5.6. RGS_fluxcombine

Program RGS_fluxcombine combines fluxed spectra, created by the XMM-Newton SAS task rgsfluxer. It has two options:

  1. Option 1: combine RGS spectra of the same detector and spectral order.

  2. Option 2: combine spectra of RGS1, RGS2 and first and second order of both (4 spectra) into one spectrum.

This is not a trivial task, due to the presence of bad pixels, CCD gaps etc, that for each individual spectrum can be slightly different, for instance because of the use of the multi-pointing mode (MPM) of the RGS, so that the same bad pixel falls at a different wavelength for each individual spectrum, or due to the transient nature of some bad pixels/columns.

We discuss both options separately. In general, if you have RGS data for multiple epochs of a source, you may have to run this program first four times with option 1 (RGS1 and 2, orders 1 and 2), and then run it ones with option 2 to get a single stacked RGS spectrum.

Warning

You must run the SAS task rgsfluxer with 3600 wavelength bins between 4–40 Å. Thus, do not use the former \beta-bins! Also, do not change these wavelength limits or number of bins.

The program needs an input file, basically telling it how many spectra should be combined, followed by one line for each spectrum (fixed format, in fortran (F9.2,1X,A) for option 1), containing the exposure time in s (unfortunately not contained in the output of rgsfluxer, but you can get it from the spectral files) and the name of the relevant output file of rgsfluxer. For option 2 there are two additional numbers, namely the RGS (1 or 2 for RGS1 and RGS2), and the spectral order (1 or 2 for first and second spectral order), in such a way that the format is (I1,1X,I1,1X,F11.2,1X,A).

5.6.1. Option 1: combining RGS spectra of the same detector and spectral order

It is important to realise that when data of a time-variable source are combined, artifacts due to missing data (bad pixels) will arise. This can be simply illustrated by an example. Suppose that source X is observed twice with RGS, with exactly the same exposure time, the first time with 100 counts/bin, the second time with 20 counts/bin. Suppose that at wavelength bin j the first observation has a bad pixel, hence no counts, while the second observation has no bad pixel at bin j. The averaged spectrum will have (100+20)/2=60 counts per bin, except for bin j where the average value is (0+20)/2=10. Now since both exposure times are the same, the model will predict 60 counts for all bins (as required), except for bin j where it will predict 30 counts (the pixel is dead for half of the exposure). Thus, the model has 30 counts while the data have only 10 counts. An innocent observeer might therefore think there is an absorption line at bin j taking awat 20 counts, but it is obvious that that is not true.

For this reason, when we combine spectra, we will weigh with the exposure time for all “normal” bins, but when in some of the datasets there is a bad pixel j, we will use a different procedure. In that case, we look to the neighbouring pixels, and assume that the spectral shape in this local neighbourhoud remains the same. From the neighbours with complete data we can estimate how much flux the spectra with good data contribute to the total flux, and we use this fraction to estimate with what factor we should scale the flux measured at pixel j in these good data sets, to obtain the best estimate of the flux at pixel j for the total spectrum.

This procedure gives reliable results as long as the spectral shape does not change locally; as there is less exposure at pixel j, only the error bar on the flux will be larger.

When there is reason to suspect that the bad pixel is at the location of a spectral line that changes in equivalent width, this procedure cannot be applied!

To alleviate this problem, the user has to enter a minimum exposure fraction. If this value is zero, for spectra with constant shape the best result is obtained. On the other hand, if this value is 1, only bins will be included that have no bad pixel in any of the observations that are combined. Advantage in that case is that there is no bias in the stacked spectrum, but a disadvantage may be that a significant part of the spectrum may be lost near important diagnostic lines (in particular for the multi-pointing mode).

Due to the binning and randomisation procedures within the SAS task rgsfluxer, it is still possible that despite careful screening on bad pixels, a few bad pixels remain in the fluxed spectrum, often adjacent or close to discarded pixels. For this reason, the present program checks for any bins that are more than 3\sigma below their right or left neighbouring bin (taking the statistical errors in both into account). Typically, the algorithm finds a few additional bad pixels in an individual observation that is discarded for combination.

The program further allows to apply two other corrections (both are done in the same step). The first correction is an effective area correction. In very high signal to noise data, there are broadband flux differences between RGS1 and RGS2 and first and second order spectra, in some parts of the spectrum, at the few percent level. A simpel model has been produced to correct for this, in the sense that when RGS1 and RGS2 are combined, the true spectrum is assumed to be the average of both. The correction is based on the monitoring campaign on Mrk 509, taken in 2009, and is found to be consistent with a large data set of Mrk 421 spectra that are present in the archive.

Local continuum fits to spectral bands that are poor of lines yield in general \chi^2 values that are too low. This is an artifact of the SAS procedures related to the rebinning of the data. Data have to be binned from the detector pixel grid to the fixed wavelength grid that we use in our analysis. The bin boundaries of both grids do not match. As a consequence of this process, the natural Poissonian fluctuations on the spectrum as a function of detector pixel are distributed over the wavelength bin coinciding most with the detector pixel and its neighbours. In addition, there is a small smoothing effect caused by pointing fluctuations of the satellite. Due to this tempering of the Poissonian fluctuations, chi^2 values will be lower for a “perfect” spectral fit.

We have quantified the effect by fitting a linear model F_\lambda = a + b\lambda to fluxed spectra in relatively line-poor spectral regions, in 1 Å wide bins in the 7–10, 17–18 and 35–38 Å ranges. The median reduced \chi^2 is 0.72, with a 67 % confidence range between 0.65 and 0.79.

The rebinning process conserves the number of counts, hence the nominal error bars (square root of the number of counts) are properly determined. The lower reduced \chi^2 is caused by the smoothing effect on the data. For correct inferences about the spectrum, such a bias in \chi^2 is not appropriate. As we cannot change the observed flux values, we opt to multiply the nominal errors on the fluxes by \sqrt(0.72) = 0.85, in order to get get acceptable fits for ideal data and models.

5.6.2. Option 2: combine spectra of RGS1, RGS2 and first and second order of both (4 spectra) into one spectrum

This procedure is similar to option 1, but with some differences.

No corrections for effective area or binning bias are allowed here, as this should be taken into account in the steps that use option 1. In case there is only one observation, the present program can also be run with only one spectrum for option 1, to get the efective area and binning corrections in.

Further, the spectra are not combined according to exposure time (that should be in general almost the same for RGS1 and RGS2), but according to signal to noise ratio at each bin. Reason is that ofteh the second order spectra have poorer statistics than the first order spectra, hence they should be weighted less in the combined spectra.

Spectra created with rgsfluxcombine can only be fitted using \chi^2 statistics. C-statistics will produce wrong values.