Table 1
Brief description of our four models of poloidal, Xshape magnetic fields in galactic halos.
Model  Shape of  Reference^{a}  Label of^{b}  Reference^{c}  Vertical^{d}  B _{ r }  B _{ z }  Free parameters^{e}^{f}  
field lines  coordinate  field lines  field  parity  


A^{g}  Eq. (12) – Fig. 1a  r_{1} > 0  z_{1} (Eq. (13))  Eq. (16)  sym  Eq. (14)  Eq. (15)  r _{1}  a  B _{1}  H 
Eq. (21)  antisym  


B  Eq. (17) – Fig. 1b  r_{1} > 0  z_{1} (Eq. (18))  Eq. (16)  sym  Eq. (19)  Eq. (20)  r _{1}  n  B _{1}  H 
Eq. (21)  antisym  


C  Eq. (26) – Fig. 1c  z_{1} = 0  r_{1} (Eq. (27))  Eq. (30)  antisym  Eq. (28)  Eq. (29)  a  B _{1}  L  


D  Eq. (31) – Fig. 1d  z_{1} =  z_{1}  sign z  r_{1} (Eq. (32))  Eq. (30)  antisym  Eq. (33)  Eq. (34)   z_{1}   n  B _{1}  L 
Eq. (35)  sym 
Notes.
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.
In general, the free parameters can vary with azimuthal angle, ϕ. However, in the particular case considered in Sect. 2.4, only B_{1} depends on ϕ (through Eq. (36)).
r_{1} is the reference radius in models A and B and  z_{1}  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 powerlaw index of field lines asymptotic to the zaxis in model B (n ≥ 1) or the raxis in model D (); B_{1} is the peak value of the reference field, taken as the normalization field (B_{1} ≷ 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 nonaxisymmetric magnetic configurations, with the addition of an azimuthal field component near the zaxis, to prevent the magnetic field from becoming singular at r = 0 (see Sect. 2.4).
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