理論懇シンポジウム
2006年12月26日＠立教大学

Anisotropy in the gamma-ray sky
and prospects for GLAST
Shin’ichiro Ando
Theoretical Astrophysics, California Institute of Technology

In collaboration withE. Komatsu (Texas), T. Narumoto, T. Totani (Kyoto)1. Introduction:
Unresolved mystery in the high-energy sky

1. Introduction:
Unresolved mystery in the high-energy sky• What are blazars?
• ~60 were detected with EGRET• What are the emission mechanisms?
• Are they beamed AGNs?—Is AGN unification picture really right?

• What is the origin of cosmic gamma-ray background?
• EGRET discovered isotropic gamma-ray background in GeV region• Can unresolved astrophysical sources explain all the flux?
• Do we have chance to see signature of dark matter annihilation?

GLAST:Gamma Ray Large Area Space Telescope• GLAST is equipped with a large volume gamma-ray
detector (LAT)• Sensitivity covers 30 MeV–300 GeV• Very large field of view (2.4 sr), enabling all sky survey• Point source flux sensitivity: 2×10−9 cm−2 s−1, 50 times
better than EGRET• Better map of (1) point sources and (2) diffuse radiation2. Point source anisotropy:
blazars for GLAST

Ando, Komatsu, Narumoto, & Totani,
MNRAS in press; astro-ph/0610155

Blazar luminosity function: How many atGLAST?

w the 68%, 95% and 99% C.L. regions for the PLE model parameters [the faint-end slope index γ1 and the mean gamma-rayg10 (Lγ /Lr )"]. The best-fit values, (!p",γ1 ) = (3.28,0.69), are shown by the cross. The dashed contours correspond to−1.33 , respectively, where η is the ratio of the normalizations of the gamma-ray to radio luminosity functions.

Narumoto & Totani 2006

GAMMA-RAY LUMINOSITY FUNCTION OF BLAZARS

1.6

dN/d(log10z)

1.2

LDDE model
PLE model
SS96 model
EGRET blazars

LDDE model
PLE model
SS96 model
EGRET blazars

0.6
0.5
dN/d(log10L!)

1.4

0.7

1.0
0.8
0.6

0.4
0.3
0.2

0.4
0.2

0.1

0.0

0.0

0.01

0.1
Redshift z

143

44

45

46

47

48

4950

log10 (L! [erg s"1])

F IG . data.
6.— TheLuminosityof theblazars.
Theforline
are the same as Figure 5. The luminosity is
he EGRET blazars. The histogram is the EGRET
solid anddistribution
dashed curves
areEGRET
the best-fitmodels
themarkings
LDDE and1σPoissonerror.
ikelihood analysis. The dotted curve is obtained from the blazar GLF model of SS96. The error bars are 1σ Poisson error.

• Luminosity-dependent density evolution (LDDE) model motivated by X-ray
AGN observation fits the data very well
• The best fit model predicts ~3,000 blazars from all sky

Is blazar clustering detectable with GLAST?
• Blazars should cluster spatially tracing the dark matter distribution• Given the large number statistics (~3,000), can the spatial clustering be
detectable with GLAST?
• We can compare data immediately with prediction of angular power spectrum• One can directly get blazar bias
• This provides an independent test of AGN unification picture• This is a very straightforward and important thing to do; nevertheless has notbeen done by anybody

pend on redshift and luminosity of blazars, we modas ξ(r; Lγ,1 , Lγ,2 |z) = ξlin (r, z)bB (Lγ,1 , z)bB (Lγ,2 , zr = |%x2 − %
x1 | is the distance between two blazars,Lγ,2 are their luminosities, and ξlin (r, z) is the 3-dtion function of linear
dark matter
fluctuations. As
22 ANGULAR
POWER
SPECTRANGULAR
POWER
SPECTRUANGULAR
POWER
SPECTRU
in this paper the angular correlation function of bla
BLAZARSBLAZARSBLAZARSbe detectable only on large scales, and thus the lin• Everything is in textbook by Peebles(1980)
relationfunction and the linear bias model would pgood approximation. By projecting the 3-d correlat
2.1 Formalism
Formalism
2.12.1
Formalism
Angularfunction:
Blazar biastion on correlation
the sky, one
obtains (Peebles 1980)! zmaxThe
angularpower
spectrumofttThe
angularpower
spectrumofblazars
blazars
The N 2 w(θ) power
spectrumd2 V
2of blazars
22=dz
χ(z) φ(z) bB (z)dzdΩ
tected byby GLAST
thesumofofofttectedGLAST0 !isis∞givengivenby
bythesumtectedGLAST
isgivenby
thesum$"#PPP2, z ,
noise term,term, C
correlation
u2 + χ(z)2 θterm,
×duξlinnoiseand thethe
correlation
term
noise
Clll ,, andandthecorrelation
term

Formulation: Angular power spectrum1980)
θ 1980)1980)

Angular power
spectrum:−∞CllCClPCPlPC
Cllwhere χ(z) is the comoving distance out to an obj
P is theCcomoving volume element per u
d2 V /dzdΩ
P + ClC
C,=Cl=C+C
Cll ,redshift,angle andrange, bB (z) is the averl per unit
−1=−1,,= N
N −1CCCClC
Cll====N!,!
! 111
2πdd cosθθ PPl (cosθ)w(θ),
2πcos(cos
2π −1 d cos θ Pll (cosθ)w(θ),θ)w(θ),−1−1

Results:(i) Angular correlation and power spectrum
Power spectrum of GLAST point sources

5LDDE1Best fit modelExplains 100%
LDDE2 of gamma-ray
background

Point source flux limit:
2, 3, 4 × 10−9 cm−2 s−1

Ando et al., astro-ph/0610155

2. (Left) Angular correlation function, w(θ), and (Right) correlation term of the angular power spectrum, l(l + 1)ClC /2π, of the2that would be detected by GLAST. Both have been divided by the average bias squared; thus plotted quantities are w(θ)/bB and2ClC /(2πbB ). The dotted, solid, and dashed lines show the predictions for the limiting flux of Fγ,lim = 2, 3, and 4 × 10−9 cm−2 s−1 ,vely. The top panels are for the LDDE1 model, while the bottom panels are for the LDDE2 model.

bB should be, in order for C
The statistical error inby the following argumentof the universe, we have 2Cl = |alm |2 (with different
is the spherical harmonic cblazars on the sky. One ma!
l2|a|/(2l + 1). Thelmm=−l(ii) Errors of angular power spectrum
Ando et al., astro-ph/0610155

gure 1. Redshift distribution of blazars that would be detected
GLAST, for LDDE1 (solid) and LDDE2 (dashed) models. (Seeble 1 for the model parameters as well as for the expectedmber of blazars.) The thick solid line shows the LDDE1 modelh Lγ,min = 1041 erg s−1 , while the thin solid lines show theDE1 model with Lγ,min = 1040 erg s−1 and 1042 erg s−1 :larger the Lγ,min is, the fewer the low-z blazars would beected.

2Cl2=(δCl ) =(2l + 1)∆lfsky(2where ∆l is the bin size inthe sky covered by observat
GLAST, we may adopt fsk• We can detect blazar
source sensitivity becomes w
correlation at large
cause of strong galactic fore
angular scalependent of l and depends on
density of blazars, one can• This directly
tells usmeasured
Cl , leaving
only
biasthe contributi
stillblazar
contains
is important to detect as ma
reduce ClP as much as possi
Figure 3 shows the 1-σ0.5l for the LDDE1 and LD
for the average bias of b =(iii) Dependence on blazar bias and otherobservations• Average over large
scale: 2 ≤ l ≤ 30
• Correlation isdetectable for bB > 1.2(LDDE1), and bB > 0.5(LDDE2)• Optical quasar gives:bQ ~ 0.8 at relevant
redshift range• X-ray AGNs seem morestrongly clustered withb ~ 3–4
Ando et al., astro-ph/0610155

Discussion:
Example strategy for GLAST point source survey
1. Source detection
2. Removing galaxy clusters
Catalog may contain galaxy clusters. These can be removed by using theFIRST radio survey
3. Updating blazar luminosity function
According to the source number, we may update the luminosity function
4. Analysis of angular power spectrum
We can constrain the blazar bias, even before follow-up observations
5. Completion of follow-ups: beginning of precision study
Analysis with more precise luminosity function. One may also use 3D
power spectrum

3. Anisotropy of cosmic gammaray background (CGB) anddark matter annihilation

Ando & Komatsu, Phys. Rev. D 73, 023521 (2006)
Ando, Komatsu, Narumoto, & Totani, astro-ph/0612467

bound at the most interesting masses, shows that dark matter halos cannot be significantly moby annihilations, and can be improved by a factor of 10–100 with existing neutrino experimen

Dark matter (WIMP) annihilation

PACS numbers: 95.35.+d, 98.62.Gq, 98.70.Vc, 95.85.Ry

elf-annihilation cross section is a fundamental• If darkmatter
is WIMP,it mayof darkmatter.
For thermal
relics,it sets thetter massdensity, Ωinto0.3, and in these andannihilates
visibleDM !
neral non-thermal
photons scenarios, also the annihilain gravitationally-collapsed dark matter halos]. How large can the dark matter annihilation
WIMP
is likely
tion •be?
Theremass
are twogeneralaroundconstraints that
he rate GeV–TeV,of dark matter
disappearance.
so GLAST
might (Throughmean havethe crosssectionaveragedover the halo
goodchance
to detect−3
distribution,i.e.,"σv#,wherev
∼
10c.)
Arms
the signature

rst is the unitarity bound, developed for the earlycase by Griest and Kamionkowski [2], and for• WIMPin In the plane ofuniverse
halo annihilationcase by Hui [3].
darkhalosmayonly thend darkcosmologicalmatter mass mallows
χ , this2(this will be made moreelow a line
"σcontributethus
A v# ∼ 1/mχ significantlybelow).toTheis provided by the model
the second
CGB flux
nghat, Knox, and Turner (KKT) [4], in which
nt dark matter annihilation is invoked to resolvet between predicted (sharp cusps) and observedχ

χ










“All StandardModel=GeV-γfinal states“

perity,Annihilation of dark matter previnFIG. 1:Since all final states except neutrinos pr(see text), we can bound the total cross setrino signal limit, i.e., assuming Br(“InvisTheas tΦE (We will show that the most difficu
to detect is neutrinos; but that surpri
limits can be derived from recent whe
higand that we may interpret these as exp
borighnal states, and hence the dark matter
Usicross section. To be robust and genera
theto brived with very conservative assumptio

TCGB anisotropy from dark matter annihilation• Astrophysical sources like blazars and clusters of galaxies cannot
fully explain the observed CGB• but only 25–50% using the latest blazar luminosity function(Narumoto & Totani 2006)• If dark matter annihilation contributes significantly, it might beobserved through anisotropy signature of the CGB• Potentially a smoking gun of dark matter annihilation• Energy spectrum might not be sufficient for such a strong claim

Angular power spectrum
Dark matter halo

• Projected along the line of sight is theCGB intensity• Angular power spectrum, Cl, is related
to the spatial power spectrum via
Limber’s equation• 3D correlation can be modeled, using• halo mass function, andθ (= π / l)• density profile in each halo

Result: angular power spectrum
Ando et al., astro-ph/0612467• At 10 GeV for 2-year
observation• If dark matter annihilation
contributes > 30% of theCGB, GLAST should beable to detect anisotropy• Detector background isnegligible• Galactic emission(foreground) is small at
10 GeV4. Conclusions I:
Point source anisotropy• Blazars are the most promising source for GLAST: 1,000–10,000 are expectedfrom all-sky survey• We calculated angular power spectrum of these blazars and showed that• it would be detectable at large angular scales, dominated by low-redshift(faint blazars);• spatial clustering would be measurable if blazar bias were larger than 1.2(0.5) for the best-fit (optimistic) luminosity function• This would be a first direct measurement of blazar bias, and could provide
further test of AGN unification picture

4. Conclusions II:
Anisotropy of background radiation• The CGB anisotropy would be a key to revealing the origin of CGB, andpotentially be a smoking gun of annihilating dark matter• The resulting angular spectrum would be very different from the case of othersources• We developed a new formalism for that calculation• We showed that if the annihilating dark matter is a main CGB constituent,
GLAST can detect anisotropy in a few years• This is also true even with the existence of other sources like blazars, if thecurrent dark matter contribution exceeds 30% at 10 GeV

Appendix: Supplementary materials

Redshift distribution of blazars

Bias modelingEffective bias

Clusters of galaxies
10S. Ando et al.

Table 2. Model parameters, α and ", the expected
N , the surface density, N , the average bias, bC
clusters that would be detected by GLAST. The l
the expected signal-to-noise ratio for detecting
power spectrum averaged over 2 ! l ! 30.
Modelαp,e"p,eN

N (sr−1 )

bC

pp1
pp2
pp3
IC1
IC2
IC3

2.2
2.2
2.2
22
2.2

0.5
0.1
0.01
0.05
0.01
0.01

6600
1100
633700430
62530
885.029034
4.9

2.0
2.53.31.4
1.7
2.2

Mixed case of blazars and galaxy clusters

Since the gamma-ray emissivity from the dark-matter22
2annihilation
isproportional
tothedensity
squared,ρχ,
where f = δ − "δ # and the energy index in the function#the CGB intensity (number per unit area, time, solid
WA isfew
suppressedforrange)
simplicity.
To direction
clarify ourequations...,if youwant
angle,and energy
towardthen̂ canformulabe
˜tion, generally
we here expresseddefine thequantity
fk as the Fourier transasw

Gamma-ray intensity:formationof f (r), andvi! its power spectrum Pf (k) by the
3 2(3)#(Ntio)!
#=(2π)
δ(k+k)P(k),whereδ
relation "f˜Ikγ f(˜n̂,k Eγ ) =f γ , r),
dr δ (r, n̂r)W ([1 + z]E(1)
threpresents the N -dimensional delta function. We note
scSphericalharmonic
expansion:that where
k is aE comoving
wavenumber,since
it is ar theFourieristhegamma-rayenergy,z
theredshift,γ!
variableto the comoving distance r.
ThecomovingtoδIcorresponding
γ (n̂) distance, δ the overdensity at n̂r compared
2=aY(n̂)lm
lm" power
C=!|a|
thetheuniversal
average,andsomel functionof gammagoal ofpaper
isW
toisevaluate
the lmangular!Iγ "presentlm
rayenergyandthat
given below.
Note tothat
label by 1
spectrum Cl ≡ "|arlm|2 #,iswhichis shown
bewegiven
Limber’s
equation:timeby r (or redshift z used interchangeably), and space# of the $" We first derive the concrete formby r = n̂r.
drl2
2generalformulaforthe intensity
isgiven"Iγfunction# Cl =W . The{W([1+z]E,r)}
Pk=;r ,γf2rr(8)22f = δ − "δ #where the detailed derivation is summarized in Ap-

What are backgrounds?
!"#$%&"#%&'()*+,-./012#$#&345+678+9'(+67:784(;&.+57<8&=+>7+?@&A48B4(;&C@&DEED

34,N<()B8O&=+*+,-7)8&=+5B6-5•Detector
background!
=+JB7(+:+8-F&PQER&,)8-4:784-7)8&)S&-T+&:+45B(+O&+U-(4<464,-7,&O7SSB5+&S6BU&S)(&
0VQEE&W+X=+57OB46&Y4,N<()B8O&75&MR&)S&-T+&
O7SSB5+&Z[R&78&-T+&78-+(>46&Y+-?++8&QEE&W+X 48O&Q&!+X\I&&L:])(-48-&+U]+(7:+8-46&T48O6+F&64(<+&>4(74-7)8&)S&Y4,N<()B8O&
S6BU+5&)>+(&)(Y7-&^ ,):]4(+&O7SSB5+&(+5B6-5&)>+(&)(Y7-I3+6)?&QEE&W+X _8)&(+JB7(+:+8-`@&?7-T)B-&48;&-B878<&)S&,B-5&S)(&6)?&+8+(<;@&S(4,-7)8&(75+5&-)&QGRI&&%T75&?766&7:]()>+I'+4N&+SS+,-7>+&4(+4F&QE@EEE&,:DZ4-&aQE&!+X\I
0SS+,-7>+&4(+4&4-&HEE&!+XF&C@EEE9
QE@EEE&,:D@&O+]+8O78<&)8&4846;575&5+6+,-7)85I#-&DE&W+X@&+SS+,-7>+&4(+4&4S-+(&)8Y)4(O&5+6+,-7)85&75&[HE&,:DI&&.7SS+(+8-&]T;57,5&-)]7,5&?766&(+JB7(+&O7SS+(+8-&Z48O&<+8+(466;&
6+55&5-(78<+8-\&Y4,N<()B8O&(+*+,-7)8&)8&-T+&<()B8OI&

From http://www-glast.stanford.edu/!"##$%&'#($)*'+#,&-'.$,%*'%.+(&/',0'
1&2&-+,&/'3+.41-0$2/!
•Negligible,
being 5%of the CGB above
100 MeV (even!
smallerat 10 GeV)!
!
!

(01567'.0--&.,&/'58&97!""#$%&!#'%&!"#'%&!""#'%&

10-3

ICEBIC-3-3

EB

10EB

10!"

"!
!"

bremssbremss10 bremss
1
10-4
10
1
10-4

10

10

66-4

What are backgrounds?
10

2

2

10

10

3

3

10

4

5

10
10
energy, MeV
45
10
10energy, MeV

10

10

6

1

galdef ID 44_500180-1-2-1-2-2

10-2

10

2

1010"!
bremssbremss"!
bremss-411010210

11010210

33451010energy, MeV
451010energy, MeV

610sr s MeV-1-1-2-22total

EBIC!"-410110210

310

4510
10energy, MeV

Strong et al. 2004

102

10

310

4

51010energy, MeV

610•The flux is about one order ofmagnitude smaller than CGB
for |b| > 20 deg, safely
negligible

10-3

1

60.25<l<179.75 , 180.25<l<359.75-89.75<b<-60.25 , 60.25<b<89.75

60–90 deg

1010galdef ID 44_500180
1010•It strongly depends on thegalactic latitude
EBIC!"-1

E . intensity, cm

total

10-4

6-2

10EB-410•Galactic cosmic rays — aforeground

-3

EB

ICIC

9.75
9.75

610

total

10

6

50.25<l<179.75 , 180.25<l<359.75-59.75<b<-20.25 , 20.25<b<59.75

2

total

-3

1010-10.25<l<179.75 , 180.25<l<359.75-59.75<b<-20.25 , 20.25<b<59.75

20–60 deg-1

sr s MeV

-1

-3

104

10
10
energy, MeV

galdef ID 44_500180

10106310-10.25<l<179.75 , 180.25<l<359.75-19.75<b<-10.25 , 10.25<b<19.75

galdef ID 44_500180

E . intensity, cm

2-1
E . intensity,cm cm
sr -2 ssr -1MeV
E . intensity,s MeV

9.75
9.75

102

1010-1

69.75
5106610

Substructure with disruptionHost-halo dominated case