Signatures of Cosmic Reionization on the 21cm 3-Point Correlation

Transcription

1 Tsinghua Center for Astrophysics (Beijing) Signatures of Cosmic Reionization on the 21cm 3-Point Correlation Kai Hoffmann collaborators: Yi Mao, Houjun Mo, Benjamin D. Wandelt

2 Motivation 21cm clustering statistics can constrain Reionization models (Shimabukuro et al. 2017, ) possibly cosmological models at high z (see conclusions) Credit: Kaurov

3 Motivation 21cm clustering statistics can constrain Reionization models (Shimabukuro et al. 2017, ) possibly cosmological models at high z (see conclusions) Why going beyond 2-point statistics? 21cm 2pc probes scale dependence of 21cm clustering, while 3pc is sensitive to additional information on shape of ionized regions matter fluctuations (Suman Majumdar et al. 2017, arxiv: ) tighter model constraints

4 Motivation 21cm clustering statistics can constrain Reionization models (Shimabukuro et al. 2017, ) possibly cosmological models at high z (see conclusions) Why going beyond 2-point statistics? 21cm 2pc probes scale dependence of 21cm clustering, while 3pc is sensitive to additional information on shape of ionized regions matter fluctuations tighter model constraints no theory model for the 21cm 3pc

5 21cmFast simulations matter 21cm brightness fluctuations Temperature [mk] Global neutral fraction (768 Mpc)3 box 200 realizations ( 21cmFAST: Mesinger et al )

6 2- and 3-point correlations fluctuations: ρ m ρ m δ m= ρ m δ T δ T δδ T = δ T 2-point correlation (2pc): ξ (12) spherically symmetric not sensitive to shape of fluctuations 3-point correlation (3pc): ζ r δ 1 δ 2 (r) (123) δ 1 δ 2 δ 3 (r 1, r 2, r 3 ) provides additional shape info r1 r3 r2

7 2pc measurements mean measurements over 200 realizations symbols: 21cm 2pc ( ξ δ T ) dashed lines: matter 2pc ( ξ ) solid lines: fits to bias model m Leading-order bias model 2 1 ξ δ T =b ξ m fitting range: 40 < r < 90 Mpc

8 3pc measurements matter matter dots: 3pc ζ δ 1 δ 2 δ 3 line: hierarchical 3pc H ζ (ξ (12) (13) m m ξ r1 +2 perm.) r3 r2

9 3pc measurements matter matter dots: 3pc ζ δ 1 δ 2 δ 3 line: hierarchical 3pc H ζ (ξ 21cm 21cm (12) m ξ (13) m r1 +2 perm.) r3 r2

10 quadratic bias model Assumption: 21cm brightness temperature is deterministic function of underlying matter density N n m δ δ δ T =F (δ m ) bn n! n=0 (Taylor expansion of F around δ m 0 )

11 quadratic bias model Assumption: 21cm brightness temperature is deterministic function of underlying matter density n m N δ δ δ T =F (δ m ) bn n! n=0 (Taylor expansion of F around δ m 0 ) Leading-order approximations for biased correlation functions 2pc 3pc 2 ξ δ T b1 ξ m ζ δ T b ζ m +b b 2 ζ H m (Fry & Gaztanaga 93)

12 quadratic bias model Assumption: 21cm brightness temperature is deterministic function of underlying matter density n m N δ δ δ T =F (δ m ) bn n! n=0 (Taylor expansion of F around b2 Q δ T (Q m + ) b1 b1 )1 Leading-order approximations for biased correlation functions H 3pc 2 ξ δ T b1 ξ m 3 1 <= > 2pc Q ζ / ζ with δ m ζ δ T b ζ m +b b 2 ζ H m (Fry & Gaztanaga 93)

13 21cm 3pc fits dots: 21 3pc ζ δ 1 δ 2 δ 3 lines: 3pc bias model fit 3 2 H ζ δ T b1 ζ m +b1 b 2 ζ m (fitting range: 30<r<90 Mpc)

14 21cm 3pc fits model fails at r3 < 20 Mpc dots: 21 3pc ζ δ 1 δ 2 δ 3 lines: 3pc bias model fit 3 2 H ζ δ T b1 ζ m +b1 b 2 ζ m (fitting range: 30<r<90 Mpc)

15 21cm 3pc fits triangle configurations, defined by (r1, r2) triangle opening angle triangle scale black dots: colored dots: 3pc measurements fits to bias model prediction in triangle scale bins 1/ 3 (r 1 r 2 r 3 )

16 21cm 3pc covariance 15 configurations X 18 opening angles = 270 triangles

17 linear bias measurements ~10% agreement between linear bias from 2pc and 3pc

18 Linear bias comparison with 2pc ~10% agreement between linear bias from 2pc and 3pc

19 Bias model validation δ δ T =F (δ m )?

20 Bias model validation grey dots: fluctuations in 24 Mpc cubical grid cells in one realization

21 Bias model validation grey dots: fluctuations in 24 Mpc cubical grid cells in one realization black dots: mean δ δ T over 200 realizations in δ m bins

22 Bias model validation grey dots: fluctuations in 24 Mpc cubical grid cells in one realization black dots: mean δ δ T over 200 realizations in δ m bins red line: quadratic bias model with b1 and b2 from 3pc measurements δ δ T =b 0 +b1 δ m +b2 δ 2 m ( δ δ T =0 b0= b2 δ 2m )

23 Bias model validation quadratic bias model with b1 and b2 from 21cm 3pc: 2 2 δ δ T =b1 δ m +b2 (δ m σ m ) b1 = slope of δ δ T at δ m =0 positive at early times negative at late times δ T ρ HI x HI (1+δ m )

24 Bias model validation

25 Bias model validation δ m β Fitting model δ δ T =α erfc ( γ )(1+δ m ) 1

26 conclusions Quadratic bias model explains shape of 21cm 2pc & 3pc at large scales and early times of reionization (neutral fraction > 60%, r> 20 Mpc) b1 from 2pc and 3pc consistent at 10% level b1 and b2 measurements might allow for extracting physical information on EoR from 21cm observations Combining 21cm 2pc & 3pc can break growth-bias degeneracy ξδ T ( z) D ( z 0 )2 b1 ( z 0 )2 ξδ T ( z 0 ) D ( z )2 b1 ( z)2 cosmological constraints from growth measurements at high z arxiv:

27 conclusions Quadratic bias model explains shape of 21cm 2pc & 3pc at large scales and early times of reionization (neutral fraction > 60%, r> 20 Mpc) b1 from 2pc and 3pc consistent at 10% level b1 and b2 measurements might allow for extracting physical information on EoR from 21cm observations Combining 21cm 2pc & 3pc can break growth-bias degeneracy ξδ T ( z) D ( z 0 )2 b1 ( z 0 )2 ξδ T ( z 0 ) D ( z )2 b1 ( z)2 cosmological constraints from growth measurements at high z Thanks! arxiv: