銀河形成と高エネルギー現象
井上進（国立天文台）
長島雅裕（長崎大教育）※井上さん作成の過去のスライドを改変して使用しております。

Gamma-rays from merging halos
ダークハローが合体すると、中の hot gas にショックが立ち、γ線を放射するであろう→ハロー内 diffuse baryon 測定に使える？
ハロー内のhot gas

shock が立つ
→γ線が出るはず

ハロー同士の合体

structure formation (SF) shocks
During the hierarchical formation of large-scale structure through mergers and accretion,
shocks inevitably form in the gas induced by gravity of the dark matter. Besides heating thegas, these structure formation (SF) shocks can accelerate nonthermal electrons and protons
and generate nonthermal emission.

shock surfaces

thermal emission• acceleration of nonthermal particles (e, p, …)-> nonthermal radiation• heating of baryonic gas

cosmological hydro simulations by Miniati et al. 00

virialization shocks, merger shocks, accretion shocks…

electron inverse Compton γ-rays from SF shocks
High energy electrons accelerated in SF shocks promptly emit γ-rays via inverse Compton (IC)upscattering of CMB photons. The spectra should be a broken power-law with a cooling break
and a maximum energy. The spectral photon index depends on the shock strength (Machnumber M), becoming E-2 above the break for strong shocks (M>>1).
Lschematicspectrum(clusters)

Ec(tIC~tshock)Emax“prompt” γ-rays(tIC<<tshock)(tIC~tacc)

strong shock E-2

LIC >~ Lsyn if
B < 3µG(1+z)2

weak shockeVkeV

MeVGeV

TeV

EγLoeb & Waxman ‘00 proposed that such emission may be the origin of the cosmic γ-ray
background, assuming that all SF shocks are strong. Is this plausible?

今回の計算ダークハローのtreeのみ使う(1st step)● ハローとして同定する最小Vcirc=Vlow● 冷却が起こる最大Vcirc=Vcut● baryonのうち、銀河になっている割合f_GF● 等を仮定し、ガンマ線背景放射を計算する● 将来的には三鷹モデルに実装（したい）● 次頁でメインの図を見せてから、式をちょっと見せて、いろいろまた図を見せます。
●

Gamma-rays from merging halos
今のところ、簡単にハロー内の hot gas fraction をパラメータにして計算
次のステップとして、SA model に入れる予定

In o u e & N a g a s h im a (2 0 0 5 ; a s tr o -p h /0 5 0 2 3 3 8 )shock formation & particle acceleration during SF
In fact, not all SF shocks are equal. Major mergers i.e. between virialized objects of similar
masses result in relatively weak(low M) shocks and soft spectra (p>2), as the preshock gas
T is already high. Conversely, minor mergers i.e. between virialized objects of very unequalmasses can produce relatively strong (high M) shocks and hard (p~2) spectra. Diffuse
accretion shocks should also be strong.
Gabici & Blasi ‘03

majormerger

minor merger,accretion
weak shock (low M)
soft spec.(p>2)

strong shock (high M)
hard spec. (p~2)

p=2(1+M-2)(1-M-2)-1
Modeling of these shocks and resulting emission requires knowledge of the preshock Tdistribution, and hence the progenitor mass distribution. This is not possible analytically,
pointing to either numerical simulations (Miniati ‘02, Keshet et al. ‘03) or semi-analyticmethods (Gabici & Blasi ‘03, THIS WORK).

Press-Schechter based semi-analytic methods for SF
Compared to simulations, semi-analytic methods are:-inexpensive & fast-simple, clear & flexible

but-no information on spatial distribution-need care with artificial effects e.g. timestep-need simplified, prudent description of subhalo physics

Monte Carlo merger trees
warning:
Lacey & Cole ‘93 “merger” rate
= probability of halo with mass M increasing its mass by ∆M
through mergers within time interval dt≠rate of binary mergers for halos of masses M and ∆M!

known problems with binary merger trees
1. does not treat all progenitors equally
2. does not reproduce Press-Schechter mass function!
3. cannot describe diffuse accretion
WE EMPLOY
multiple merger trees + accretion algorithmof Somerville & Kolatt 99

which does not entirely solve 1, but solves 2 & 3

Multiple mergers inN-body simulationsWechsler et al. ‘02

-v

main model assumptionsv

MB• An effective Mach no. is assigned to each merger shock,MAsimilar to GB03; however, we allow for uncertainty in theactual value of Ms by including a parameter f0. Takizawa
MBMA(priv.comm.) estimates a range Ms~1.9-3.1( f0~0.6-1.2) for
equal mass mergers. Diffuse accretion shocks are alwaysf (M /M )+1
1
assumed to be strong.
v2=2G(MA+B) 0 B A
RA+RB
RA+B• The electron injection efficiency is fiducially a fractionξe=0.05 of the shock-dissipated energy, i.e. the difference
f0: どれだけのめり込むか
between the postshock and preshock thermal energies.
With the injection index p given by Ms, the electron distribution
is described as a standard, cooling broken power-law.
• Employing the Monte Carlo algorithm of SK99, we assume
that the multiple merger corresponds to an ensemble of binary
mergers with the most massive progenitor. Mass remaining
below a certain scale (see below) is treated as diffuse
accretion. The fiducial time step is taken to be ∆z=0.05(1+z),
approximately the dynamical time.
• A very accurate mass function extracted from highres N-body simulations by Yahagi et al. ‘04 is adopted,
which is used for every timestep (since merging
histories are not essential for the current problem).The
power spectrum includes baryonic effects as inSugiyama ‘95.
equal M merger simulations (Takizawa 99)
Ms~1.9-3.1 → parameter f0~0.6-1.2

MDMBMAMC=(MA⇔MB), (MA⇔MC), (MA⇔MD)

c.f. Gabici & Blasi 03

non-gravitational effects due to galaxy formation and feedback Madau & Kuhlen ‘03

1. post-reionization Jeans (filtering) massfilteringmassboundary betwenn clumpy merging and diffuse accretionparameter Vacc (~20-70 km/s)
Gnedin ‘00

2. cooling dropout (galaxy formation) mass range

Jeans mass↑reionization

efficient cooling, gas to star conversion (galaxy formation)→ shock suppression
removal of fraction fGF of halos in range Vacc-Vcut
M, Tparameters fGF, Vcut (~150-250 km/s)

accretionconnection with baryon fraction in cool IGM V+warm-hot IGM (‘missing baryons’)
3. feedback (pre-)heating c.f. Totani & Inoue ‘01broken self-similarity in cluster/group
X-ray scaling relations

future workacc~5*1010MΘ
~105K

fGF
1-fGF
nomerger
Vcut shock~3*1012MΘ
~106Kmergerdiffuse: T<105 K
condensed: galaxies
warm-hot: 105<T<107 K
hot: T>107 K

Vacc
Vcut

Dave et al. ‘01 simulations withcooling and galaxy formation
accretion
fGF

1-fGF

noshock merger
mergerfGF=1 Vacc=40 Vcut=200
diffusefractionwarm-hot IGM = SF shock heated‘missing baryons’condensed
warm-hothotz

shock statistics (luminosity weighted Mach number distribution)
shock-dissipatedluminosity

dependence on z, f0

radiated luminosity• M~1.5-3 shocks dissipate majority of energy• M>~3 shocks contribute to nonthermal emission

c.f. Ryu et al. ‘03

γ-ray background: vary Vacc=Vcut (no cooling dropout)

EGRET background data:
Sreekumar et al. ‘98 (S98)

Vacc=Vcut

accretion

Vacc=Vcut
merger

Vacc=Vcut ~20 ⇔ T0 ~104K, no GF ~ simulations~100% of S98, minor merger dominantc.f. Miniati ‘02
Keshet et al. ‘03

γ-ray background: Vacc=40km/s fixed, fGF=1 (complete cooling dropout)vary Vcut

accretion
Vcut

VfGF acc
no shockVcut

mergereffect of Vcut (max. cooling mass):Vcut ↑, monotonically↓‘best bet’ Vacc =40km/s, Vcut=200km/s: ~10% of S98
c.f. Gabici & Blasi ‘03
merger ~ accretion ~1/2
probe Vacc?

baryons in the universe

diffusediffusecondensed
warm-hotfraction

fGF=0.4 Vacc=40 Vcut=200

fractionfGF=1 Vacc=40 Vcut=200

warm-hotcondensed
hothotzz

Fukugita ‘04, Stocke et al. ‘04
stars+cold gas w. galaxies~8%hot cluster gas~5%cool IG gas~30%warm-hot gas
rest?

γ-ray background: Vacc=40km/s, Vcut=200km/s fixed, vary fGF

accretion

Vacc
fGF

1-fGF

no merger
shock

Vcutmerger

effect of fGF (global GF efficiency):fGF ↑, monotonically↓‘best bet?’ fGF=0.4 (fcond~0.1): ~50% of S98 (more of SMR04)
min. merger dominantgamma-ray background = indirect ‘baryometer’ of the universeIF ξe=0.05

γ-ray cluster source counts: Vacc=40km/s, Vcut=200km/s fixed, vary fGF

GLAST

EGRET <1
GLAST ~100EGRET

5@5 100h

fGF=1 (fcond~0.25, fWH~0.25):
ξe=0.01<<1~10ξe=0.005<<1~4

fGF=0.4 (fcond~0.1, fWH~0.4):
EGRET a few
GLAST ~400

ξe=0.01<1~40ξe=0.005<<1~10IF ξe=0.05
ξe must be determined fromindividual sources

gamma-rays from SF shocks
can indirectly probe the missing baryons

summary: IC γ-rays from SF shocks, a semi-analytic study• Simulation-like: ~100% of S98 background (if ξe=0.05)• Important dependence on non-gravitational effects,
Jeans scale, max. cooling scale, global GF efficiency;with ‘best bet’ values ~50% of S98 (more of SMR04) background (if ξe=0.05)• γ-ray background and γ-ray source counts can probe these effects,
and hence warm-hot IGM fraction (‘missing baryons’)• Effective application of semi-analytic methods
Must be checked with simulations!

長島的まとめ
宇宙における高エネルギー放射に対し構造形成起源のγ線は無視できない寄与があり得る● ハローmajor merger よりも、accretion的なminor merger の方が重要●– Mach number が増大する– high-E particles が生成されやすい●

最小ハロー質量、冷却可能最大質量に（原理的には）制限がつく– 独立な制限●

非熱的粒子による銀河形成への影響？
– 加熱源→cooling flow suppression?