Numerical simulations of cosmic structure formation

Liang Gao

NAOC

PlanPlan

A basic overview of Cosmological A basic overview of Cosmological simulations.simulations.

Dark side of the UniverseDark side of the Universe

Simulations of visible side of the Simulations of visible side of the UniverseUniverse

Available numerical data in NAOCAvailable numerical data in NAOC

85%

15%

Dark Matter

Baryons

Cosmological Constant

“Dark Energy”

Matter

tot= 1

flat space-time

Simulations need to account for the full cosmic matter-energy content

MATERIAL IN THE UNIVERSE

Recreating the Universe in a Recreating the Universe in a computercomputer

Creating initial matter distribution of Creating initial matter distribution of the Universe according to the observed the Universe according to the observed Microwave background.Microwave background.

Start evolution from a time shortly after Start evolution from a time shortly after big bangbig bang

Follow the matter in an expanding cubic Follow the matter in an expanding cubic regionregion

Cosmological N-body simulations have grown rapidly in size over the last three decades

"N" AS A FUNCTION OF TIME

Computers double their speed every 18 months

(Moore's law)

N-body simulations have doubled their size

every 16-17 months

Recently, growth has accelerated

further.

The large N-body dark matter with uniform mass resolution like the MS may be not ideal to study internal structure of galaxy size halo ~1e12 solar masses.

To reliably revolve inner structure of dark halo, one needs least million particles.

We need a simulation 1000 times bigger than the Millennium simulation!

A resimulation will help here!

4 stages:

(1) Identify object of interest in existing simulation(2) Create high resolution smooth mass distribution of the region the object originates from.(3) Add old power keeping phases/amplitudes the same +add extra power(4) Feed initial conditions to n-body code

10^9 particles simulation of a galaxy sized halo Springel et al. 2008

10^9 particles simulation of a cluster sized halo

Gao et al. 2010

Structure of dark matter halosStructure of dark matter halos

Halos extend to more than 10 times the Halos extend to more than 10 times the visible radius of galaxies and contain more visible radius of galaxies and contain more than about 10 times the mass in the visible than about 10 times the mass in the visible regionsregions

Halo are not spherical but approximate Halo are not spherical but approximate triaxial ellipsoidstriaxial ellipsoids

Cuspy density profiles with outwardly Cuspy density profiles with outwardly increasing slopes.increasing slopes.

Substantial number of self-bound subhalos Substantial number of self-bound subhalos contain about 10% of the halo mass.contain about 10% of the halo mass.

Small scale structure in halosSmall scale structure in halos

A ‘Milky haloA ‘Milky halo’ Springel et ’ Springel et al. 2008al. 2008 A rich galaxy cluster halo A rich galaxy cluster halo

Gao et al. 2010Gao et al. 2010

Dark halo tests of LCDMDark halo tests of LCDM

Measures of the shape and density profile of Measures of the shape and density profile of halos from Lensing and dynamics of visible halos from Lensing and dynamics of visible tracers (stars, satellite galaxies)tracers (stars, satellite galaxies)

Limits on the central cusps from galaxy rotation Limits on the central cusps from galaxy rotation curvescurves

Limits on amount of substructure from Observed Limits on amount of substructure from Observed satellites number counts and image distortion of satellites number counts and image distortion of background lensed objects.background lensed objects.

Predictions for all these properties require Predictions for all these properties require simulations.simulations.

Density Density profiles of profiles of

dark matter dark matter haloshalos

Density profile Density profile slopeslope

Slope evolves much slower as radius for clusters than galaxies.

Inner slopers are quite noisy for clusters

A couple of Phoenix clusters tentatively haveasymptotic inner slopes up to the numerically trusted scales.

Einasto versus Einasto versus NFWNFW

Some Phoenix cluster are better fitted with Einasto profile, while some are better with NFW, still some can not be well fitted with both fits.

Subhalo abudance Subhalo abudance (Gao et al. 2010)(Gao et al. 2010)

There are more subhalos in clusters than in There are more subhalos in clusters than in galactic halos. The subhalo mass function is galactic halos. The subhalo mass function is close to N(m)~m^(-1.9x). Most mass of dark close to N(m)~m^(-1.9x). Most mass of dark halos are not in subhalos. Cluster have higher halos are not in subhalos. Cluster have higher abundance of subhalos (in terms of mass) and abundance of subhalos (in terms of mass) and more mass in subhalos. more mass in subhalos.

Subhalo spatial distributionSubhalo spatial distribution

Subhalo radial distribution is almost identical for cluster and galaxy.subhalo mass fraction is higher everywhere in clusters than in galaxies, especiallyin the innermost regions.

But we need to carefully interpret dark matter But we need to carefully interpret dark matter only simulationonly simulation

Missing satellites? Miss-distributed galaxies?Missing satellites? Miss-distributed galaxies?

Moore et al 1999 Diemand, Moore & Stadel 2005

By taking into account of baryon physics, there is indeed nocrisis for radial distribution of cluster galaxies

Gao et al. 2004 with SA model

Towards a realistic simulation of the Universe Can we simulate the astrophysical objects from the first principle?

The baryons in the universe can be modelled as an ideal gas

BASIC HYDRODYNAMICAL EQUATIONS

Euler equation:

Continuity equation:

First law of thermodynamics:

Equation of state of ideal monoatomic gas:

Towards ideal cosmological simulation! We need to integrate more physicsFor example:

Radiative cooling, UV background--is relatively well defined, but do we really understand UV background?

Detailed chemical enrichment--relying on feedback model.

Growth of supermassive black holes and AGN feedback--physics is not yet clear. Blackhole formation, feeding, feedback?

Phenomenological model for galactic winds--physics is not clear yet.

Radiative transfer--computational challenge. A function of 6 variables, position, photo frequency,

And direction.

Modelling star formation and subresolution multiphase model for the ISM--we have to put by hand.

1. First stars1. First stars

The cleanest simulation we can do from The cleanest simulation we can do from the first principle because ofthe first principle because of

1. Very clean initial conditions1. Very clean initial conditions

2. Very clear physics.2. Very clear physics.

What are needed to make the first What are needed to make the first starsstars

Assembly of dark matter structures to Assembly of dark matter structures to provide potential well to constrain gas.provide potential well to constrain gas.

CDM --------dark haloCDM --------dark halo

WDM ---dark halo, filaments and WDM ---dark halo, filaments and pancakes. pancakes.

Primordial Gas collapse to high density Primordial Gas collapse to high density to make a proto-star seed (central to make a proto-star seed (central density reach stellar density 10^22 cc).density reach stellar density 10^22 cc).

What we have knownWhat we have known

At T<10000k, H2 is the main coolant to At T<10000k, H2 is the main coolant to dispose primordial gas entropy:dispose primordial gas entropy:

Formation of H2Formation of H2 channel , dominates at z>200channel , dominates at z>200

H- channel, dominates at z<200 and H- channel, dominates at z<200 and

3 body reaction, very rapid reaction, 3 body reaction, very rapid reaction, dominates dominates

Dark matter Gas

density

The first star will be formed in two density peak

0.3Mpc

5pc

0.01pc A new born proto-starwith T* ~ 20,000K

r ~ 10 Rsun!

Self-gravitating cloud

Fully-molecular core

First stars in WDM

Gao & Theuns,2007, Science

Status of current cosmological hydro-dynamical simulation

Even the most sophisticated hydro-dynamical simulation failed to reproduce a right shape luminosity function seen today.

Disk formation is still an problem. (too small is disk size)

Many simulation results are resolution dependant.

Overcooling problems.

Nevertheless it is promising in future!

Why hydro-dynamical simulation still fails?

<> Unclear subgrid physics and how to integrate subgrid Physics to numerical code. Star formation, AGN, Blackhole…

<>Feedback is vital in galaxy formation. It heat baryons, redistribute metals where gas cooling rate is sensitive

to the metalicity.

<> Feedback--winds, supernova explosion in real galaxy. Different implementations of feedback often

lead to very different results (see Thacker et al. 2001).

Different implement Of star formation and Associated feedback Recipe lead to different Morphology of galaxies.

Okomoto et al. 2002

Available Available simulations in simulations in

NAOC NAOC

Phoenix ProjectPhoenix Project

A brother project of the Aquarius. Collaborating with A brother project of the Aquarius. Collaborating with Simon White, Carlos Frenk, Volker Springel and Adrian Simon White, Carlos Frenk, Volker Springel and Adrian JenkinsJenkins

A set of simulations of 9 rich clusters sized halo with A set of simulations of 9 rich clusters sized halo with mass about 1e15 Msun/h with unprecedented mass about 1e15 Msun/h with unprecedented resolutionresolution

Pure dark matter only, but will run with whole physics Pure dark matter only, but will run with whole physics in futurein future

For the most expensive simulation, it takes more than For the most expensive simulation, it takes more than 2 months on 1024 computing cores2 months on 1024 computing cores

Simulations have been performed at Supercomputer Simulations have been performed at Supercomputer center, CAScenter, CAS

10^9 particles inside virial radius; 10^9 particles inside virial radius; Mp=5e5 Msun/h resolves 200,000 Mp=5e5 Msun/h resolves 200,000

substructures. 5Mpc/h acrosssubstructures. 5Mpc/h across

Unit Mpc/h across

Phoenix Phoenix simulation simulation overviewoverview

9 clusters (Ph-[A-I]) with masses great than 5e14 9 clusters (Ph-[A-I]) with masses great than 5e14 Msun randomly selected from the MSMsun randomly selected from the MS

9 clusters have been simulated with 10^8 particles 9 clusters have been simulated with 10^8 particles inside their R200. Per DM particles ~5e6 Msun/h , inside their R200. Per DM particles ~5e6 Msun/h , force resolution 320 pc/hforce resolution 320 pc/h

The PhA halo has been simulated with 4 different The PhA halo has been simulated with 4 different resolutions. The PhA-1 has 10^9 particles inside its resolutions. The PhA-1 has 10^9 particles inside its viral radius. Mass resolution 5e-5 Msun/h, viral radius. Mass resolution 5e-5 Msun/h, softenning=150pc/hsoftenning=150pc/h

Stored 71 snapshots for all simulations.Stored 71 snapshots for all simulations.

We now already have all halo/subhalo catalogues and We now already have all halo/subhalo catalogues and merging trees for the level-4 and 2 simulations, but merging trees for the level-4 and 2 simulations, but only have catalogues for z=0 for the Ph-A-1.only have catalogues for z=0 for the Ph-A-1.

Ongoing research projectsOngoing research projects

The dark side of rich clusters. Properties of dark matter The dark side of rich clusters. Properties of dark matter component of rich clusters, i.e. density profiles, component of rich clusters, i.e. density profiles, velocities profiles, shapes, substructures etc.velocities profiles, shapes, substructures etc.

Dark matter annihilation signal from clusters Dark matter annihilation signal from clusters

Strong lensing--Strong lensing--Perturbation of giant arcs by DM halos Perturbation of giant arcs by DM halos of cluster galaxiesof cluster galaxies

Intra-cluster lightIntra-cluster light

Galaxy formation in rich clustersGalaxy formation in rich clusters

Tidal disruption of subhalosTidal disruption of subhalos

And many othersAnd many others

C4 ProjectC4 Project

One of the largest Cosmological simulations One of the largest Cosmological simulations in the world. 1Gpc/h Boxsize and 3072^3 in the world. 1Gpc/h Boxsize and 3072^3 particles. Mass resolution 2.4 e9Msun/hparticles. Mass resolution 2.4 e9Msun/h

Run with the WMAP 5 Cosmological Run with the WMAP 5 Cosmological parameters.parameters.

Collaborators: Ming Li, Longlong Feng, Collaborators: Ming Li, Longlong Feng, Yipeng Jing, Xiaohu yang, pengjie Zhang, Xi Yipeng Jing, Xiaohu yang, pengjie Zhang, Xi Kang, Jun Pan, Liang Gao etc.Kang, Jun Pan, Liang Gao etc.

Two weeks running on 2048 Cores at Super Two weeks running on 2048 Cores at Super computer center, CAS computer center, CAS

Science program Science program for the C4 projectfor the C4 project

Make good mocks for Large Make good mocks for Large observational surveies in China, for observational surveies in China, for example, LAMOST, Sub millimeter example, LAMOST, Sub millimeter survey of Dome-A.survey of Dome-A.

Large scale structure of the UniverseLarge scale structure of the Universe

Study earlier massive galaxy formationStudy earlier massive galaxy formation

Weak lensing studiesWeak lensing studies

Other Available Other Available simulation data of simulation data of

the Virgo the Virgo consortium at NAOCconsortium at NAOC

Millennium simulation (Dark matter Millennium simulation (Dark matter density, halos, subhalos, merging tree, density, halos, subhalos, merging tree, the latest galaxy catalogue) the latest galaxy catalogue)

MS2 – 125 time higher resolution than MS2 – 125 time higher resolution than MS but with 125 time less volume.MS but with 125 time less volume.

Aquarius Project—6 galactic halos with Aquarius Project—6 galactic halos with resolution up to 1000 Msun/hresolution up to 1000 Msun/h

What are What are simulations good simulations good

for?for?They compress cosmic evolution into They compress cosmic evolution into human timescaleshuman timescales

They can follow complex structures They can follow complex structures and complex physics in order to learn and complex physics in order to learn origin of cosmic systemsorigin of cosmic systems

They can be observed in exactly similar They can be observed in exactly similar ways to the real sky, enabling direct ways to the real sky, enabling direct comparison of theory and observationcomparison of theory and observation

Keep computer busy.Keep computer busy.