories.

We focus on the effects of finite temperature and finite density on fundamental matter in the holographic quark-gluon plasma, which we model as the N=2 hypermultiplet in addition to the N=4 gauge multiplet of supersymmetric Yang-Mills theory.

As a key ingredient we develop a setup in which we can describe vector meson spectra in the holographic plasma at finite temperature and either baryon or isospin density. The resulting spectral functions are valid for all values of quark mass and temperature. They show the expected features of meson melting at high temperatures and are in agreement with the previously derived spectra for the zero temperature and zero density limit. Moreover, we are able to give a description of in-medium effects of finite particle density which are in qualitative agreement with phenomenological models and experimental observations. The description of vector meson excitations furthermore allows for a demonstration of the splitting of their spectrum at finite isospin chemical potential.

In the effort to better understand transport processes in the QGP, we then study various diffusion coefficients in the quark-gluon plasma, including their dependence on temperature and particle density. In particular, we perform a simple calculation to obtain the diffusion coefficient of baryon charge and we derive expressions to obtain the isospin diffusion coefficient. Furthermore, we make use of an effective model to study the diffusion behavior of mesons in the plasma by setting up a kinetic model. The setup we chose allows to carry out computations at weak and strong coupling which we compare in order to estimate the effects of the coupling strength on mesonic diffusion and therewith

equilibration processes in the QGP.

Finally, we observe the implications of finite temperature and finite baryon or isospin density on the phase structure of fundamental matter in the holographic plasma. As one consequence we find a phase transition in the baryon diffusion coefficient which vanishes at a critical value of the particle density. The critical density we quantify matches the values of the according critical densities previously found in the phase transitions of other quantities. More important, we observe a new phase transition occurring when the isospin chemical potential excesses a critical bound, which depends on the temperature of the medium. Beyond this point we observe an instability of the system under consideration. In this way we trace out the border of a new phase in the phase diagram of fundamental matter in the holographic plasma.