18.4 Dirty Tricks

Besides flux density estimate, which, as discussed before, is a non trivial task, analyzing spectral line images may force the astronomer to face some really tricky problems. The two most obvious are moment evaluation and continuum subtraction.

18.4.1 MOMENTS

The lowest order moment of a spectral line data cubes offer very convenient ways of interpreting images. The zero $^{\mathrm{th}}$ order moment is the integrated intensity, the first order moment the velocity, the second order moment the line width. While these moments are linear combination of the channel maps, the deconvolution process is non linear. Accordingly, the two operations do not commute.

Hence, it is impossible to recommend deconvolving before computing the mean intensity, or summing up the individual cleaned channel maps. In the latter, limited signal to noise can prevent proper deconvolution. In the former, velocity gradients can spread emission over an extended area which is difficult to handle in the deconvolution. Choice can be a matter of trial (and errors).

To avoid introducing noise, a window in velocity is important. While noise on the integrated intensity only increases as the square root of the window width, the effect on the higher order moments is much more dramatic, and results in non-gaussian noise distribution on these variables. A threshold in intensity is useful to prevent spurious noisy features. The window should in principle be pixel dependent to allow for velocity gradients. Smoothing both in the spatial and spectral domains may help in obtaining better results in moment extraction. A line fitting procedure (e.g. a Gaussian line fit at each pixel) may sometimes be the best solution (under construction, check later...).

Moments can be computed using task MOMENTS and displayed using the GO VELOCITY command in GRAPHIC.

18.4.2 Continuum Subtraction

Continuum subtraction is a related problem. It is in principle needed to compute properly moment maps. However, it may be completely impossible, for example in the case of an optically thick line partially covering a continuum source. Continuum subtraction can be done in the image plane or in the $uv$ plane. $uv$ plane subtraction avoid the non linearity in the deconvolution, and thereby any amplification of errors induced in this process. Task UV_SUBTRACT performs this operation. Although signal to noise on the continuum is often much better than on the spectral line, it may be advantageous to subtract a source model rather than the measured visibilities; this is only true when thermal noise is more important than phase noise. Task UV_MODEL compute visibilities from an input image.