Morphology of Cosmological Fields during the Epoch of Reionization - PowerPoint PPT Presentation

Morphology of Cosmological Fields during the Epoch of Reionization Akanksha Kapahtia Indian Institute of Astrophysics (Joint Astronomy Program, IISc Bengaluru) With Pravabati Chingangbam (Indian Institute of Astrophysics, Bengaluru) Stephen Appleby (Korea Institue of Advanced Studies, Seoul) AK, P. Chingangbam et al JCAP 2018; AK, P. Chingangbam et al arXiv:1904.06840 1 / 36

Epoch of Reionization 21cm Cosmology for Epoch of Reionization Cosmic inflation would have amplified minute quantum fluctuations (pre-inflation) into slight density ripples of overdensity and underdensity (post-inflation) It is these fluctuations that are the seeds of structure formation in the universe. Image Credit: Roen Kelly- Discover Magazine 2 / 36

Epoch of Reionization Observational evidence of EoR Ly-alpha Spectra of distant quasars show an absorption trough. x HI ≃ 10 − 4 Ω 1 / 2 m h (1 + z ) 3 / 2 τ α Universe is highly ionized atleast till z ≃ 6. (Fan et.al. AnnRev.AA 2006) CMB The scattering of CMB photons induces polarizations and temperature anisotropies. Optical depth to last scattering, τ ls ∼ 0 . 054. (Planck 2018) 3 / 36

Epoch of Reionization The 21cm spin flip transition Transition between 1 1 s 1 / 2 & 1 0 s 1 / 2 The relative populations of hydro- gen atoms in the two spin states de- fines the spin temperature T s , ( T ∗ = 68 mK , ν 0 = 1420 MHz ): � − T ∗ � n 1 n 0 = 3 exp T s Image Credit: nrao.edu E= 5 . 87 × 10 − 6 eV , A 21 = 2 . 88 × 10 − 15 sec ∼ 11 ( Myr ) − 1 4 / 36

Epoch of Reionization Brightness temperature The transfer of radiation through thermally emitting matter can be described in terms of the specific intensity: dI ν = − I ν + B ν ( T ) d τ ν The temperature of a black body having the same specific intensity as I ν is the Brightness Temperature . In RJ regime I ν = 2 ν 2 c 2 kT and so the above equation can be written in terms of the brightness temperature, with solution: T ′ b ( ν ) = T S (1 − e − τ ν )+ T ′ R ( ν ) e − τ ν The background radiation is usually CMB, so T ′ R ( ν ) = T γ ( z ) 5 / 36

Epoch of Reionization 21cm Brightness Temperature Image Credit:lunar.colorado.edu/dare/science T S − T γ (1 − e − τν 0 ) ≈ δ T b ( ν ) = 1 + z � � 1 + z � 1 / 2 � Ω b h 2 � H � � 1 − T γ 0 . 15 � 27x HI (1 + δ nl ) mK Ω M h 2 dv r / dr + H T S 10 0 . 023 6 / 36

Epoch of Reionization Spin Temperature � � 1 − T γ δ T b ( ν ) ∝ x HI (1 + δ nl ) T S δ T b < 0 if T s < T γ : absorp- tion δ T b > 0 if T s > T γ : emission δ T b = 0 if T s = T γ : No signal Three competing processes determine T s : 1 . Absorption of CMB photons(and stimulated emission by CMB photons) 2 . Collisions with other hydrogen atoms, free electrons, and protons 3 . Scattering of Lyman alpha photons (Wouthuysen-Field Effect) + (x c + x α )T − 1 T − 1 γ k T − 1 = s 1 + x c + x α 7 / 36

Epoch of Reionization Evolution of T s and δ T b :Models 10 4 10 3 T γ T γ T γ 10 3 T k T k T k T S T S T S 10 3 T (K) 10 2 T (K) T (K) 10 2 10 2 10 1 10 1 10 1 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 6 8 10 12 14 16 18 20 z z z ζ ∼ 17 (Fid) ζ ∼ 10 . 9 (Fid) ζ X ∼ 10 56 ζ X ∼ 10 56 ζ X ∼ 10 57 0 0 −40 −40 δT b ( mK ) δT b ( mK ) −80 −80 Fiducial −120 −120 Fiducial ζ = 10.9 ζ X = 1 × 10 57 ζ = 23.3 12 12 σ T b σ T b 6 6 0 0 6 10 14 18 6 10 14 18 8 / 36 z z

Epoch of Reionization Credit:Pritchard and Loeb (2012) 9 / 36

Epoch of Reionization Observations of the 21cm brightness temperature There are two ways the signal is detected: Global Signal :EDGES,LEDA,DARE Fluctuations :GMRT,LOFAR,SKA,PAPER Observational Challenge : Foregrounds are 5 orders of magnitude greater than the signal Power spectrum → advantageous for observations. Fields are highly non-Gaussian → methods to include higher n-point statistics. Analyzing the morphology in real space → disadvantage as large sky volume is required for analysis. We use simulations to develop the method and make predictions for physical models. 10 / 36

Epoch of Reionization Morphology of cosmological fields Cosmological fields are random fluctuation fields in 2 or 3 dimensional space. Excursion set : all spatial points with field values higher than or equal to a chosen threshold. In 2D, boundaries form closed contours enclosing connected regions or holes . Betti Numbers : Topological quantities n c = no of connected regions n h = no of holes 200MPc 11 / 36

Epoch of Reionization Tensor Minkowski Functionals in 2D space Alesker 1997, Hug 2008, Beisbart et al 2002, Schroeder-Turk et al 2011 � r m d a W m = � 0 � n n d ℓ W m , n r m ⊗ ˆ = � 1 C n � n n κ d ℓ W m , n r m ⊗ ˆ = � 2 C r κ ≡ local curvature y ) ij ≡ 1 ( � x ⊗ � 2 ( x i y j + x j y i ) m + n ≤ 2 12 / 36

Epoch of Reionization Scalar Minkowski Functionals : m = 0 , n = 0 � W 0 = d a area − → � = d ℓ W 1 − → contour length C � W 2 = κ d ℓ genus − → C Cosmological application: Gott 1990 Tensor Minkowski Functionals : W 1 , 1 , W 0 , 2 , W 1 , 1 , W 0 , 2 1 1 2 2 � � W 1 , 1 T ⊗ ˆ ˆ = � r ⊗ ˆ n κ d ℓ = d ℓ T 2 C C κ = | d ˆ T / d ℓ | ( Schroeder-Turk et al 2011, Chingangbam,KP Yogendran et al 2017 ) Translation invariant Gives the size and shape information of the curve : � Trace ( W 1 , 1 ) = d ℓ 2 C 13 / 36

Epoch of Reionization Shape and Alignment measure using W 1 , 1 2 Single Curve: Many curves: : W 1 , 1 λ 1 , λ 2 , λ 1 < λ 2 � λ 1 � − → 2 ¯ β ≡ λ 1 λ 2 β ≡ λ 2 0 ≤ β ≤ 1 � � W 1 , 1 Average over all curves Λ 1 , Λ 2 − → − → 2 α ≡ Λ 1 , 0 ≤ α ≤ 1 Λ 2 14 / 36

Epoch of Reionization Shape and Alignment measure using W 1 , 1 2 β :intrinsic shape of each curve α :relative alignment of many curves 15 / 36

Epoch of Reionization Simulating EoR Messinger et. al., 2010 The brightness temperature field was generated using the publicly available code 21cmFAST . Uses a combination of the excursion set and perturbation theory to generate full 3D realizations of: ◮ Evolved density Field ◮ Ionization field - ζ and T vir ◮ Spin temperature field - ζ X and T vir ◮ Brightness temperature field Simulation Simulated δ T b , T s , δ nl and x HI . Box size = 200 Mpc, resolution = 512 3 grid. Combinations of ζ and T vir to correspond to reionization ending at z ≈ 6, τ re = 0 . 054 ( PLANCK 2018 ). 16 / 36

Epoch of Reionization Morphology of fields during EoR Physical questions How is the shape of structures related to the underlying physics of EoR? To study the morphology of δ nl , T s and x HI , and see how the morphology is reflected in δ T b . To discriminate models of reionization To trace ionization and heating history of the IGM 17 / 36

Epoch of Reionization Quantities of interest: Single curve λ 1 , λ 2 − → Eigenvalues of W 1 β ch ≡ λ 1 /λ 2 r ch ≡ ( contour length ) / (2 π ) n c ( ν ) , n h ( ν ) − → Betti Numbers at a given ν Average quantities at each threshold, ν � n x ( ν ) j =1 λ i , x ( j ) λ i , x ( ν ) ≡ n x ( ν ) � n x ( ν ) j =1 r x ( j ) r x ( ν ) ≡ n x ( ν ) � n x ( ν ) j =1 β x ( j ) β x ( ν ) ≡ n x ( ν ) 18 / 36

Epoch of Reionization Isotropic Gaussian random field The analytical forms for scalar Minkowski functionals ( Tomita 1986, Schmalzing:1998 ) and α ( Chingangbam, Yogendran et al.:2017 )for Gaussian random fields is known . Their variation with threshold is same for a gaussian random field, irrespective of it’s power spectrum. However, their amplitude depends upon σ 0 (standard deviation) and σ 1 (standard deviation of the field derivative). The variation of Betti numbers is sensitive to the power spectrum ( Park et al. 2013, Pranav 2018 ) and their analytical forms is not known. The analytical form for variation of β is not known but it is sensitive to power spectrum. r ch gives a measure of perimeter of individual curves. It is sensitive to power spectrum of the field. 19 / 36

Epoch of Reionization Isotropic Gaussian random field On varying ν from top to bottom: Isolated small connected regions around the highest peaks of the field and their number gradually increases Some of these small connected regions merge thereby decreasing their number. Connected regions all merge to form a single connected region with holes puncturing it which shrink in size and disappear as we go lower in threshold. (Image Credit:Feldbrugge and Engelen,University of Groningen (2012)) con hole 80 60 n con , hole 40 20 0 400 r con , hole ( Mpc ) 200 0 0.85 β con , hole 0.65 0.45 -4 -2 0 2 4 ν 20 / 36

Epoch of Reionization Redshift Evolution of average quantities Condense the ν dependence to get a single quantity at each redshift � ν high N x ( z ) d ν n x ( ν, z ) ≡ ν low � ν high ν low d ν n x ( ν, z )¯ λ i , x ( ν ) λ ch i , x ( z ) ≡ N x ( z ) � ν high ν low d ν n x ( ν, z )¯ r x ( ν ) r ch x ( z ) ≡ N x ( z ) � ν high ν low d ν n x ( ν, z )¯ β x ( ν ) β ch x ( z ) ≡ N x ( z ) ν high and ν low can be suitably chosen based on physical interpretation. 21 / 36