Saturday, 1 August 2015

spectroscopy - Why do linear velocity redshifts correspond to linear pixel shifts when the spectra are binned in constant log wavelength?

All this means is that you need to bin your spectra in equal intervals of log wavelength for each pixel to be a constant interval in velocity.



First consider the case whereeachpixel is worth a constant interval in linear wavelength. Here we have
fracDeltalambdalambda=fracDeltavc,


and the Deltav represented by each pixel depends on lambda, which changes across the spectrum.



But now if you bin in equal increments of
Deltaloglambda=fracDeltalambdalambda=fracDeltavc


and each pixel has the same fixed velocity interval, Deltav=cDeltaloglambda, independent of lambda.



This log wavelength binning is a prerequisite for cross-correlation procedures that yield velocities.

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