Statistical Analyses of Data Cubes

Transcription

1 Statistical Analyses of Data Cubes Erik Rosolowsky University of British Columbia, Okanagan Campus FCRAO survey of Taurus

2 1. Whence datacubes 2. Things that I m not going to talk about 3. Analyses from theory 4. Analyses from observations 5. Examples 6. A plea

3 Astronomical Images ν1 Iν (α, δ, ν, t) dν ν0 Usually: - Ignore t - Ignore Q,U,V Hα image from the Local Group Survey (Massey et al. 2008)

4 13 CO Image from COMPLETE Survey (Ridge et al. 2005)

5 Spectral Line Data Cubes (spectral hypercubes) ν0 +δν ν 0 I ν (α, δ, ν, t) dν I ν (α, δ, ν 0,t) δν

6 Other Spectral Data Cubes Optical Spectroscopy (IFUs, sparely sampled spectroscopy via fiber) Geophysics (satellite data e.g., AVIRIS) Materials Physics (electron energy loss spectroscopy) Other cubes are out there: medical imaging, biological and geological studies, engineering (fluids)

7 δν 10 9 ν 0 Focus on radio δν ν

8 Atacama Large Millimeter Array: now! Square Kilometer Array: 2020 (?) (7 Pb/s)

9 We typically resolve spectral lines, so Doppler gives us: c δν ν 0 = v r Thus, position-position-velocity (PPV) cubes

10 Ignore sparse data sets

11 There are many two-dimensional treatments of integrated PPV cubes - Fractals - Wavelets / Delta Variance Some exceptions ψ i (x, y)φ j (v) See Fermi application in Starck s talk

12 Star formation from molecular clouds Narayanan et al. (2008)

13 Simulations of the Interstellar Medium v t +(v )v = F 1 ρ p + B2 8π + (B )B 4πρ + ν 2 v What makes it hard: ν 2 v Viscosity F Gravitation (B )B 4πρ Magnetic field

14 N 2 He + N +400 other Also should include chemistry HCO species and HCN 4500! e HCO + H 3 + H 3 O + H reactions CN e H 2 CN + e HNC Young Owl et al. (2000) And radiative transfer

15 Physical Domain Simulated Physical Domain Radiative Transfer, Telescope Effects Radiative Transfer, Telescope Effects Observations Statistical Tools Simulated Observations

16 (Relatively) Easy Physics

17 SDSS Real SDSS Simulation How well do simulations match data?

18 Sample Data S1 Padoan et al. (2006) MHD S2 Offner et al. (2008) HD+Gravity IC 348 Ridge et al. (2005) SFR, d=260 pc NGC 1333 Ridge et al. (2005) SFR, d=260 pc Ophiuchus A Ridge et al. (2005) SFR, d=120 pc

19 S1 S2 Images View Oph A NGC 1333 IC348

20 2+1= 3 But nevertheless...

21 Three-dimensional volumes

22 Visualization of 3D density fields is well-explored. Osirix 3D Slicer Insight Toolkit

23 Can we design one or more sensible distance functions? d(o 1,O 2 ) 0 for similar regions d(o 1,S 1 ) 0 for a dissimilar simulations Simulations are tuned to reproduce observational PDFs of variables

24 Theoretically Motivated Statistics Turbulent flows O [(v )v] O (ν 2 v) Re = VL ν 108 Structure Functions D p (l) = v(r) v(r + l) p Kolmogorov Theory (1941) gives D 2 () 2/3

25 694 Structure functions: PPPVVV space Observations: PPV space R. Shetty et al. Figure 4. Images of (a) N CO, (b) W, (c) NH2 and (d) the X factor of model n300-z03. Each side has a length of 20 pc. In (a) and (b), solid contours indicate log(n CO ) = 12, 14 and log(w) = 3, 1; dashed contours are log(n CO ) = 16.5 and log(w) = 1.5 (see the text and Fig. 2d). by 1 order of magnitude. Since the X factor directly depends on 21 Shetty et al. (2011) 5 10 cm, the X factor varies from 1020 to 1023 cm 2 K 1 1 2

26 Retrieving the Structure Function in PPV Velocity Channel Analysis and Velocity Coorindate Spectra by Lazarian, Pogosyan et al. (ref. 1,2) Principal Component Analysis by Heyer, Brunt and Scloerb (ref 3,4) σ jk = 1 n n i=0 I(r i,v j )I(r i,v j ) Variance Matrix σu = λu Solve eigenvalue problem

27 Identify eigenspectra which account for the variance Generate images using eigenspectra as weights PC n (r) = j u n (v j )I(r,v j ) D 2 (l) from autocorrelation width of u n l from autocorrelation width of PC n Heyer et al. (2006)

28 Observationally Motivated Statistics

29 Spectral Correlation Function Goodman, Rosolowsky, Padoan S p (l) = 1 v I(r,v) I(r + l,v) p v I(r,v) p + v I(r + l,v) p

30 SCF Results Observations agree Simulations don t

31 Structure Identification Algorithms Intensity Position Gaussclumps (Stutzki, Güsten and Kramer, ref. 1, ref. 2) like PSF Fitting Clumpfind (Williams, de Geus Blitz) like SExtractor

32 Clumpfind s default segmentation What are the objects?

33 Clumpfind Analysis Compare to stellar distributions Ikeda, Sunada, & Kitamura (2007)

34 Source extraction algorithms are not robust Clumpfind -- parameter changes C i = max j (V i V j ) 2 V i V j (c) Power Law Exponent (α) E. Lada et al. (1991) Salpeter Stutzki & Guesten (1990) Stepsize (Units of σ) Pineda, Rosolowsky & Goodman (2009)

35 Creating an Intensity Dendrogram (a.k.a. Reeb Graphs) Intensity Intensity Position arbitrary Emission Profile Dendrogram

36 1) Identify Local Maxima Intensity Intensity Position arbitrary Emission Profile Dendrogram

37 2) Contour emission from high to low; assign emission to maxima Intensity Intensity Position arbitrary Emission Profile Dendrogram

38 2) Contour emission from high to low; assign emission to maxima Intensity Intensity Position arbitrary Emission Profile Dendrogram

39 2) Contour emission from high to low; assign emission to maxima Intensity Intensity Position arbitrary Emission Profile Dendrogram

40 2) Contour emission from high to low; assign emission to maxima Intensity Intensity Position arbitrary Emission Profile Dendrogram

41 3) When regions join, connect branches of dendrogram Intensity Intensity Position arbitrary Emission Profile Dendrogram

42 3) When regions join, connect branches of dendrogram Intensity Intensity Position arbitrary Emission Profile Dendrogram

43 3) When regions join, connect branches of dendrogram Intensity Intensity Position arbitrary Emission Profile Dendrogram

44 4) Iterate until zero intensity is reached Intensity Intensity Position arbitrary Emission Profile Dendrogram

45

46 Dendro-fu = Every point on a dendrogram represents a simply connected contour in the data. The (statistical) moments over these contours give us properties. L CO = δa i C I i σ 2 v = i C (v i v) 2

47 Dendrogram-based Genus Measurement G(I 0 )=N region (I>I 0 ) N region (I<I 0 ) Normalize by PPV volume

48 Estimating Energetics: α VIR = 2U kin = 5σ2 vr U grav GM B=0; uniform density profile 4 15 Oph A 3 T mb (K) 10 5 Virial Parameter

49 S T mb (K) 4 2 Virial Parameter

50 The Orion Molecular Complex Wilson, et al.(2005)

51 !"#$%&(!"#$%&' )$%$*+"$, -./0102 /"$,,3$%+, CHAFF -$"45+"%&6#789+%4 -"&./%&#* 0)123%#. 5&"''9"#%'!"#"$%&"' Identifying GMCs in blended data using self-gravitation -45*6768 (&)"#*, (&)"#*+ Rosolowsky et al. (2008)

52 Moving into the realm of needing good statistics. To steal from one person is plagiarism, to steal from many is research. -- Steven Wright Feedback: