銀河形成シミュレーションの現状と展望
Takashi Okamoto (NAOJ)

Talk plan
• 銀河形成シミュレーションの現状、SA model との関係
• 例えばこんな simulation• AGN feedback– SA を眺めながらモデルを組んだ例• 現在の simulation の問題点
• 展望？

「動く」ことによるメリット• Local physics– Multi-zone• Dynamics– Gaining angular momentum through tidal field– Interactions• Tidal interaction• Mergers– Outflows• Fountains• Winds

デメリット• Expensive• Numerical effects• SA model と同じくらいのパラメーター数– 「動く」せいで不定性は増す

The initial condition for galaxyformation• Background cosmology– WMAP– LSS (2dF, SDSS)– Type Ia SNe– ΛCDM
Tegmark et al. 2003

The abundance of dark halos
ΛCDM Hubble Volume Simulation

ΛCDM
Halo mass function

Millennium run

Jenkins+99
3000 Mpc/h

Virgo consortium

Galaxy formation

Dark halos(const M/L)

The galaxy luminosity function

galaxies
Baryonic physics is very
important!
Benson+03

A standard picture of galaxy
formation
cooling

Disc formation throughgas accretion fromtidally torqued halo

merging

A galaxy merger destroys discs
and leads to bulge formation

Further cooling forms anadditional disc.

Two ways for studying galaxy
formation in cosmological context• Semi-analytic models– Halo formation histories (merger tree) from either
the extended Press-Schechter theory or
cosmological N-body simulations– Simple parameterized physics for baryons (SF,cooling, FB, etc.)– Fast! -> statistics• Cosmological simulations (N-body + Hydro)– Including hydrodynamics– But still modelling is needed for sub-resolution
physics (SF, FB, multiphase ISM, etc)
– Computationally expensiveCosmological model(Ω, Λ, h) dark matterPrimordial fluctuations
δρ/ρ(M, t)
Dark matter halos(N-body simulations)
Gas processes(cooling, star formation, feedback)Gasdynamic simulations

Semi-analytics

Formation and evolution of galaxies

Difficulties in cosmologicalsimulations of galaxy formation• Wide dynamical range– From large scale structure to the ISM• Not well-understood processes– Star formation, supernova feedback, etc.
– These processes operate well below
numerical resolution of cosmologicalsimulations• Need large sample for verifying galaxy
formation models

Roles of tidal field• Spin up proto-halos

White 1984

r = a (t )x(t ) ≈ a (t )[q − D(t )∇Φ ],2∂ΦLi (t ) = a 2 D& ε ijk∂q′j ∂ql′ ′32 &′′′qqdqa
Dε ijk Tjl I lk ,=−lk∫|L|q =0 Γ∂ 2Φwhere Tij = −∂qi′∂q′jq′= 0and I ij = ∫ qi′q′j d 3 q′.
Γt• Accelerate/deaccelerate collapse of proto-halos
Porciani et al. 2002b

Angular momentum profile

Bullock+02

Interstellar medium

2 kpc

Wada & Norman 99• The ISM has complicated multiphase structure.
• The box size of this 2D simulation is comparable
to the size of one numerical element in typicalhigh-resolution cosmological simulations used tostudy galaxy formation.

Modeling the ISM
Halo gas

解ける

ISM
解けない

• Isothermal gals with T = 104K
– Standard (many authors)• Multiphase (2-phase) model– Springel & Hernquist (2003)– Okamoto et al. 2005

• Sticky particle– Booth, Theuns, & Okamoto 2006

Star formation & feedback insimulations• Star formation

ρ gas > ρ th ,

ρ gas
1.5
ρ&* = C*∝ ρ gastdyn ( ρ gas )– Simulations of elliptical galaxies• Large C* (~1) and strong feedback for halting SF(e.g. Kobayashi 2004; Kawata & Gibson 2005)– Simulations of disc galaxies• Small C* (~0.03) and relatively weak feedback(e.g. Steinmetz & Navarro 1999; Thacker & Couchman 2001;
Abadi et al. 2003a; Governato et al. 2004; Robertson et al.
2004)– Combined• Sommer-Larsen+03, Okamoto+05

Two kinds of cosmologicalsimulations• Box– Simulate whole periodic simulation box– Galaxy population– Intergalactic medium– Low resolution• Zoom– Multi-resolution– Put high-resolution and gas particles into theregion of interest.
– Single objects– High resolution

An example of box-sim

Kobayashi+06

So far..
• Box simulations– Insufficient resolution– Insufficient box size
– Gaining little insight into physical processes– Expensive• 観測屋さんは喜ぶことも• 将来的にはやらないといけない– 必要最小限の resolution を見極める必要あり

Zoom simulation• 一つ一つ心を込めて– 比較的詳しく形成過程を見られる– 統計量が求まらない– 観測と比較できない– 初期条件？
– モデルに制限がつかない• モデルが固まって計算機が速くなったら box
simulation に以降する必要ありSimulations of single objects(Zoom simulations)Initial conditions

Problems• Angular momentum problem– Simulations based on CDM produce too
many bulge-dominated galaxies.
– Simulated discs are too small in CDM
simulations.

• Satellite problem– CDM predicts too many sub-halos comparedto observed satellite galaxies

Simulated Tully-Fisher relation

MI - 5log(h)• Simulated galaxies in CDM have toocompact.

Angular momentum problem

High coolingrate at high-z

Lose angularmomentum!!

Cooled baryons loose their angular momenta throughdynamical friction and spiral into the centre.

Satellite problem• Simulated galaxies
have too manysub-halos.

Some successes• Sommer-Larsen et al. 2003

– Using two distinct star formation modes• Early star formation - High star formation efficiency & verystrong feedback• Late star formation – low star formation efficiency & nofeedback• Governato et al. 2004

– Numerical resolution is matter.

• Robertson et al. 2004

– Stiffer EQS for the ISM stabilises gas disc.

• Okamoto et al. 2005 (This talk)– Multi-phase ISM– Two distinct star formation modes – quiescent & bursts

An example

Multi-phase

Iso-thermalAngular momentum problem
problemsolution

coolingHigh coolingrate at high-z

Lose angular Keep them hot Disc formation
at high-z
momentum!!

Star formation & feedback insimulations• Star formation

ρ gas > ρ th ,

ρ gas
1.5
ρ&* = C*∝ ρ gastdyn ( ρ gas )– Simulations of elliptical galaxies• Large C* (~1) and strong feedback for halting SF(e.g. Kobayashi 2004; Kawata & Gibson 2005)– Simulations of disc galaxies• Small C* (~0.03) and relatively weak feedback(e.g. Steinmetz & Navarro 1999; Thacker & Couchman 2001;
Abadi et al. 2003a; Governato et al. 2004; Robertson et al.
2004)

Two star formation modes• Quiescent– Self-regulated star formation– Salpeter IMF• Burst– High star formation efficiency– Top-heavy IMF– Trigger?

Top-heavy IMF in bursts?
• Recent version of GALFORM– More luminous

high-z populations (Baugh et al. 2005)– More α−elements

ICM and Es (Nagashima et al. 2005a, b)

Also more feedback energy for merging galaxies!!

Two star formation modes• Quiescent– Self-regulated star formation– Salpeter IMF• Burst– High star formation efficiency– Top-heavy IMF– Trigger?

SF & FB

cooling
FBevaporation

SFSSPM*

The Kennicutt law

Kennicutt 98

The Kennicutt law

What triggers bursts?
• In SA models– Merger• In simulations– High density (ρ > ρburst)• Nuclear starbursts– Strong shock• Extended starbursts.

Simulations
ΛCDM:– Box-size L= 35.335 h-1 Mpc– Halo with a quiet merger history.
No-burst (only quiescent SF)
3 models Density-induced burst
Shock-induced burstSame initial conditions in all cases!

50 h-1 kpc

Stars: edge on

Stars: face on

Gas: edge on

Gas: edge on

Dynamical decomposition• Abadi et al. 2003

– Calculate the angularmomentum of co-rotating
circular orbit Jc(E) for agiven binding energy.
– Define an orbital
circularity, Jz/Jc(E).
– Decompose each galaxy
into a spheroid and a disk
assuming non-rotating
spheroids.

Probability distribution oforbital circularity.

Birthplaces of stars
comoving 2 h-1 Mpc

comoving 200 h-1 kpc

no-burst

density-burst
Less SF
Continuous
trajectories
shock-burst
More SF
discontinuous!

No-burst• SF peaks at high z andconstant SFR at low-z forms
a tiny disk.
Density-induced bursts• Similar to no-burst model until
gas density reaches threshold.
• Once bursts occur, SF
strongly suppressed.
• Almost no SF after z = 0.5
Shock-induced bursts• Burst fraction high at high-z→ SF strongly suppressed.
• Burst fraction gradually ÌSFR (Mo/yr)

Star formation historiest (yr)Birthplaces of stars

Galactic winds
No burstNo-burst• Almost no gas lost
• Gal baryons: 2/3 cold, 1/3 hot
Density-induced bursts• 2/3 of gas lost in winds• Gal baryons: all cold
Shock-induced bursts• 1/3 of gas lost in winds• Gal baryons: 1/3 hot, 2/3 cold

Density- burst

Shock- burst

Feedback & morphology
Density-burst

spheroid

Shock-burst

diskcooling

SF & feedback strongly affect galaxy
evolution

Simulated satellites

Libeskind & Okamoto et al. 2006

Flattening plots

c/ab/aShape of the satellite systems

MW satellites
Satellite systems
in simulations.

Flattened satellite distribution is consistent with earlier studies by N-bodyand N-bod/SAM simulations (Libeskind et al. 2005, Zentner et al 2005,Kang et al 2005)

Orientation of a forming disc
• Fixed viewing angle(edge-on at z = 0)
• Orientation of thedisc can significantly
change through its
formation.

J-alignments• Jgal is well alignedwith JhaloSummary• The angular momentum problem can be
avoided if starbursts are triggered bystrong shocks and stars are born with a
top-heavy IMF in the bursts.
• Results are too sensitive to assumed
physics.
• We have to understand small scale
physics and how to model it.
• The model that successfully produces adisc also explains LF of satellites.

Need of AGN feedback(BH → galaxy)• Luminosity function of galaxies
ｺｺ!!

tdyn ≈ tcool

Benson et al. 03

Magorrian (MBH-Mbulge)
relation

dMbulge/dt ∝ dMBH/dt?
Galaxy → BH

Marconi & Hunt 03

Growth of BH andAGN feedback• The Maggorian relation– dMBH/dt ∝ SFR at galactic centre• If LFB ∝ dMBH/dt– No characteristic mass scale appears.

AGN feedback – local
luminosity functions• LFB ∝ MBHMhottH– Feedback energy
ejection rate is
proportional to the
product of thetotal mass of hot
gas and the blackhole mass(just a model!! nophysics behind)

Croton et al. 2005

AGN feedback – down sizing

Bower et al. 06

What we can learn from semianalytic models?
• If AGN feedback is preferentiallyeffective in large halos where tcool >tdyn, the model can explain– Luminosity function– Cooling flow
– Down sizing• SNe feedback alone can account for the
faint end of the luminosity functions

Simulations
Cluster scale

Dalla Vecchia et al. 2004

Galaxy scale
2&LFB ∝ Mc
This model doesn’t have atypical mass above which
cooling is suppressed.

Di Matteo et al. 2005

Motivation• Construct a physically motivated, selfconsistent AGN feedback model whichefficiently shut off cooling solely inmassive halos.
• No cosmological simulations withevolving BHs and AGN feedback.
• Study roles of BHs in galaxy formationand vise versa.
• Make predictions

Mass accretion on to central
BHs• Radiation drag model by Kawakatu & Umemura 2002

LSFR (t )−τ SFR ( t )&M = η drag(1−e),2c3χ d M cloudandwhere τ SFR ≈24π rSFR

χ d = 300 cm 2 g -1 (αd /0.1μm)-1 ( ρs /g cm -3 ) ( Z/0.3Z sun )• Roughly speaking,M& ∝ M& SF– Magorrian relation– If LFB∝dM/dt, LFB∝SFRAGN feedback• In order to have strong feedback in large halo
where tcool > tdyn, here we consider two modesof accretion.
& >M& ≈ 0.01−0.1M
&– M
crit
Edd
Radiatively efficient thin accretion flow
– M& < M& crit
Radiatively inefficient thick accretion flow

• Only the latter associates with radio jets (e.g.
Narayan & Quataert 05)−5 & 2Thin
L ≈ 5 × 10 Mc ,FBLThickFB2&≈ 2.5 × 10 Mc (Meier 2001)−1

Simulation• ΛCDM• 35.325 h-1Mpc periodic box• Target halo
– Mvir ～ 2x1012 h-1 Msun
– zmajor ～ 1– zhalf ～ 1.5• UV background• Type Ia & II SNe• Metallicity dependent radiative coolingResults

SFR

Peaked at z = 2.

BH evolution• The BH mass roughly agrees
with that inferred from theMagorrian relation.
• The accretion mode changes
after the star burst. phase.

Relative importance of the AGN
1. Bolometric luminosities

Relative importance of the AGN
1. Feedback energy

Summary• Code is almost ready.
– Almost…

• By assuming two modes of accretion flow
– The AGN becomes a dominant source of feedback
after the starburst phase.
– The AGN is luminous only in the starburst phase.

• Future work
– Groups and clusters– Slim disc at M& > M& Edd ?
– Effects of radiation

数値シミュレーションの最大の不定性• Feedback– Cooling function が温度の関数なので、同じEFB を与えてもそれを空間的・時間的にどう配分するかで結果が大きく変わる• 小さな質量を加熱→高温→strong FB• 同様に instantaneous FB の方がまじめに星の寿命を計算して少しずつ熱を注入するよりずっと強い FBの効果

展望• Higher resolution– 天の川プロジェクト？

• Better code

– さよなら SPH• More physics– Conduction– Radiation– Magnetic field• よりよい理解につながるのか？
• まあほどほどに個人的には…
• 星形成のモデルはなんであれ、観測 (Kennicuttlaw) を再現できる程度のもので十分• ISM からどのくらいのガスがどのくらいの速度でハローに逃げるかが一番大事。
– High-resolution の simulation で調べられるかも？

• 本当に星形成のモードが複数あるのか？あるならどんな物理で切り替わるのか？
– 分子雲形成入りの high-resolution の simulation• 銀河をまわしたりぶつけたりて MH2/Mgas と local の物理量の関係を見てみるとか…