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5 Data merging

The only prominent line present in all spectra is H$\alpha$, so only this line has had its line-index calculated and used for the subsequent analysis. Due to differences in S/N and resolution the individual sets of spectra are very different. However, the total flux in a spectral line (i.e. the EW) should be independent of resolution.

As mentioned in Sect. 2.1, a given line index will be proportional to the EW of the line, so that for H$\alpha$:

$$\Lambda_i^{{\rm H}\alpha} = k_i^{{\rm H}\alpha} EW({\rm H}\alpha),$$ (8)

where the index i refers to the choice of filter and the proportionality constant $k_i^{{\rm H}\alpha}$ will depend on the FWHM (in wavelength units) of the filter. In order to be able to combine all observations, we had to make sure that the proportionality constant in Eq. (8) was the same for all sets.

Figure 6: Spectrum from VBO. Clear H$\alpha$ and atmospheric bands.

Figure 7: Spectrum from McD. The order containing H$\alpha$. Again low counts due to high resolution. The throughput was measured to be only $\sim$1.7%

The line-index was calculated with a fixed filter width (in pixels) for each individual observatory's data, chosen so that the mean value of the line-index divided by the filter width was the same throughout the full data set. This means that the line-index filter integrates the same part of the line in all data sets regardless of resolution and it ensures that the resulting amplitudes are directly comparable. The filter was indeed found to have approximately the same width in Ångströms for all the individual sets, as expected.

The full data set can then be normalized by scaling each subset to a common mean value, which amounts to transforming the individual pixel units of the line-indices to a common unit.

Finally, the scaled data points were assigned statistical weights calculated from the local scatter in the series.

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