The IVM measures the Q and U Stokes parameters to estimate the tansverse magnetic field. There is a 180 degree ambiguity in the field direction. This note describes some aspects of the azimuth definition and the effects of ambiguity resolution.
Azimuths are defined as the position angle of the transverse field, measured East from Earth North. The angles range -90 to +90 degrees. The azimuth is computed as
The factor of 2 indicates the ambiguity, as only half of all angles are available.
This definition is used uniformly in all IVM magnetogram codes: BJEFF6, IVM_WAVGRAM, and IVM_TRIPLET_GRAM. The azimuths obtained from the various codes differ by a few degrees, as would be expected from their different models of the Stokes profiles in terms of the magnetic parameters.
The simple sunspot in AR8525 on 04-May-1999 was observed with the IVM. The images are continuum intensity, longitudinal field (cube root scaling), transverse field magnitude (square root scaling), and azimuth.
The transverse field is usually expressed in Cartesian coordinates. The observed field components are computed as
Oy = COS( azimuth * !DTOR ) * Bt
The observed field vector (Ox, Oy) is ambiguous with the vector (-Ox, -Oy). A common mistake is to try to resolve ambiguity by switching the sign of only 1 component; that is wrong.
The resolution of the ambiguity is a complex task and required assumptions about the nature of the fields. There are two large ambiguity codes in use for Mees data:
The simplest resolution is to assume the fields are potential, with no currents. The transverse components of the potential field can be computed from the convolution of the longitudinal field with the gradient of a Green's function (T.Sakurai, Solar Phys., 76, 301, 1982.) A simple approximation is
Py = - d Bl / dy
The AR8525 gram was processed to generate the images of Ox, Oy are at the top; the inferred Px, Py from longitudinal field are at the bottom.
The vector product of the potential and observed fields,
is positive if the vectors are parallel and negative if they are antiparallel. The signs of the observed vector (Ox, Oy) can then be switched to give a first guess at the resolved field (Bx, By).
The derived vectors (Px, Py) are plotted at the top. The "resolved" vectors (Bx, By) are plotted at the bottom.
Contours of constant azimuth will be radial if the fields are radial, from some field concentration. If the contours of constant azimuth "twist" counterclockwise (right-hand), then the azimuth is decreasing outward, and therefore the field lines twist clockwise (left-hand). The converse also holds. This gives a simple visual check on the sense of the vector field to make sure there are no sign errors in the field vector or ambiguity computations.
Last modified: Wed Jun 25 17:42:11 HST 2003