21cm線によるBAO測定のための⾮線形バイアスモデリング
第６回観測的宇宙論ワークショップ @ 弘前

安藤 梨花

(名古屋⼤学 宇宙論研究室 M1)
⻄澤 淳

⻑⾕川賢⼆
2017.10.24

⽥代寛之

目次

• 目的
• 中性水素の分布の観測• 本研究で行ったこと• 結果• まとめ2 /15

(AASKA14)024

目的

The SKA will be able to measure theBAO in two ways (Fig. 1). The first, using the intensity mapping (IM) technique,seeks to reconstruct the cosmological density field in three dimensions over unprecedentedly large volumes, using the 21cm spinflip transition of neutral hydrogen to trace thedensity field in redshift space. The second
is a more conventional galaxy redshift survey, which will detect many millions of disMeasuring BAO with future SKA surveys
Philip Bu
crete sources over a wide range of redshifts,
with accurate redshift determinations comBull et al (2015)
ing from the 21cm line. Of the two, IM is 1.0
the newer and less-tested method – galaxy
surveys have been used to great effect asprobesそのためにof LSS over the past several decades,
whereas the first IM experiments are only
0.0
just coming online, and are subject to a num-a
ber of potential foregrounds and systematics
that are yet to be fully quantified. Nevertheless, an IM survey is the best prospect for
doing transformative cosmology with Phase-1.0
Figure 1: Constraints on the BAO ‘wiggles’,1 of the SKA – surpassing all existing BAO
-1.3
-0.7
fBAO
(k) = P(k)/Pref (k) 1-1.0(where Pref (k) is a BAOconstraints at low redshift, and strongly comfree reference spectrum), combined
0 over all available
plementing future surveys at higher redshift.
redshiftbins
three SKA galaxy/IM surveys. FullFigure 4: Forecastconstraintson (wfor0 , wa ) for several SKA configurations and Euclid, in combination wiPlancktheand BOSS.forecasts
All other parameters
haveinbeen
marginalised,
In this chapter, we will review
are givenSection
4. including WK , and the bias is free per z bi
physics of the BAO, its suitability for use as
Expected constraints on the dark energy equation of state parameters (Eq. 2.3) are showna standard ruler, and the current state of theart in BAO measurements from optical and Lyman-a/15

将来のSKAでの観測によるダークエネルギーの状態方程式パラメータの制限予測

w

中性水素のパワースペクトルでのBAOのピーク位置のw
線形パワースペクトルからのずれを見る

3Fig. 4 for a subset of these configurations, combined with forecast Planck CMB and BOSS lodark energy
ダークエネルギーの状態方程式パラメータ( p = w⇢ )w = w0 + (1a)wa

先行研究での制限領域 Philip B

Measuring BAO with future SKA surveys

への制限の予測を行いたい

Bull et al (2015)

1.0

wa 0.0宇宙の膨張史を調べる
-1.0

-1.3

-1.0

w0

-0.7
4 /15

Figure 4: Forecast constraints on (w0 , wa ) for several SKA configurations and Euclid, in combination w

バリオン音響振動(BAO)
脱結合前の光子とバリオンは強結合してダークマターの重力ポテンシャル中で音響振動している
振動スケールはCMBの観測から精密に測定
BAO→ DA→ H(z)BAOの測定から宇宙論パラメータを制限できる
5 /15

21-cm線
中性水素の超微細構造のエネルギー差に由来する電磁波

21-cm線は赤方偏移空間で物質の分布のトレーサー
21-cm線

21-cm線でBAOを見る

6 /15

Square Kilometre Array(SKA)2020年から初期科学運用が始まる大規模電波干渉計
HI galaxy redshiM survey (gal)‣ 大量の星形成銀河のredshiMを測定
z ⇠ 0.5 (SKA1)

0.18 < z < 1.84 (SKA2)Intensity mapping survey (IM)‣ 21-cm線源からの強度を観測
0<z<3

from
h'p://japan.skatelescope.org/africa/
SKA MID

7 /15

Assuming that HI is a linearly-biased tracer of the total matter
eld, we can relate fluctuations in the brightness temperature to the (Fourier-transformed)
pace matter density perturbation,

Square Kilometre Array(SKA)
d Tb =mapping
T b dHI (k) =survey
T b (bHI + f µ )eintensity
21 2 24 k sNL (z,µ)

dM (k),(3.4)

e anisotropic terms are due to RSDs
(Eq. 3.1). One can then3 and non-linear growth
23hc
A
(1+z)
10
⇤ (k0 )i = (2p)3 d (3) (k0 )P(k),the 3D redshift-spacematterpower
spectrum,hd(k)dkMM⇢¯Tb =HI HI
232⇡ kB mH(z)ng out the brightness temperature
distribution
angle and frequency, n = nHI /(1 + z).
p ⌫21 inTinst [K]zminzmax
nmin [MHz]nmax [MHz]Ddish [m]d n [kHz]
Wsur [103 deg2 ]Ndish ⇥ Nbeam

SKA1-MID
Band 1 Band 2
28
20
0.35
0.00
3.05
0.49
350
950
1050
1760
15155050
2525254 ⇥ 1 254 ⇥ 1A14)024,0 , in neutral hydrogen.

Bull et al (2015)
SKA1-SUR
Band 1 Band 2
50
30
0.58
0.00
3.05
1.18
350
650
900
1670
1212-5dz~105050
dχ~300[kpc/h]
252560 ⇥ 36 60 ⇥ 368 /15

本研究では…
ダークマターと中性水素のBAOのピークの位置の検証@z=3.0 – 0.1‣ wiggleのないパワースペクトル(Eisenstein & Hu '98)
‣ 線形/非線形パワースペクトル(camb)‣ ダークマター/HIのパワースペクトル(Illustris SimulaUon)

h = 0.704

WMAP

バリオンも考慮したシミュレーション⌦0 = 0.2726 ⌦⇤ = 0.7274
9 /15密度ゆらぎのmap(Illustris)
dark ma^er

HI1pixel~290[kpc/h]

z=3.01Ume

75[Mpc/h]

z=0.5

10 /15

実空間でのパワースペクトル10z=0.1z=0.1
Eisenstein&Hu'98
53

P[(Mpc/h) ]104
103102101

Eisenstein’98
0 illustris HI
10 illustris dark matterCAMB linear-1 CAMB non-linear
10 -3-2

1010

Large scale

HInon-linear
dark ma^erlinear
10-1
k[h/Mpc]

100

101

Small scale
11 /15

パワースペクトルz=3.01

104

103

102

102

P[(Mpc/h)3]

103

101
100

Eisenstein’98-1 illustris HI
10 illustris dark matter
CAMB linear
CAMB non-linear
10-2 -3-2

10

10

z=1.0

10-1
k[h/Mpc]

100

101

Eisenstein’98-1 illustris HI
10 illustris dark matter
CAMB linear
CAMB non-linear
10-2 -3-210104

104

HInon-linear

102
101

dark ma^er0Eisenstein’98
illustris HI-1 illustris dark matter
10 CAMB linear
CAMB non-linear
10-2 -3-2

1010linear
10-1
k[h/Mpc]

10z=0.1

z=1.0

103

100

101

z=2.0

100

10

10

z=2.0

101

510

P[(Mpc/h)3]z=3.01

P[(Mpc/h)3]P[(Mpc/h)3]

104

10-1
k[h/Mpc]

100

101

100

101

z=0.1

5103
102
101

Eisenstein’98
illustris HI
100 illustris dark matter
CAMB linear
CAMB non-linear
10-1 -3-2

101010-1
k[h/Mpc]

12 /15

wiggle P/Psmooth

1.00

0.500.00

-0.50

-1.00

illustris HI
illustris dark matter
CAMB linear
CAMB non-linear

1.00

z=1.00.00-0.50

illustris HI
illustris dark matter
CAMB linear
CAMB non-linear

z=0.1✓cosmic varianceの影響

k[h/Mpc]
z=0.1

1.00

PBAO/Psmooth-1

0.00

-1.00

z=2.0

-1.00
0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
✓Box sizeが足りない

0.50

-0.50

z=2.0

dark ma^er HI0.50

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k[h/Mpc]

z=1.0PBAO/Psmooth-1

z=3.01

PBAO/Psmooth-1

PBAO/Psmooth-1

1.00

z=3.01

1

illustris HI
illustris dark matter
CAMB linear
CAMB non-linear

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k[h/Mpc]

0.50

0.00

-0.50

-1.00

illustris HI
illustris dark matter
CAMB linear
CAMB non-linear

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50
k[h/Mpc]

13 /15

Summary目的‣ SKAの観測によるダークエネルギーの状態方程式パラメータの制限予測

SKAの21-cm線の観測によってBAOを測定
本研究では…

‣ 中性水素のパワースペクトルにおけるBAOのピーク位置のずれの検証

IllustrisでBAOを考えるのは難しいかもしれない

14 /15

Future work
✓中性水素の赤方偏移空間歪みの検証✓Fisher解析による制限予測

15 /15補⾜実空間と赤方偏移空間
21-cm線は振動数の関数として観測
s3

赤方偏移空間での分布を考える必要(s1 , s2 , s3 ) = (x1 , x2 , x3 + (z))
real spaceでの座標

box内での boxまで

座標

⇣

座標の距離

⌘
v3000
(s1 , s2 , s3 ) = x1 , x2 , x3 + (z) +aH

redshiM spaceでの75[Mpc/h]

特異速度によるずれ

視線方向

s2

s118 /15

Power spectrum
power spectrum
104
z=3.01(HI)z=3.01(matter)z=1.0(HI)z=1.0(matter)z=0.1(HI)z=0.1(matter)

33P(k) [Mpc / h ]103102101dashed line
dark ma^er

Ume

100
10-1 -210solid line
HI

Ume
10

Large scale-1010
k [h/Mpc]

10

1102

Small scale
19 /15

scale- and redshift- dependent bias
2bias

b (k, z) = PHI /Pmatterb(k)

10.00

Ume
1.00

0.10 -2
1010-1
Large scale

100
k[h/Mpc]

z=3.01
z=2.0
z=1.6
z=1.0
z=0.5
z=0.35z=0.1
110Small scale

102

20 /15