rdgen    4 October 2004

uc  (no parameters) - determine upper limit column densities for an ion given a redshift and the Doppler parameter of another ion which was used to determine the redshift.

Any additional information is prompted for:

1:   xn, xb, nminf, pchslim, ctype, and vres (km/s), where:

    xn is a threshold for inclusion in the fit statistic,

    xb is the halfwidth of the search area in units of the test Doppler parameter

    nminf is the minimum number of pixels which are used to determine the fit statistic

    pchslim is the approximate chi-squared probability for acceptance (pchslim=0.16 corresponds to one-sided 1-sigma)

    cmin is the default - it means determine the minimum column density consistent with the noise. The alternative 'nocmin' results in a list with the raw minimum column density as stepped, which may be lower if the continuum level is set slightly too high. If the continuum level is set a little low, then the result is the maximum of the minimum value consistent with the noise or the maxumum consistent with the data.

    vres is the FWHM in km/s for the data. Default is 6.7 km/s.
   

2. Reference ion, Doppler parameter, redshift, search ion (rest wavelength, rest wavelength,   ....)


The routine allows the determination of upper limits to column densities for ions for which the transitions to be used may be blended with lines from other redshift systems. The redshift and Doppler parameter are assumed to be known from one species, and these are used to determine a maximum allowed column density for another specified ion.

The method is as follows: given the redshift and the Doppler parameter for the reference ion, a series of trial profiles are created
for the search ion at the wavelengths specified using a range of Doppler parameters from pure thermal to pure turbulent broadening. Each of these is compared with the data in the range -xb to +xb times the trial Doppler parameter, using only those pixels for which the trial profile is at most xn-sigma above the data values, or, if there are fewer than nminf pixels satisfying this criterion, the nminf pixels for which the quantity (data - fit)/error is the largest. Using these pixels a chi-squared value is determined. The trial column density is increased for each trial Doppler parameter until the normalized chi-squared starts to increase and the probability that the fit matches the data falls below pchslim.  The maximum column density allowed for the range of possible Doppler parameters is determined.

In some cases, particularly for narrow lines, there is never an acceptable fit over the minimum pixel range. For these the trail fits are such that some data pixels fall far below the trial fit, and some above, and the upper limit is a conservative one. Trials using clean profiles with xn=1.0, xb=2.0 nminf=5 and pchslim=0.16 show that the limits are close to those expected from fitting the lines directly. The default if no rest wavelengths are specified is to choose the first two for the specified ion from the atomic data file, and if there is only one line it that file then only that one will be chosen.

There is a restriction on its use - the error estimate and the rms fluctuations must be the same, or similar. This is because the rms is used in determining the chi-squared value for finding an acceptable fit, and the error estimates used to determine the minimum column density consistent with the noise. If the rms scatter in the data is significantly different from the error estimate, then you'll need to run the program once for the internal error array set as the rms estimate, and once for the independent pixel error estimate, and choose the appropriate column density limit depending on the relationship between rms and error estimate (which I have not thought about).