Lorentz Center - Advanced School and Workshop on Computational Gravitational Dynamics from 3 May 2010 through 13 May 2010
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    Advanced School and Workshop on Computational Gravitational Dynamics
    from 3 May 2010 through 13 May 2010


Projects Advanced School on Computational Gravitational Dynamics


Title: Testing formation scenarios of ultra-compact dwarf galaxies
Supervisor: Dr. Holger Baumgardt

Ultra-compact dwarf galaxies (UCDs) are compact stellar systems with masses between 106 and 108 Msun which are intermediate between globular clusters and dwarf galaxies. Their formation mechanism is largely unknown, with four major scenarios being discussed at the moment:

 1) UCDs are simply bright and massive globular clusters
 2) UCDs form by the merging of several globular clusters which formed close together in a major starburst event
 3) UCDs form from dark-matter dominated sub-structures  4) UCDs are the nuclei of dwarf galaxies that were stripped due to a close passages of a large galaxy

While little or no rotation is expected in the first three scenarios, the fourth scenario could lead to UCDs which are strongly rotating due to preferential stripping of stars on pro-grade orbits. The idea of the project is therefore to test if the measurement of rotation profiles of UCDs could give clues on their origin.

Recommended literature:
Dabringhausen J., Hilker M. & Kroupa, P. 2008, MNRAS, 386, 864: From star clusters to dwarf galaxies: The properties of dynamically hot stellar systems

Evstigneeva E.A., Drinkwater M.J., Peng C.Y., Hilker, M., et al. 2008, AJ, 136, 461: Structural Properties of Ultra-Compact Dwarf Galaxies in the Fornax and Virgo Clusters

Mieske S., Hilker M., Jordan A., et al. 2008, A&A, 487, 921: The nature of UCDs: Internal dynamics from an expanded sample and
homogeneous database

Required software:


You can download the latest version of AMUSE via:



Title: Exploring galaxy collision products
Supervisor: Prof. dr. Chris Boily

Description: We will explore the dataset of galaxy collisions compiled by Igor in his GalMER [1] project. The idea is to look at mergers, first observationnally (really) through snaphots of compiled runs, using on-line tools such as topcat [2] (or aladin and VOspec) to reconstruct spectra. There are several aspects to explore, include direct comparisons with SDSS galaxies. After this observational consensus, the students will try their hand at simulating galaxy mergers using a tree code, such as in AMUSE [3].

Recommended literature:

Requires software:
 [1] http://galmer.obspm.fr/

 [2] http://www.star.bris.ac.uk/~mbt/topcat

 [3] http://www.amusecode.org


You can download the latest version of AMUSE via:


Title: Toomre & Toomre Redux
Supervisor: John Dubinski

The goal of this project is to re-model the interacting galaxy systems as described in Toomre and Toomre 1972 - M51, The Mice, and The Antennae - using modern methods.  I will describe some current methods for setting up realistic, equilibrium initial conditions for disk galaxies and we will use a parallelized treecode with the N-body visualization package MYRIAD to recreate animations of these classic systems.  After determining an appropriate orbital geometry for these model systems, we will explore the role of stellar:dark matter mass ratio, disk extent and dark matter halo extent in controlling the phenomenology in interacting galactic disks and the structural properties of tidal tails.

Recommended Literature:
Interacting Galaxies
[1] Toomre & Toomre 1972 http://adsabs.harvard.edu/abs/1972ApJ...178..623T
[2] Eneev, Kozlov, Sunyaev 1973 http://adsabs.harvard.edu/abs/1973A%26A....22...41E
[3] Barnes 1988 http://adsabs.harvard.edu/abs/1988ApJ...331..699B
[4] Barnes 1989 http://adsabs.harvard.edu/abs/1989Natur.338..123B
[5] Salo and Laurikainen 2000 (M51) http://adsabs.harvard.edu/abs/2000MNRAS.319..377S

Initial Conditions for Galaxies
[5] Binney & Tremaine 2008, Chapter 4
[6] Kuijken & Dubinski 1995  http://adsabs.harvard.edu/abs/1995MNRAS.277.1341K
[7] Widrow, Pym, Dubinski 2008 http://adsabs.harvard.edu/abs/2008ApJ...679.1239W

Parallel Treecodes and N-body Visualization
[8] Dubinski, J 1996 http://adsabs.harvard.edu/abs/1996NewA....1..133D
[9] Dubinski, J 2008 http://adsabs.harvard.edu/abs/2008NJPh...10l5002D

Tidal Tails and Halos
[10] Dubinski, Mihos, Hernquist 1999 http://adsabs.harvard.edu/abs/1999ApJ...526..607D
[11] Springel and White 1999 http://adsabs.harvard.edu/abs/1999MNRAS.307..162S

Will be provided by John Dubinski



Title: Orbital Dynamics of Multi-Planet Systems w/ GPUs
Supervisor: Prof. Eric B. Ford

Description: The discovery of dozens of distant planetary systems has reinvigorated the field of planetary orbital dynamics. The resonant and/or secular interactions can provide insights into the formation processes of extrasolar planetary systems [1-4]. Due to their chaotic evolution, one can not study the long-term evolution of a specific system. Instead, one studies the statistical properties of ensembles of planetary systems. In practice, observational uncertainties make it even more important to consider the orbital evolution of large ensembles of planetary systems. Astronomers have developed tools for efficiently performing thousands of small-n-body integrations in parallel using highly modern graphics processing units (GPUs). We will use GPUs to explore the orbital dynamics of ensembles of planetary systems similar to some of the particularly interesting multi-planet systems discovered by Doppler planet searches [e.g., 1,3].

The exact nature of the project(s) will depend upon students' interests and programming skills. To facilitate rapid progress, a
library (written in CUDA 3.0 and C++) and trivial demonstration programs will be provided, so that students can harness GPUs to
perform n-body integrations using plain C/C++, without having to learn a language specific for GPUs. (Programing in other languages like Fortran or Python is possible, but will require some additional coding by students.) Students with CUDA [5,6] experience will be encouraged to improve the libraries to increase computational efficiency and/or add functionality. Another possibility is for students to study the dynamics of planets in clusters by coupling GPU codes written for studying planetary dynamics (many few-body systems) with GPU codes written studying star clusters (one many-body system).

Recommended literature on planetary dynamics:

[1] Correia et al. 2009 A&A 496,521-526. "The HARPS search for southern extra-solar planets. XVI. HD 45364, a pair of planets in a 3:2 mean motion resonance" (http://adsabs.harvard.edu/abs/2009A%26A...496..521C)

[2] Ford et al. 2005 Nature 434, 873-876 "Planet-planet scattering in the upsilon Andromedae system"

[3] Lee et al. 2006 ApJ 641, 1178-1187. "On the 2:1 Orbital Resonance in the HD 82943 Planetary System"

[4] Veras & Ford 2009 ApJ 690, L1-4.
"Secular Evolution of HD 12661: A System Caught at an Unlikely Time"

Recommended literature on GPU programming:

[5] Farber, Rob "CUDA, Supercomputing for the Masses" Dr. Dobb's Journal, April 15, 2008.

[6] nVidia CUDA Developer Zone http://developer.nvidia.com/object/cuda_training.html (e.g., 4x10
minute "CUDAcasts - Downloadable CUDA Training Podcasts", and/or "Introductory CUDA Technical Training Courses, Volume I: Introduction to CUDA Programming")

Requires software:
[1] CUDA SDK 3.0 [http://developer.nvidia.com/object/cuda_3_0_downloads.html]
[2] AstroGpu Swarm (first release coming soon, will be provided)



Title: The Final Parsec Problem
Supervisor: Stefan Harfst

Supermassive black holes (SMBHs) are found in the center of most, if not all, massive galaxies. When two galaxies merge two SMBHs are brought together to form a binary. Observations indicate that the binary must coalesce on a short time scale but the theory for this process is inconclusive. In gas-free galaxies in particular, N-body simulations have shown that binary SMBHs may stall at a separation of order of 1pc (the "final parsec problem") [1]. However, this may be partly due to the arbitrary and simplified choice of the galaxy model [2]. The aim of this project is to study and compare the evolution of binary SMBHs in various galaxy models (spherical, non-axisymmetric, rotating) in order to find conditions suitable for rapid coalescence. The required N-body simulations will be carried out using phiGRAPE [3] in AMUSE [4] on (parallel) GRAPE/GPU machines.

[1] Berczik P., Merritt D., Spurzem R., Bischof H.-P., 2006, ApJ, 642, L21 "Efficient Merger of Binary Supermassive Black Holes in
  Nonaxisymmetric Galaxies"

[2] Berczik P., Merritt D., Spurzem R., 2005, ApJ, 633, 680 "Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies"

[3] Harfst S., Gualandris A., Merritt D., Spurzem R., Portegies Zwart S., Berczik P., 2007, NewA, 12, 357 "Performance analysis of
  direct N-body algorithms on special-purpose supercomputers"

Required software:
[4] http://www.amusecode.org

You can download the latest version of AMUSE via:

Title: Collisional dynamics with a tree code
Supervisor: prof. dr. D.C. Heggie

Tree codes greatly accelerate the computation of gravitational accelerations, but they are not used for collisional simulations (e.g. for star clusters) because (it is believed) they conserve
energy too poorly. And yet several investigations [1,2] show that they correctly exhibit such collisional effects as core collapse. The aim of this project is to check the collisional evolution of a tree code against results of N-body simulations [3], with particular regard to mass segregation. Any tree code would be suitable, but with a view to subsequent implementation of stellar evolution, AMUSE offers appropriate flexibility [4].

Recommended literature:
 [1] McMillan, Stephen L. W. & Aarseth, Sverre J., 1993 An O(N log N)
   integration scheme for collisional stellar systems, The
   Astrophysical Journal, 414, 200-212

 [2] Arabadjis, John S. & Richstone, Douglas O., 1998 ArXiv
   Astrophysics e-prints, arXiv:astro-ph/9810192

 [3] Khalisi, E., Amaro-Seoane, P., and Spurzem, R., 2007 A
   comprehensive NBODY study of mass segregation in star clusters:
   energy equipartition and escape, Monthly Notices of the Royal
   Astronomical Society, 374, 703-720

Requires software:
 [4] http://www.amusecode.org

You can download the latest version of AMUSE via:



Title: Core collapse with black holes
Instructor: David Merritt

A stellar system undergoes core collapse in a time of order 100 central relaxation times. On the other hand, if a stellar system contains a massive central black hole, a density cusp forms near the center, in a time roughly equal to the relaxation time measured at the black hole radius of influence. There is no core collapse. If one imagines making the black hole smaller and smaller, eventually the BH will be no more massive than a single star, and there should be a transition from one regime (cusp formation) to the other (core collapse).

We can study this transition by making a series of initial models, containing central BHs with various masses, and evolving them for several relaxation times. A tree code is probably adequate for this project, as long as the central BH is given a large enough

Background reading:
Preto, M., Merritt, D., & Spurzem, R. 2004, ApJL, 613, L109 Spurzem, R., & Aarseth, S. J. 1996, MNRAS, 282, 19



Title: Planetary system stability
Supervisor: prof. dr. A Quillen

Stability of planetary systems. Consider a planetary system with N-planets initially started in circular orbits all in the same plane. The stability or instability timescale can be measured as
 the time to first planetary close approach or orbit crossing. In the literature [1,2] exponentially long stability timescales have been numerically measured for this problem for low planet mass ratios. It is likely that resonances lead to instability, however the types of resonances responsible in these idealized settings have not been identified. Identification of resonances leading to instability will differentiate between secular chaotic and Arnold
diffusion instability (from 3 and 4 body mean motion resonances) scenarios and identify the dimension and regime if a Nekhoroshev  type of limit is appropriate. For larger mass planets it has been proposed that resonances lead to increased stability timescales as
subresonances are required to develop instability. This proposal can also be explored. Code needed for this would be mercuri or swift or symba or any accurate few planet system integrator. Outputs would need to be frequent so that fixed angular combinations associated
 with different resonances can be identified.

Recommended literature:
 [1] Chambers J.~E., Wetherill G.~W., Boss A.~P., 1996, Icar, 119, 261

 [2] Chatterjee S., Ford E.~B., Matsumura S., Rasio F.~A., 2008, ApJ, 686, 580

Requires software:

 AMUSE: http://www.amusecode.org

You can download the latest version of AMUSE via:

 MERCURY: http://www.arm.ac.uk/~jec/home.html
 SWIFT: http://www.boulder.swri.edu/~hal/swift.html



Title: Galactic Disks and Bar Formation

Supervisor: dr. P.J. Teuben



The initial conditions of an N-body simulation are arguably the most important part of your project [4]. Sometimes these are however tied to the integration code being used, making comparisons with other integrators hard.


In this project were are investigating the stability of galactic disks. Many papers have been written on this [5,6,7]. We will be looking into quiet starts, and how initial conditions with a certain symmetry create certain patterns, such as bars, which are known to exist in nearly every galactic disk in some form.  These bars spin, and slow down.  What are the properties of these bars? What are the stellar orbits in such bars? [8]


Of historic amusement, the disks used by Eric Holmberg in his famous 1941 semi-analog N-body calculation [3], have properties we can now better understand.


Required software:

[1] http://www.astro.umd.edu/nemo

[2] http://www.amusecode.org


Recommended literature: (also on http://adsabs.harvard.edu/abs/)


[3] Holmberg, Erik


    On the Clustering Tendencies among the Nebulae. (II)


[4] Sellwood, J. A.      


    The art of N-body building - Section 9 (p180-182)


[5] Kuijken, K.; Dubinski, J.    


    Nearly Self-Consistent Disc / Bulge / Halo Models for Galaxies


[6] Boily, Christian M.; Kroupa, Pavel; Pearrubia-Garrido, Jorge     


    Efficient N-body realisations of axisymmetric galaxies and halos.


[7] Dubinski, John; Berentzen, Ingo; Shlosman, Isaac


    Anatomy of the Bar Instability in Cuspy Dark Matter Halos


[8] Sparke, Linda S.; Sellwood, J. A. 


    Dissection of an N-body bar


Title: Do spiral galaxies contain a dark matter disc?
Supervisor: Tom Theuns


Simulations have made considerable progress in successfully modelling how galaxies form. They use a combination of a hierarchical tree and a particle-mesh to compute how dark matter haloes form in a cosmological context, and use grid or particle techniques to follow the hydrodynamics of the gas. Other important effects such as gas cooling, star formation, energy injection from super novae, stellar evolution, and enrichment of gas by metals are also modelled with increasing sophistication.

To win the continuous battle between modelling a representative cosmological volume, while at the same time resolving the forming galaxy in sufficient detail, it is possible to perform zoomed simulations, that is modelling the formation of a single galaxy in a cosmological setting. This project uses such a simulation of a spiral galaxy, examining its properties. Rather unexpectedly the galaxy contains a disc in the dark matter. This project will examine how and when this disc forms, and whether it affects the dynamics of the stars. Below details for suggested reading.

Recommended literature:
The simulation code is based on Volker Springel's Gadget code, (http://www.mpa-garching.mpg.de/gadget/right.html),
with details about the physics of galaxy formation given in

[1] Schaye, J., et al 2010 (http://adsabs.harvard.edu/abs/2010MNRAS.402.1536S)

The simulated galaxy is taken from the GIMIC simulations, described in

[2] Crain, R, et al 2009 (http://adsabs.harvard.edu/abs/2009MNRAS.399.1773C)

2) Previous discussion of dark matter discs in spiral galaxies are

[3] Read et al (http://adsabs.harvard.edu/abs/2009MNRAS.397...44R)

[4] Purcell et al (http://adsabs.harvard.edu/abs/2009ApJ...703.2275P)