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+\newcommand{\this}{\mbox{\tt \task}} +\newcommand{\shorttype}{\mbox{COMPTEL}} +\newcommand{\doctype}{\mbox{COMPTEL interface}} +\newcommand{\version}{\mbox{draft}} +\newcommand{\calendar}{\mbox{17 January 2021}} +\newcommand{\auth}{\mbox{J\"urgen Kn\"odlseder}} +\newcommand{\approv}{\mbox{J\"urgen Kn\"odlseder}} +\def\sun{\hbox{$\odot$}} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Document definition +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\documentclass{article}[12pt,a4] +\usepackage{epsfig} +\usepackage{../manual} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Begin of document body +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} +\frontpage + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Introduction +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Introduction} + +The present document describes the COMPTEL specific interface that is implemented in \this. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Definitions +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Definitions} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Time} + +COMPTEL times are defined by two integers: TJD (Truncated Julian Days) and tics (1/8 ms). +COMPTEL times are given in UTC, and TJD:tics = 8393:0 converts into 1991-05-17T00:00:00 UTC +(see COM-RP-UNH-DRG-037). + +At 8798:28800000 (1992-06-25T01:00:00) the CGRO clock was corrected, before that date the +CGRO clock was 2.042144 seconds too fast. + +Conversion of COMPTEL times to a {\tt GTime} object is implemented by the {\tt gammalib::com\_time()} +function. The function applies the CGRO clock correction before 8798:28800000 and stores the +corrected time as UTC time. Specifically +\begin{equation} +{\rm MJD} = {\rm TJD} + 40000 + {\rm tics} \times \frac{0.000125}{86400} +\end{equation} +and for ${\rm TJD} < 8798$ or ${\rm TJD} = 8798$ and ${\rm tics} < 28800000$: +\begin{equation} +{\rm MJD}_{\rm corr} = {\rm MJD} - \frac{2.042144}{86400} +\end{equation} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Pulsar analysis +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Pulsar} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Barycentre correction} + +A Barycentre correction is applied to the event times. The formulae were extracted from the COMPASS +code {\tt pulphi01.pulphi.f}. + +{\tt pulphi01.pulphi.f} reads the pulsar ephemeris from a PPT using the {\tt ppptrd.f} function. Specifically +the following parameters are read +\begin{itemize} +\item $t_0$ is the reference epoch of the pulsar ephemeris (specified as TJD and tics); +\item $\nu_0$ is the frequency at the reference epoch; +\item $\dot{\nu}_0$ is the first frequency derivative at the reference epoch (specified in units of $10^{-15}$); +\item $\ddot{\nu}_0$ is the second frequency derivative at the reference epoch (specified in units of $10^{-20}$); +\item $\alpha$ is the Right Ascension of the pulsar; +\item $\delta$ is the Declination of the pulsar; +\item $\nu_{\rm obs}$ is the observed frequency at radio; +\item $DM$ is the radio Dispersion measure; +\item $\Phi_0$ is the zero phase defining main peak for EGRET. +\end{itemize} + +The function computes then the centre time of the observation using +\begin{equation} +t_{\rm obs} = \frac{1}{2} (t_{\rm start} + t_{\rm end}) +\end{equation} +where $t_{\rm start}$ and $t_{\rm end}$ are the start and stop time of the EVP dataset of +interest. +Using the {\tt pula32.f} function, the pulsar frequency and frequency derivative as well as the zero phase +are extrapolated to this centre time using +\begin{equation} +\nu = \nu_0 + \dot{\nu}_0 (t_{\rm obs} - t_0) + \frac{\ddot{\nu}_0}{2} (t_{\rm obs} - t_0)^2 , +\end{equation} +\begin{equation} +\dot{\nu} = \dot{\nu}_0 + \ddot{\nu}_0 (t_{\rm obs} - t_0) , +\end{equation} +and +\begin{equation} +\Phi = \Phi_0 + \nu_0 (t_{\rm obs} - t_0) + \frac{\dot{\nu}_0}{2} (t_{\rm obs} - t_0)^2 + \frac{\ddot{\nu}_0}{6} (t_{\rm obs} - t_0)^3 +\label{eq:phase-ephemeris} +\end{equation} +with $\Phi$ put in the interval $[0,1]$. +Note that the second frequency derivative is not updated, as it would required a third frequency derivative for +that. + +The subroutine then retrieves the Solar System Barycentre to CGRO spacecraft vector $\vec{s}$ based on the +information provided in the {\tt BVC} file. +Based on the event time $t_{\rm utc}$, given in the UTC time system, the routine uses the {\tt pulbcv.f} routine +to perform a linear interpolation between the two vectors $\vec{s}(i)$ and $\vec{s}(i+1)$ that enclose the event +time using +\begin{equation} +\vec{s} = (\vec{s}(i+1) - \vec{s}(i)) \frac{t_{\rm utc} - t(i) }{t(i+1) - t(i)} + \vec{s}(i) +\end{equation} +where $t(i)$ and $t(i+1)$ are the UTC times to which the vectors $i$ and $i+1$ correspond to. +If $t_{\rm utc}