Étienne Artigau edited section_Results_subsection_Analysis_As__.tex  over 8 years ago

Commit id: 76f62ee7355c448c6a8b3ba11099ed49b2924de6

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$\frac{\delta V_{RMS}(i)}{c} = \frac{[A(i)-A_0(i)]_{RMS}}{\lambda(i)(\delta A_0(i)/\delta \lambda(i)}$.  And that the radial velocity accuracy attainable with a given wavelength domain is (Eq. 13 in {\color{red}Bouchy2001})  : $\overline{\delta V_{\rm RMS} } = \frac{1}{\sum{(\frac{1}{ \delta V_{\rm RMS}(k) })^2}}$  Assuming a contant SNR through the domain, then one gets the following  $\overline{\delta V_{\rm RMS} } = \frac{1}{c\middot SNR}$  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.