Alignment of interacting haloes in the Horizon Run 4 simulation L’Huillier, Park & Kim MNRAS submitted Benjamin L’Huillier (KIAS → KASI) with Changbom Park , Juhan Kim (KIAS) XII th Rencontres du Vietnam, ICSE, Quy Nhon
Model-independent measurement of H 0 L’Huillier & Shafieloo, arXiv:1606.06832 H ( z ) /h ( z ) H 0 = H ( z ) c/ (1 + z ) D ( z ) /d A ( z ) h ( z ) 80 H 0 (kms − 1 Mpc − 1 ) CMASS H ( z ) , d A ( z ) from BAO (BOSS, 75 Cuesta et al 2016) 70 h ( z ) = 1 / D ′ ( z ) , D ( z ): D ( z ) c H 0 = model-independently 1+ z d A ( z ) 65 reconstructed from supernovae (JLA, Betoule et al 2014) 60 60 65 70 75 80 H 0 (kms − 1 Mpc − 1 ) LOWZ Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 2 / 14
Outline Motivations 1 Simulation and Method 2 Alignment of the major axes of interacting pairs 3 Summary and perspectives 4 Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 3 / 14
Motivations 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 Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 4 / 14
The Horizon Run 4 simulation Horizon Run 4 (J. Kim et al 2015, JKAS) N -body: L = 3 . 15 h − 1 Gpc , N = 6300 3 (¯ d = 0 . 5 h − 1 Mpc ), WMAP5 cosmology 8000 CPU cores, 2000 timesteps, 50 days at KISTI (Korea). Catalogues Haloes detected with OPFOF, and subhaloes with PSB Minimum subhalo mass (20 particles): 1 . 8 × 10 11 h − 1 M ⊙ Target ( M T > 5 × 10 11 h − 1 M ⊙ ) and neighbour ( M N > 2 × 10 11 h − 1 M ⊙ ) catalogues Hereafter, “haloes” refer to PSB subhaloes ( ↔ galaxies) Interactions A target T is interacting if it is located with the virial radius of its neighbour N M N > 0.4 M T At z = 0: N Target = 225 406 978; N interactions = 14 267 922 Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 5 / 14
Large-scale density All haloes 10 < 1 + δ < 30 1 + δ > 100 B. L’Huillier, C. Park and J. Kim 2015, MNRAS 451, 527 z = 0 150 To quantify the environment: ρ 20 : density over 20 neighbours 100 y ( h − 1 Mpc) 20 � ρ 20 = M i W ( r i , h ) , 50 i =1 where r i is the distance to the i th neighbour, M i 0 0 50 100 150 x ( h − 1 Mpc) its mass, W the SPH spline kernel, and h the z = 1 150 smoothing length. Normalisation by ¯ ρ = � N M i : 100 y ( h − 1 Mpc) 1 + δ = ρ 20 / ¯ ρ 50 0 0 50 100 150 x ( h − 1 Mpc) Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 6 / 14
Method B. L’Huillier, C. Park & J. Kim MNRAS submitted 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 � N R ( θ ) � for N rand ≃ 200, calculate and σ θ the mean and std deviation of random permutations of u . � N R ( θ ) � We look at f ( θ ) = N ( 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) � N R ( θ ) � the strength of the signal (error bars) is given by σ θ / . Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 7 / 14
Shapes a N ε N r γ a T T γ = ( a T , r ): angle between major axis (target) and direction neighbour ε = ( a N , r ): angle major between the major axis of the neighbour and the direction of the target Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 8 / 14
γ = ( a T , r ); q T < 0 . 8 Dependence on mass and environment z = 0 Density Mass 10 1 5 . 00 × 10 11 h − 1 M ⊙ < M T 1 . 53 × 10 12 h − 1 M ⊙ 1 . 53 × 10 12 h − 1 M ⊙ < M T 4 . 68 × 10 12 h − 1 M ⊙ 4 . 68 × 10 12 h − 1 M ⊙ < M T 1 . 43 × 10 13 h − 1 M ⊙ 10 0 f (cos γ ) 0 . 02 < 1 + δ 0 . 21 0 . 21 < 1 + δ 2 . 27 2 . 27 < 1 + δ 24 . 13 10 -1 24 . 13 < 1 + δ 256 . 92 1 . 43 × 10 13 h − 1 M ⊙ < M T 4 . 39 × 10 13 h − 1 M ⊙ 256 . 92 < 1 + δ 2735 . 15 4 . 39 × 10 13 h − 1 M ⊙ < M T 1 . 34 × 10 14 h − 1 M ⊙ 2735 . 15 < 1 + δ 29118 . 66 1 . 34 × 10 14 h − 1 M ⊙ < M T 1 . 34 × 10 14 h − 1 M ⊙ 29118 . 66 < 1 + δ 310000 . 00 10 -2 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 cos γ cos γ Alignment increase with mass; little density dependence Major axis aligned with the direction of the neighbour Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 9 / 14
γ = ( a T , r ); q T < 0 . 8 Higher densities δ < ∆ 1 ( z ) ∆ 1 ( z ) < δ < ∆ 2 ( z ) δ > ∆ 2 ( z ) 10 1 M 0 ( z ) < M < M 1 ( z ) f (cos γ ) 10 0 10 -1 10 1 Higher masses M 1 ( z ) < M < M 2 ( z ) f (cos γ ) 10 0 10 -1 10 1 z = 4.0 z = 1.5 z = 0.5 z = 3.1 z = 1.0 z = 0.0 M > M 2 ( z ) f (cos γ ) z = 2.0 10 0 10 -1 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 cos γ cos γ cos γ Alignment stronger at low- δ and low- z ; little mass dependence Major axis aligned with the direction of the neighbour
γ = ( a T , r ); ε = ( a N , r ); Alignment of prolate pairs z = 0.0 z = 1.0 90° 90° 135° 45° 135° 45° γ γ 180° 0° 180° 0° 225° 315° 225° 315° 270° 270° 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 Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 11 / 14
γ = ( a T , r ); ε = ( a N , r ); Alignment of prolate pairs z = 0.0 z = 1.0 90° 90° 135° 45° 135° 45° γ γ 180° 0° 180° 0° 225° 315° 225° 315° 270° 270° 0.00 < p < 0.66 0.85 < p < 1.00 Neighbours are drawn at their angular 10 1 γ = 8.1 ◦ γ = 8.1 ◦ γ = 59.3 ◦ γ = 59.3 ◦ position γ proportionaly to P ( γ ). γ = 89.4 ◦ γ = 89.4 ◦ PDF 10 0 Neighbours located in the direction of 10 -1 z = 0 z = 0 10 1 the major axis PDF 10 0 Neighbours point toward the Target 10 -1 z = 1 z = 1 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 cos ǫ cos ǫ Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 11 / 14
Spins J N φ J T N r α T α = ( J T , r ): angle between spin target and direction neighbour φ = ( J T , J N ): angle between target and neighbour neighbour spins Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 12 / 14
φ = ( J T , J N ) Higher densities δ < ∆ 1 ( z ) ∆ 1 ( z ) < δ < ∆ 2 ( z ) δ > ∆ 2 ( z ) 2.5 M 0 ( z ) < M < M 1 ( z ) 2.0 f (cos φ ) 1.5 1.0 Higher masses 2.5 0.5 M 1 ( z ) < M < M 2 ( z ) 2.0 f (cos φ ) 1.5 1.0 2.5 0.5 z = 4.0 z = 1.5 z = 0.5 2.0 z = 3.1 z = 1.0 z = 0.0 M > M 2 ( z ) f (cos φ ) z = 2.0 1.5 1.0 0.5 0.5 0.0 0.5 0.5 0.0 0.5 0.5 0.0 0.5 cos φ cos φ cos φ At high- z : anti-parallel or no alignment At low- z : aligned
Summary and perspective The unprecedented statistics of HR4 enable us to study the alignment as a function of the environment The angular position neighbour is aligned with the major axis of the target Alignment increases with mass, independent of large-scale density Alignment signal stronger at low redshift Flip in the spin alignemtn at z ≃ 2 Compare with observations: need for hydro simulations Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 14 / 14
Summary and perspective The unprecedented statistics of HR4 enable us to study the alignment as a function of the environment The angular position neighbour is aligned with the major axis of the target Alignment increases with mass, independent of large-scale density Alignment signal stronger at low redshift Flip in the spin alignemtn at z ≃ 2 Compare with observations: need for hydro simulations Cảm ơn! Benjamin L’Huillier (KASI) Halo interactions Quy Nhon, 2016–01-11 14 / 14
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