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Compton Polarimetry In Gamma ray Astronomy

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Compton Polarimetry In Gamma ray Astronomy Powered By Docstoc
					Compton Polarimetry
  In Gamma-ray
    Astronomy

                  Jeng-Lwen, Chiu
       Institute of Physics, NTHU
                       2006/01/12
                   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
                    Introduction
   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.

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




Synchrotron Emission
Bremsstrahlung Radiation
Compton
Scattering
Magnetic photon splitting
     Potential Astronomical Sites of
    Polarized Gamma-Ray Emission

 Gamma-Ray Bursts
 Pulsars
 Solar Flares
 Other Possible Sites for Polarized Emission
   Crab Nebula
   AGNs
   Galactic Black Hole Candidates
           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.
• 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 ?!
γ-Ray Polarization Instrumentation
   The measurement of the degree of linear polarization of
    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.

   Several X-ray polarimeters but few dedicated gamma-
    ray polarimeters have been launched.
• 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.




   ξ/(ξ‘) : electric vector of the incident/(scattered) photon
   Φ : the angle between incident and scattered photons
   r0 : classical electron radius
   me : mass of an electron
   θ: the angle between the incident photon direction and the scattered photon
        direction.
   η: the azimuthal angle of the scattered photon with respect to the electric
        vector of the incident photon
   electric vector




angle between the incident
photon direction and the
scattered photon direction




                     azimuthal angle of
                     the scattered photon
                     wrt. the electric vector of
                     the incident photon
• 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.
used to scatter photons
from the source into a
detector at B.




  rotated about η until a maximum is
  found in the coincidence counts
  between A and B.
Q polarimetric modulation
factor : the response of the
polarimeter to a 100%
polarized beam of photons
(Suffert 1959)
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
Computer and Laboratory Tests of
 Novel Polarimetric Techniques
   Polarization Dependent M-C Code
   Polarization Data Analysis
     The Moving Mask Technique (MMT)
     The Radial Bin Technique (RBT)
   Systematic Modulation Effects
     Effect of Non-Uniform Polarimetric Response
     Effect of Off-Axis Incidence
     Effect of Background Noise
     Effect of Pixellation
   Laboratory Tests with Pixellated Detector Arrays
   The Geometrical Optimization of a Pixellated Planar
    Polarimeter
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
  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).
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.
              Problem of MMT
1) the most significant is the non-independence of Nn(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.
               The Radial Bin Technique (RBT)
                                                                                                  1.1%   2.9%      10%


       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. )

                                                                                                   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.
    All of the N(Φ) points are independent
  and thus the errors in each parameter can be                                                Degree of
  simply determined from the variance of the                                                  linear
  points from the fitted curve.                                                               polarization
• 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
Systematic Modulation Effects
  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.
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)
            Effect of Background Noise
   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.

                                                                    If background is not removed
                                                                     Reduced Q value &
                                                                    introduce pseudo polarimetric
                                                                    modulation


The minimum detectable polarization (MDP), at n-σ level.
 SF: the source flux in units of (photons/s*cm2),                     In order to minimize the
 B: the background flux in units of (counts/s),                     background effect, its distribution
 Q100: the modulation factor of the polarimeter to 100% polarized
         photons,                                                   has to be measured by an on/off
 A: the detection area in cm2,                                      observation strategy or derived by
 ε: the detection efficiency                                        detailed modeling.
 T: the observation time in seconds.
                   Effect of Pixellation
• 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).

        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.
                          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 ring, as this is where the smearing is most apparent.
                         Effect of Pixellation
                                                           Q=0.215
                                                           1DR




                                                           Q=0.393
                                                           2DR




(By RBT)




           The de-coupled ring method can be used, so as to maximise the sensitivity of the polarimeter.
   Laboratory Tests
with Pixellated Detector Arrays
         Experiment                          (Hills 1997)


 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.
                                                                          The experimental setup of the polarization measurement.

37 discrete CsI(Tl)-photodiode detectors housed in a spark eroded aluminum honeycomb structure.
Non-pol   Polarized
                          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 Q100 = 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
The Geometrical Optimization
  of a Pixellated Planar Polarimeter
  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
Pixel size --- Depth
                       5~7 cm
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).
Optimum pixel configuration
maximizing the polarimetric sensitivity of a
   planar polarimeter using CsI pixels
                Conclusion (1)
 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.
 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.
 Polarimetric modulation factor Q
                      Conclusion (2)
  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.
 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).
 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 Optimum pixel configuration has been tested by FOM. (a long
    bar)
                  Reference
   Lei, F., Dean, A. J., and Hills, G. L.: 1997,
    Space Science Reviews 82, 309.




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