COMPTEL response functions

Formulation

A COMPTEL event is characterised by an instrument direction spanned by the angles \((\chi, \psi, \bar{\varphi})\). \((\chi, \psi)\) is the direction of the photon after scattering in the upper detector plane, which is determined from the photon interaction locations in both detector planes, and

\[\bar{\varphi} = \arccos \left( 1 - \frac{m_\mathrm{e}c^2}{E_2} + \frac{m_\mathrm{e}c^2}{E_1+E_2} \right)\]

is the Compton scattering angle as inferred from the energy deposits \(E_1\) and \(E_2\) in the upper and lower detector planes, respectively. The measured energy of the photon is estimated from the sum

\[E' = E_1 + E_2\]

of the energy deposits in both detector planes. The probability that a photon which interacted in the upper detector plane will encounter a detector of the lower plane is described by \(DRG(\chi, \psi, \bar{\varphi})\), which also includes any cuts related to the removal of events coming from the Earth limb.

The COMPTEL response is factorised using

\[R(p',E',t'|p,E,t) = \frac{\tau}{T} \frac{DRX(p)}{T} \times DRG(\chi, \psi, \bar{\varphi}) \times IAQ(\chi, \psi, \bar{\varphi} | p, E)\]

where \(\tau\) is the lifetime in units of \(s\), \(T\) is the ontime in units of \(s\), \(DRX(p)\) is the exposure in units of \(cm^2 \, s\), and \(IAQ(\chi, \psi, \bar{\varphi} | p, E)\) quantifies the interaction probability for a Compton scattering in the upper detector plane followed by an interaction in the lower detector plane.

We note that \(IAQ(\chi, \psi, \bar{\varphi} | p, E)\) is azimuthally symmetric about the source direction, and the IAQ file is stored as a 2D FITS image providing the interaction probabilities as function of \(\bar{\varphi}\) and \(\varphi_\mathrm{geo}\) for a given energy range, where \(\varphi_\mathrm{geo}\) is the angular separation between \((\chi, \psi)\) and \(p\).

Analytical Instrument Response Functions

COMPTEL instrument response functions may be computed analytically, taken into account ground calibration information. Analytical computation is implemented in GammaLib, and is automatically performed when comobsbin is executed.

Simulated Instrument Response Functions

Alternatively, simulated instrument response functions can be used for the data analysis. Simulated instrument response functions can be specified in the observation definition file through the IAQ parameter as illustrated below.

<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
  <observation name="Crab" id="100001" instrument="COM">
    <parameter name="DRE" file="m50438_dre.fits"/>
    <parameter name="DRB" file="bgdlix_drb.fits"/>
    <parameter name="DRG" file="m34997_drg.fits"/>
    <parameter name="DRX" file="m32171_drx.fits"/>
    <parameter name="IAQ" value="SIM2(0.75-1.00)MeV(2)deg"/>
  </observation>
  ...
</observation_list>

A number of simulated Instrument Response Functions are shipped together with GammaLib. The table below specifies the possible options for the value field of COMPTEL observation definition files.

value

Energy range

Phibar binning

Type

SIM2(0.75-1.00)MeV(2)deg

0.75-1 MeV

2 deg

Continuum

SIM2(1.00-3.00)MeV(2)deg

1-3 MeV

2 deg

Continuum

SIM2(3.00-10.00)MeV(2)deg

3-10 MeV

2 deg

Continuum

SIM2(10.00-30.00)MeV(2)deg

10-30 MeV

2 deg

Continuum

SIM2(0.75-30.00)MeV(2)deg

0.75-30 MeV

2 deg

Continuum

SIM2(1.00-30.00)MeV(2)deg

1-30 MeV

2 deg

Continuum

SIM2(1.809)MeV(2)deg

1.809 MeV

2 deg

Line

SIM3(0.75-1.00)MeV(2)deg

0.75-1 MeV

2 deg

Continuum

SIM3(1.00-3.00)MeV(2)deg

1-3 MeV

2 deg

Continuum

SIM3(3.00-10.00)MeV(2)deg

3-10 MeV

2 deg

Continuum

SIM3(10.00-30.00)MeV(2)deg

10-30 MeV

2 deg

Continuum

SIM3(0.75-1.00)MeV(1)deg

0.75-1 MeV

1 deg

Continuum

SIM3(1.00-3.00)MeV(1)deg

1-3 MeV

1 deg

Continuum

SIM3(3.00-10.00)MeV(1)deg

3-10 MeV

1 deg

Continuum

SIM3(10.00-30.00)MeV(1)deg

10-30 MeV

1 deg

Continuum

SIM3(1.00-1.25)MeV(1)deg

1-1.25 MeV

1 deg

Continuum

SIM3(1.25-1.50)MeV(1)deg

1.25-1.5 MeV

1 deg

Continuum

SIM3(1.50-2.00)MeV(1)deg

1.5-2 MeV

1 deg

Continuum

SIM3(2.00-2.50)MeV(1)deg

2-2.5 MeV

1 deg

Continuum

SIM3(2.50-3.00)MeV(1)deg

2.5-3 MeV

1 deg

Continuum

SIM3(3.00-4.00)MeV(1)deg

3-4 MeV

1 deg

Continuum

SIM3(4.00-6.00)MeV(1)deg

4-6 MeV

1 deg

Continuum

SIM3(6.00-8.00)MeV(1)deg

6-8 MeV

1 deg

Continuum

SIM3(8.00-10.00)MeV(1)deg

8-10 MeV

1 deg

Continuum

SIM3(10.00-15.00)MeV(1)deg

10-15 MeV

1 deg

Continuum

SIM3(15.00-30.00)MeV(1)deg

15-30 MeV

1 deg

Continuum

SIM3(0.75-0.90)MeV(1)deg

0.75-0.9 MeV

1 deg

Continuum

SIM3(0.90-1.06)MeV(1)deg

0.9-1.06 MeV

1 deg

Continuum

SIM3(1.06-1.28)MeV(1)deg

1.06-1.28 MeV

1 deg

Continuum

SIM3(1.28-1.50)MeV(1)deg

1.28-1.50 MeV

1 deg

Continuum

SIM3(1.50-1.70)MeV(1)deg

1.50-1.70 MeV

1 deg

Continuum

SIM3(1.70-1.90)MeV(1)deg

1.70-1.90 MeV

1 deg

Continuum

SIM3(1.90-2.10)MeV(1)deg

1.90-2.10 MeV

1 deg

Continuum

SIM3(2.10-2.30)MeV(1)deg

2.10-2.30 MeV

1 deg

Continuum