The Source and Lens of B

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1 The Source and Lens of B New Polarization Radio Data to Constrain the Source Structure and H 0 with LensCLEAN Olaf Wucknitz Astrophysics Seminar Potsdam University, Germany 5 July 2004

2 The source and lens of B The System B Time-delay and Hubble constant Radio interferometry LensCLEAN Lens model fits & Source structure Optical HST Data New radio data Polarization in B & in jets in general Summary titlepage introduction summary contents bonus back forward previous next fullscreen 1

The Lens B0218+357 titlepage introduction summary

3 The Lens B titlepage introduction summary contents bonus back forward previous next fullscreen 2

4 The Lens JVAS B (Facts) Time-delay known: 10.5 ± 0.4 d Smallest separation of all resolved lenses (335 mas) Two subcomponents each with separation of 1.4 mas Jet with potential components from ca. 1 mas to 1 arcsec Einstein ring with diameter 335 mas Single galaxy lens, no external shear Position of lensing galaxy not known with high accuracy titlepage introduction summary contents bonus back forward previous next fullscreen 3

B0218+357 with VLBI 8.4 GHz global VLBI (VLBA + EVN + 2 DSN) (Biggs et al.

5 B with VLBI 8.4 GHz global VLBI (VLBA + EVN + 2 DSN) (Biggs et al., 2003) titlepage introduction summary contents bonus back forward previous next fullscreen 4

6 Time Delay as Measure for H 0 true source different light paths α additional Shapiro-delay lens different light travel times ( time-delay T ) α α measurable if source variable observer H 0 T = f (lens model) titlepage introduction summary contents bonus back forward previous next fullscreen 5

7 Time Delay in B measurements of intensity linear polarization polarization angle simultaneous fit to all T = 10.5 ± 0.4 d (Biggs et al., 1999) titlepage introduction summary contents bonus back forward previous next fullscreen 6

8 Unknown Galaxy Position simple lens model: SIE H 0 depends on lens position 1 mas 1 % no constraint! titlepage introduction summary contents bonus back forward previous next fullscreen 7

9 Radio Interferometry titlepage introduction summary contents bonus back forward previous next fullscreen 8

10 Principles of Radio Interferometry Interferometers measure the Fourier transform Ĩ(u, v) of the true brightness distribution I(l, m). Ĩ(u,v) = dl dmi(l,m)e 2πi(ul+vm) Derive brightness distribution from inverse transform? I(l,m) = dudvĩ(u,v)e 2πi(ul+vm) u, v: separations of telescopes [λ] earth rotation tracks one track for each telescope pair titlepage introduction summary contents bonus back forward previous next fullscreen 9

w j Ĩ(u j,v j )e 2πi(u j l+v j m) w j e 2πi(u j l+v j m) I D (l,m) = (I B)(l,m)

11 Dirty Map, Dirty Beam Do the inverse transform including the measured visibilities only. Dirty map : I D (l,m) = j Dirty beam : B(l,m) = j Dirty map is convolution: w j Ĩ(u j,v j )e 2πi(u j l+v j m) w j e 2πi(u j l+v j m) I D (l,m) = (I B)(l,m) titlepage introduction summary contents bonus back forward previous next fullscreen 10

12 The CLEAN Method (Högbom 1974) Start with the dirty map Subtract dirty beam from the residual map shifted to the peaks Use loop gain of 0.1 to scale dirty beam Iterate until residuals become sufficiently small Add all the CLEAN components as δ peaks Convolve with a Gaussian titlepage introduction summary contents bonus back forward previous next fullscreen 11

13 0, 100, 2500 Iterations of CLEAN titlepage introduction summary contents bonus back forward previous next fullscreen 12

14 The LensCLEAN method Proposed by Kochanek & Narayan (1992) Improved by Wucknitz (2002, 2004) The idea arbitrary components in CLEAN consistent with lens model in LensCLEAN use residuals to find best lens model best fitting self-consistent model for source and lens Works for arbitrary source structure! titlepage introduction summary contents bonus back forward previous next fullscreen 13

15 LensCLEAN: Some More Details start scan of all lens positions start initial model for LensClean: classical fit of remaining parameters vary model parameters select next lens position LensClean with fixed lens model load uv data and calc./select Stokes fit compact components vary source position of compact comp. (re)grid and invert subtract all components from ungridded visibilities image plane loop find max. in residual dirty map find secondary images for all pixels (LenTil) calc. image positions & magnifications fit source flux analytically calculate residuals position converged? no convolve and grid visibilities inverse FFT divide by inv. FT of gridding conv. function calc. optimal source flux S for this position yes regrid? no subtract shifted beams from dirty map calc. final residuals yes continue? no yes (convolve with clean beam, build maps) self calibration loop self calibration with LensClean emission model build LensClean emission model no lens pos. converged? yes smooth residual function and fit for minimum lens mod. converged? yes no yes selfcal converged? no finished inspect maps of residuals as function of lens position yes all positions done? no titlepage introduction summary contents bonus back forward previous next fullscreen 14

16 Published Results for B : Lens Models Lens position (a) uniform weighting (b) natural weighting (Wucknitz, Biggs & Browne, 2004) titlepage introduction summary contents bonus back forward previous next fullscreen 15

17 Published Results for B : H 0 H 0 = 78 ± 6 kms 1 Mpc 1 titlepage introduction summary contents bonus back forward previous next fullscreen 16

18 Optical HST Data 5% 10% 5% 10% orbits of HST with ACS/WFC deepest image before Hubble UDF accuracy ca. 10 mas consistent with LensCLEAN York et al. (2004), astroph/ titlepage introduction summary contents bonus back forward previous next fullscreen 17

19 New VLA + Pie Town Data (2003) combination of Very Large Array Pie Town (VLBA) 14 h long track at 15 GHz improved resolution and sensitivity titlepage introduction summary contents bonus back forward previous next fullscreen 18

20 New CLEAN Maps natural weighting uniform weighting titlepage introduction summary contents bonus back forward previous next fullscreen 19

21 Lens Position old VLA dataset confidence limits 1,2,3,4,5σ new VLA+Pt dataset very very preliminary! confidence limits 5,10,15,20,25σ! titlepage introduction summary contents bonus back forward previous next fullscreen 20

Published Results for B0218+357: Source Structure lensed centre: 8.

22 Published Results for B : Source Structure lensed centre: 8.4 GHz VLA (Biggs et al., 2003) left: 15 GHz VLA (Wucknitz et al., 2004) right: 8.4 GHz VLBI (Biggs et al., 2003) new method to reconstruct source plane with LensCLEAN (Wucknitz et al., 2004) unlensed titlepage introduction summary contents bonus back forward previous next fullscreen 21

23 Source Structure from VLA+Pie Town data titlepage introduction summary contents bonus back forward previous next fullscreen 22

24 Polarization Most radio telescopes measure circular waves right-handed: R left-handed: L Stokes parameters I: total intensity I = (RR + LL )/2 V : circular pol. V = (RR LL )/2 Q, U: linear pol. Q = (RL + LR )/2 iu = (RL LR )/2 Linear polarization m: fractional linear pol. m = Q 2 +U 2 /I Q = mi cos2φ U = mi sin2φ titlepage introduction summary contents bonus back forward previous next fullscreen 23

25 Polarization in B GHz VLA (Biggs et al., 2003) 15 GHz VLA+Pt (new) titlepage introduction summary contents bonus back forward previous next fullscreen 24

26 Polarization Source Structure titlepage introduction summary contents bonus back forward previous next fullscreen 25

27 Polarization Source Structure (Core Removed) titlepage introduction summary contents bonus back forward previous next fullscreen 26

28 Polarization in Relativistic Magnetic Jets (Ch. Fendt) (Pariev et al., 2003) titlepage introduction summary contents bonus back forward previous next fullscreen 27

29 Summary LensCLEAN fits lens models position consistent with new optical data Hubble constant H 0 = 78 ± 6 kms 1 Mpc 1 Source structure Improved resolution and sensitivity with VLA + Pie Town Formally very high accuracy for lens position Polarization of ring & source Additional power-law models extinction, variability + time-delay Work continues... titlepage introduction summary contents bonus back forward previous next fullscreen 28

30 Contents 1 Contents 2 The Lens B The Lens JVAS B (Facts) 4 B with VLBI 5 Time Delay as Measure for H 0 6 Time Delay in B Unknown Galaxy Position 8 Radio Interferometry 9 Principles of Radio Interferometry 10 Dirty Map, Dirty Beam 11 The CLEAN Method (Högbom 1974) 12 0, 100, 2500 Iterations of CLEAN 13 The LensCLEAN method 14 LensCLEAN: Some More Details 15 Published Results for B : Lens Models 16 Published Results for B : H 0 titlepage introduction summary contents bonus back forward previous next fullscreen 29

31 17 Optical HST Data 18 New VLA + Pie Town Data (2003) 19 New CLEAN Maps 20 Lens Position 21 Published Results for B : Source Structure 22 Source Structure from VLA+Pie Town data 23 Polarization 24 Polarization in B Polarization Source Structure 26 Polarization Source Structure (Core Removed) 27 Polarization in Relativistic Magnetic Jets 28 Summary 29 Contents 31 Interferometrie: Grundlagen 32 Die visibilities titlepage introduction summary contents bonus back forward previous next fullscreen 30

32 Interferometrie: Grundlagen Signal von einer Quelle in Richtung k: E(r,t) = E 0 e i(k r+ωt) Korrelator kombiniert Signale zweier Teleskope: E(r 1 )E (r 2 ) = E 0 2 e ik (r 1 r 2 ) k = 2π λ 2π λ E 0 2 I 0 Intensität (l, m, 1 l 2 m 2 ) (l, m, 1) (kleines Feld) titlepage introduction summary contents bonus back forward previous next fullscreen 31

33 Die visibilities u = x 1 x 2 λ v = y 1 y 2 λ w = z 1 z 2 λ Messung Ĩ(u,v) = e 2πiw E(r 1 )E (r 2 ) Quelle Ĩ(u,v) = I 0 e 2πi(ul+vm) Für eine ausgedehnte Quelle mit Helligkeitsverteilung I(l, m): Ĩ(u,v) = dl dmi(l,m)e 2πi(ul+vm) Das ist eine Fourier-Transformation! titlepage introduction summary contents bonus back forward previous next fullscreen 32

Difference imaging and multi-channel Clean

Difference imaging and multi-channel Clean Olaf Wucknitz wucknitz@astro.uni-bonn.de Algorithms 2008, Oxford, 1 3 Dezember 2008 Finding gravitational lenses through variability [ Kochanek et al. (2006)