Transcript I – The NEXUS+ Algorithm - INAF

Tracing the
Halo – Cosmic Web
Connection
Marius Cautun
Kapteyn Astronomical Institute
Rien van de Weygaert, Wojciech Hellwing,
Carlos Frenk, Bernard J. T. Jones
September 6th 2012
CosmoComp 2012, Trieste
Introduction
Sloan Digital Sky Survey galaxies
Outline
I - The NEXUS+ algorithm
Outline
I - The NEXUS+ algorithm
II – Halos and the Cosmic Web
I – The NEXUS+ Algorithm
Challenges:
• Multiscale distribution
• No clear defined boundaries
• Orders of magnitude variation in the
density field
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
filter
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
2 f ( x)
Hij ( x ) 
has eigenvalues: 1  2  3
xi x j
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
3. Use the Hessian eigenvalues to assign an environment signature to
each point.
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
3. Use the Hessian eigenvalues to assign an environment signature to
each point.
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
3. Use the Hessian eigenvalues to assign an environment signature to
each point.
4. Repeat steps 1-3 for a range of filter scales.
increasing filter size
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
3. Use the Hessian eigenvalues to assign an environment signature to
each point.
4. Repeat steps 1-3 for a range of filter scales.
5. Combine the environmental signatures of each scale to get a scale
independent result.
I – The NEXUS+ Algorithm
The NEXUS+ algorithm
1. Apply a filter to the input field.
2. Compute the Hessian of the filtered field f.
3. Use the Hessian eigenvalues to assign an environment signature to
each point.
4. Repeat steps 1-3 for a range of filter scales.
5. Combine the environmental signatures of each scale to get a scale
independent result.
6. Use physical criteria to identify the valid clusters, filaments and walls.
I – The NEXUS+ Algorithm
NEXUS+ results
I – The NEXUS+ Algorithm
Cosmic Web evolution
3
20  20  2 (Mpc h1 )volume
rendering.
Using the data from CosmoGrid simulation (Ishiyama+ 2011).
II – Halos and the Cosmic Web
Halos and environments
Halo fraction
Halo mass function
II – Halos and the Cosmic Web
Halos and environments
Angular momentum direction
Major axis of halo shape
Aragon-Calvo+ (2007), Hahn+ (2007), Codis+ (2012), Trowland+ (2012)
II – Halos and the Cosmic Web
Environment characteristics
II – Halos and the Cosmic Web
Environment characteristics
Filament diameter
II – Halos and the Cosmic Web
Environment characteristics
Filament diameter
Filament linear density
II – Halos and the Cosmic Web
Halo angular momentum vs. environment
Dependence on filamentary density
II – Halos and the Cosmic Web
Closer to home: Milky Way
Wang, Frenk, Navarro, Gao and Sawala (2012):
• 3 MW satellites with maximum velocity > 30 km/s
40% for a MW mass  1012 M 0
5%
for a MW mass  2·1012 M 0
II – Halos and the Cosmic Web
Closer to home: Milky Way
Wang, Frenk, Navarro, Gao and Sawala (2012):
• 3 Milky Way (MW) satellites with maximum velocity > 30 km/s
40% for a MW mass  1012 M 0
5%
for a MW mass  2·1012 M 0
II – Halos and the Cosmic Web
Substructure and environment
MW resides in a wall-like environment (Tully+ 2008)
For MW-like halos in the
Millennium 2 simulation:
90% in filaments
10% in walls
II – Halos and the Cosmic Web
Substructure and environment
Number of subhalos with maximum velocity
larger than 30km/s for a MW-like halo with
200km/s.
7% of halos in filaments
14% of halos in walls
II – Halos and the Cosmic Web
Conclusions
•
The NEXUS+ algorithm: a tool for multiscale and automatic Cosmic Web
environment detection.
•
Very successful in following the evolution of the cosmic environments.
•
Ideal tool for measuring the influence of the Cosmic Web on dark matter
halos and galaxies.
•
Understanding how the Cosmic Web influences the formation and evolution
of halos and galaxies.
II – Halos and the Cosmic Web