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The bug lay in the code that computes the exposure averaged PSF. This is given by
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{latex}
\newcommand{\e}{\varepsilon}
\newcommand{\Int}{{\displaystyle \int}}
\begin{eqnarray}
P(\psi, \e) &=& \frac{\Int dt P(\psi, \e, \theta) A(\e, \theta)}
{\Int dt A(\e, \theta)}\\
&=& \frac{\Int d\theta P(\psi, \e, \theta(t))
A(\e, \theta(t))|\partial\theta/\partial t|^{-1}}
{\Int d\theta A(\e, \theta(t))
|\partial\theta/\partial t|^{-1}}
\end{eqnarray}
{latex} |
Here
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$P${latex}$P${latex} |
and
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$A${latex}$A${latex} |
are the PSF and effective area, respectively, and
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{latex}$\theta=\theta(t)${latex} |
is the angle of the source relative to the instrument z-axis. The phi-dependence of
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$P${latex}$P${latex} |
and
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$A${latex}$A${latex} |
is suppressed for clarity.
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{latex}$\psi${latex} |
is the angle between true and measured photon direction, and
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{latex}$\varepsilon${latex} |
is the photon energy. In the second line of the above equation, the integrals have been recast as integrations over theta. These integrations are performed using the livetime cubes computed with gtltcube.
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One can estimate the impact of the theta=70 deg cutoff by running gtexpcube2 with the option thmax=180 in the nominal case (this is the default) and thmax=70 in the truncation case. Assuming a photon index of -2, which Josh used in his gtobssim runs, one can estimate the expected fractional offset in measured flux (Fmeas) relative to the MC value (Fmc), (Fmeas - Fmc)/Fmc, using the spectrally weighted exposures, exposure
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{latex}$= \left.\int \varepsilon^{-2} A(\varepsilon, \theta(t)) dt d\varepsilon\right/\int \varepsilon^{-2} d\varepsilon${latex} |
, and computing (exposure180 - exposure70)/exposure70.
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