Some thoughts on intrinsic alignments (IA)(my talk is for discussion)
Masahiro Takada(Kavli IPMU)
Based on collaborations with Kazu Akitsu (IAS), Toshiki Kurita (IPMU), Jingjing Shi (IPMU),
Ken Osato (Kyoto/IAP), Takahiro Nishimichi (Kyoto), Rensei Tateishi

Intrinsic alignment (IA): a contamination to weak lensing<latexit sha1_base64="YmVltyPk1+7Ss8iSQF58abWqarM=">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</latexit>obs(z2 ) = GL (z2 )z2<latexit sha1_base64="pL6dGIn8+cU9jfVpd05X2wLzRuo=">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</latexit>• Hirata & Seljak (2004)
h obs (z1 ) obs (z2 )i = h GL (z1 ) GL (z2 )i + h IA (z1 ) GL (z2 )i<latexit sha1_base64="Ab2yxYXBZeE1x5MR7NgZSS747jI=">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</latexit>

cosmic shear

IA contaminationh IA (z1 ) GL (z2 )i =6 0<0<latexit sha1_base64="JG3TvSYeQ/a8Qqddzs00N25l3Mo=">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</latexit><latexit sha1_base64="FxGwSPBVF/lwiV+vw92B4mNpU4w=">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</latexit>

obs(z1 ) = GL (z1 )+ IA (z1 )z1IA contamination needs to be considered in cosmic shear cosmology<latexit sha1_base64="AYXJtBfgXQQQ+JQnKN/+coRRNM8=">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</latexit>

halo

halo

• Galaxy-galaxy lensing is NOT contaminated by IA
h g (x; z1 ) GL (z2 )i<latexit sha1_base64="N29v89p9Mt+fMQaXJZfyckamYMQ=">AAAC83ichVE7b9RAEB6bVzCPHNAgaCyOoAuFNTYXuEATQQEFRR5cEikO1tq3Z6xbr83ad+LO8h+goKVIRQRCCPEraPgDFPkJiDKRaCiY8x3iIQVmtTuz3873zeyun4ooyxH3NP3I0WPHT8ycNE6dPnN2tnbu/HqW9FXA20EiErXps4yLSPJ2HuWCb6aKs9gXfMPv3Rufbwy4yqJEPsqHKd+OWSijbhSwnCCv9sL1eRjJgj+VTCk2vF4ahVvJFr5gQa90BZOh4Ibb4SJnXuGq2AzLRuH6XfNZeWfk2fOl4fqJ6GTDmFzhhiyOWfm4yrz/sGyMPGf+b1FViZrE5LLzW3GvVkdrcRGbzZaJ1gI6TnOBArzhtFq2aVtYWR2mtpzU3oILHUgggD7EwEFCTrEABhmNLbABISVsGwrCFEVRdc6hBIO4fcrilMEI7dEa0m5rikrajzWzih1QFUFTEdOEOfyM73AfP+F7/ILfD9UqKo1xL0Py/oTLU2/2+cW1b/9lxeRzePKL9c+ec+hCq+o1ot7TChnfIpjwB6OX+2u3V+eKa7iLX6n/V7iHH+kGcnAQvFnhqztg0Af8fGXz8GDdseybVnPFqS/dnX7FDFyGK9Cg974FS/AAlqFNdQ+0S1pdu6r39R19V389SdW1KecC/GH6hx+dO8Gf</latexit>h g (x; z1 ) IA (x0 ; z1 )i<latexit sha1_base64="oEYZ8dQj0ccHQHbeadn96INEshk=">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</latexit>• IA correlation function
foreground, shared large-scale structure (z<z_1)
that causes weak lensing distortions in images ofbackground galaxies
observerIntrinsic alignments of galaxy shapes<latexit sha1_base64="6s+ONyBwS1H6q2H+5KlLs0W+zLM=">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</latexit>"ij (x2 )ü Intrinsic alignment = intrinsic correlations ofgalaxy “shapes” with surrounding large-scale
structureü Here we want to consider IA up to O(100)Mpc/h ⇒ gravity/primordial origin
ü Galaxy shapes have to be estimated fromimaging data
ü Large-scale structure needs to be estimatedfrom spectroscopic data (e.g. using 3D
distribution of galaxies)<latexit sha1_base64="tNrixdxnMcmyAwOl2ppPnpA0xwk=">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</latexit>"ij (x1 )ü For IA measurements, we need both imaging
and spectroscopic data for the same region of
the sky• IA effect has been detected by SDSS data for early-type, redgalaxies, NOT for blue, star-forming galaxies• So far all the measurements are in real (configuration) space• See Toshiki’s (Kurita-san’s) talk for an attempt of the Fourierspace measurement

101

Halo+NLA joint fit, AI =5.2±0.4
NLA-smooth+Halo, AI = 5.2, ah = 0.08

wg+ [Mpc/h]

LOWZ-LOWZ

100

Okumura+ 09

10−1
g

10−2
10−1

100

shape

101

102

r p [Mpc/h]

Singh & Mandelbaum 15

Landscapes in 2020s cosmology
2030

2029

2028

2027

2026

2025

2024

2023

2022

2021

2020

now
Subaru HSC

under consideration
Subaru PFS (8m)commissioning

science operation (SSP)

DES (US, imaging), KiDS (EU, imaging)
DESI (US, 4m, spectroscopy)
4MOST (EU, 4m, spectroscopy)
MOONS (EU, 8m VLT, spectroscopy)
Euclid (EU, imaging/spec.)
Vera C. Rubin Observatory’s LSST (US, imaging)
Roman space tel. (NASA, imaging/spec.)

“adiabatic” ΛCDM model• All cosmological data are consistent with “adiabatic” ΛCDM model that is predicted by thesimplest, single-field inflation model• “single”-field inflation initial conditions ⇒ a “single” degree of freedom in large-scale structure
fields on linear scales

z~1000<latexit sha1_base64="pREEA0I2Gor+wOHpB4cKieIGptA=">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</latexit><latexit sha1_base64="I8NfpSnvYCuZvRNRDAVRAK9FriY=">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</latexit>

inf (k) ! ⇣(k)quantum
fluctuations

primordial
curvature
perturbationT= T (k)⇣(k)T̄⌫ (k) = T⌫ (k)⇣(k)⇥ (k) ⌘In late universe (matter dominated)on large scales (>100Mpc)⇢m<latexit sha1_base64="bIEWOtsDNtv+ANsfBeX4UexNe0c=">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</latexit>⇢im (k) = Tm (k)⇣(k)

cdm (k) = Tcdm (k)⇣(k)galaxy (k) = bgalaxy m (k)b (k) = Tb (k)⇣(k)

BH (k) = bBH m (k), . . .

“adiabatic” ΛCDM model• For any primordial-origin scalar field, its power spectrum (or 2pt correlation function)
should obey the following, in the matter dominated era and on linear scales:<latexit sha1_base64="EEkABu68LAHj7xiTteLgLRdfYUc=">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</latexit>hF (k)F ( k)i
PF F (k)=h m (k) m ( k)i
Pmm (k)! k 0 for k ⌧ kNL• “m”: weak lensing, RSD. “F” can be any field (galaxy, shape, SZ, kSZ, luminosity, ...
AGN jet … ): a “correlation” method is very powerful to test the cosmology origin• Hence if any scale-dependence is observed, it should be a smoking-gun signature of“new physics”, compared to ΛCDM model• Secondary primordial field or new degree freedom: e.g., primordial non-Gaussianity and darkenergy perturbation• Modified gravity• … anything else?

Parfrey, Hui & Sheth 11

1020

3.0

M0 (MØ/h)

1019

1018

1017

1016

1015

=

5 ⇥ 1014 h 1 M<latexit sha1_base64="1ovF7fu3txbBXoFOcEzUnitzIt0=">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</latexit>

Mh

=
=

2.5

=
=
=

1014

5 ⇥ 1013
1013

5 ⇥ 1012
1012

b1

2.0
<latexit sha1_base64="Y/NLKn6rwlSBjRrjLSoyim1Vy7s=">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</latexit>↵ = 1,

1.5

1.0<latexit sha1_base64="vp/tpxxp4nsxCJrXnnNgzUumRt0=">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</latexit>⇢(r) =
0.5 °3
10

GN
1+↵

Z

0

⇢¯ m (r )d3 r0|r r0 |⇢

10°2

1 + ↵ exp

k0 (h/Mpc)

✓

0

|r

r|

◆

Note the effect of massive neutrinos,
which can be accurately modeled (seeNishimichi-san’s talk)r = ax<latexit sha1_base64="HaSkN/BTvmLG/kfUDZwziRgis1Q=">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</latexit>= 10 h 1 Mpc

10°1Issue: An estimator of “shapes”• Need an estimator to quantify “shape” form galaxy images• E.g., the following is one choice of the estimator (here, to keep
generality, it is for “3D” shape, but what is usually observed is a“projected (2D)” shape):
Z<latexit sha1_base64="ywFlcYss+3YCshDO3P+V7bEhuV8=">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</latexit>

Iij /d2 r b(r)w(r) xi xj

e.g. star distribution

radial weight• The 3D shape carries 6 degrees of freedom (Vlah et al. 20):
2 scalar (2 equivalent to 1 scalar in ΛCDM), 2 vector and 2 tensor
modes = the same degrees as the metric perturbations (see Kazu
Akitsu-san’s talk)• What is an optimal estimator? What is an optimal choice of the weight?
• Note that the estimator needs not be super-accurate unlike weaklensing (the shape bias parameter absorbs an uncertainty in shapeestimator; see later)

Kurita, MT+20
1.0

(`)

P± , P±E [(h°1Mpc)3]10

z = 0.484
Mh = 1012-12.5h°1MØ

4

0.8

103

<latexit sha1_base64="QfyVEQt3EVbyQh60RBFXPQWoWTU=">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</latexit>

Pmm (k)100.62P±(0)<latexit sha1_base64="nkxa/p2QuLI0+cL/HCuZmoyK77Y=">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</latexit>

`=0
PmE
(k)

°P±E

100.41<latexit sha1_base64="TtWMLJGrjkHZE1mdS7kCr+acUv8=">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</latexit>

(2)

P±E

errorbars for 1 (Gpc/h)3

Ratio

0.2

10°2

obs
ij = (1 + h ) ij

• IA signal gamma~O(0.01), the intrinsic
shape O(0.1); noisy on individual halobasis
• Indeed confirmed

10°1<latexit sha1_base64="I+ReO4kHybX+wumlM2eqvYzh5vE=">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</latexit>(0)°P±E /P±

0.0

0.0 °2
10• Run simulation for ΛCDM model• Identify halos, by Rockstars• Quantify “shapes” of individual halos (forprojected shapes)• Measure the power spectrum, after E/B
decomposition• Note that the halo shape is measured at
the halo position (the density-weighted
shape field)

0.2

10°1 0.6
k [hMpc°1]

0.4

(2)
P±E /P±0.8

101.00PmE (k)! k 0 for k ⌧ kNL
Pmm (k)• What are properties of IA for different
types of galaxies?
• Central vs. satellite galaxies• Early-type (quiescent) and late-type(star-forming) galaxies• Environments (filaments, voids, nodes)• See Jingjing’s talk

Joachimi+15

Comment on tidal torque theory• No primordial vector mode in the standard ΛCDM scenario• A progenitor region of galaxy would acquire angular momentum
via coupling between the mass inertia and the surrounding tidal
field (White 84; Eisenstein & Loeb 97) ⇒ the origin of “disk”
galaxy or galaxy spinLij<latexit sha1_base64="RPEXKsaK7pol9h9BAARjqmF5dLM=">AAACzXichVFNb9NAEJ2ar2I+GuCCxGVF1AhxsCZWUxpOFb0UCYl+JG2lurJsd5tuY6/Neh0puOaK1D/AgRNICCF+BhdO3Dj0J6AeW6kXQEycIMKhMJZ3Zt++N/t2109CkWrEwwnj3PkLFy9NXjavXL12fapy4+ZaGmcq4O0gDmO14XspD4XkbS10yDcSxb3ID/m6310YrK/3uEpFLFu6n/CtyOtIsSMCTxPkVnYdn3eEzPkz6Snl9e8X5hM3F3sFqzmJihMdsxp7TEi3YC037+4VjoxlFvlcMcdh5hirNc5ipsPl9lhbt1JFC+25BjYZWjYlu0FFA+vN2SarW1hGFUaxFFfegwPbEEMAGUTAQYKmOgQPUvo2oQ4ICWFbkBOmqBLlOocCTNJmxOLE8Ajt0tih2eYIlTQf9ExLdUC7hPQrUjKYxq/4AY/xM37Eb/j9zF552WPgpU/ZH2p54k4d3F49/a8qoqxh94/qn5417MBc6VWQ96REBqcIhvre81fHqw9XpvMavsUj8v8GD/ETnUD2ToJ3y3zlNZj0AL9vmZ1drNlWfdaaWbar849GTzEJd+Au3KP7fgDzsAhL0KZ9v8AJ/ICfxlMjM/aNF0OqMTHS3IK/wnj5C5bPsuM=</latexit>//

Iik Tkj
Tik Tkj• Therefore, a correlation of galaxy spins, if exists, should be “nonlinear” origined (not primordial-origined)
4
Pss (k) / hLij Ljk i / hO( m)i / (Pmm (k))2<latexit sha1_base64="lVc+ssQWpQZQOKzMTMSHelcyQ7w=">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</latexit><latexit sha1_base64="9+hHTIyVOBucgmErrjaTVG6URYo=">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</latexit>

Pss (k)! Pmm (k) ! 0 for k ! 0 Emission line galaxies (main targets for PFS andPmm (k)
DESI) are mainly star-forming (disk-like) galaxies⇒ no IA signal for ELGs? (see Jingjing’s talk)Linear alignment model• Intrinsic shapes of galaxies are determined by the tidal field at the time during galaxy
formation (matter dominated era) (Catelan, Kamionkowski & Blandford 00; Hirata &Seljak 04)
!
K
C1
ij
(x;
z)
=
@i @j
r2
ij
P (x)
4⇡G
3
0
<latexit sha1_base64="VjrBRgAaOGfiAS2m2T7pUHCAKUI=">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</latexit><latexit sha1_base64="tU8YS79PqLGFJNwXDJgt4+vGexw=">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</latexit>

primordial gravitational potential field:⌦m (kx2
AIA C1 ⇢cr0
D(z)<latexit sha1_base64="WaDGiawtGDbeVQgGeMWWYeLMjAY=">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</latexit>

!

proj

(k; z) =ky2 , 2kx ky )m (k, z)k2

P (x; z) / a

assume that the l.o.s. direction is along z-direction (see Toshiki’s talk)• If the primordial linear IA model is valid, we should find, on linear scales
AIA / a0<latexit sha1_base64="FeYLrDhR1TuVhMkR7KgUPM2dSao=">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</latexit>• Q: How do the scale- and redshift-dependences of IA signals look like?

Kurita, MT+20

30

AIA (k < 0.05 hMpc°1)<latexit sha1_base64="FeYLrDhR1TuVhMkR7KgUPM2dSao=">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</latexit>

AIA / a25
200

• Mass-limited halo sample = thefixed Lagrangian volume

15
Mh [h°1 MØ ]

10
0.00

0.25

0.50

[1012 , 1012.5 ][1013 , 1013.5 ][1012.5 , 1013 ][1013.5 , 1014 ]

0.75
z

1.00

1.25

1.50

• A_IA is estimated for each halosample, from P_mE(k)/P_mm(k) at
k<0.05 h/Mpc• Halos shapes at higher redshift,just after formed, have theconstant IA amplitude; that is, theprimordial IA model seems valid

The largest IA signal should be from “shapes” of primordial density peaks that lead togalaxies (halos) at later epochs, for the standard ΛCDM model

BBKS 86
Bond & Efstathiou 87

Comment: linear “shape” bias parameter
Kurita, MT+20
Mh [h°1 MØ ]0.25

[1012 , 1012.5 ][1013 , 1013.5 ][1012.5 , 1013 ][1013.5 , 1014 ]• Other commonly-used definition, justlike the linear density bias
(Schmidt+15; Vlah+20); on linear
scales
!

°bK

0.20

<latexit sha1_base64="+KlIj7XsB5LSmHsEaWvU1WZOqIE=">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</latexit>

0.15

IA
2
(x)
=
b
@
K
ij

@i @j

K
ij

3

r2

m (x)

0.10
0.05
0.00

0.25

0.50

0.75
z

1.00

1.25

• The linear shape bias parameter has
greater amplitude for higher redshifts
1.50
and more massive halos (Akitsu, Li &Okumura 2021)

A calibration of linear bias parameters withseparate universe simulation• Recall: a linear halo density parameter is given by the “response”
of halo mass function to the large-scale overdensity (Li, Hu &MT
16; Bauldauf+16; Lazeyras+16)<latexit sha1_base64="z9mWauLB2nXlnpTc0qJQjS5tz7s=">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</latexit>b (t)d ln nhd ln nh
L
b1 =
/
d b
d⌦K
<latexit sha1_base64="g0Lm1yZxMhx5Zz3YbUGLVcljMIg=">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</latexit>• Linear shape bias parameter is given by the response of halo
shapes to the large-scale tidal field (Akitsu, Li & Okumura 21)<latexit sha1_base64="O2KGb7NOx/9rFBLzDe7sgnCa4Nc=">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</latexit>ai (t)• Large-scale tidal field is described by anisotropic-expansion SU background

d ij
bK =
dKij

<latexit sha1_base64="rPirL2vLvB4mO//psnYV6evvNC8=">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</latexit><latexit sha1_base64="rPirL2vLvB4mO//psnYV6evvNC8=">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</latexit><latexit sha1_base64="PxcedMceuMxn0NM2zQRS30dW/6Q=">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</latexit>aj (t)<latexit sha1_base64="O2KGb7NOx/9rFBLzDe7sgnCa4Nc=">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</latexit>ai (t)aj (t)

Comment: complementarity between density and IA fields
Kurita, MT+20
no-wiggle
PXY /Plin(arbitrarily scaled)

1.8
P±lin
1.6

P±h
(0)

z = 0.484
Mh = [1012, 1012.5] h°1MØ

P±E
1.4

• The standard density power spectrum arises
more
1.8 from “high” density field (like galaxycluster regions)P±lin
z = 0.484
13
13.5
°1
M
=
[10
,
10
]
h
MØ
P
h
• On
the
other
hand,
galaxy(subhalo)shapes±h
1.6(0)
in high-density
P±E regions get randomized due
to mass accretion and mergers. Satellite
1.4
galaxies
have smaller IA• The IA power spectrum would arise more
1.2 “isolated” galaxies (halos) or halos infromlow-density regions (like filaments)

1.2<latexit sha1_base64="5gYZi8dkKlm+NU8Xij3tfeSNBis=">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</latexit>

1.0

1.0

0.8
0.0

0.8
0.0

0.1

0.2
k [hMpc°1]

0.3

P E (k)0.1

h h (1 + h ) IA i
0.2
k [hMpc°1]

0.3

Issue: Any optimal estimator?

<latexit sha1_base64="ywFlcYss+3YCshDO3P+V7bEhuV8=">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</latexit>

Iij /Kurita, MT+20°P±E (k) [(h°1Mpc)3]103

z = 0.0
Mh = [1012, 1012.5] h°1MØ

Ratios

(0)

102

101

Red-Iter-AC (default)
Red-Iter-VC
Red
Red-AllParts

Sim-Iter-AC
Sim-Iter-VC
Sim
Sim-AllParts

10°1
k [hMpc°1]

d2 r b(r)w(r) xi xj• A choice of “weight”: w(r) ∝ r^0 or r^-2
• A choice of the integration range:
spherical or ellipsoid• Changes in the IA power spectrum
due to the different shape definitions
are absorbed by changes in the linear
shape bias amplitudes

1.0
0.5
10°2

Z

100

Expected signal-to-noise ratios
LRG/CMASS-like sample

Kurita, MT+20

Cumulative S/N

500
400

500
V = 1 (h°1Gpc)3

400

300

300

200

200

100

100

(2)

Phh

PhE

(0)

PEE

PhE

(0)

z = 0.484
0
0.0

0.2

0.4
0.6
kmax [hMpc°1]0.8

z = 0.0
1.0

0
0.0

0.2

0.4
0.6
kmax [hMpc°1]

0.8

IA power spectrum carries descent signal-to-noise ratios (about
60% of density power spectrum)

1.0IA: a new probe of primordial anisotropic non-Gaussianity• Tests of different types of primordial non-Gaussianity (ΛCDM predicts f_NL<1)<latexit sha1_base64="D9orWmbud8nQLGXCi4umWFvAYQU=">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</latexit>⇣

NG(x) = ⇣(x) + fNL ⇣(x)<latexit sha1_base64="6jHriaNB8sPPCeI6Y9qOFiUCikE=">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</latexit>

⇣

NG

⇥

s=2
(x) = ⇣(x) + fNLh( ij )

2

2

2

h⇣ i

⇤

2

h( ij ) ii2ij (x) ⌘ r

K
ij

@i @j

3

r2

!

105

s=2
fNL
= 500

Dalal+08

k2

k 2<latexit sha1_base64="fZc2DW0+Ik87bqFOwG59xEZUmmw=">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</latexit>

103

Density power spectrum

10°2

k [hMpc°1]

10°1

104

Akitsu et al.
3 21

10

(0)

<latexit sha1_base64="fZc2DW0+Ik87bqFOwG59xEZUmmw=">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</latexit>

104

(0)

10

5

PEE (k) [(h°1Mpc)3]

PNG(s = 2)

°P±E (k) [(h°1Mpc)3]

P±h(k) [(h°1Mpc)3]<latexit sha1_base64="T27UOFyMDFX11rgBwFrW3Coxg00=">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</latexit>

Gaussian
PNG(s = 0)⇣

Shape (IA) power spectrum

10°2

k [hMpc°1]

10°1

102

Subaru HSC (imaging) and PFS (spectroscopy)

HSC

PFS (2400 fibers)

HSC image of Andromeda galaxy

PFS will populate2394 individual fibers
for simultaneous spectroscopy
over this hexagonal field.

~1.5 degSubaru HSC (2014-) and PFS (2023-) surveys• Subaru Hyper Suprime-Cam survey: thanks to large aperture, wide field-of-viewand superb image-quality, the ongoing Subaru HSC will deliver high-quality, deep
images of all galaxies (g~26mag for stars) over ~1,200 sq. degrees• PFS Cosmology survey will carry out a spectroscopic follow-up observation of [OII]
emission-line galaxy candidates, selected from the multi-color HSC images, over
0.6<z<2.4 (~20 arcmin-2 HSC galaxies, compared to ~1 arcmin-2 PFS ELGs)• Various, exciting opportunities of many science cases with Subaru HSC and PFS(see Taruya-san and Teppei’s talks)• Stringent test of ΛCDM models• Dark matter & dark energy• Neutrino masses• PNG

Can we measure IA signals for ELGs?
• Used the Illustris-TNG galaxy to simulate HSC-like images of ELG region (including
Maunakea sky noise, CCD noise, PSF, … ) (see Jingjing’s talk)Original

1000

Shi+ 21
Simulated (PSF + Noise)

Simulated (PSF + Noise)

z=1.5, galaxy ID=18349

Pixels with S/N> 3x2[h°1kpc]

800
600
400

log M? =11.54
log Mhalo =13.87
R? =46.54[h°1kpc]
R200 =1009.25[h°1kpc]

ELG-like (star-forming galaxy)

200
0
0

250

@z=1.5500
750
x1[h°1kpc]

1000
0

250

500
750
x1[h°1kpc]

1000
0

250

500
750
x1[h°1kpc]

1000

Discussion items during WS• How useful is IA (spin-2 field) signal for cosmology (and galaxy physics),
compared to the standard density (spin-0; scalar) information?
• How can we measure the IA signal? (real- vs. Fourier-space, weight, shapemeasurement method)• What is an optimal estimator of galaxy “shapes”?
• How can we use the IA signals to do cosmology?
• Cosmological parameters, primordial non-Gaussianity, anything else?

• Optimal strategy and survey designs for Subaru HSC/PFS (or DESI, Euclid, …)
to maximize the scientific returns?