8.3 Continuum subtraction

Most spectral-line observations contain a certain amount of frequency-independent, continuum radiation in addition to the frequency-dependent line signals. In most (all?) cases, it is probably best to separate the two signals at this stage of the data processing. In this way, a single continuum image can be constructed to apply to all frequencies. It will probably be necessary to apply Clean or other expensive deconvolution techniques to determine the best estimate of this continuum image. To do this for each channel individually would not only be considerably more time consuming, but would result in different models for the continuum in each channel. Since Clean is a data-adaptive non-linear algorithm, minor disturbances in its progress causes it to converge to surprisingly different solutions. Such “disturbances” could be caused by differing noise and line signals in different channels. (It can be caused simply by differing computational order on identical data using different computers.) Clean also increases the noise in an image in the areas at which there are sources. If the continuum is removed from the line data before Cleaning, then this increase in noise is also removed. To determine the continuum from separately Cleaned channel images is to use noisier individual determinations to get the final estimate. If the imaging and deconvolution were a linear process, then this would not matter. But the deconvolution is non-linear, making it better to start with the best possible estimate of the continuum.

In many cases, the continuum signal is stronger by far than the line signal. In such cases, it is best to use as many channels as possible to estimate the continuum and to remove that estimate as early as possible. The remaining line signal may be of fairly low signal-to-noise ratio and, therefore, not need the same processing that the continuum signal requires. In particular, it may not be necessary to Clean the channel images particularly deeply, if at all.

All of the arguments above suggest that the continuum should be estimated and subtracted in the visibility domain. This has the unfortunate attribute that we can use only those channels which are free of line signal over the entire field of view. (This is because the Fourier transform relation mixes signals from all directions in the field into every visibility sample.) In the image domain, the dirty images also have this unfortunate attribute, in this case because the dirty beam mixes signals from all parts of the field into every pixel. The above arguments suggest that the only time one should determine the continuum in the image domain is when the observations have essentially no channels which are free of line signal over the full field of view. In that case, the continuum at each position will have to be determined from deconvolved images using those channels which are free of line signal at that position.

 provides three separate tasks for fitting and subtracting the continuum in the uv plane. All three fit a linear “baseline” to a selected group of channels and subtract that from the data. The reasons for a linear baseline are (1) a continuum source offset from the field center will produce a linear phase slope across the passband, (2) minor other changes in the visibility with baseline may be approximately linear over narrow passbands, and (3) minor passband variations with time appear also to be approximately linear. Higher-order fits can be done by UVLSF, but they do not seem to be justified and are often not well constrained. The first reason suggests that one should do the fit in amplitude and phase, an algorithm implemented by the task UVBAS. This should be used only if you have good signal-to-noise in all of your visibility samples. The reason for this very stringent requirement is that visibility amplitudes have Ricean rather than Gaussian noise statistics. As a result, very biased estimates are produced in moderate to low signal-to-noise cases. For these, the two tasks UVLSF and UVLIN should be used. They do the fits in the real and imaginary parts of the visibilities and, hence, do not produce biased estimates in the absence of signal. Both tasks allow you to shift the visibilities to move a strong source to the center of the field before doing the fits (and then shift the visibilities back to the original phase center). This changes sinusoidal real and imaginary parts to linear for an accurate fit, but only for those cases where a single source dominates the field. Both tasks offer the option to flag discrepant data, but they differ in the details of how they do this. UVLSF offers the option to write out a “best-fit” single-channel data set as well as subtracting it from the line data; see §8.1 for an sample inputs to UVLSF.

There are also a number of ways to remove the continuum in the image domain, all of which assume that the channels have been imaged similarly and placed into a three- or more dimensional “cube.” The “classical” method to subtract the continuum, which is the least useful, is to average those image planes which contain no line signals using SQASH on each set of line-free planes and COMB to average those averages. Finally, COMB is used to subtract the resulting plane from each plane of the initial cube. In this method, the cube is in the “natural” transposition with the frequency axis third. The other two methods require you to use the task TRANS (see §8.5.2) to transpose the frequency axis to the first (most-rapidly varying) axis. Then IMLIN may be used to fit polynomial baselines (linear is usually all that is justified) to the line-free parts of each spectrum. This task, like all of the other tasks so far mentioned in this section, requires you to use a fixed set of channels for all positions in the field. Many objects (e.g., rotating galaxies) have spatially-dependent spectra in which each pixel has a rather narrow line width compared to the object or objects as a whole. In such cases, the task XBASL may be used. This task requires some endurance on your part to complete, but it allows you to specify the baseline region for each pixel interactively using the  TV or Tek graphics windows.