Tracing the Tracing the Halo – Cosmic Web Halo – Cosmic Web Connection Connection Marius Cautun Marius Cautun Kapteyn Astronomical Institute Kapteyn Astronomical Institute Rien van de Weygaert, Wojciech Rien van de Weygaert, Wojciech Hellwing, Hellwing, Carlos Frenk, Bernard J. T. Jones Carlos Frenk, Bernard J. T. Jones September 6 th 2012 CosmoComp 2012, Trieste
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Tracing the Halo – Cosmic Web Connection Marius Cautun Kapteyn Astronomical Institute Rien van de Weygaert, Wojciech Hellwing, Carlos Frenk, Bernard J.
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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