21cm-LAE cross-correlationによる宇宙再電離期の観測可能性の調査
久保田賢志(熊本大学)!

共同研究者
吉浦伸太郎(熊本大学)
高橋慶太郎(熊本大学)
長谷川賢二(名古屋大学)
大内正己(東京大学・宇宙線研)

Ongoing 21cm observation
MWA(Australia)

LOFAR(Netherland)

1/15
PAPER(South Africa)2/15
Future21cm
observation
Future 21cm observation
SKA1-LOW(2015/10/28段階,オーストラリアに建設予定)
SKA1-Low(Australia)
frequency•

50-350MHz

周波数：50-350MHz

frequency~1kHzresolution• 周波数分解能：~1kHz
angular~1arcmin• 角度分解能：~1分角
resolution•視野：>44平方度
ﬁeld of view
>4 4deg^2•

最大基線長(core)：~700m
maximumbase line length~700m

3/15

4/15

5/15

Lyman-α emitter(LAE)

6/15・high-z galaxy bright in Lymanα-line
・one of the ionizing sources
・narrow band survey by HSC @z=6.6, 7.3
・Ultra Deep, Deep ﬁeld → 2D cross-correlationΔz~0.1・+PFS → 3D cross-correlationΔz~0.0007◎Check qualitative feature of cross-spectrum
under our realistic IGM simulation→ Hasegawa et al. 2016(1603.01961)◎Detectability of 2D and 3D cross-spectrum
・Comparison ultra deep with deep ﬁeld
・necessity of PFS

of the standard model of cosmology, and test for exotic variations such as deviations from the predictions ofGeneral Relativity on cosmological scales. Studies of the highest-redshift galaxies and quasars discoveredin this survey will lead to a deeper understanding of reionization, a key event in the thermal history of theUniverse.

7/15

LAE modeling

Table 1: Summary of HSC-Wide, Deep and Ultradeep layers
Layer
Wide
Deep
18UltradeepArea[deg2 ]
1400
27
3.5

# ofHSC fields
916
15
2

Filters & Depth
grizy (r ≃ 26)
grizy+3NBs (r ≃ 27)
grizy+3NBs (r ≃ 28)

Comoving volume Key Science[h−3 Gpc3 ]∼ 4.4 (z < 2)
WL cosmology, z ∼ 1 gals, clusters< 2 gals, reionization, WL calib.
∼ 0.5 (1 < z < 5)z∼
> 2 gals,with reionization,
Hyper Suprime-Cam∼ 0.07Wide-field(2 < z < 7)imagingz∼
SNeIa

The experience of the Sloan Digital Sky Survey (SDSS; York et al. 2000), and the tremendous success ofTable 6:Suprime-Cam
LAE and LAB (MiyazakiSamples
the current prime-focus camera on Subaru,
et al. 2002a), have demonstrated theaa
NB816aNB101
power of wide-field narrow-bandimaging to makeNB387
science breakthroughs
in NB921
a broadrangeof topics.
The SDSS imaged
2.180.02
5.71 ±6.57(5σ± 0.05
± 0.04It has produced morein five broad-bandsredshift(u, g, r, i, andz),±toa depthof 0.05r ≈ 22.5
point7.30
source).
b– any other3.9k observational(60)
1.7k (30)39 (0)
highly cited papersNinUD
recent years thanfacility, including
the Keck Telescopes
NDb Telescope (Madrid
9.0k (730)
14k (360)2009).
5.5kThe(100)SDSS characterized–
and the Hubble Space& Macchetto
the nature andcVUD–
1.2
1.2
distribution of galaxies
in the local present-day
Universe.
Observations
with0.79
Suprime-Cam have led theVDc distant Universe,
6.0 and have shown
9.6– Subaru telescope has theworld in studies of thethat an9.8imager on thed–
2.5
potential to extend L(Lyα)
SDSS low-redshift
discoveries
in1.5
the field of cosmology
and6.8galaxy formation/evolution
UDd2.7
2.9HSC survey4.1– cover SDSS-like volumes
to the intermediate-L(Lyα)
and high-redshift
Universe. The
we propose willDescience
LA large-scaleLA, survey
CR of LA,LA, CR
at high redshift, making
it the first truly
the CRdistant Universe.
Notes– a)top-level
We will usescientificthese narrow-band
downHSCto thesurvey
4σ limits,
The
goals data
for theare:following the convention in the literature. b) Expectedc)
numberofLAEs,
withnumbersofLABs
inparentheses,in
eachredshift
slice.
The comoving
volumeof observables
each redshift slice
inthe• To derivestringentdark
energyconstraints
fromthecombinationoftheHSC
WLandunits of 106 (h−1 Mpc)3 . d) Limiting Lyα luminosity in units of 1042 erg s−1 . e) Key science cases. LA: evolution of LAEs andgalaxy clustering information from the BOSS survey to precisions of σ(wpivot ) ≃ 0.03 and the dark energy
LABs (Section 5.2), CR: cosmic reionization (Section 5.4).

5.1

Galaxy evolution in dark matter halos

22|6|(mK)|6221,gal|(mK)|621,gal|(mK)
21,gal2|6 21,gal|(mK)raged ionwhereρ(r)agalaxy
galaxydensity
fieldandρ̄gal
ismeanmean
dengalwhere(r)(r)
density
fieldanddenwhereρρgalisis aisa galaxy
density
fieldandρ̄ρ̄gal
isis mean
dengalgal⟩ 0.75=0.75
i=0.75i⟩⟩ =xxi⟨xsity.
Defining
δ̂(k)
(k)
the
Fouriertransform
δ(k),(k),21
21sity.
Defining
(k)
toto
bebe
the
Fouriertransform
ofof(k),
21
21
sity.
Definingδ̂δ̂21tobe
theFouriertransformofδδ21
mulationbox
lation21cm-LAE
box
8/15
21cm-LAE
cross-power
spectrum
ation
box
the
cross-power
spectrum
isgivenby
21cm-LAE
cross-power
spectrumthecross-power
spectrum
isgivenbycross-power
spectrumthecross-powerspectrum
isgiven
by−1−1 Mpc−1906h06hMpc
6h Mpc** *++ +33 3 δD (k1 + k2 )P21,gal (k1 ),
δ̂(k)
δ̂(k)
≡(2π)
21
12gal(k11))δ̂δ̂gal(k22)) ≡≡(2π)(2π) δδDD(k(k11++kk22)P)P21,gal(k11),), (5)(5)(5)
21(kδ̂δ̂21
gal(k21,gal(khave
QcellveQ
Qcellve!! !
celle ionized
where
δ(k)
(k)
isthe
the
Dirac
deltafunction.
The
dimensionlessionizedbyby
Dcrosswhereδ
(k)is
Diracdeltafunction.
Thedimensionless
21cm-LAE
cross
power
spectrumonizedbyD
whereδ
isthe
Dirac
delta
function.
The
dimensionless
21cm-LAE
power
spectrum
21cm-LAE
cross
power
spectrumD
21cm-LAE
cross
power
spectrum
223210 the
10r
to
find
cross-power
spectrum・negative
large
scale
10 thetofindthecross-power
spectrum・negative
onon
large
scale
o findcross-power
spectrum
isis is・negative
on
large
scale
Qell
field
usfieldus2usfieldllcell・signchanges
ina
scale
10 1
3k 3
・sign
changesina
scale
3・signchanges
ina
scale
1110
kk
2 2diusR(with102∆us(with(k)=P21,gal(k).
(6)
s RR10(with21,gal∆21,gal(k)== (2πP
(k).
(6)
∆(k)
P(k).
(6)
21,gal21,gal221,gal122)) ) !! !
10 ion(2πoothedion(2πothed
thed ion01000101010

Turnoverscale
depends
Turnoverscale
depends
onon
Turnoverscale
dependsonredshift.
redshift.
redshift.

0-1
10-1-1-1
10
1010

!! !

10-2
-2-2-2
1010-3
10z=7.5(nHI=0.53)
z=9.2(nHI=0.77)
z=9.2(n=0.77)
z=9.2(n=0.77)
HI
z=7.3(n=0.36)HI
z=8.5(nHI HI
HI=0.70)z=8.5(n=0.70)
z=8.5(n=0.70)HI
z=7.8(nHI=0.54)
z=7.8(n=0.54)
z=7.0(nz=7.8(n=0.54)
HIHIHI=0.13)
z=7.3(nHI-3=0.18)
z=7.3(nHI=0.18)
z=7.3(nHI=0.18)
z=6.6(n=8.2×10) ) -3)
z=6.6(n=2.7×10-3-3
HI =2.7×10HI
z=6.6(n10-3-3-4
101010 10-3

0.1
0.10.10.1

1 1

1-1-1-1-1
k[Mpck[Mpck[Mpc ]] ]z=6.6(nHIHI=2.7×10 )1

Turnoverscale
corresponds
Turnoverscale
corresponds
Turnoverscale
corresponds
sizeionizedbubble.
toto
size
ofofionizedbubble.
tosizeofionized
bubble.
10 10
10k[Mpc ]

Wecould
couldconﬁrm
conﬁrmthethebasic
basicfeaturefeatureWe
could
conﬁrmthebasic
featureWe
previousstudy
studyunder
underourourrealistic
realisticsimulations.
simulations.
ininprevious
previous
study
under
ourrealisticsimulations.
in9/15

MWA : 1000h, 256tiles

MWA-ultra deep

10/15

ultra deep : 3.5deg^2, σ̲z=0.1(=Δz)

ultra deep+PFS : 3.5deg^2, σ̲z=0.0007

z=6.6(f̲HI=8.2 10^-3)
Expected errors on cross power spectrum(z=6.6)
103

102

102

101

101
6221,gal(mK)

6221,gal(mK)103

z=7.3(f̲HI=0.36)

100
10-1
10-2
10

100
10-1
10-2

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

Expected errors on cross power spectrum(z=7.3)

0.1-1

1

10

10-4

k[Mpc ]

Depending on sample variance,
detectable at large scale@z6.6

sample variancesignal(z=7.3,nHI=0.36)
error(PFS,without sample variance)
error(without sample variance)

-3

0.1

-1

1k[Mpc ]red : signal
blue : error(ultra deep+PFS)
black : error(ultra deep)

SKA1 : 1000h, 512tiles

SKA1-ultra deep

11/15

ultra deep : 3.5deg^2, σ̲z=0.1(=Δz)

ultra deep+PFS : 3.5deg^2, σ̲z=0.0007

z=6.6(f̲HI=8.2 10^-3)
Expected errors on cross power spectrum(z=6.6)103102102

101

101
6221,gal(mK)2

6 21,gal(mK)103

z=7.3(f̲HI=0.36)

100
10-1
10-2
10

100
10-1
10-2

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

Expected errors on cross power spectrum(z=7.3)

0.1

-1

1

k[Mpc ]

detectable on mid scale@z7.3
PFS is powerful on small scale.

10

sample variancesignal(z=7.3,nHI=0.36)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

0.1

-1

1

k[Mpc ]

red : signal
blue : error(ultra deep+PFS)
black : error(ultra deep)

12/15※deep : 27deg^2

MWA-deep(z=6.6)
Expected errors on cross power spectrum(z=6.6)

103

102

102

101

101
6221,gal(mK)

6221,gal(mK)103

MWA-ultra deep(z=6.6)

100
10-1

100
10-1
10-2

10-2
sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

10-3
10-4

Expected errors on cross power spectrum(z=6.6)

0.1

-1

1

k[Mpc ]In deep we can detect
the signal on large scale.
→ Deep is advantageous.

10

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

0.1

-1

1

k[Mpc ]

red : signal
blue : error(deep+PFS)
black : error(deep)

13/15※deep : 27deg^2

SKA1-deep(z=6.6)
Expected errors on cross power spectrum(z=6.6)

10

3

102

102

101

101
6221,gal(mK)

6221,gal(mK)103

SKA1-ultra deep(z=6.6)

100
10-1
10-2
10

100
10-1
10-2

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

Expected errors on cross power spectrum(z=6.6)

0.1

-1

1

k[Mpc ]We are likely to see turnover.

10

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

0.1

-1

1

k[Mpc ]

red : signal
blue : error(deep+PFS)
black : error(deep)

14/15Comparison of models on MWA-deep(z=6.6)
・mid model(f̲HI=8.2 10^-3)
Expected errors on cross power spectrum(z=6.6)103102102

101

101
6221,gal(mK)

6221,gal(mK)103・late model(f̲HI=0.11)

100
10-1
10-2
10

100
10-1
10-2

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

Expected errors on cross power spectrum(z=6.6)

0.1

-1

1k[Mpc ]※late model … emissivity/1.5

10

sample variancesignal(z=6.6,nHI=0.11)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

0.1

-1

1

k[Mpc ]

red : signal
blue : error(deep+PFS)
black : error(deep)

Summary

15/15

・Cross-correlation reduces foreground problem.
!

・We conﬁrm qualitative feature of cross-spectrumin our realistic simulation.
!

・Deep ﬁeld is advantageous than ultra deep in detection.
→ Survey volume is key to the detection.
MWA-deep has ability to detect the signal on large scale.
!

・PFS enhances SKAʼs ability.
PFS allows us to detect on small scale.

Back up・midExpectedmodel(f̲HI=8.2
10^-3)
errors on cross power spectrum(z=6.6)
10102

1021011016221,gal(mK)

106221,gal(mK)

3

100
10-1
10-2
10

Expected errors on cross power spectrum(z=6.6)

100
10-1
10-2

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

3

0.1

-1

10-3
10-4

1

sample variancesignal0.1

k[Mpc ]

・late
Expectedmodel(f̲HI=0.11)
errors on cross power spectrum(z=6.6)
10

3

102

102

101

101

100
10-1
10-2
10

Expected errors on cross power spectrum(z=6.6)

100
10-1
10-2

sample variancesignal(z=6.6,nHI=0.11)
error(PFS,without sample variance)
error(without sample variance)

-3

10-4

1

k[Mpc ]

6221,gal(mK)

6221,gal(mK)

10

3

-1

0.1

-1

k[Mpc ]

110-3
10-4

sample variancesignal0.1-1

k[Mpc ]

1

error budget
1 2
2
A = [P21,gal + (P21 + N )(Pgal + g )]2
1 2
= [P21,gal + P21 Pgal + P21 g + N Pgal +2

N g]

N : thermal noise

z=7.3
z=7.3
・midmodel(f̲HI=8.210^-3)1001010-1

z=6.6(MWA-deep)210-1mA(mK)

1mA(mK)mA

1010-2z=6.6
z=6.6
・late model(f̲HI=0.11)

100

10-3
100
10-4
10-1
10-5

10-2

0.1

k[Mpc-1]

1

101

10-3

100

1010-4

P21,gal2 2P21
PP21,galgal
P21mg
PPgal
21
mN P
gal
mNPm21g mg

mNPgalm N mg-2mA

10z=6.6(MWA-deep)2

g : shot noise, z error

10
10P21,gal2
2P21Pgal P21,galP21mg
P P
mNPgal 21 gal
mNmg P21mg

-1

10-5

0.1

10-2

k[Mpc-1]

mNPgal10m N mg1

k[Mpc ]
k[Mpc ]
・thermal noise
is dominant on all scale @z=7.3
0.1-1

1

0.1-1

1

2D cross-power spectrum(z=6.6)
103

102

Expected errors on cross power spectrum(z=6.6)
10

MWA-Ultra deep(2D)

102

100
10-1

10-1
10-2-3-3

10-4

MWA-Ultra deep(3D)

100

10-2
10

Expected errors on cross power spectrum(z=6.6)

1016221,gal(mK)

1016221,gal(mK)3Δz=0.1~40Mpc

sample variancesignal(z=6.6,nHI=8.2×10-3)
error without sample variance

0.1

-1

10

10-4

1

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

0.1

k[Mpc ]
10

3

102

Expected errors on cross power spectrum(z=6.6)
10

MWA-Deep(2D)

Expected errors on cross power spectrum(z=6.6)

MWA-Deep(3D)

1016221,gal(mK)

6221,gal(mK)

3102

100
10-1

100
10-1

10-2

10-2-3-3

10-4

1

k[Mpc ]

101

10-1

sample variancesignal(z=6.6,nHI=8.2×10-3)
error without sample variance

0.1-1

k[Mpc ]

1

10

10-4

sample variancesignal(z=6.6,nHI=8.2×10-3)
error(PFS,without sample variance)
error(without sample variance)

0.1

-1

k[Mpc ]

1

MWA-Deep(2D)
z=6.6(MWA-deep)

102

101

101

100

100

P21,gal2
P21Pgal
P21mg
mNPgalm N mg

10-1

10-2

0.1

-1

k[Mpc ]

z=6.6(MWA-deep)

102

mA

mA

MWA-Deep(3D)1

P21,gal2
P21Pgal
P21mg
mNPgalm N mg

10-1

10-2

0.1

-1

k[Mpc ]

1