On the Weak Field Approximation for Ca 8542 Å

The weak field approximation (WFA) is a conceptually simple and computationally light method for inferring the magnetic field strength and its orientation in the Sun's atmosphere. In this work, we study the validity and limitations of this tool when applied to full Stokes Ca II 8542 angstrom profiles to extract information about the chromospheric magnetic field. We find that the range of validity of the WFA depends, among other things, on the component of the magnetic field that one is trying to infer. The retrieval of the line-of-sight component of the chromospheric magnetic field from the core of the spectral line is reliable for field strengths up to similar to 1200 G, even when moderate velocity gradients are present. The horizontal component, on the other hand, is suitably derived using the wing-core boundary of the spectral line, but typically yields systematic errors of greater than or similar to 10%. The effects of scattering polarization further compound the problem by rendering the transverse field inference problematic in quiet Sun areas, and for observing geometries within 30 degrees of the limb. Magneto-optical effects disproportionately challenge the determination of the magnetic field azimuth in the transverse plane, leading to errors of similar to 10 degrees Typical noise levels of sigma(n) = 10(-3) relative to the continuum intensity preclude the accurate retrieval of the transverse field strength and its azimuth below a threshold of a few hundred Gauss. Striving for a noise level of sigma(n) 10(-4) significantly improves the diagnostic capability of the WFA with this spectral line, at which point the magnetic field inference becomes limited by systematic errors.