Simulations of the formation of tidal dwarf galaxies [Elektronische Ressource] / presented by Markus Wetzstein

Dissertationsubmitted to theCombined Faculties for the Natural Sciences and for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byDipl. Phys. Markus Wetzsteinborn in Idar-Oberstein (Germany)Oral examination: February 16th, 2005Simulations of the FormationofTidal Dwarf GalaxiesReferees: Prof. Dr. Andreas BurkertProf. Dr. Rainer SpurzemSimulationen zur Entstehung von Gezeiten-Zwerggalaxien — Wir pra¨sentieren dieErgebisse von numerischen Simulationen der Gezeitenarme in wechselwirkendenGalaxien. Die Entstehung von Zwerggalaxien in diesen Gezeitenarmen wurde mitsehr hoher Auflo¨sung untersucht. Wir stellen fest, daß in reinen N-body Simula-tionen keine kollabierten Objekte in den Gezeitenarmen entstehen, wa¨hrend Gas ef-fizientdengravitativen KollapsinGezeitenarmen triggert, soferndieGasscheibederVorga¨nger Galaxie hinreichend grosse Ausdehnung besitzt. Mittels einer Analyse-methode, die der von Beobachtern verwendeten nachempfunden ist, bestimmen wirdie kinematischen Eigenschaften des massereichsten kollabierten Objekts in unsererGas-Simulation.Ausserdem pra¨sentieren wir numerische Projekte, die fu¨r solch hochaufl¨osende Sim-ulationen no¨tig sind. VINE, ein neuer N-body SPH Code fu¨r astrophysikalischeTeilchensimulationen wurde in diesem Zusammenhang entwickelt. Der Code ver-wendet eine binaere Baumstruktur zur Berechnung von Gravitationskr¨aften.
Publié le : samedi 1 janvier 2005
Lecture(s) : 17
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Source : D-NB.INFO/974085154/34
Nombre de pages : 152
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Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
Dipl. Phys. Markus Wetzstein
born in Idar-Oberstein (Germany)
Oral examination: February 16th, 2005Simulations of the Formation
of
Tidal Dwarf Galaxies
Referees: Prof. Dr. Andreas Burkert
Prof. Dr. Rainer SpurzemSimulationen zur Entstehung von Gezeiten-Zwerggalaxien — Wir pra¨sentieren die
Ergebisse von numerischen Simulationen der Gezeitenarme in wechselwirkenden
Galaxien. Die Entstehung von Zwerggalaxien in diesen Gezeitenarmen wurde mit
sehr hoher Auflo¨sung untersucht. Wir stellen fest, daß in reinen N-body Simula-
tionen keine kollabierten Objekte in den Gezeitenarmen entstehen, wa¨hrend Gas ef-
fizientdengravitativen KollapsinGezeitenarmen triggert, soferndieGasscheibeder
Vorga¨nger Galaxie hinreichend grosse Ausdehnung besitzt. Mittels einer Analyse-
methode, die der von Beobachtern verwendeten nachempfunden ist, bestimmen wir
die kinematischen Eigenschaften des massereichsten kollabierten Objekts in unserer
Gas-Simulation.
Ausserdem pra¨sentieren wir numerische Projekte, die fu¨r solch hochaufl¨osende Sim-
ulationen no¨tig sind. VINE, ein neuer N-body SPH Code fu¨r astrophysikalische
Teilchensimulationen wurde in diesem Zusammenhang entwickelt. Der Code ver-
wendet eine binaere Baumstruktur zur Berechnung von Gravitationskr¨aften. Er
kann in Verbindungmit der Spezialhardware GRAPE verwendet werden undist fu¨r
Shared Memory Supercomputer parallelisiert worden. Sowohl ein Leapfrog als auch
ein Runge-Kutta-Fehlberg Integrator wurden implementiert, die beide ein Schema
fu¨rindividuelleZeitschrittederTeilchenverwendenk¨onnen. Weitereimplementierte
Merkmale sind z.B. periodische Randbedingungen und kosmologische Expansion.
Wir pra¨sentieren detaillierte parallele Zeitmessungen des Codes.
Simulations of the Formation of Tidal Dwarf Galaxies — We present results of
numerical simulations of the tidal arms in interacting systems of galaxies. The for-
mation of new dwarf galaxies inside the tidal arms has been studied with very high
resolution. WefindthatinpureN-bodysimulations,nocollapsedobjectsareformed
and that gas efficiently triggers the onset of collapse in tidal tails if the gas distri-
bution in the progenitor disk is extended enough. Using an analysis which closely
matches the procedure observers use, we determine detailed kinematical properties
for the most massive object formed in the tidal tails of our simulation with gas.
Numericaltools forsuchhighresolution simulations arealsopresented. Wehave de-
veloped VINE, a new N-body SPH code for astrophysical particle simulations. The
code uses a binary tree structure for the computation of gravitational interactions.
Itcan make efficient useofthespecialpurposehardwareGRAPEandis parallelized
for shared memory supercomputers. A leapfrog and a Runge-Kutta-Fehlberg inte-
gratorhavebeenimplementedtogetherwithanindividualparticletimestepscheme.
Other implemented features include periodic boundary conditions and cosmological
expansion. We present detailed parallel timings of the code.Contents
1 Introduction 1
2 Tidal Dwarf Galaxies and their Formation 3
2.1 Observations of Tidal Tails in Interacting Galaxies . . . . . . . . . . . . . . 6
2.2 Theoretical Modelling of Tidal Tails . . . . . . . . . . . . . . . . . . . . . . 22
3 VINE - a New N-body / SPH Simulation Code 29
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Time Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 The Runge-Kutta-Fehlberg (RKF) Integrator . . . . . . . . . . . . . 31
3.2.2 The Leapfrog Integrator . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Time Step Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Smoothed Particle Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.1 Momentum Equation and Artificial Viscosity . . . . . . . . . . . . . 35
3.3.2 Energy Equation and Equation of State . . . . . . . . . . . . . . . . 37
3.3.3 Variable Smoothing Lengths. . . . . . . . . . . . . . . . . . . . . . . 37
3.3.4 Symmetrization of Pairwise Quantities . . . . . . . . . . . . . . . . . 39
3.3.5 Additional Time Step Criteria for SPH Simulations . . . . . . . . . . 40
3.4 Cosmological Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Optimizations for Efficient Simulations . . . . . . . . . . . . . . . . . . . . . 42
3.5.1 The Individual Time step Scheme . . . . . . . . . . . . . . . . . . . 42
3.5.2 Practical Issues Relevant for Obtaining Good Performance on Mi-
croprocessors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5.3 The Tree Structure – Organizing Particles for Quick Access . . . . . 47
3.6 Calculation of Gravitational Forces . . . . . . . . . . . . . . . . . . . . . . . 50
3.6.1 Use of the Tree Structure to Obtain Gravitational Forces . . . . . . 50
3.6.2 Multipole Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.6.3 Node Acceptance Criteria . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6.4 Finding Neighbor Particles for SPH . . . . . . . . . . . . . . . . . . 55
3.6.5 Parallelization of the Tree Traversals . . . . . . . . . . . . . . . . . . 55
3.6.6 The GRAPE Hardware . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.6.7 Gravitational Forces Obtained from the GRAPE Hardware . . . . . 57
3.6.8 Gravitational Forces from the Combined Tree Based and GRAPE
Based Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.6.9 Softening the Forces and Potential . . . . . . . . . . . . . . . . . . . 59
III CONTENTS
3.7 Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.8 Accuracy Tests of Gravitational Forces . . . . . . . . . . . . . . . . . . . . . 63
3.8.1 The Tree Alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.8.2 The GRAPE/Tree Combination . . . . . . . . . . . . . . . . . . . . 66
3.9 Simulation of a Test Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.10 Performance of the Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 GRACE - Reprogrammable Hardware for SPH 72
4.1 Field Programmable Gate Arrays (FPGA) . . . . . . . . . . . . . . . . . . . 73
4.2 Motivation for using Reprogrammable Hardware . . . . . . . . . . . . . . . 74
4.3 Precision Requirements for SPH on FPGAs . . . . . . . . . . . . . . . . . . 78
4.4 Discussion of the Current State of the GRACE Project. . . . . . . . . . . . 81
5 Simulations of Tidal Dwarf Galaxy Formation 83
5.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.2 Numerical Parameters of the Simulations . . . . . . . . . . . . . . . . . . . 87
5.3 Resolution Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Influence of Increased Progenitor Resolution . . . . . . . . . . . . . . 88
5.3.2 Influence of Progenitor Dark Matter Halo . . . . . . . . . . . . . . . 103
5.4 Gas Dynamical Effects on the Formation of TDGs . . . . . . . . . . . . . . 108
5.4.1 Effects of Gas Distribution in Progenitor Disk . . . . . . . . . . . . . 108
5.4.2 Properties of best TDG Candidate Object . . . . . . . . . . . . . . . 117
6 Summary and Discussion 121
List of Figures 125
Bibliography 127Chapter 1
Introduction
The research topic of this thesis are the so called tidal dwarf galaxies or TDGs. Whether
these objects actually exist or not has been a highly debated matter until today. At the
timeof this writing, thenumberof TDGsystems for which reliable observational evidence
exists can easily be counted on one hand. The difficulties in observing these systems are
intimately coupled to their formation process. In systems of interacting galaxies, the tidal
forces acting from one galaxy on the other can lead to the tidal ejection of significant
amounts of matter from the parent galaxy into a tidal arm. Tidal dwarf galaxies are
believed to form inside such tidal arms. They can either be ejected from the interacting
systemor could stay gravitationally boundtotheremnantof theinteraction. Inthelatter
case, they would orbit the remnant until they either fall back into it or are gradually
disruptedby tidal forces. Theobservation of tidal dwarf galaxies is a difficulttask. Either
the objects have to be detected inside a surroundingtidal arm in order to be sure of their
tidal origin, or the are detected among other dwarf galaxies and their specific properties
point to a tidal origin. If an object is detected inside a tidal arm, the observational proof
that a it has become a self-gravitating entity and has decoupled from the surrounding
arm is hard to obtain. High resolution spectroscopic data is needed to infer the internal
kinematics of the object and prove that it is more than just a simple transient density
feature of the tidal arm. On the other hand, a dwarf galaxy which is not located inside a
tidal arm is not easily recognized as a tidal dwarf galaxy, as the internal properties of the
galaxy have to distinct it from dwarf galaxies which have been formed outside of the tidal
debris of a gravitational interaction between galaxies. Without detailed knowledge of the
observational properties of tidal dwarf galaxies, identifying a tidal dwarf galaxy inside a
given population is a difficult task as well. Especially as that knowledge without having
observed tidal dwarf galaxies inside their hosting tails before is rather limited.
The theoretical models of tidal dwarf galaxies which exist so far do not agree on a well
studied formation mechanism for those objects yet. The theoretical models have not yet
reachedthelevel wheretheycouldbeusedtodetermineTDGpropertiesliketheirinternal
velocity dispersion,rotationvelocity, etc. Hencethereisquitesomeroomforimprovement
in this field.
The current state of research on tidal dwarf galaxies from both observational as well as
theoretical sideisreviewed inChapter2. Ourownnumericalsimulations ontheformation
of tidal dwarf galaxies will be presented in Chapter 5. We will show there that the
numerical study of these objects requires much higher resolution than was previously
12 CHAPTER 1. INTRODUCTION
used.
In order to perform numerical simulations with that level of spatial as well as mass
resolution, it has become necessary for the work presented here to use a state of the art
astrophysical simulation code. We have developed such a code, called VINE, during the
past years. At the time of this writing, it is about to be published and will afterwards be
madeavailabletotheastrophysicalcommunitysothatotherscanprofitfromourextensive
work on the development of VINE as well. We will describe our new simulation code in
detail in Chapter 3.
An effort in the same direction as the development of VINE is the GRACE project,
whichstartedduringtheworkforthisthesisasanefforttospeedupnumericalsimulations
which use the Smoothed Particle Hydrodynamics (SPH) approach for the simulation of
gas. The aim of the project is the development of a flexible, reprogrammable hardware
device which can carry out otherwise time consuming parts of numerical simulations in a
much shorter time. The applications which could make efficient use of such a hardware
solution are either SPH codes or collisional N-body codes which use the Ahmad-Cohen
neighbor scheme. GRACE is an ongoing project and we give a detailed description of its
goals and the current state of development in Chapter 4.
Our results about the formation of tidal dwarf galaxies and their properties will be
summarized in Chapter 6, as well as the most important results about thenumerical tools
developed during the work for this thesis, VINE and GRACE.

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