hfs_nh3

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hfs_nh3 is an interactive graphic procedure for fitting simultaneously up to 9 velocity components of a pair of NH₃(1,1) and (2,2) spectra.

• It is a menu-driven program, and uses the PGplot Graphics Subroutine Library to display the spectral data, fit, and residual.

Example of a hfs_nh3 run:

• Help is available, explaining the program options and parameters.
• The spectra to fit are read from two ASCII files, each one with a pair of values (velocity, intensity) per line. Lines beginning with "#" or "!" are ignored. The files can be given as arguments to hfs_nh3:

$ hfs_nh3 <source_11>.dat <source_22>.dat

• An optional Hanning smoothing of the spectrum can be performed prior to fitting.
• The six parameters fitted for each velocity component are
  • Δv, hyperfine line FWHM;
  • v_LSR1, central velocity of the (1,1) main line;
  • A(1 - e^-τ_1m), intensity of the (1,1) main line;
  • 1 - e^-τ_1m, where τ_m is the optical depth of the (1,1) main line;
  • v_LSR2, central velocity of the (2,2) main line;
  • A(1 - e^-τ_2m), intensity of the (2,2) main line.

with the additional constraints

• 0 < Δv,
• 0 < 1 - e^-τ_1m < 1.
• 0 < A(1 - e^-τ_1m),
• 0 < A(1 - e^-τ_2m),

For each set of fit parameters, the optical depth of the (2,2) transition, τ_2m, is obtained from

[1-e^-τ_2m] = [1-e^-τ_1m] × [A(1-e^-τ_2m)] / [A(1-e^-τ_1m)],

and used to evaluate the (2,2) synthetic spectrum.

• The initial values for the fit are guessed from the intensity, position, and width of the data peak for the first component, and of the residual (data minus previous components) for the rest of components. The opacity is set arbitrarily to 0.7 (1 - e^-τ_m = 0.5). Alternatively, you can use the cursor to add or delete components. The position of a new component is set at the cursor position, its intensity is the intensity at the cursor position, and the FWHM is estimated around the cursor position.
• Values for the initial search ranges is proposed, but they can be changed. Any ofthe parameters can be kept constant by setting its range to 0.
• The fit is performed by sampling the parameter space of dimension 4×Ncomp (the number of components) using a Sobol pseudo-random sequence and finding the minimum residual rms. The parameter space is defined by a search range for each parameter, centered on the initial values (and taking into account the constraints given above).
• The uncertainties in the parameters are found from the increase of residual rms with each parameter deviation.
• See an example of fitting a NH₃ (1,1) and (2,2) with one velocity components: hfs_nh3.log.
• The synthesized spectra are saved to ASCII files <source_11>.synt and <source_22>.synt. The files have a header (lines beginning with "!") with the values of the parameters of the fitted spectrum for each velocity component. The file is readable by GREG. The file is overwritten for every new fit.
• A plot showing the data, the components fitted, and the residual is saved in a file <source>.eps. The file is overwritten for every new fit. See an example (data in black, synthetic in magenta, residual in green, residual rms = 0.0015):