An optimized filter to detect galaxy clusters in optical surveys

Transcription

1 An optimized filter to detect galaxy clusters in optical surveys Alexander Gelsin Institute for Theoretical Astrophysic Heidelberg under supervision of Prof. Matthias Bartelmann and Dr. Matteo Maturi

2 Outline 1 Motivation 2 The Model 3 Detection Method 4 Applications

3 Motivation for the work Detection of Galaxy Clusters

4 Motivation for the work Detection of Galaxy Clusters ˆ Cosmologogical constraints i.e. σ 8 & Ω m through mass function.

5 Motivation for the work Detection of Galaxy Clusters ˆ Cosmologogical constraints i.e. σ 8 & Ω m through mass function. ˆ Investigation of Evolution and Properties of these objects.

6 What do we know? Big structures as result of primordial density fluctuations Source: Volker Springel (Millenium Simulation)

7 Expected Properties of Galaxies in a Cluster

8 Expected Properties of Galaxies in a Cluster ˆ Red and blue sequence of Galaxies

9 Expected Properties of Galaxies in a Cluster ˆ Red and blue sequence of Galaxies ˆ Number Density Profile and Richness of the Cluster

10 Expected Properties of Galaxies in a Cluster ˆ Red and blue sequence of Galaxies ˆ Number Density Profile and Richness of the Cluster ˆ Luminosity Distribution of Galaxies

11 Expected Properties of Galaxies in a Cluster ˆ Red and blue sequence of Galaxies ˆ Number Density Profile and Richness of the Cluster ˆ Luminosity Distribution of Galaxies ˆ Brightest Cluster Galaxy (BCG)

12 Matched Optimal Filter Data is composed of signal, which has a shape τ and a strength Λ and noise n, which contaminates the data D( θ) = Λτ( θ) + n( θ). (1)

13 Matched Optimal Filter Data is composed of signal, which has a shape τ and a strength Λ and noise n, which contaminates the data D( θ) = Λτ( θ) + n( θ). (1) The convolution Λ est ( θ cl ) = D( θ)ψ( θ cl θ) d 2 θ, (2) results in a signal strength weighted by he filtering function Ψ

14 Optimal Filtering Optimal means: The signal estimate is enforced ˆ to be unbiased Λ est ( θ cl ) Λ = B = 0, and

15 Optimal Filtering Optimal means: The signal estimate is enforced ˆ to be unbiased Λ est ( θ cl ) Λ = B = 0, and ˆ to have a minimal variance σ 2 (Λ est ( θ cl ) Λ) 2,

16 Optimal Filtering Optimal means: The signal estimate is enforced ˆ to be unbiased Λ est ( θ cl ) Λ = B = 0, and ˆ to have a minimal variance σ 2 (Λ est ( θ cl ) Λ) 2, whereas the second condition results from δl δψ = with the Lagrangian multiplier λ. δ ( σ 2 + λb ) = 0, (3) δψ

17 Matched Optimal Filter Such a matched optimal filter has the following form: ˆΨ(k) = 1 [ ] ˆτ(k) 2 1 ˆτ(k) (2π) 2 P N (k) d2 k P N (k). (4) This filter is matched to the model τ.

18 Matched Optimal Filter Such a matched optimal filter has the following form: ˆΨ(k) = 1 [ ] ˆτ(k) 2 1 ˆτ(k) (2π) 2 P N (k) d2 k P N (k). (4) This filter is matched to the model τ. Thus giving ˆ strong signal estimate when data shape is like the model, and

19 Matched Optimal Filter Such a matched optimal filter has the following form: ˆΨ(k) = 1 [ ] ˆτ(k) 2 1 ˆτ(k) (2π) 2 P N (k) d2 k P N (k). (4) This filter is matched to the model τ. Thus giving ˆ strong signal estimate when data shape is like the model, and ˆ weak signal when the noise P N (k) dominates.

20 Properties of the Cluster Cluster- Model Properties Mass M Redshift 0.4 N R Mpc h 1

21 Properties of the Cluster Cluster- Model Properties Mass M Redshift 0.4 N R Mpc h 1 Cosmological Parameters Ω m 0.25 Ω b 0.04 Ω Λ 0.75 h 0.7 σ 8 0.8

22 simple model ˆ τ(r, z) = p red (r)g(z z cl, σ z ) + p blue (r)g(z z cl, σ z ) = p(r)g(z z cl, σ z ) ˆ ˆΨ(k, z) = ˆΨ(k) G(z z cl,σ z) G 2 (z z cl,σ z)dz, and ˆ ˆΨ(k) = 1 (2π) 2 [ ˆτ(k) 2 ] 1 ˆτ(k) PN z (k) d2 k PN z (k).

23 1000 model cluster given this good statistic and ˆ no contamination by field galaxies: Λ est results in 1020 and S/N = 1118, where the only noise is poissonian due to realizations of the cluster, ˆ some artificial field fluctuations and resolution noise: Λ est decreases to 938 and S/N to 813.

24 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice

25 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice DEC in deg Cluster search in a smooth artificial field at 0.3 Signal RA in deg 0

26 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice

27 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice Cluster search in a smooth artificial field at 0.3 Signal to Noise DEC in deg RA in deg

28 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice ˆ Signal Map One Cluster z = 0.3 slice

29 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice ˆ Signal Map One Cluster z = 0.3 slice DEC in deg Cluster search at 0.3 in a smooth artificial field with a cluster Signal RA in deg

30 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice ˆ Signal Map One Cluster z = 0.3 slice ˆ S/N Map One Cluster z = 0.3 slice

31 Smooth Field + one model cluster comparison Field parameters: 1 1 deg 2, without structures, realistic redshift distribution and errors (CARS, CFHTLS) with additional model cluster ˆ Signal Map Smooth z = 0.3 slice ˆ S/N Map Smooth z = 0.3 slice ˆ Signal Map One Cluster z = 0.3 slice ˆ S/N Map One Cluster z = 0.3 slice DEC in deg Signal to Noise Cluster search at 0.3 in a smooth artificial field with a cluster RA in deg 0.5 0

32 Thank you, any questions?