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Analyzing profiles

The CLASS user may analyse spectra by fitting profiles. The fitting commands are available from the FIT language. The minimization method is taken from the MINUIT system of CERN, modified and optimized for this purpose. Reliability proved to be good. Five types of profiles are presently available, and can be selected by the METHOD command:

METHOD SHELL in details. The fitted function is:


\begin{displaymath}f(\nu) = \frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}}\,
\frac{1+4H\,[(\nu-\nu_0)/\ensuremath{\Delta \nu}]^2}{1+H/3}
\end{displaymath}

where the fitted parameters are:
  1. \ensuremath{{\cal A}}: the area under the profile (in K MHz),
  2. $\nu_0$: the middle frequency (in MHz),
  3. \ensuremath{\Delta \nu}: the full width at zero level (in MHz),
  4. $H$: the Horn/Center parameter (dimensionless, see below)

The central value is $f(\nu_0) = \frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}}\frac{1}{1+H/3}$ whilst the value at the edge is $f(\nu_0+\ensuremath{\Delta \nu}/2) =
\frac{\ensuremath{{\cal A}}}{\ensuremath{\Delta \nu}}\frac{1+H}{1+H/3}$. The edge-to-center intensity ratio value is thus dictated by the Horn/Center parameter $H$ according to

\begin{displaymath}\frac{f(\ensuremath{\Delta \nu}/2)}{f(0)} = 1 + H\end{displaymath}

The center-to-edge frequency shift corresponds to an expanding velocity

\begin{displaymath}
v_{\rm exp} = c\,\frac{\ensuremath{\Delta \nu}/2}{\nu_0}
\end{displaymath}

Figure [*] shows synthetic shell-like profiles, for which the area takes values $\ensuremath{{\cal A}}=5$ to 20 by 5 K MHz. The full width at zero level is $\ensuremath{\Delta \nu}=3.83$ MHz in all cases, which corresponds to $v_{\rm exp}=2.49$ km.s \ensuremath{^{-1}}at 230.537 GHz. The Horn/Center parameter is $H=5$ (top) or $H=-1$ (bottom, for which the intensity at the edge is zero).

Figure: Four synthetic shell-like profiles, corresponding to increasing areas $\ensuremath{{\cal A}}=5$ to 20 by 5 K MHz, a \ensuremath{\Delta \nu} of 3.83 MHz or $v_{\rm exp}=2.49$ km.s \ensuremath{^{-1}}at 230.537 GHz. The results of fitted shell profiles are indicated at the top. The upper scale is km.s \ensuremath{^{-1}}. Top: The Horn/Center parameter is $H=5$. Bottom: Same as above for $H=-1$.
Image class-shell-1



Image class-shell-2


The FIT commands are:

Fit results are always saved by a WRITE command and made available through the corresponding variable section (see SET VARIABLE help).


next up previous contents index
Next: Gridding Spectra on a Up: Spectra Line Processing Previous: Adding Spectra   Contents   Index
Gildas manager 2018-11-13