halo interactions in the horizon run 4...

Halo interactions

in the Horizon Run 4 simulationB. L’Huillier, C. Park & J. Kim (2015), MNRAS 451, 527

B. L’Huillier, C. Park & J. Kim (2016) MNRAS subm.

Benjamin L’Huillier (KIAS→ KASI)

(루이리예, 벤자민)

with Changbom Park & Juhan Kim (KIAS)

Future Sky Surveys and Big Data

2016-04-25, KASI

Outline

1 Introduction

2 Simulation and method

3 Halo interaction rate in the Horizon Run 4

4 Alignment of interacting haloes

Benjamin L’Huillier (KIAS) Halo interactions 2016-04-25 2 / 26

Outline

1 Introduction





Motivations

ΛCDM predicts hierarchical structure formation: halo mergers

Galaxy mergers and interactions are observed

Merger can trigger star-formation, morphological transformations, fuel central

black-hole, . . .

Distant interactions also matter (Park et al 2008, Hwang & Park 2015)

Major merger have a dramatic impact (morphology transformation, significant mass

increase; e.g., Toomre & Toomre 1972)

Minor mergers also matter: more frequent (Bournaud et al 2007)

How about flybys? Not much studied (notable exception: Sinha &

Holley-Bockelmann 2012)

Role of the environment: voids, walls, filaments, clusters


Motivations

ΛCDM predicts hierarchical structure formation: halo mergers

Galaxy mergers and interactions are observed

Merger can trigger star-formation, morphological transformations, fuel central

black-hole, . . .

Distant interactions also matter (Park et al 2008, Hwang & Park 2015)

Major merger have a dramatic impact (morphology transformation, significant mass

increase; e.g., Toomre & Toomre 1972)

Minor mergers also matter: more frequent (Bournaud et al 2007)

How about flybys? Not much studied (notable exception: Sinha &

Holley-Bockelmann 2012)

Role of the environment: voids, walls, filaments, clusters

Main questions

How do haloes interact within the large-scale structures?

How do interactions shape haloes?


Flybys in cosmological simulations

Sinha & Holley-Bockelmann (2012):

importance of flybys?

N-body simulation:

Merger dominant at high z

For massive haloes (> 1011) and

z < 2, flybys important

Small box (50 h−1Mpc: large-scale

effects?)

Down to z = 1

Observationally: close pairs as a

proxy for merger rate. What about

flybys? (cf. Tonnensen & Cen 2012)


Outline

1 Introduction


The Horizon Run 4 simulation

Background density

Definitions




The Horizon Run 4 simulation

Horizon Run 4 (J. Kim et al 2015, JKAS)

N-body simulation using the GOTPM code in a WMAP5 cosmology

8000 CPU cores, 50 days at KISTI (Korea).

L = 3.15 h−1Gpc, N = 63003 (d̄ = 0.5 h−1Mpc)

2LPT, zini = 100, 2000 timesteps

70 outputs, lightcone up to z = 1.39, merger trees

Catalogues

Haloes detected with OPFOF, and subhaloes with PSB

Minimum subhalo mass (20 particles): 1.8 × 1011 h−1M⊙

Use of a target (MT > 5 × 1011 h−1M⊙) and neighbour (MN > 2 × 1011 h−1M⊙)

catalogue

Hereafter, “haloes” refer to PSB subhaloes (↔ galaxies)


Large-scale densityB. L’Huillier, C. Park and J. Kim (2015) MNRAS 451, 527

To quantify the environment: ρ20: density over

20 neighbours

ρ20 =

20∑

i=1

MiW (ri , h),

where ri is the distance to the i th neighbour, Mi

its mass, W the SPH spline kernel, and h the

smoothing length.

Normalisation by ρ̄ =∑

N Mi :

1 + δ = ρ20/ρ̄

0 50 100 150x (h−1Mpc)

0

50

100

150

y(h−1Mpc)

z=0

0 50 100 150x (h−1Mpc)

0

50

100

150

y(h−1Mpc)

z=1

All haloes 10<1+δ<30 1+δ>100


Definitions

InteractionsA target T is interacting if

it is located with the virial radius of its neighbour N

if MN> 0.4 MT


Outline

1 Introduction



Influence of the large-scale density

Interaction rate as a function of the mass and density

Dependence on the mass ratio and distance

A closer look at the oblique branch



Interaction rate: background densityB. L’Huillier, C. Park and J. Kim 2015, MNRAS 451, 527

10-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1100

Ptarget(δ)

z=0.0

z=0.5

z=1.0

z=1.5

10-5

10-4

10-3

10-2

10-1

100

Γ(δ)

z=2.0

z=3.1

z=4.0

z=5.0

10-2 10-1 100 101 102 103 104 105

1+δ

100101102103104105106107

Ninter

Targets = all subhalos with

M > 5 × 1011 h−1M⊙

Background density: smoothed over 20

neighbours:

ρ20 =

20∑

i=1

Mi W (ri , h),

Top: PDF of the density of interacting

targets

Middle: fraction of targets that are

interacting

Bottom: Number of interaction per bin

Interactions occurs at 1 + δ ≃ 103


Mass and density dependence of the interaction fractionB. L’Huillier, C. Park and J. Kim 2015, MNRAS 451, 527

Fit:Γ(M|δ, z) = A0 erfc

(

b log10

(

M

M∗

))

10-1

100

101

102

103

104

1+δ

Targets Interactions

1012 1013 1014 1015

M (h−1M⊙)

10-1

100

101

102

103

104

1+δ

Interaction rate

1012 1013 1014 1015

M (h−1M⊙)

Fit

100

101

102

103

104

105

106

f(M,δ)

10-4

10-3

10-2

10-1

100

Γ(M

,δ)

z=0.0

A0, M∗, and b dependence on (δ, z):

1012

1013

1014

M∗(h

−1M

⊙) z=0.0

z=0.5

z=1.0

z=1.5

z=2.0

10-3

10-2

10-1

100

A0

10-1 100 101 102 103 104

1+δ

012345

b




(

b log10

(

M

M∗

))

10-1

100

101

102

103

104

1+δ


1012 1013 1014 1015

M (h−1M⊙)

10-1

100

101

102

103

104

1+δ

Interaction rate

1012 1013 1014 1015

M (h−1M⊙)

Fit

100

101

102

103

104

105

106

f(M,δ)

10-4

10-3

10-2

10-1

100

Γ(M

,δ)

z=0.5


1012

1013

1014

M∗(h

−1M

⊙) z=0.0

z=0.5

z=1.0

z=1.5

z=2.0

10-3

10-2

10-1

100

A0

10-1 100 101 102 103 104

1+δ

012345

b




(

b log10

(

M

M∗

))

10-1

100

101

102

103

104

1+δ


1012 1013 1014 1015

M (h−1M⊙)

10-1

100

101

102

103

104

1+δ

Interaction rate

1012 1013 1014 1015

M (h−1M⊙)

Fit

100

101

102

103

104

105

106

f(M,δ)

10-3

10-2

10-1

100

Γ(M

,δ)

z=1.0


1012

1013

1014

M∗(h

−1M

⊙) z=0.0

z=0.5

z=1.0

z=1.5

z=2.0

10-3

10-2

10-1

100

A0

10-1 100 101 102 103 104

1+δ

012345

b




(

b log10

(

M

M∗

))

10-1

100

101

102

103

104

1+δ


1012 1013 1014 1015

M (h−1M⊙)

10-1

100

101

102

103

104

1+δ

Interaction rate

1012 1013 1014 1015

M (h−1M⊙)

Fit

100

101

102

103

104

105

106

f(M,δ)

10-4

10-3

10-2

10-1

100

Γ(M

,δ)

z=1.5


1012

1013

1014

M∗(h

−1M

⊙) z=0.0

z=0.5

z=1.0

z=1.5

z=2.0

10-3

10-2

10-1

100

A0

10-1 100 101 102 103 104

1+δ

012345

b




(

b log10

(

M

M∗

))

10-1

100

101

102

103

104

1+δ


1012 1013 1014 1015

M (h−1M⊙)

10-1

100

101

102

103

104

1+δ

Interaction rate

1012 1013 1014 1015

M (h−1M⊙)

Fit

100

101

102

103

104

105

106

f(M,δ)

10-3

10-2

10-1

100

Γ(M

,δ)

z=2.0


1012

1013

1014

M∗(h

−1M

⊙) z=0.0

z=0.5

z=1.0

z=1.5

z=2.0

10-3

10-2

10-1

100

A0

10-1 100 101 102 103 104

1+δ

012345

b


Time evolution of the interaction rateB. L’Huillier, C. Park and J. Kim 2015, MNRAS 451, 527

0.0

0.2

0.4

0.6

0.8

1.0

Γinter

δ<∆1

∆1 δ<∆2

δ≥∆2

A=0.6892, B=0.006, γ=4.41

A=0.6448, B=0.021, γ=3.85

A=0.5910, B=0.157, γ=3.15

0.0

0.2

0.4

0.6

0.8

1.0

Γinter

δ<∆1

∆1 δ<∆2

δ≥∆2

A=0.6865, B=0.005, γ=4.34

A=0.6421, B=0.018, γ=3.70

A=0.5767, B=0.140, γ=3.08

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

a

0.0

0.2

0.4

0.6

0.8

1.0

Γinter

δ<∆1

∆1 δ<∆2

δ≥∆2

A=0.6433, B=0.006, γ=3.54

A=0.5970, B=0.019, γ=3.14

A=0.5624, B=0.078, γ=2.75

M0<M

TM

1M

1<M

TM

2M

T>M

2

Γ/B

Γ(a) = B exp

(

−

(

1 − a

A

)γ)

Increasing rate

At “fixed” mass bin

Final interaction rate (B)

higher for higher density

Rates saturates earlier at lower

densities

At “fixed” density

B decreases with MT for the

largest density bin


10-2

10-1

100

p=d/R

vir,nei

δ<∆1 ∆1 δ<∆2 δ≥∆2

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

100 101 102 103

q=MN/MT

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

f(p,q|δ,M

T,z)

MT>M

2(z)

M1(z)<M

TM

2(z)

M0(z)<M

M1(z)

z=2.0

d2N = f (p, q|MT, δ, z)dp dq

Sep

arat

ion

Mass ratio

10-2

10-1

100

p=d/R

vir,nei

δ<∆1 ∆1 δ<∆2 δ≥∆2

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

100 101 102 103

q=MN/MT

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

f(p,q|δ,M

T,z)

MT>M

2(z)

M1(z)<M

TM

2(z)

M0(z)<M

M1(z)

z=1.0


Sep

arat

ion

Mass ratio

10-2

10-1

100

p=d/R

vir,nei

δ<∆1 ∆1 δ<∆2 δ≥∆2

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

10-2

10-1

100

p=d/R

vir,nei

100 101 102 103

q=MN/MT

100 101 102 103

q=MN/MT

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

f(p,q|δ,M

T,z)

MT>M

2(z)

M1(z)<M

TM

2(z)

M0(z)<M

M1(z)

z=0.0


Sep

arat

ion

Mass ratio

A closer look at the oblique branch

1.0 0.5 0.0 0.5 1.0

cosθ

10-1

100

101

PDF

0.4<p<0.6

q<1.0

q>3.0

1.0 0.5 0.0 0.5 1.0

cosθ

10-1

100

1011<q<3

p<0.4

p>0.6

θ = (r, v)

Low q: flatter distribution: more

random; fewer infalling orbits

Low p: flatter distribution, fewer

receding orbits

100 101 102 103

q=MT/MN

10-1

100

p=d/R

vir,nei

cosθ>0.5

100 101 102 103

q=MT/MN

−0.5<cosθ<0.5

100 101 102 103

q=MT/MN

cosθ<−0.5

1012 1013 1014 1015

MN (h−1M⊙)

10-2

10-1

100

d(h

−1Mpc

1012 1013 1014 1015

MN (h−1M⊙)

1012 1013 1014 1015

MN (h−1M⊙)

10-19

10-18

10-17

10-16

10-15

10-14

10-13

f(p,q|δ,M

T,z)

the oblique branch corresponds to

radial orbits: 1st infall

0.5 < cos θ < 0.5: random motions

after 1st infall, oblique branch less

prominent.


Outline

1 Introduction




Motivations

Alignment of the major axes of interacting pairs


MotivationsL’Huillier, Park & Kim MNRAS subm.

Galaxies form within the cosmic web: properties must be related to their

environment

The study of the alignment of the spins and shapes of haloes can shed light

on galaxy formation within their environments

Alignment as a probe of the large-scale structures

Intrinsic alignment: source of systematics for weak lensing analysis

From simulations: spins aligned with the intermediate axis of the tidal tensor

Wang et al (2011)

mass dependence: low-mass (massive) haloes have their spin parallel

(orthogonal) to filaments Hahn et al (2007),

Haloes in sheets have their spin in the plane


MethodL’Huillier, Park & Kim MNRAS subm.

To detect an alignment signal of an angle θ = (u, v) , following Yang et al 2006,

we used the normalised pair count:

Count the number of pairs N(θ) with angle θ

for Nrand ≃ 200, calculate⟨

NR(θ)⟩

and σθ the mean and std deviation of

random permutations of u.

We look at f (θ) = N(θ)/⟨

NR(θ)⟩

If f ≡ 1: No alignment (random)

If f (cos θ ≃ ±1) ≫ 1 : Alignment (parallel/anti parallel)

If f (cos θ ≃ 0) ≫ 1: Anti-alignment (orthogonal)

the strength of the signal (error bars) is given by σθ/⟨

NR(θ)⟩

.


Shapes

T

N

γ

ε

aT

aN

r

γ = (aT, r): angle between major axis (target) and direction neighbour

ε = (aN, r): angle major between the major axis of the neighbour and the direction

of the target


10-1

100

101

f(cosγ)

δ<∆1(z) ∆1(z)<δ<∆2(z) δ>∆2(z)

10-1

100

101

f(cosγ)

0.2 0.4 0.6 0.8

cosγ

10-1

100

101

f(cosγ)

z=4.0

z=3.1

z=2.0

0.2 0.4 0.6 0.8

cosγ

z=1.5

z=1.0

0.2 0.4 0.6 0.8

cosγ

z=0.5

z=0.0

M0(z)<M<M

1(z)

M1(z)<M<M

2(z)

M>M

2(z)

Higher densities

Hig

her

masses

γ = (aT, r); qT < 0.8

Alignment stronger at low-δ and low-z; little mass dependence

Major axis aligned with the direction of the neighbour

Spins

T

N

φ

JT

α

JN

r

α = (JT, r): angle between spin target and direction neighbour

φ = (JT, JN): angle between target and neighbour neighbour spins


0.5

1.0

1.5

2.0

2.5

f(cosφ)

δ<∆1(z) ∆1(z)<δ<∆2(z) δ>∆2(z)

0.5

1.0

1.5

2.0

2.5f(cosφ)

0.5 0.0 0.5

cosφ

0.5

1.0

1.5

2.0

2.5

f(cosφ)

z=4.0

z=3.1

z=2.0

0.5 0.0 0.5

cosφ

z=1.5

z=1.0

0.5 0.0 0.5

cosφ

z=0.5

z=0.0

M0(z)<M<M

1(z)

M1(z)<M<M

2(z)

M>M

2(z)

Higher densities

Hig

her

masses

φ = (JT, JN)

Strong time evolution, inversion of tendence: towards an alignment of spins.

High-δ: weak alignment → strong

Low-δ: spins para and anti-para → para

Alignment of prolate pairs

0°

45°

90°

135°

180°

225°

270°

315°

γ

z=0.0

0°

45°

90°

135°

180°

225°

270°

315°

γ

z=1.0

γ = (aT, r); ε = (aN, r);

Neighbours are drawn at their angular

position γ proportionaly to P(γ).

Neighbours located in the direction of

the major axis

Neighbours point toward the Target


Alignment of prolate pairs

0°

45°

90°

135°

180°

225°

270°

315°

γ

z=0.0

0°

45°

90°

135°

180°

225°

270°

315°

γ

z=1.0

10-1

100

101

PDF

z=0

0.00<p<0.66

γ=8.1 ◦

γ=59.3 ◦

γ=89.4 ◦

z=0

0.85<p<1.00

γ=8.1 ◦

γ=59.3 ◦

γ=89.4 ◦

0.0 0.2 0.4 0.6 0.8cosǫ

10-1

100

101

PDF

z=1

0.0 0.2 0.4 0.6 0.8cosǫ

z=1

γ = (aT, r); ε = (aN, r);

Neighbours are drawn at their angular

position γ proportionaly to P(γ).

Neighbours located in the direction of

the major axis

Neighbours point toward the Target


Summary and perspectives

The unprecedented statistics of HR4 enable us to study the the interaction rate and

the halo alignment as a function of the environment

The angular position neighbour is aligned with the major axis of the target

Alignment signal stronger at low redshift, increases with density, independent of

mass

Comparison with observations: SDSS (in progress)

Inclusion of hydrodynamics: morphological transformation, star formation,

misalignment galaxy/halo:

How does modified gravity affects interactions? (In progress)


Summary and perspectives

The unprecedented statistics of HR4 enable us to study the the interaction rate and

the halo alignment as a function of the environment

The angular position neighbour is aligned with the major axis of the target

Alignment signal stronger at low redshift, increases with density, independent of

mass

Comparison with observations: SDSS (in progress)

Inclusion of hydrodynamics: morphological transformation, star formation,

misalignment galaxy/halo:

How does modified gravity affects interactions? (In progress)

감사합니다!


Target selection

At z = 4, find M2(z = 4) the median mass

of the targets. This defines two subsamples

of equal numbers.

Divide them into three equal subsamples

according to the density with ∆2,1, ∆2,2.

At lower z , find Mi(z) and

∆j,i(z) (i ∈ {0, 1, 2}, j ∈ {1, 2}) that yield

the same number of targets per bin.

About 4M targets per bin of (M, δ)

1 2 3 5 61011

1012

1013

M(z)h−1

M⊙

M0 (z)

M1 (z)

M2 (z)

1 2 3 4 5

1+z

100

101

102

103

∆i,j(z)

∆1,0(z)

∆1,1(z)

∆1,2(z)

∆2,0(z)

∆2,1(z)

∆2,2(z)

Redshift-evolution of Mi (z) and ∆j,i (z)


halo interactions in the horizon run 4...

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