Brief description of our four models of poloidal, X-shape magnetic fields in galactic halos.
|Model||Shape of||Referencea||Label ofb||Referencec||Verticald||B r||B z||Free parametersef|
|field lines||coordinate||field lines||field||parity|
|Ag||Eq. (12) – Fig. 1a||r1 > 0||z1 (Eq. (13))||Eq. (16)||sym||Eq. (14)||Eq. (15)||r 1||a||B 1||H|
|B||Eq. (17) – Fig. 1b||r1 > 0||z1 (Eq. (18))||Eq. (16)||sym||Eq. (19)||Eq. (20)||r 1||n||B 1||H|
|C||Eq. (26) – Fig. 1c||z1 = 0||r1 (Eq. (27))||Eq. (30)||antisym||Eq. (28)||Eq. (29)||a||B 1||L|
|D||Eq. (31) – Fig. 1d||z1 = | z1 | sign z||r1 (Eq. (32))||Eq. (30)||antisym||Eq. (33)||Eq. (34)||| z1 |||n||B 1||L|
Prescribed radius or height at which field lines are labeled by their height or radius, respectively.
For each model, the first line refers to the original parity in Sect. 2.2, and, when present, the second line refers to the reversed parity.
r1 is the reference radius in models A and B and | z1 | the modulus of the reference height in models C and D; a is the parameter governing the opening of quadratic field lines in models A and C (a > 0); n is minus the power-law index of field lines asymptotic to the z-axis in model B (n ≥ 1) or the r-axis in model D (); B1 is the peak value of the reference field, taken as the normalization field (B1 ≷ 0); H is the exponential scale height (in models A and B) and L the exponential scale length (in models C and D) of the reference field (H > 0 and L > 0).
Model A can only be used in non-axisymmetric magnetic configurations, with the addition of an azimuthal field component near the z-axis, to prevent the magnetic field from becoming singular at r = 0 (see Sect. 2.4).
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