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@@ -0,0 +1,798 @@ +% hp-20240104.pdf - Lecture Slides on Low-Level Programming +% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024 Peter Gerwinski +% +% This document is free software: you can redistribute it and/or +% modify it either under the terms of the Creative Commons +% Attribution-ShareAlike 3.0 License, or under the terms of the +% GNU General Public License as published by the Free Software +% Foundation, either version 3 of the License, or (at your option) +% any later version. +% +% This document is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this document. If not, see <http://www.gnu.org/licenses/>. +% +% You should have received a copy of the Creative Commons +% Attribution-ShareAlike 3.0 Unported License along with this +% document. If not, see <http://creativecommons.org/licenses/>. + +% README: Dunkle Materie und angewandte hardwarenahe Programmierung + +\documentclass[10pt,t,fleqn]{beamer} + +\usepackage{pgslides} +\usepackage{utfsym} +\usepackage{gnuplot-lua-tikz} + +\newcommand{\vfilll}{\vspace{0pt plus 1filll}} +\newcommand{\scientistimage}[2]{\hfill + \raisebox{#1}{\makebox(0,0)[tr]{\includegraphics[width=2.5cm]{#2}}}} +\newcommand{\fr}[2]{{\textstyle\frac{#1}{#2}}} + +\title{\textcolor{black}{\textbf{Dunkle Materie}}\\ + {\large und} {\Large\emph{angewandte}}\\ + hardwarenahe Programmierung} +\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski} +\date{4.\ Januar 2024} + +\begin{document} + +\maketitleframe + +\title{Dunkle Materie und angewandte\\hardwarenahe Programmierung} + +\nosectionnonumber{\inserttitle} + +\begin{frame} + + \shownosectionnonumber + + \vspace{-1.5\smallskipamount} + \begin{itemize} + \item[\textbf{1}] \textbf{Was ist dunkle Materie?} + \hfill\makebox(0,0)[br]{\url{https://gitlab.cvh-server.de/pgerwinski/hp}} + \begin{itemize} + \item[1.1] Rotationskurven + \item[1.2] Virialsatz + \item[1.3] Gravitationslinsen + \item[1.4] Strukturbildung von Materie + \end{itemize} + \item[\textbf{2}] \textbf{Erklärungsansätze} + \begin{itemize} + \item[2.1] MACHOs + \item[2.2] WIMPs + \item[2.3] Modifizierte Gravitation + \end{itemize} + \item[\textbf{3}] \textbf{Das Bullet-Cluster} + \item[\textbf{4}] \textbf{Neue Erkenntnisse} + \begin{itemize} + \item[4.1] Nichtkommutative Geometrie + \item[4.2] Konforme Gravitation + \item[4.3] Verfügbare Daten + \item[4.4] Hardwarenahe Programmierung + \end{itemize} + \item[\textbf{5}] \textbf{Fazit und Ausblick} + \end{itemize} + \vspace*{-1cm} + +\end{frame} + +\section{Was ist dunkle Materie?} + +\begin{frame} + + \showsection + + Materie im Weltraum, die wir nicht sehen können\pause,\\ + auch nicht im IR-, UV-, Radar-, Röntgen-, Radio- oder Gamma-Bereich\pause,\\ + die wir aber indirekt über ihre Schwerkraft nachweisen können\pause: + \begin{itemize} + \item Rotationskurven + \item Virialsatz + \item Gravitationslinsen + \item Strukturbildung von Materie + \end{itemize} + +\end{frame} + +\subsection{Rotationskurven} + +\begin{frame} + + \showsubsection + + Kapteyn (1904):\scientistimage{0ex}{kapteyn.jpg} + \begin{itemize} + \only<1>{\item + Sterne bewegen sich.} + \only<2->{\item + Die Sterne in den Galaxien rotieren\\ + um ein gemeinsames Zentrum.} + \only<3->{\item + Über das Newtonsche Schwerkraftgesetz\\ + können wir auf die Masse dessen schließen,\\ + was sich innerhalb der Bahn des Sterns befindet.} + \end{itemize} + + \vfilll + + \only<3->{\begin{quote} + "`We therefore have the means of estimating\\ + the mass of the dark matter in the universe."' + \end{quote}} + + \medskip + + Kapteyns Stern + \begin{center} + \begin{minipage}{3.5cm} + \begin{center} + \includegraphics[width=3.5cm]{kapteyns-stern-1894.jpg}\\ + 1894 + \end{center} + \end{minipage}\quad + \begin{minipage}{3.5cm} + \begin{center} + \includegraphics[width=3.5cm]{kapteyns-stern-1904.jpg}\\ + 1904 + \end{center} + \end{minipage}\quad + \begin{minipage}{3.5cm} + \begin{center} + \includegraphics[width=3.5cm]{kapteyns-stern-2024.jpg}\\ + 2024 + \end{center} + \end{minipage} + \end{center} + +\end{frame} + +\begin{frame} + + \showsubsection + + Rubin (1970):\scientistimage{0ex}{rubin.jpg} + \begin{itemize} + \item + Galaxien rotieren außen wesentlich schneller,\\ + als es das Newtonsche Schwerkraftgesetz vorhersagt. + \arrowitem + Die Masse in den Galaxien ist deutlich größer\\ + als die Masse der sichtbaren Materie. + \end{itemize} + + \vfilll + + \only<1>{\includegraphics[width=9.4cm]{dark-matter.jpg}\\[\smallskipamount] + \hbox{\hbox to 4.7cm{\hss berechnet\hss}\hbox to 4.7cm{\hss beobachtet\hss}}} + + \only<2>{\includegraphics[width=9.4cm]{triangulum.jpg}} + +\end{frame} + +\subsection{Virialsatz} + +\begin{frame} + + \showsubsection + + Zwicky (1933):\scientistimage{0ex}{zwicky.jpg} + \begin{itemize} + \item + Die Galaxien im Coma-Galaxienhaufen bewegen sich\\ + zu schnell, als daß sie zusammenbleiben könnten. + \arrowitem + Die Masse in den Galaxien ist mindestens 400mal\\ + größer als die Masse der sichtbaren Materie. + \end{itemize} + + \vfilll + + \only<1>{\includegraphics[width=9.4cm]{coma-haufen.jpg}} + +\end{frame} + +\subsection{Gravitationslinsen} + +\begin{frame} + + \showsubsection + + Galaxienhaufen\\ + Abell 1689 + \begin{itemize} + \item<1-> + Sterne:\\ + ca.~$4{,}7\cdot10^{12}\,M_\odot$ + \item<2-> + Intergalaktisches Gas:\\ + ca.~$3{,}6\cdot10^{13}\,M_\odot$ + \item<3-> + Gesamtmasse,\\ + ermittelt über Gravi-\\ + tationslinseneffekt:\\ + ca.~$6{,}4\cdot10^{14}\,M_\odot$ + \only<4->{\arrowitem + 0,7\,\%\ Sterne\\ + 5,6\,\%\ Gas\\ + \hspace*{-0.56em}93,7\,\%\ dunkle Materie} + \end{itemize} + + \vfilll\strut\hfill\makebox(0,0)[br]{% + \only<1>{\includegraphics[width=7.8cm]{abell-1689.jpg}}% + \only<2>{\includegraphics[width=7.8cm]{abell-1689-roentgen.jpg}}% + \only<3->{\includegraphics[width=7.8cm]{abell-1689-masse.jpg}}} + +\end{frame} + +\begin{frame} + + \begin{center} + \small + \input{abell-1689-smd-1308.1958.tex} + \end{center} + + Quelle: arXiv:1308.1958\hfill Abell 1689 + +\end{frame} + +\subsection{Strukturbildung von Materie} + +\begin{frame} + + \showsubsection + + Kosmische Hintergrundstrahlung + \begin{itemize} + \item + Erstes Licht nach dem Urknall + \item + Schwarzkörperstrahlung mit Farbtemperatur $2{,}7\,\text{K}\pm0{,}1\,\%$ + \item<2-> + Fouriertransformation\\ + \textarrow\ Wellenlängen\\ + \phantom{\textarrow\ }der Schwankungen + \item<2-> + Daraus sind kosmische\\ + Strukturen entstanden. + \item<3-> + Vergleich mit realen\\ + kosmischen Strukturen\\ + \textarrow\ zusätzliche Masse\\ + \phantom{\textarrow\ }erforderich + \only<3->{\arrowitem + ca.~fünfmal so viel dunkle\\ + wie sichtbare Materie} + \end{itemize} + + \vfilll\strut\hfill\makebox(0,0)[br]{% + \only<1>{\includegraphics[height=6cm]{hintergrundstrahlung.jpg}}% + \only<2->{\includegraphics[height=6cm]{spektrum.png}}} + +\end{frame} + +\section{Erklärungsansätze} +\subsection{MACHOs} + +\begin{frame} + + \showsection + \showsubsection + + Dunkle Materie = "`normale"', nicht selbst leuchtende Materie\\ + MACHO = \emph{Massive Astrophysical Compat Halo Object} + \begin{itemize} + \item Planeten ohne Sonne + \item Gas- und Staubwolken + \item Schwarze Löcher + \end{itemize} + + \pause + + \vspace*{-0.6cm}\strut\hfill + \begin{minipage}{7.5cm} + \begin{flushright} + Problem: Davon müßte es sehr viel geben.\\ + Bis heute (2024) hat man jedoch nichts entdeckt. + \end{flushright} + \end{minipage} + + \vfilll\strut\hfill\makebox(0,0)[br]{% + \includegraphics[height=4cm]{hubble.jpg}% + \includegraphics[height=4cm]{jwst.jpg}} + +\end{frame} + +\subsection{WIMPs} + +\begin{frame} + + \showsection + \showsubsection + + Dunkle Materie = neue Teilchen\\ + WIMP = \emph{Weakly Interacting Massive Particle} + \begin{itemize} + \item sterile Neutrinos + \item Axionen + \item \emph{Little Higgs\/}-Teilchen + \item supersymmetrische\\Partnerteilchen + \end{itemize} + + \medskip + + \only<2->{Problem: Man hatte erwartet,\\ + diese Teilchem am LHC zu\\ + finden. Bis heute (2024) hat\\ + man jedoch nichts entdeckt.} + + \vfilll\strut\hfill\makebox(0,0)[br]{% + \only<1>{\includegraphics[height=6cm]{standardmodell.png}}% + \only<2->{\includegraphics[height=5.6cm]{cern.jpg}}} + +\end{frame} + +\subsection{Modifizierte Gravitation} + +\begin{frame} + + \showsection + \showsubsection + + Es gibt keine dunkle Materie.\\ + Die Gravitation verhält sich anders. + \smallskip + \begin{itemize} + \item + Newton: $\displaystyle F = \frac{m\cdot M\cdot G}{r^2}$ + \smallskip + \item + Einstein: leichte Abweichungen nahe der Sonne\\ + \textarrow\ Periheldrehung des Merkur + \pause + \smallskip + \item + Modifizierte Graviation (verschiedene Theorien):\\ + leichte Abweichungen in sehr großen Entfernungen\\ + \textarrow\ Wir benötigen keine dunkle Materie. + \smallskip + \only<2>{% + \begin{itemize} + \item Rotationskurven + \item Virialsatz + \item Gravitationslinsen + \item Strukturbildung von Materie + \end{itemize}} + \only<3->{% + \begin{itemize} + \item[\color{medgreen}\usym{2714}] Rotationskurven + \item[\color{medgreen}\usym{2714}] Virialsatz + \item[\raisebox{-1pt}{\color{red}\large\usym{2718}\kern0.5pt}] Gravitationslinsen + \item[\color{medgreen}\usym{2714}] Strukturbildung von Materie + \end{itemize}} + \end{itemize} + +\end{frame} + +\section{Das Bullet-Cluster} + +\begin{frame} + + \showsection + + Galaxienhaufen 1E 0657$-$56 "`Bullet Cluster"' + \begin{itemize} + \item + Tatsächlich: 2 Galaxienhaufen, Kollision vor ca.~100 Millionen Jahren + \item + Masse: ca.~10\,\% Galaxien, 90\,\% Gas + \begin{onlyenv}<2-3> + \smallskip + \item + Galaxien: durchdringen\\ + sich kollisionsfrei + \item + Gas: kollidiert, bremst,\\ + heizt sich auf + \begin{onlyenv}<3> + \smallskip + \item + Gravitationslinseneffekt:\\ + Schwerkraft maximal\\ + bei den Galaxien,\\ + nicht beim Gas + \arrowitem + Es gibt dunkle Materie,\\ + bei den Galaxien,\\ + kollisionsfrei. + \arrowitem + nicht erklärbar durch\\ + modifizierte Gravitation + \end{onlyenv} + \end{onlyenv} + \begin{onlyenv}<4-> + \smallskip + \item + Relativgeschwindigkeit\\ + der Galaxien + \arrowitem + nicht erklärbar\\ + durch dunkle Materie\\ + (zu hoch) + \arrowitem + erklärbar duch\\ + modifizierte Gravitation + \begin{onlyenv}<5-> + \bigskip + \arrowitem + {\Large\textbf{\raisebox{-0.3ex}{?\raisebox{-0.2ex}{?}\raisebox{0.2ex}{?}}}} + \end{onlyenv} + \end{onlyenv} + \end{itemize} + \vspace*{-1cm} + + \vfilll\strut\hfill\makebox(0,0)[br]{% + \begin{minipage}{7.5cm} + \begin{flushright} + \only<3>{Quelle: arXiv:astro-ph/0608407\\[\smallskipamount]} + \only<4->{\phantom{p}Quelle: arXiv:0704.0381\\[\smallskipamount]} + \includegraphics[width=7.5cm]{bullet-cluster.jpg} + \end{flushright} + \end{minipage}} + +\end{frame} + +\section{Neue Erkenntnisse} +\subsection{Nichtkommutative Geometrie} + +\newcommand{\sheets}[1]{% + \begin{tikzpicture}[scale=#1] + \draw [fill=blue!50!white,xshift=2mm,yshift=-4mm] (2,3) + .. controls +(2,0) and +(-2,0) .. (6,2) + .. controls +(-1,-0.5) and +(0.5,1) .. (4,0) + .. controls +(-2,0) and +(2,0) .. (0,1) + .. controls +(0.5,1) and +(-0.5,-1) .. cycle; + \draw [fill=green!50!white,xshift=1mm,yshift=-2mm] (2,3) + .. controls +(2,0) and +(-2,0) .. (6,2) + .. controls +(-1,-0.5) and +(0.5,1) .. (4,0) + .. controls +(-2,0) and +(2,0) .. (0,1) + .. controls +(0.5,1) and +(-0.5,-1) .. cycle; + \draw [fill=red!50!white,xshift=0mm,yshift=0mm] (2,3) + .. controls +(2,0) and +(-2,0) .. (6,2) + .. controls +(-1,-0.5) and +(0.5,1) .. (4,0) + .. controls +(-2,0) and +(2,0) .. (0,1) + .. controls +(0.5,1) and +(-0.5,-1) .. cycle; + \draw [fill=yellow!50!white,xshift=-1mm,yshift=2mm] (2,3) + .. controls +(2,0) and +(-2,0) .. (6,2) + .. controls +(-1,-0.5) and +(0.5,1) .. (4,0) + .. controls +(-2,0) and +(2,0) .. (0,1) + .. controls +(0.5,1) and +(-0.5,-1) .. cycle; + \end{tikzpicture}} + +\begin{frame} + + \showsection + \showsubsection + + Connes (1996): "`Weltformel"'\scientistimage{1.5ex}{connes.jpg} + % https://commons.wikimedia.org/wiki/File:Alain_Connes.jpg + \begin{itemize} + \pause + \item + diskrete Extradimensionen:\\ + Das Universum hat mehrere "`Blätter"'. + \begin{picture}(0,0) + \only<2>{\put(-2,-0.5){\makebox(0,0)[t]{\sheets{1.0}}}} + \only<3->{\put(1.2,0.2){\makebox(0,0)[t]{\sheets{0.4}}}} + \end{picture}% + \pause + \smallskip + \alt<3>{\item[]}{\item} + \visible<4->{Aus} + \begin{displaymath} + \mathcal{A} = C^\infty(M) \otimes + \bigl(\mathbb{C} \oplus \mathbb{H} \oplus M_3(\mathbb{C})\bigr) + \end{displaymath} + \pause + folgt: + \begin{picture}(0,0) + \only<5->{% + \color{medgreen} + \put(4.1,-0.20){\makebox(0,0)[b]{Allgemeine Relativitätstheorie}} + \put(3.9,-0.25){\makebox(0,0)[tr]{\tikz{\draw[medgreen,-latex](0,0)--(-1,-0.3);}}} + \put(7.7,-2.8){\shortstack{Standardmodell der\\Quantenfeldtheorie}} + \put(7.6,-2.4){\makebox(0,0)[br]{\tikz{\draw[medgreen,-latex](0,0)--(-0.7,0.3);}}}} + \only<6->{% + \color{red} + \put(7.7,-0.6){\shortstack{\hspace*{-2em}Neu!\\Dunkle Materie?}} + \put(7.6,-0.6){\makebox(0,0)[tr]{\tikz{\draw[red,-latex](0,0)--(-1.1,-0.5);}}}} + \end{picture}% + \begin{align} + \mathcal{L} =~& \fr{c^4}{16\pi G} (R - 2\Lambda) + \nonumber\\*&\strut + + a\,(5R^2 - 8R_{\mu\nu}R^{\mu\nu} - 7R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}) + \nonumber\\*&\strut + + i\bar{e}^n_L \gamma^\mu\partial_\mu e^n_L + + i\bar{e}^n_R \gamma^\mu\partial_\mu e^n_R + + i\bar\nu^n_L \gamma^\mu\partial_\mu \nu^n_L + + \dots + \nonumber + \end{align} + \vspace*{-1.3\bigskipamount} + \bigskip\smallskip + \pause + \pause + \pause + \item + bisher: wenig beachtet, weil "`nicht quantisierbar"'\\ + {\color{red}\textarrow\ mit meiner Methode schon} + \end{itemize} + \vspace*{-1cm} + +\end{frame} + +\subsection{Konforme Gravitation} + +\begin{frame} + + \showsection + \showsubsection + + Allgemeine Relativitätstheorie:\quad + $\mathcal{L} = \frac{c^4}{16\pi G} (R - 2\Lambda)$ + \vspace{-\medskipamount} + \begin{displaymath} + \Rightarrow V(r) \approx -\frac{GM}{r} + \qquad + \text{(Newton)} + \end{displaymath} + + Konforme Gravitation:\quad + $\mathcal{L} = a\,(5R^2 - 8R_{\mu\nu}R^{\mu\nu} + - 7R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma})$ + \vspace{-\medskipamount} + \begin{displaymath} + \Rightarrow V_{\text{CC}}(r) \approx -\frac{c^2\beta}{r} + \fr12 c^2 \gamma\,r + \qquad + \text{(Newton + \only<2->{winzige }konstante Kraft)} + \end{displaymath} + \pause + Für unsere Sonne: $\gamma \approx 5.42\cdot10^{-39}\,\text{m}^{-1}$ + + \pause + \bigskip + + \begin{itemize}\itemsep0pt + \item[\color{medgreen}\usym{2714}] Rotationskurven + \item[\color{medgreen}\usym{2714}] Virialsatz + \item[\raisebox{-1pt}{\color{red}\large\usym{2718}\kern0.5pt}] Gravitationslinsen + \textarrow\ Was geht schief? + \item[\color{medgreen}\usym{2714}] Strukturbildung von Materie + \end{itemize} + +\end{frame} + +\begin{frame} + + \begin{center} + \small + \input{abell-1689-acc-1808.06923.tex} + \end{center} + + Quelle: arXiv:1808.06923\hfill Abell 1689 + +\end{frame} + +\begin{frame} + + \showsection + \showsubsection + + Mein Ansatz: + \begin{itemize} + \item + Allgemeine Relativitätstheorie:\\[\smallskipamount] + $\mathcal{L} = \frac{c^4}{16\pi G} (R - 2\Lambda)$\quad + $\longleftarrow$ enthält $R$ + \medskip + \item + Konforme Gravitation:\\[\smallskipamount] + $\mathcal{L} = a\,(5R^2 - 8R_{\mu\nu}R^{\mu\nu} + - 7R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma})$\quad + $\longleftarrow$ enthält $R^2$ + \medskip + \arrowitem + Konforme Gravitation ist nur bei sehr starker Gravitation relevant.\\ + \pause + \arrowitem + Konforme Gravitation ist nur bei schwarzen Löchern relevant,\\ + nicht jedoch bei Sternen und Gaswolken. + \pause + \arrowitem + \begin{picture}(0,0) + \put(0,0.45){\makebox(0,0)[bl]{\tikz{\draw[red,line width=1pt](0,0)--(9.5,0.8); + \draw[red,line width=1pt](0,0.8)--(9.5,0);}}} + \put(9.7,0.8){\makebox(0,0)[l]{\color{red}\textbf{falsch}}} + \end{picture}% + Konforme Gravitation ist nur bei Sternen relevant,\\ + nicht jedoch bei (sehr viel schwereren) Gaswolken. + \arrowitem + Bullet-Cluster erklärbar + \end{itemize} + +\end{frame} + +\begin{frame} + + \begin{center} + \small + \input{abell-1689-acc-20231101.tex} + \end{center} + + PG, 1.~November 2023\only<2>{% + \begin{picture}(0,0) + \put(0,5.7){\makebox(0,0)[bl]{\tikz{\draw[red,line width=1pt](0,0)--(7.9,2.3); + \draw[red,line width=1pt](0,2.3)--(7.9,0);}}} + \put(6.5,4.8){\makebox(0,0)[l]{\color{red}\textbf{falsch}}} + \end{picture}}, 9:40 Uhr\hfill Abell 1689 + +\end{frame} + +\begin{frame} + + \begin{center} + \small + \input{abell-1689-smd-20231226.tex} + \end{center} + + PG, 26.~Dezember 2023\hfill Abell 1689 + +\end{frame} + +\begin{frame} + + \vfilll + + \begin{center} + \includegraphics[width=0.9\textwidth]{1e0657-558-kappa.png} + \end{center} + + \vfilll + + Quelle: arXiv:astro-ph/0608407\hfill Bullet Cluster + +\end{frame} + +\begin{frame} + + \vfilll + + \begin{center} + \includegraphics[width=0.9\textwidth]{1e0657-558-smd-cg-42.png} + \end{center} + + \vfilll + + PG, 27.~November 2023\hfill Bullet Cluster + +\end{frame} + +\subsection{Verfügbare Daten} + +\begin{frame} + + \showsection + \showsubsection + + Web-Suche + \begin{itemize} + \item + Wissenschaftliche Veröffentlichungen:\\ + Meßkurven aus Abbildungen extrahieren + \item + VizieR: veröffentlichte Meßwerte + \item + sonstige veröffentlichte Meßwerte (z.\,B.\ zum Bullet-Cluster) + \end{itemize} + + \medskip + + Astronomische Daten: Position und Leuchtkraft von Galaxien + \begin{itemize} + \item + Gehören die Galaxien überhaupt zum Galaxienhaufen?\\ + \textarrow\ Leuchtkraft in verschiedenen Farben ("`Bändern"') vergleichen\\ + \textarrow\ tatsächlich: möglicherweise nicht so wichtig + \item + Welche Masse haben die Galaxien?\\ + \textarrow\ Leuchtkraft mit sinnvoller Konstanten multiplizieren\\ + \textarrow\ schwerste Galaxie ungefähr so schwer wie M87 + \item + Position: nur zweidimensional\\ + \textarrow\ plausible dritte Koordinate (pseudo-)zufällig generieren + \end{itemize} + +\end{frame} + +\subsection{Hardwarenahe Programmierung} + +\begin{frame}[fragile] + + \showsection + \showsubsection + + \vspace{-\smallskipamount} + \begin{itemize} + \item + \file{adl2xsm.c}\\ + astronomische in kartesische Koordinaten\\ + und Leuchtkraft in Masse umrechnen + \item + \file{xym2xyzm.cpp}\\ + plausible dritte Koordinate (pseudo-)zufällig generieren + \item + \file{xyzm2aca2smd.cpp}\\ + aus den Koordinaten und Massen der Galaxien\\ + zunächst dreidimensionales Gravitationsbeschleunigung berechnen,\\ + davon die Divergenz berechnen, als Massendichte interpretieren,\\ + daraus dann eine Oberflächenmassendichte + (\emph{surface mass density}, SMD)\\ + berechnen + \medskip + \item + \file{run-smd.sh}\\ + alles compilieren und in einer Pipe aufrufen + \item + parallelisiertes Rechnen mit OpenMP:\\ + \lstinline{#pragma omp parallel for reduction (+: result_x, result_y, result_z)} + \end{itemize} + +\end{frame} + +\section{Fazit und Ausblick} + +\begin{frame} + + \showsection + + Konforme Gravitation + \begin{itemize} + \item + quantitativ richtige Ergebnisse für Abell 1689, + $R \approx 100$--1000\,kpc + \item + qualitativ richtige Ergebnisse für das Bullet Cluster + \arrowitem + dunkle Materie = Divergenz des konformen Gravitationsfeldes + \end{itemize} + \begin{itemize}\itemsep0pt + \item[\color{medgreen}\usym{2714}] Rotationskurven + \item[\color{medgreen}\usym{2714}] Virialsatz + \item[\color{medgreen}\usym{2714}] Gravitationslinsen + \item[\color{medgreen}\usym{2714}] Strukturbildung von Materie + \end{itemize} + + \medskip + + Ausblick + \begin{itemize} + \item + Abell 1689: 2d-Betrachtungen + \item + Vergleich mit Messungen über das\\ + hydrostatische Gleichgewicht der Gaswolken + \item + Optimierung der Ergebnisse für das Bullet Cluster + \item + Überprüfung für weitere Galaxienhaufen + \arrowitem + alles aufschreiben und veröffentlichen + \end{itemize} + +\end{frame} + +\end{document} diff --git a/20240104/hubble.jpg b/20240104/hubble.jpg new file mode 120000 index 0000000000000000000000000000000000000000..57ec9f1dfab9b96b5b8ffdfa2b6cb92744fece05 --- /dev/null +++ b/20240104/hubble.jpg @@ -0,0 +1 @@ +Hubble_01_Cropped.jpg \ No newline at end of file diff --git a/20240104/jwst.jpg b/20240104/jwst.jpg new file mode 120000 index 0000000000000000000000000000000000000000..020173d860a93f3cb0532fb9c9b1b3c027e8f4e6 --- /dev/null +++ b/20240104/jwst.jpg @@ -0,0 +1 @@ +960px-James_Webb_Space_Telescope_2009_top.jpg \ No newline at end of file diff --git a/20240104/kapteyn.jpg b/20240104/kapteyn.jpg new file mode 100644 index 0000000000000000000000000000000000000000..6ef3ed0edbb129da41bdc3666ea042709c0ef584 Binary files /dev/null and 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