Tracing the Tracing the Halo – Cosmic WebHalo – Cosmic Web

ConnectionConnection

Marius CautunMarius Cautun

Kapteyn Astronomical InstituteKapteyn Astronomical Institute

Rien van de Weygaert, Wojciech Hellwing, Rien van de Weygaert, Wojciech Hellwing,

Carlos Frenk, Bernard J. T. JonesCarlos Frenk, Bernard J. T. Jones

September 6th 2012CosmoComp 2012, Trieste

Sloan Digital Sky Survey galaxies

Introduction

Outline

I - The NEXUS+ algorithm

Outline

II – Halos and the Cosmic Web

I - The NEXUS+ algorithm

I – The NEXUS+ Algorithm

Challenges:

• Multiscale distribution

• No clear defined boundaries

• Orders of magnitude variation in the density field

The NEXUS+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

filter

I – The NEXUS+ Algorithm

The NEXUS+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

I – The NEXUS+ Algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

2

1 2 3

( )( ) has eigenvalues: ij

i j

f xH x

x x

The NEXUS+ algorithmThe NEXUS+ algorithm

I – The NEXUS+ Algorithm

The NEXUS+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

3. Use the Hessian eigenvalues to assign an environment signature to each point.

I – The NEXUS+ Algorithm

The NEXUS+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

3. Use the Hessian eigenvalues to assign an environment signature to each point.

I – The NEXUS+ Algorithm

The NEXUS+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

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+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

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+ algorithmThe NEXUS+ algorithm

1. Apply a filter to the input field.

2. Compute the Hessian of the filtered field ff.

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+ resultsNEXUS+ results

I – The NEXUS+ Algorithm

Cosmic Web evolutionCosmic Web evolution

I – The NEXUS+ Algorithm

volume rendering.Using the data from CosmoGrid simulation (Ishiyama+ 2011).

1 320 20 2 ( )Mpc h

Halos and environmentsHalos and environments

II – Halos and the Cosmic Web

Halo mass functionHalo fraction

Halos and environmentsHalos and environments

II – Halos and the Cosmic Web

Angular momentum direction Major axis of halo shape

Aragon-Calvo+ (2007), Hahn+ (2007), Codis+ (2012), Trowland+ (2012)

Environment characteristicsEnvironment characteristics

II – Halos and the Cosmic Web

Environment characteristicsEnvironment characteristics

Filament diameter

II – Halos and the Cosmic Web

Environment characteristicsEnvironment characteristics

Filament diameter

II – Halos and the Cosmic Web

Filament linear density

II – Halos and the Cosmic Web

Dependence on filamentary density

Halo angular momentum vs. environmentHalo angular momentum vs. environment

II – Halos and the Cosmic Web

Closer to home: Milky WayCloser to home: Milky Way

Wang, Frenk, Navarro, Gao and Sawala (2012):

• 3 MW satellites with maximum velocity > 30 km/s

120

120

40% for a MW mass 10

5% for a MW mass 2·10

M

M

II – Halos and the Cosmic Web

Closer to home: Milky WayCloser to home: Milky Way

Wang, Frenk, Navarro, Gao and Sawala (2012):

• 3 Milky Way (MW) satellites with maximum velocity > 30 km/s

120

120

40% for a MW mass 10

5% for a MW mass 2·10

M

M

II – Halos and the Cosmic Web

Substructure and environmentSubstructure 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 environmentSubstructure and environment

7% of halos in filaments

14% of halos in walls

Number of subhalos with maximum velocity larger than 30km/s for a MW-like halo with 200km/s.

ConclusionsConclusions

• 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

II – Halos and the Cosmic Web