Étienne Artigau edited section_Results_subsection_Analysis_As__.tex  over 8 years ago

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Assuming a contant SNR through the domain, then one gets the following  $\overline{\delta V_{\rm RMS} } = \frac{1}{c\middot SNR}$ \frac{1}{c SNR}\frac{1}{ \sum{\lambda(i) (\delta A_0(i)/delta\lambda(i))^2 } }$  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 mean $\delta V$ at unit signal-to-noise. This value, $\rho_{\delta V}$ 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 $\rho_{\delta V} = 1$\,km/s observed over a $(\Delta \lambda/\lambda)=20$\% at a SNR=200 should lead to an intrinsic accuracy of $1000\times20^{-\frac{1}{2}}\times200^{-1}\sim1.1$\,m/s.