X-ray Imaging Polarimetry

Transcription

1 X-ray Imaging Polarimetry Jacco Vink University of Amsterdam

2 Introduction >2020: A new era in X-ray astronomy: high resolution spectroscopy (XARM + Athena) X-ray polarisation X-ray polarisation: magnetic field topology & scattering process geometry This talk A bit on supernova remnant X-ray polarisation Exploring imaging polarimetry How to make optimum use of data 2

3 X-ray imaging polarimetry Imaging: Important for isolating source and background: point sources For exploring spatial variation in extended sources C.f.: imaging spectroscopy really started with ASCA Allowed the identification of X-ray synchrotron emission from SNRs Imaging polarisation Necessary if extended sources not uniformly polarised! Variation in polarisation signal Enhance signal to noise of signal: get rid of contamination from unpolarised regions Chandra ASCA Koyama+ 1995, Nature 3

4 Color: polarisation direction Braun, Gull, Perley, Nat ApJ A Cassiopeia A in Radio Polarised intensity Anderson, Keohane, Rudnick, 1995 Young SNRs: radial 4% level Old SNRs: tangential polarisation Extracting large region: no polarisation signal 4

5 Measured polarisation fraction young SNRs Tycho s SNR, Dickel+ 91 Object Typical Peak Orientation B Remarks References RCW 86 8% 15% radial 22 cm some regions < 3% Dickel et al. (2001) SN % 60% mostly radial 20 cm peak not in X-ray rims Reynoso et al. (2013) SN % 25% radial/fine structured (4 00 ) 6 cm peak at limbs Dickel et al. (1991) SN % 12% (?) radial/fine structured (20 00 ) 6 cm DeLaney et al. (2002) Cas A 5% 20% radial 6 cm outer plateau 9% Braun et al. (1987); Anderson et al. (1995) G % 17 ± 3% radial 6 cm Faraday rotation a ected? De Horta et al. (2014) 5

6 Supernova remnants Lower surface brightness/larger/older Polarization degree Dickel 1990 Younger SNRs have lower polarisation degree: Magnetic fields are more turbulent! 6

7 X-ray polarisation fraction: similar or not to radio? XMM In blue: X-ray synchrotron dominated likely polarised Why less polarised: Probe region near shock front more turbulence less polarised Why more polarised: Smaller regions less line of sight depolarisation Steeper synchrotron spectrum more magnetic field sensitive 7

8 Sensitivity to magnetic field topology Assume magnetic field is highly turbulent db/b 1 Electron spectrum near cut-off At peaks: emitting X-ray synchrotron At troughs: no X-ray synchrotron Hence: X-ray synchrotron does not sample total magnetic field but only peaks! More polarisation expected even though field turbulent Depends sensitively on spatial scale of turbulence (see Bykov+ 2009) 8

9 How to deal with X-ray imaging polarisation data? Muleri χ 2 / ndf / 97 C 608 ± 4.4 M ± 7.5 Phase ± Phi (rad) Traditional approach: Extract data from region Make modulation curve and fit using X^2 minimisation Disadvantage: Assume prior knowledge about suitable regions Depolarisation due to regions of opposite polarity Time consuming (how many regions do you want to try?) 9

10 X-ray Imaging polarimetry p Advocated here: use estimators of Stokes parameters I, Q, U Definition Stokes parameters based on electric field: E x =E 0x cos(kz E y =E 0y cos(kz!t + x (t)),!t + y (t)). I = c 8 < E2 0x > + < E2 0y >, Q = c 8 < E2 0x > < E2 0y >, U = c 8 < 2E 0xE 0y cos >, V = c 8 < 2E 0xE 0y sin >, X-ray polarimetry (gas detector), indirect probe of E-field: photo-electron direction cos 2 modulated with E-field photo-electron direction detected with certain error 10

11 Photon-by-photon estimator of polarisation Take alpha=direction of photo-electron See Kislat et al Taking into account cos 2 modulation one finds the following estimators I N = Q N =2 U N =2 NX 1 = N, i=1 NX X cos 2 ( i ) sin 2 ( i ) = 2 cos(2 i ), i=1 XNX X X 2 sin i cos i = 2 sin(2 i ). i=1 i i The reason Xfor introducing an Xadditional factor 2 Note the factor 2! (it corrects for the cos 2 modulation of alpha) Very similar to Rayleigh method for pulsation detection! The variance is given by NX < IN 2 >= 1 = N, i=1 NX X < Q 2 N >=2 (cos 2 ( i ) sin 2 ( i )) 2 = 4 cos 2 (2 i ), i=1 NX X < UN 2 >=2 (2 sin i cos i ) 2 = 4 sin 2 (2 i ). i=1 i i The question is now whether Eq. 19 are proper estim This can be calculated for each pixel: polarisation maps As this concerns summations: images can be easily rebinned! 11

12 Monte-Carlo simulation Cas A Set-up: heuristic model test if pdf dilutes signal opposite polarisation angles Input model: Outer ring 15% polarised Inner region 5% polarised Opposite angles Output: directions recovered only S/N>3 shown polarisation fractions lower than input (as expected) Stokes I Polarised fraction Polarised intensity Significance 12

13 Monte-Carlo simulation Cas A Stokes Q Stokes U 13

14 Monte-Carlo of Bykov s model Model for slice of Tycho s SNR shock Full calculations assuming B-field turbulence model 14

15 Photo-electron direction errors Xipe Yellow Book Photo-electron direction difficult to measure: dilutes polarisation signal At 4 kev: a 100% polarised source will have 45% polarisation 15

16 Photo-electron direction errors II blue: monte carlo using Δα red: measurements (Muleri+ 2010) In simulation: attach random errors to alpha Needed some reverse engineering Ansatz: error scales with 1/ E 1/ N el (N electrons in electron cloud) Error in simulation assumed to be gaussian: = / p E/4keV Reproduces calibration measurements reasonably 16

17 Correcting for polarisation errors How to go from measured X polarisation/modulation fractions to intrinsic fractions? For narrow band Ximages: Correct for error after data extraction But what if signal is weak and one needs whole 2-7 kev band pass? One way: correct on a photon by photon base! X Q N =2 X U N =2 i i f (E i ) cos(2 i ), f (E i ) sin(2 i ). < Q 2 N >=4 X < U 2 N >=4 X i i f (E i ) 2 cos 2 (2 i ), f (E i ) 2 sin 2 (2 i ). f(e i ) is energy dependent correction factor estimate for f(e): f(e) =1/ 43%(E 1.5keV) 0.4 future: event list could contain f that depends on quality of electron cloud 17

18 Further applications This talk: concentrated on imaging However, method can also be applied to spectra: calculate Q, U in each spectral bin timing: calculate Q, U in each time bin For spectra: one can obtain a spectral/polarisation intensity For line-rich Cas A: pick out polarisation signal outside 4-6 kev band Software issues/data and modeling event lists formats should be agreed upon: - alpha column? - alpha definition (raw + ra/dec definition data and modelling: - xspec/spex etc should be able to model polarisation -for example: fit two power laws with different polarisation fraction 18

19 Summary XIPE/IXPE/eXTPE: for the first time X-ray imaging polarimetry Important for SNRs and PWNe (see Bucciantini talk) and perhaps later: clusters of galaxies For SNRs: probe B-field turbulence near shock fronts (Cas A, Tycho, SN1006 ) Not a priori clear whether polarisation fraction higher or lower than radio How to deal with polarisation? Advocated here: - Making maps of Q,U estimators based on photon-by-photon statistics - Allowing energy-dependent correction factor f(e) Method also applicable for: spectra and timing To think about: further extensions of spectral modelling codes 19