Commit 642919010ffd6380ac2b288a6b14923e3776a8aa
1 parent
751b558b
Add document describing the COMPTEL interface
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doc/dev/inst/com/com-pulsar-phase.eps
0 → 100644
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| 2038 | +stroke | |
| 2039 | +grestore | |
| 2040 | +0.800 setlinewidth | |
| 2041 | +0 setlinejoin | |
| 2042 | +[] 0 setdash | |
| 2043 | +0.000 setgray | |
| 2044 | +gsave | |
| 2045 | +57.6 38.016 m | |
| 2046 | +57.6 304.128 l | |
| 2047 | +stroke | |
| 2048 | +grestore | |
| 2049 | +gsave | |
| 2050 | +414.72 38.016 m | |
| 2051 | +414.72 304.128 l | |
| 2052 | +stroke | |
| 2053 | +grestore | |
| 2054 | +gsave | |
| 2055 | +57.6 38.016 m | |
| 2056 | +414.72 38.016 l | |
| 2057 | +stroke | |
| 2058 | +grestore | |
| 2059 | +gsave | |
| 2060 | +57.6 304.128 m | |
| 2061 | +414.72 304.128 l | |
| 2062 | +stroke | |
| 2063 | +grestore | |
| 2064 | + | |
| 2065 | +end | |
| 2066 | +showpage | ... | ... |
doc/dev/inst/com/gammalib_com.tex
0 → 100644
| 1 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 2 | +% GammaLib COMPTEL Interface | |
| 3 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 4 | + | |
| 5 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 6 | +% Definitions for manual package | |
| 7 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 8 | +\newcommand{\task}{\mbox{GammaLib}} | |
| 9 | +\newcommand{\this}{\mbox{\tt \task}} | |
| 10 | +\newcommand{\shorttype}{\mbox{COMPTEL}} | |
| 11 | +\newcommand{\doctype}{\mbox{COMPTEL interface}} | |
| 12 | +\newcommand{\version}{\mbox{draft}} | |
| 13 | +\newcommand{\calendar}{\mbox{17 January 2021}} | |
| 14 | +\newcommand{\auth}{\mbox{J\"urgen Kn\"odlseder}} | |
| 15 | +\newcommand{\approv}{\mbox{J\"urgen Kn\"odlseder}} | |
| 16 | +\def\sun{\hbox{$\odot$}} | |
| 17 | + | |
| 18 | + | |
| 19 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 20 | +% Document definition | |
| 21 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 22 | +\documentclass{article}[12pt,a4] | |
| 23 | +\usepackage{epsfig} | |
| 24 | +\usepackage{../manual} | |
| 25 | + | |
| 26 | + | |
| 27 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 28 | +% Begin of document body | |
| 29 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 30 | +\begin{document} | |
| 31 | +\frontpage | |
| 32 | + | |
| 33 | + | |
| 34 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 35 | +% Introduction | |
| 36 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 37 | +\section{Introduction} | |
| 38 | + | |
| 39 | +The present document describes the COMPTEL specific interface that is implemented in \this. | |
| 40 | + | |
| 41 | + | |
| 42 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 43 | +% Definitions | |
| 44 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 45 | +\section{Definitions} | |
| 46 | + | |
| 47 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 48 | +\subsection{Time} | |
| 49 | + | |
| 50 | +COMPTEL times are defined by two integers: TJD (Truncated Julian Days) and tics (1/8 ms). | |
| 51 | +COMPTEL times are given in UTC, and TJD:tics = 8393:0 converts into 1991-05-17T00:00:00 UTC | |
| 52 | +(see COM-RP-UNH-DRG-037). | |
| 53 | + | |
| 54 | +At 8798:28800000 (1992-06-25T01:00:00) the CGRO clock was corrected, before that date the | |
| 55 | +CGRO clock was 2.042144 seconds too fast. | |
| 56 | + | |
| 57 | +Conversion of COMPTEL times to a {\tt GTime} object is implemented by the {\tt gammalib::com\_time()} | |
| 58 | +function. The function applies the CGRO clock correction before 8798:28800000 and stores the | |
| 59 | +corrected time as UTC time. Specifically | |
| 60 | +\begin{equation} | |
| 61 | +{\rm MJD} = {\rm TJD} + 40000 + {\rm tics} \times \frac{0.000125}{86400} | |
| 62 | +\end{equation} | |
| 63 | +and for ${\rm TJD} < 8798$ or ${\rm TJD} = 8798$ and ${\rm tics} < 28800000$: | |
| 64 | +\begin{equation} | |
| 65 | +{\rm MJD}_{\rm corr} = {\rm MJD} - \frac{2.042144}{86400} | |
| 66 | +\end{equation} | |
| 67 | + | |
| 68 | + | |
| 69 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 70 | +% Pulsar analysis | |
| 71 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 72 | +\section{Pulsar} | |
| 73 | + | |
| 74 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 75 | +\subsection{Barycentre correction} | |
| 76 | + | |
| 77 | +A Barycentre correction is applied to the event times. The formulae were extracted from the COMPASS | |
| 78 | +code {\tt pulphi01.pulphi.f}. | |
| 79 | + | |
| 80 | +{\tt pulphi01.pulphi.f} reads the pulsar ephemeris from a PPT using the {\tt ppptrd.f} function. Specifically | |
| 81 | +the following parameters are read | |
| 82 | +\begin{itemize} | |
| 83 | +\item $t_0$ is the reference epoch of the pulsar ephemeris (specified as TJD and tics); | |
| 84 | +\item $\nu_0$ is the frequency at the reference epoch; | |
| 85 | +\item $\dot{\nu}_0$ is the first frequency derivative at the reference epoch (specified in units of $10^{-15}$); | |
| 86 | +\item $\ddot{\nu}_0$ is the second frequency derivative at the reference epoch (specified in units of $10^{-20}$); | |
| 87 | +\item $\alpha$ is the Right Ascension of the pulsar; | |
| 88 | +\item $\delta$ is the Declination of the pulsar; | |
| 89 | +\item $\nu_{\rm obs}$ is the observed frequency at radio; | |
| 90 | +\item $DM$ is the radio Dispersion measure; | |
| 91 | +\item $\Phi_0$ is the zero phase defining main peak for EGRET. | |
| 92 | +\end{itemize} | |
| 93 | + | |
| 94 | +The function computes then the centre time of the observation using | |
| 95 | +\begin{equation} | |
| 96 | +t_{\rm obs} = \frac{1}{2} (t_{\rm start} + t_{\rm end}) | |
| 97 | +\end{equation} | |
| 98 | +where $t_{\rm start}$ and $t_{\rm end}$ are the start and stop time of the EVP dataset of | |
| 99 | +interest. | |
| 100 | +Using the {\tt pula32.f} function, the pulsar frequency and frequency derivative as well as the zero phase | |
| 101 | +are extrapolated to this centre time using | |
| 102 | +\begin{equation} | |
| 103 | +\nu = \nu_0 + \dot{\nu}_0 (t_{\rm obs} - t_0) + \frac{\ddot{\nu}_0}{2} (t_{\rm obs} - t_0)^2 , | |
| 104 | +\end{equation} | |
| 105 | +\begin{equation} | |
| 106 | +\dot{\nu} = \dot{\nu}_0 + \ddot{\nu}_0 (t_{\rm obs} - t_0) , | |
| 107 | +\end{equation} | |
| 108 | +and | |
| 109 | +\begin{equation} | |
| 110 | +\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 | |
| 111 | +\label{eq:phase-ephemeris} | |
| 112 | +\end{equation} | |
| 113 | +with $\Phi$ put in the interval $[0,1]$. | |
| 114 | +Note that the second frequency derivative is not updated, as it would required a third frequency derivative for | |
| 115 | +that. | |
| 116 | + | |
| 117 | +The subroutine then retrieves the Solar System Barycentre to CGRO spacecraft vector $\vec{s}$ based on the | |
| 118 | +information provided in the {\tt BVC} file. | |
| 119 | +Based on the event time $t_{\rm utc}$, given in the UTC time system, the routine uses the {\tt pulbcv.f} routine | |
| 120 | +to perform a linear interpolation between the two vectors $\vec{s}(i)$ and $\vec{s}(i+1)$ that enclose the event | |
| 121 | +time using | |
| 122 | +\begin{equation} | |
| 123 | +\vec{s} = (\vec{s}(i+1) - \vec{s}(i)) \frac{t_{\rm utc} - t(i) }{t(i+1) - t(i)} + \vec{s}(i) | |
| 124 | +\end{equation} | |
| 125 | +where $t(i)$ and $t(i+1)$ are the UTC times to which the vectors $i$ and $i+1$ correspond to. | |
| 126 | +If $t_{\rm utc}<t(0)$ then the first vector in the file is returned, if $t_{\rm utc}\ge t(N)$ then the last vector | |
| 127 | +is returned, where $N$ is the number of BVC vectors in the {\tt BVC} file. | |
| 128 | +Note that the {\tt BVC} file specifies $\vec{s}$ in units of micro light seconds. | |
| 129 | + | |
| 130 | +The celestial vector of the pulsar position is then computed using | |
| 131 | +\begin{equation} | |
| 132 | +\vec{p} = \left\{ \cos \delta \cos \alpha, \cos \delta \sin \alpha, \sin \delta \right\} | |
| 133 | +\end{equation} | |
| 134 | +where $\alpha$ and $\delta$ are the Right Ascension and Declination of the pulsar. | |
| 135 | + | |
| 136 | +The photon arrival time in the Solar System Barycentre $t_{\rm sbb}$, given in Barycentric Dynamic | |
| 137 | +Time (TDB), is then computed from the event time $t_{\rm utc}$ in the subroutine {\tt pula04.f} using | |
| 138 | +\begin{equation} | |
| 139 | +t_{\rm sbb} = t_{\rm utc} + \Delta t_{\rm travel} - \Delta t_{\rm relativistic} + \Delta t_{\rm system} | |
| 140 | +\end{equation} | |
| 141 | +where | |
| 142 | +\begin{equation} | |
| 143 | +\Delta t_{\rm travel} = 10^{-6} \times \vec{s} \cdot \vec{p} | |
| 144 | +\end{equation} | |
| 145 | +is the light travel time from the CGRO to the Solar System Barycentre along the pulsar direction, | |
| 146 | +\begin{equation} | |
| 147 | +\Delta t_{\rm relativistic} = -2 t_{\sun} \log \left( 1 + \frac{ \Delta t_{\rm travel} }{10^{-6} | \vec{s} |} \right) | |
| 148 | +\end{equation} | |
| 149 | +is the relativistic delay due to the Sun, also known as Shapiro delay, with | |
| 150 | +$t_{\sun} \equiv G M_{\sun} c^{-3} = 4.9254909 \times 10^{-6}$ s | |
| 151 | +being half the Schwarzschild radius of the Sun divided by the speed of light, and | |
| 152 | +\begin{equation} | |
| 153 | +\Delta t_{\rm system} = N_{\rm leaps} + 32.184 + \Delta t_{TT \to TBD} | |
| 154 | +\end{equation} | |
| 155 | +converts from UTC to the TDB time system, with $N_{\rm leaps}$ being the number of leap seconds. | |
| 156 | +In all equations, time is expressed in units of seconds. | |
| 157 | + | |
| 158 | +The pulse phase $\Phi_{\rm COMPTEL}$ for COMPTEL is then evaluated using | |
| 159 | +\begin{equation} | |
| 160 | +\Phi_{\rm COMPTEL} = \theta_0 + \Phi + \nu (t_{\rm sbb} - t_{\rm obs}) + \frac{\dot{\nu}}{2} (t_{\rm sbb} - t_{\rm obs})^2 + \frac{\ddot{\nu}_0}{6} (t_{\rm sbb} - t_{\rm obs})^3 | |
| 161 | +\label{eq:phase-comptel} | |
| 162 | +\end{equation} | |
| 163 | +with $\Phi_{\rm COMPTEL}$ put in the interval $[0,1]$, where | |
| 164 | +\begin{equation} | |
| 165 | +\theta_0 = \frac{-DM \times 10^{4}}{2.41 \times \nu_{\rm obs}^2} | |
| 166 | +\end{equation} | |
| 167 | +is the phase shift of radio pulsars due to the dispersion in the Interstellar Medium, with $DM$ in units of g/cm$^3$, | |
| 168 | +and $\theta_0=0$ for infinite frequency pulsar ephemerides. | |
| 169 | + | |
| 170 | +Figure \ref{fig:pulsar-phase} compares the phase computation using Eq.~(\ref{eq:phase-comptel}) to the one using | |
| 171 | +Eq.~(\ref{eq:phase-ephemeris}), i.e.~without passing through an intermediate reference time $t_{\rm obs}$. | |
| 172 | +Obviously the phase difference is negligible, and the computation, implemented in {\tt pula32.f}, of an intermediate | |
| 173 | +reference time can be avoided. | |
| 174 | + | |
| 175 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 176 | +\begin{figure}[!t] | |
| 177 | +\center | |
| 178 | +\epsfig{figure=com-pulsar-phase.eps, width=12cm} | |
| 179 | +\caption{Maximum phase difference between computing the phase via an intermediate | |
| 180 | +reference time $t_{\rm obs}$ using Eq.~(\ref{eq:phase-comptel}) or via using the ephemeris | |
| 181 | +reference time $t_0$ using Eq.~(\ref{eq:phase-ephemeris}). The phase difference is negligible.} | |
| 182 | +\label{fig:pulsar-phase} | |
| 183 | +\end{figure} | |
| 184 | +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |
| 185 | + | |
| 186 | + | |
| 187 | + | |
| 188 | +\end{document} | ... | ... |