...V

For a given noise level N, the SNR in Stokes V is always smaller than in Stokes I because the circular polarization signal is smaller than the intensity signal. As an example, take  $N = 10^{-3}~I_{\rm c}$ and  $V_{\rm max}/I_{\rm c} \sim 3 \times 10^{-3}$ (these values correspond to the profiles depicted in Fig. 4). The SNR in the continuum intensity is $S/N = I_{\rm c}/(10^{-3}~I_{\rm c}) = 1000$. The SNR in Stokes V is only $3\times 10^{-3}~I_{\rm c}/(10^{-3}~I_{\rm c}) \sim 3$. The minimum detectable polarization signal (the polarimetric sensitivity) is usually estimated from the noise of the observations. However, the important quantity determining the reliability of the inferred magnetic field is the SNR in Stokes V.

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