1. Compton Polarimetry In Gamma-ray Astronomy Jeng-Lwen, Chiu Institute of Physics, NTHU 2006/03/16 (following 2006/01/12)

2. Outline 1. Introduction 2. Polarized Gamma-Ray Emission Mechanisms 3. Potential Astronomical Sites of Polarized Gamma-Ray Emission 4. A Review of Gamma-Ray Polarimetric Instrumentation 5. Computer and Laboratory Tests of Novel Polarimetric Techniques 6. Conclusion

3. Introduction For the most part, the analysis of compact X-ray and gamma-ray sources has been confined to spectral characteristics and time variability. For the most part, the analysis of compact X-ray and gamma-ray sources has been confined to spectral characteristics and time variability. This analysis often allows two or more very different models to successfully explain the observations. This analysis often allows two or more very different models to successfully explain the observations. It is possible to double the number of observational parameters through measurements of the polarization angle and degree of linear polarization of the source emission to discriminate between the various models. It is possible to double the number of observational parameters through measurements of the polarization angle and degree of linear polarization of the source emission to discriminate between the various models.

4. Polarized Gamma-Ray Emission Magneto-Bremsstrahlung Radiation Magneto-Bremsstrahlung Radiation Cyclotron Emission Cyclotron Emission Synchrotron Emission Synchrotron Emission Curvature Radiation Curvature Radiation Bremsstrahlung Radiation Bremsstrahlung Radiation Compton Scattering Compton Scattering Magnetic Photon Splitting Magnetic Photon Splitting

5. Cyclotron Emission Synchrotron Emission

6. Bremsstrahlung Radiation

7. Compton Scattering

8. Magnetic photon splitting

9. Potential Astronomical Sites of Polarized Gamma-Ray Emission Gamma-Ray Bursts Gamma-Ray Bursts Pulsars Pulsars Solar Flares Solar Flares Other Possible Sites for Polarized Emission Other Possible Sites for Polarized Emission Crab Nebula Crab Nebula AGNs AGNs Galactic Black Hole Candidates Galactic Black Hole Candidates

10. Gamma-ray Pulsars Only 7 gamma-ray pulsars are known to exist. (e.g. Crab, Vela, Geminga (radio-quiet) ) Polarization characteristics of gamma-ray pulsars: rare information & difficult to collect. Optical polarization of Crab pulsar (Smith et al. 1988). Observations of the polarization of the pulsed optical emission: both the angle and the degree of polarization change during the period of the pulses.

14. The similarities in the polarization characteristics indicate that the pulses originate from two separate sources with the same emission mechanism. Polarization: the key to differentiating between polar cap models & outer gap models ?!

15. γ-Ray Polarization Instrumentation The measurement of the degree of linear polarization was first reported in 1950 by Metzger and Deustch, when they exploited the Compton scattering process to measure the asymmetry in the azimuthal distribution of scattered gamma-rays. The measurement of the degree of linear polarization was first reported in 1950 by Metzger and Deustch, when they exploited the Compton scattering process to measure the asymmetry in the azimuthal distribution of scattered gamma-rays. Since then polarimeters have been constructed with ever increasing sensitivities. Since then polarimeters have been constructed with ever increasing sensitivities. Several X-ray polarimeters but few dedicated gamma- ray polarimeters have been launched. Several X-ray polarimeters but few dedicated gamma- ray polarimeters have been launched.

16. The differential Compton cross-section, dσ, is the probability that a photon of energy E will suffer a collision with an electron in a medium in which the electron density is 1 cm -3. r 0 : classical electron radius m e : mass of an electron ξ/(ξ‘) : electric vector of the incident/(scattered) photon Θ : the angle between the electric vectors of incident and scattered photons θ/(Φ): the angle between the incident photon direction and the scattered photon/(electron) direction. η: the azimuthal angle of the scattered photon with respect to the electric vector of the incident photon

17. azimuthal angle of the scattered photon wrt. the electric vector of the incident photon electric vector angle between the incident photon direction and the scattered photon direction

18. After averaging over the electric vector of the scattered photon, the differential cross-section can be rewritten as (4.2) (Evans, 1955) For a fixed scattering angle, the cross-section will be at a maximum for those photons scattered at right angles to the direction of the electric vector of the incident photon. This will lead to an asymmetry in the number of photons scattered in directions parallel and orthogonal to the electric vector of a beam of photons incident on some scattering medium. By a suitable arrangement of detector elements this asymmetry can be used to determine the direction and degree of polarization of the beam.

20. Q polarimetric modulation factor : the response of the polarimeter to a 100% polarized beam of photons (Suffert 1959)

21. The theoretical form of the Q factor at an angle Φ with respect to the X’-axis, for a given polarization vector angle with respect to the X’-axis, Ψ ← ( Derived from (4.1) )

22. Computer and Laboratory Tests of Novel Polarimetric Techniques Polarization Dependent M-C Code Polarization Dependent M-C Code Polarization Data Analysis Polarization Data Analysis The Moving Mask Technique (MMT) The Moving Mask Technique (MMT) The Radial Bin Technique (RBT) The Radial Bin Technique (RBT) Systematic Modulation Effects Systematic Modulation Effects Effect of Non-Uniform Polarimetric Response Effect of Non-Uniform Polarimetric Response Effect of Off-Axis Incidence Effect of Off-Axis Incidence Effect of Background Noise Effect of Background Noise Effect of Pixellation Effect of Pixellation Laboratory Tests with Pixellated Detector Arrays Laboratory Tests with Pixellated Detector Arrays The Geometrical Optimization of a Pixellated Planar Polarimeter The Geometrical Optimization of a Pixellated Planar Polarimeter

23. Polarization Dependent M-C Code a Si(Li) detector is used as the scattering element and two Ge detectors are used as the analysers. the Swinyard et al. (1991) method: the Compton polarization algorithm is applied only to the first scattering of the incident photon

24. The scattering of even unpolarized photons will in general produce linearly polarized photons, which will in turn produce an azimuthally anisotropic distribution of subsequently scattered photons.  Any simulation in which Compton scattering is likely to play an important role should in principle include polarization effects. Several of the popular codes: Matt et al. (1996) for MCNP (Briesmeistel et al., 1993), Namito et al. (1993) for EGS4 (Nelson et al., 1985), Lei et al. (1995) and Garcia-Raffi et al. (1995) for GEANT3 (Brun et al., 1994) For energies below 750 keV where the chance of multiple scattering within the Si(Li) is high, the simulations have under predicted the Q factor.  The simulation predicts a lower performance than is measured experimentally below 750 keV. The velocity vectors of low-energy photons undergoing multiple scatters will tend to remain in the original plane of scattering. The azimuthal distribution of the second generation of scattered photons will also be anisotropic and will contribute to the Q factor. However, as stated above, the Compton polarization algorithm is only active for the first interaction, the simulation then reverts to its normal non-polarized state for any successive interactions. For higher energies, where a single scatter is more likely than multiple scatters, the simulations have successfully reproduced the experimental data as the distortion from this effect is small

25. Polarization Data Analysis The simple determination of the Q factor used in the classic Compton polarimeter data analysis cannot be used with non-rotational polarimeters such as COMPTEL. Consequently two analysis routines for determining the Q factor have evolved the Moving Mask Technique (MMT) and the Radial Bin Technique (RBT).

26. The Moving Mask Technique (MMT) each event is transformed onto a displacement plane showing the deviation in the detector X and Y-axis directions (ΔX, ΔY) between the two interactions. A mask is then applied to the data dividing the displacement plane into quadrants. The mask is rotated, usually in 2 ∘ or 5 ∘ steps, and the resultant distribution of Q(Φ) is fitted to the cos2Φ form given by Equation (4.10) to find the maximum Q factor and the angle of the polarization vector. (Nn(Φ) is the number of counts detected in the nth quadrant when the mask X-axis is at an angle Φ to the X-axis of the scatter plane )

27. Problem of MMT 1) the most significant is the non-independence of N n (Φ). 2) the smearing effect due to the broad binning size. A single event will be sampled many times during the analysis.  The Q(Φ) points will also be non-independent and so the variance in Q(Φ) cannot be used to obtain the errors in the determined Q factor and the polarization angle. One way to avoid the non-independent data points problem is to reduce the mask size (e.g., to 15 ∘ ) and move the masks in step size equals to the mask size. the smearing effect is also significantly reduced.

28. The Radial Bin Technique (RBT) The RBT tackles the problem of determining the Q factor by dividing up the displacement plane into a number of equal sized radial bins, usually 15 ∘ or 24 ∘ in size giving 24 or 15 radial bins, respectively. Each event is placed into its corresponding bin and the radial distribution is fitted to the expression : (P1: the amplitude of the curve; P2: the polarization angle; P3: the average height of the curve. ) All of the N(Φ) points are independent and thus the errors in each parameter can be simply determined from the variance of the points from the fitted curve. Minimum degradation in the Q factor vs. sufficiently large size as to ensure the best possible statistics for the Q(Φ) points.  Bin sizes of between 10 ∘ and 30 ∘ are suitable. Degree of linear polarization 1.1%2.9%10%

29. The above comparisons with analytical calculations have shown the validity of using either the Moving Mask Technique (MMT) or the Radial Bin Technique (RBT) to analyze the polarimetric distribution for a continuous and uniform detector plane in an ideal case. Practical limitations of a polarimeter & ways of removing their undesired side effects

30. Systematic Modulation Effects

31. Non- uniform As the distribution of events on the displacement plane is highly dependent upon the detector geometry, this will result in the distortion of the Q distribution, masking the polarimetric signature or even possibly creating a false result. Polarimeter calibration: The effect of the non- uniformity can be removed using the detector response to non-polarized photons.

32. Off-axis It is necessary to transform each point on the displacement plane onto a new displacement plane normal to the incident photon direction so the true polarimetric distribution. Assuming the incident direction is at (α,β) azimuth and zenith angles; (ΔX, ΔY, ΔZ) is the displacement in the coordinates of the polarimeter (or telescope) (ΔX’, ΔY’, ΔZ’) is the displacement in a coordinates whose Z’-axis is in the direction of the incident photon and the X’- axis is in the X-Y plane of the telescope coordinates. After the transform, one can proceed with the removal of off-axis and non-uniform response effects and perform the polarimetric analysis using either the MMT or RBT techniques. (By RBT)

33. Effect of Background Noise The minimum detectable polarization (MDP), at n-σ level. S F : the source flux in units of (photons/s*cm 2 ), B: the background flux in units of (counts/s), Q 100 : the modulation factor of the polarimeter to 100% polarized photons, A: the detection area in cm 2, ε: the detection efficiency T: the observation time in seconds. If background is not removed  Reduced Q value & introduce pseudo polarimetric modulation In order to minimize the background effect, its distribution has to be measured by an on/off observation strategy or derived by detailed modeling. Background noise, if well understood and properly removed, will not degrade the polarimetric characteristics, such as the detection efficiency and modulation factor, of a polarimeter. It will, however, reduce the sensitivity of a polarimeter statistically.

34. There are three principle pixel shapes which will tessellate to form a continuous detection plane: triangular pixels, square pixels and hexagonal pixels. The polarimetric analysis of a pixellated detector plane requires significant alteration of the RBT and takes the form of the Decoupled Ring Technique (DRT). Effect of Pixellation The DRT analysis is conducted by first selecting only those events where energy is deposited in two pixels. One pixel is then transformed onto the central pixel of a pixellated displacement plane. In this technique, the resultant distribution shows the displacement as pixels rather than in terms of ΔX and ΔY. Unfortunately, using pixellated detectors, it is impossible to determine the exact location of the interaction site. Thus, for the purposes of the DRT, the interaction is generally assumed to occur at the centre of the pixel. Radial binning cannot be applied in this technique because of the centering that has occurred due to pixellation.  The N(Φ) points occurring at the wrong Φ.

35. Effect of Pixellation In the DRT, the number of events in a displacement plane pixel is used instead of the number of events in a radial bin: Azimuthal distribution: N(Φ)  P(Φ) ( P(Φ): the number of events in a displacement plane pixel whose centre is Φ from the X-axis. ) Complications: 1) The pixels subtend a finite angle. The first ring of pixels that surround the central pixel, 1DR (1st Decoupled Ring), subtend the greatest angle, whilst those in subsequent rings subtend increasingly smaller angles. The important effect is that in general the 1DR ring will contain the highest number of events and will thus have the best statistics for fitting. The 1DR ring also subtends the largest angle and will thus suffer the greatest degree of smearing. 2). Events detected in the 1DR have a much broad range of scattered angle, while events detected in the 2DR or higher will have more narrowly restricted around 90 ∘, due to the finite thickness of the detector plane. cf. Fig 4.3  lead to higher Q factor. It is impossible to completely decouple the P(Φ) distribution for these cases. In practice the DRT is best suited to hexagonal pixels It is usually sufficient to only decouple the 1DR, as this is where the smearing is most apparent.

36. Effect of Pixellation (By RBT) Q=0.215 1DR Q=0.393 2DR The de-coupled ring method can be used, so as to maximise the sensitivity of the polarimeter.

37. Laboratory Tests with Pixellated Detector Arrays

38. The experimental setup of the polarization measurement. The electronic system has been set to only accept those events that occur in triple coincidence. 1). A signal must be received from the photomultiplier tube, indicating that one of the two emitted photons has been detected. 2). A second signal must be received from the central pixel due to the alignment of the collimator 3). Final signal must be received from one of the surrounding pixels. The selected photons are ~17% polarized (Hills, 1997), a polarization angle of approximately 120 ∘ to the module X- axis. Experiment (Hills 1997) 37 discrete CsI(Tl)-photodiode detectors housed in a spark eroded aluminum honeycomb structure.

39. Non-polPolarized

40. About the Test Simulation: GEANT M-C simulations were used to determine the module’s response to 100% polarized photons. For 1.173 and 1.332 MeV photons it yields Q 100 = 0.263.  For a 17% polarized beam as was used in the measurement, the expected Q factor is 0.0444. Results: The experimentally determined Q factor of 0.0356±0.0040 is in good agreement with this prediction and corresponds to Π=(13.6±1.7)% which is again in good agreement with the 17% polarization expected. The polarization angle should be approximately 120 ∘ and the determined value of (129.0±3.3) ∘ is only 2.7σ away.  A good agreement!! Conclusion: 1). it has demonstrated the ability of the simulations to successfully match both experimental data and analytical predications based on nuclear theory. This validates the calibration/correction approach developed for the analysis of data from more intricate detectors and telescopes, such as COMPTEL and INTEGRAL. 2). it has conclusively shown that a pixellated detector plane, such as those adopted for the INTEGRAL telescope is an effective polarimeter

41. The Geometrical Optimization of a Pixellated Planar Polarimeter

42. The product of the modulation factor Q and detection efficiency ε is normally called the figure of Merit (FOM) In general optimizing the design of a polarimeter is simply the process of achieving the best combination of the Q factor and the efficiency. Unfortunately an increase in one generally leads to a reduction in the other. Choice of scintillator: A single material for all elements shifts the effective energy band towards the higher energy. Such a behavior is due to the impossibility for the same material to be both a high efficiency scatter (for which low Z is recommended) and a highly efficient absorber (for which high Z is required).  To lower this limit, it is necessary to use different materials as scattering and absorbing elements. (e.g. CsI, CsF2, and Plastic ) Low-energy threshold: The low-energy threshold of the individual pixels is another crucial factor which determines the operational energy range of a polarimeter and it performance. 1). Hills (1997) studied the FOM as a function of the low-energy threshold for various incident energies in the case of a CsI-based polarimeter. It was found that the peak value of the FOM in CsI occurs at higher incident photon energies as the low-energy threshold increases, but remains at roughly a constant value. 2). Costa et al. (1995) found that the FOM dropped by a factor of 5 for a CaF2 polarimeter to Crab spectrum type incident photons by increasing the low-energy threshold from 5 keV to 30 keV.  the low energy threshold of individual pixels should be kept as low as possible so as to ensure that the polarimeter operates at low energies where astronomical sources are strongest and mostly polarized. Pixel size: Both the length (depth) and cross-section size of the pixel of the detector plane will greatly affect the performance of a polarimeter. The FOM tends towards a maximum for depths In terms of the pixel design, the scintillator depth should be kept as shallow as possible A smaller pixel size leads to better FOM

43. Pixel size --- Depth 5~7 cm 7 cm: option may offer an 8% better FOM 5 cm: the lower mass of the option should allow the area of the polarimeter to be approximately 40% larger  the expected sensitivities of polarimeters built around two such options should be very similar. The 5 cm bars will experience less optical photon attenuations and will be technically easier to manufacture.

44. Pixel size --- AF-distance Hexagonal: its size is represented by the Across-Flats (AF) distance (from one edge of the hexagon to the opposite edge). A smaller pixel size leads to better FOM The larger the pixel size the flatter (broad) the FOM curve For a 3 mm AF size the sensitive range is between 300 and 800 keV.

45. Optimum pixel configuration maximizing the polarimetric sensitivity of a planar polarimeter using CsI pixels

46. Conclusion (1) The measurements of the polarization angle and degree of linear polarization of the source emission will help us identify the mechanism. The measurements of the polarization angle and degree of linear polarization of the source emission will help us identify the mechanism. Optical polarization of Crab helps identify the mechanism. Optical polarization of Crab helps identify the mechanism.  Gamma-ray polarization will be the key to differentiating between polar cap models and outer gap models The Compton scattering process can be exploited to measure the asymmetry in the azimuthal distribution of scattered gamma rays. The Compton scattering process can be exploited to measure the asymmetry in the azimuthal distribution of scattered gamma rays.  Polarimetric modulation factor Q

47. Conclusion (2) The recent developments in polarimetric techniques, in both data The recent developments in polarimetric techniques, in both data analysis and instrumentation, have been discussed. It is important to incorporate the Compton polarimetric algorithm into a M-C code in full, otherwise significant discrepancies from experimental results will occur at low energies. It is important to incorporate the Compton polarimetric algorithm into a M-C code in full, otherwise significant discrepancies from experimental results will occur at low energies. For a continuous detection plane, analytical calculations have shown the validity of using either the MMT or the RBT to analyse polarimetric distributions. For a continuous detection plane, analytical calculations have shown the validity of using either the MMT or the RBT to analyse polarimetric distributions. For pixellated detector plane, it is necessary to use the DRT and this type of analysis is best suited to hexagonal tessellation (square also). For pixellated detector plane, it is necessary to use the DRT and this type of analysis is best suited to hexagonal tessellation (square also). Systematic Modulation Effects (e.g. Non-Uniform Polarimetric Response, Off- Axis Incidence, Background Noise, Pixellation) could be removed or reduced by calibration. Systematic Modulation Effects (e.g. Non-Uniform Polarimetric Response, Off- Axis Incidence, Background Noise, Pixellation) could be removed or reduced by calibration. The results of the tests made by Hills (1997) & Kroeger et al. (1997) showed the good agreement among simulations, experimental data, and analytical prediction. The results of the tests made by Hills (1997) & Kroeger et al. (1997) showed the good agreement among simulations, experimental data, and analytical prediction. The Optimum pixel configuration has been tested by FOM. (a long bar) The Optimum pixel configuration has been tested by FOM. (a long bar)

48. Reference Lei, F., Dean, A. J., and Hills, G. L.: 1997, Space Science Reviews 82, 309. Lei, F., Dean, A. J., and Hills, G. L.: 1997, Space Science Reviews 82, 309. ~ Thank You ~

50. 1DR

54. used to scatter photons from the source into a detector at B. rotated about Φ until a maximum is found in the coincidence counts between A and B.

59. X’ Y’ Z’ Φ