# What does “the depth of the 13.0 Å feature differs by 7 sigma from zero” mean?

In a paper I've read, I have seen the following:

In view of the noise levels, it is difficult to perform such a search effectively using statistical significance criteria only. We will therefore appeal to spectroscopic consistency arguments when assessing apparent absorption features in the spectrum. As a guide, however, we estimated the significance of the features by fitting each with a simple gaussian profile, optimizing the continuum, and evaluating their significance in terms of the amplitude of the gaussian. In the early-phase spectrum, the depth of the 13.0 Å feature differs by 7 sigma from zero, whereas those of the 25.3, 26.3 and 26.9 Å features differ by 3–4 sigma.

What does "the depth of the 13.0 Å feature differs by 7 sigma from zero" mean?

How these significance level calculate? The line seems weak and could not fit with normal fitting method. So use chi-squared method seems do not work.

And another way to calculate such weak line significance level is to use equivalent width divide the uncertainty, but to the so narrow absorption line, how to calculate or get the uncertainty of the equivalent width?

## 1 Answer

1. In this case itseems to mean that the depth of the line is 7 times its error bar below the continuum level.

2. Impossible to answer. You say it can't be done, but the authors say that they fitted a Gaussian.

3. You either use a rough estimate (attributable to Cayrel de Strobel 1988) of $$\Delta {\rm EW} \sim 1.5\frac{\sqrt{RP}}{{\rm SNR}},$$ where $$R$$ is the resolution element (the FWHM) of your instrumental wavelength response, $$P$$ is the pixel size (both in the same wavelength units) and SNR is the signal-to-noise ratio per pixel. Or you use an integration method and combine the SNR of each pixel used to find the uncertainty in the integral. Or you fit a Gaussian but using the area under the Gaussian as one of the fitting parameters.

• Since from that paper figure 1, the line in 13.0A do not seems have 7 times 1sigma error bar below continuum, so i'm puzzled with the statement. And in your fomula, how to get SNR if the spectra is Chandra HEG/MEG grating spectrum? And could you give me more about the details of the last two processing methods? I'm a little slow in accepting them. – Chen Jul 19 '20 at 14:01
• The gaussian component can be fitted by curve fitting tools like matlab and other peak fitting tools but since the width is nearly or even smaller than the resolution of Chandra spectra, so in the tools like xspec or sherpa, it give out uncertainty 0. So i curious about how the uncertainty of EW and sigma be calculated. – Chen Jul 19 '20 at 14:53