Hard X-Ray Solar Flare Polarimetry

with RHESSI

M.L. McConnell1, D.M. Smith2, A.G. Emslie3, R.P. Lin2, and J.M. Ryan1

1Space Science Center, University of New Hampshire, Durham, NH2Space Sciences Laboratory, U.C. Berkeley, Berkeley, CA

3Physics Department, University of Alabama, Huntsville, AL

Polarization of Bremsstrahlung Radiation

Photons tend to be emitted perpendicular to electron’s plane of motion.

The polarization vector tends to be parallel to the direction of acceleration.

Degree of linear polarization can reach 80%.

Polarization in Solar Flares

The hard X-ray continuum is dominated by electron bremsstrahlung emission.

Measurements of hard X-ray polarization can shed light on the geometry of the acceleration process.

Models predict polarization levels as high as 20 or 30%.

Model parameters include :

1) pitch angle distribution

2) geometry of the B-field

3) viewing angle

Predictions for Solar Flare Polarization

Langer and Petrosian (1977)

Single vertical flux tube

Leach and Petrosian (1983)

Integrated over a loop

Basic Principles of Compton Polarimetry Basic Principles of Compton Polarimetry ((10 keV – 30 MeV)

Polarimetry relies on the fact that…

photons tend to Compton scatter at right angles to the

incident polarization vector

€

dσ =ro

2

2dΩ

′ E Eo

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

2Eo

′ E +

′ E Eo

−2sin2θcos2η⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

′ E =Eo

1+Eo

mc2 1−cosθ( )

is the Compton Scatter Angle

is the Azimuthal Scatter Angle

X

Y

Z

Eok

k'

incident photon

scattered photon

The Polarization SignatureThe Polarization Signature

For a fixed Compton scatter angle (), the azimuthal distribution of scattered photons contains the polarization signature.

The amplitude of the modulation defines the level of polarization.

The scattering angle corresponding to the minimum of the distribution defines the plane of polarization.

2000

1500

1000

500

0

Counts

350300250200150100500

Azimuthal Scatter Angle (degs)

C-max

C-min

polarization angle

€

C η( ) = A cos2(η−ϕ)+B

1

10

100

Asymmetry Ratio

1201008060Scattering Angle (degrees)

50 keV

100 keV

250 keV

500 keV

1 MeV

Asymmetry Ratio

Modulation FactorModulation Factor

2000

1500

1000

500

0

Counts

350300250200150100500

Azimuthal Scatter Angle (degs)

C-max

C-min

polarization angle

€

Q =Cmax−CminCmax+Cmin

=AB

Modulation Factor for a 100% polarized beam represents a figure-of-merit for the polarimeter :

€

C η( ) = A cos2(η−ϕ)+B

A

B

Minimum Detectable Polarization (MDP)Minimum Detectable Polarization (MDP)

S = source counting rate

B = background counting rate

T = observation time

= modulation factor for 100% polarization

€

MDP =nσ

Q100SS+B

T

Sensitivity can be improved by :

1) Increasing S (efficiency or geometric area)

2) Decreasing B

3) Increasing T

4) Increasing Q (optimizing geometry)

RHESSI as a Polarimeter (20 – 100 keV)

In the case of RHESSI, the scattering medium is a small (3 cm diameter by 3.5 cm high) cylinder of Be placed within the array of Ge detectors. The Ge detectors measure the distribution of the scattered radiation. The rotation of the spacecraft rotation provides an effective method for fine sampling of the scatter distribution, as well as a means of minimizing systematic effects.

Segmented Ge detectors

The segmented nature of the Ge detectors means that low energy photons can reach the rear Ge segments only by scattering off other material.

Monte Carlo Simulations

We have used a modified version of GEANT3 to carry out Monte Carlo simulations of the polarimetric capabilities of RHESSI.

A valid polarimeter event is one which produces a measurable energy deposit in the rear segment of Ge detectors 1, 8, or 9.

Detector 2 is not included because it is not currently operating as a segmented detector.

Detectors 3, 4, 5, 6 and 7 do not contribute significantly to the polarization signal and are therefore also excluded from the analysis.

We have simulated a very narrow beam (just covering the front surface area of the Be) to study the intrinsic polarimetry parameters of RHESSI.

A broader beam (covering the full front surface of the telescope tube) has been used to study the effects of scattering into the rear Ge segments.

The Polarization Signal - Simulated Results

40 keV

40 keV

80 keV

80 keV

Top row shows results for narrow incident

beam (no spacecraft scattering).

Bottom row shows results for wide

incident beam (with spacecraft scattering). Note the significant degradation of signal

at 80 keV.

Polarimeter Mode – Effective Area

The effective area is defined for both a narrow beam

directed towards the front surface of the Be scattering

block and a broad beam directed across the full front of the HESSI telescope tube.

The broad beam simulation incorporates the effects of

scattering of solar flux into the rear Ge segments, which

leads to an increase in effective area at higher

energies .

0.01

0.1

1

10

Effective Area (cm

2 )

10 100

Energy (keV)

RHESSI Polarimeter ModeEffective Area

Narrow Beam

Broad Beam

Polarimeter Mode – Modulation Factor

The modulation factor is a measure of the quality of the

polarization signal.

Here we can see that scattering of incident solar flux reduces the quality of the polarization signal. (The scattered flux is not

modulated.)

1.0

0.8

0.6

0.4

0.2

0.0

Modulation Factor (Q)

10 100

Energy (keV)

RHESSI Polarimeter ModeModulation Factor

Narrow Beam

Broad Beam

Polarimeter Mode – Figure of Merit

The figure-of-merit is a measure of the intrinsic capability to measure

polarization.

Here, it is defined as the product of (effective area)1/2 and the modulation factor.

As defined here, it does not incorporate the effects of

detector background.

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Effective Area (cm

2 )

10 100

Energy (keV)

RHESSI Polarimeter ModeFigure of Merit

Narrow Beam

Broad Beam

Ambient (Non-Flare) Background

The measured detector background at lower

energies is somewhat lower than was

expected based on pre-flight estimates using

data from the Ge detector on Wind/TGRS.

Data are shown here for the three detectors that are used in polarization

studies.0.01

2

4

6

80.1

2

4

6

81

2

4

6

810

cts s

-1

keV

-1

detector

-1

102 3 4 5 6 7 8

1002 3 4 5 6

Energy (keV)

Detector #1 - rear segment Detector #8 - rear segment Detector #9 - rear segment Pre-flight bgd estimate

HESSI Sensitivity to Solar Flare Polarization

Minimum Detectable Polarization (MDP)

For M-class flares, sensitivity levels of 20-40% may still be achievable in the lowest energy bands.

Candidate Flare EventsThere have been two X-class flares since the launch of RHESSI. Both

are currently under study, but no results have yet been attained. Shown below are the count rate time histories covering each event.

21-Apr-2002 : Class X1.5 : 00:59-02:51 UT

20-May-2002 : Class X2.1 : 15:08 - 15:38 UT

time intervalof flare

time intervalof flare

Summary

Addition of a Be scattering block provides HESSI with significant polarimetric capability.

Despite detrimental impact of the scattering of incident solar flux by the spacecraft, HESSI retains significant polarization sensitivity.

Polarization sensitivity can be less than a few percent for some X-class flares.

Work in progress:

1. Estimate of polarization sensitivities for specific flares.

2. Study of the impact of Earth-scattered flux.

3. Development of analysis tools.

4. Investigation of polarization sensitivity for non-solar sources (gamma-ray bursts and the Crab pulsar).