Étienne Artigau edited section_Results_subsection_Analysis_As__.tex  over 8 years ago

Commit id: ad391ee85b7355fb3db560a437b23c7bd2a515d5

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$\frac{\delta V_{RMS}(i)}{c} = \frac{[A(i)-A_0(i)]_{RMS}}{\lambda(i)(\delta A_0(i)/\delta \lambda(i)}$.  Considering, for the sake of establishing a comparison metric between spectra, we assume that over the wavelength interval the signal-to-noise ratio (SNR) is constant, we define a local radial-velocity information metric that is the local integral over a $\Delta\lambda/lambda=1$\% for a constant signal-to-noise of 100. This value, $\delta V_{1\%}$ can readily be scaled for a given wavelength domain and SNR. The radial velocity accuracy achieved with scale as $(\Delta \lambda/lambda)^-{\frac{1}{2}}$ and as the inverse of SNR. A spectrum with a $\delta V_{1\%} = 20$\,m/s observed over a $(\Delta \lambda/lambda)=20$\% at a SNR=200 should lead to an intrinsic accuracy of $20\times20^\frac{-1}{2}\times(200/100)^{-1}\sim2.2$\,m/s.