deletions | additions       diff --git a/section_Results_subsection_Analysis_As__.tex b/section_Results_subsection_Analysis_As__.tex  index 2bf0096..f549c85 100644  --- a/section_Results_subsection_Analysis_As__.tex  +++ b/section_Results_subsection_Analysis_As__.tex 
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$\overline{\delta V_{\rm RMS} } = \frac{1}{\sum{(\frac{1}{ \delta V_{\rm RMS}(k) })^2}}$  Assuming a contant constant  SNR through the domain, then one gets the following $\overline{\delta V_{\rm RMS} } = \frac{1}{c SNR}\frac{1}{ \sum{\left(\lambda(i) \delta A_0(i)/\delta\lambda(i)\right)^2 } }$ }$.  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 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. :  $$\rho_{\delta V^2} = \left(\lambda(i) \delta A_0(i)/\delta\lambda(i)\right)^2$,  which corresponds to a local density of information content in the spectrum at unit signal-to-noise ratio.   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, $\rho_{\delta V^2}$ 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.