Errors and Uncertainties

It is a well-established rule of scientific investigation that the first time an experiment is performed the results bear all too little resemblance to the "truth" being sought. (Bevington,1969)

Oh dear. But this isn't the first time any of these contributors have measured spectra, and we now have almost 300, so we can at least hope to get close to the "truth" and we don't have to use an "alternate truth" (Orwell,1949). But anyway we will have errors and uncertainties in our data. However, we certainly have errors and uncertainties in our data, and we'd like to estimate their magnitudes.

We call error a deviation from a known value.

An uncertainty can only be determined from many measurements. We hope that the mean of our measurements will then be close to the desired value. We use the standard deviation of the measured values as the uncertainty.

For the individual measurement points in our spectra, we need to determine two values.

• the position of the pixel, i.e., its wavelength
• the measured value, i.e., the flux, the number of photons in the pixel, and the measured ADUs.

We'll with start the first, simpler one.

Wavelength uncertainty

The wavelength of the pixels is usually determined using the emission spectrum of a gas discharge lamp, neon, starter, or ThAr. The software used creates a second- or third-degree polynomial based on the known line positions and wavelengths, with which the corresponding wavelength is calculated for each pixel. The software then always provides an incredibly reassuring RMS error. This error applies only to the measured lines and not to any individual wavelength. The error includes neither random, statistical deviations nor certainly systematic errors, such as skewed coupling of the light from the reference lamp. At least the latter error does not occur if the spectrum is calibrated with terrestrial lines in wavelength. Water vapor in the atmosphere does move, but much slower than our desired accuracy of < 1 km/s.

Almost all of our spectra from alpha Cam actually contain a fixed wavelength, the interstellar absorption at approximately 6614 Å This allows us to check our entire calibration chain. We have almost 300 spectra. This allows us to do some statistical work.

The following video shows, on the left, 'lamp', the spectra already calibrated by participants from August 2022 to March 2023. 12 spectra were calibrated with atmospheric water lines.
In the middle, 'lamp, bary' shows the same spectra barycentrically corrected. The specutils algorithm was used.
On the right, 'tellu, bary, smooth' the spectra were corrected again with the telluric lines before the barycentric correction. See a detailed description here.