CRT Supplied Fields

CRT incorporates many types of magnetic fields: Spiral Symmetric, Uniform , Dipole , Simple Random , Ring Model, and toroidal. We have recently added the JF12 model and framework for simulating Kolmogorov spectrum turbulent field realizations. All magnetic fields are assumed well defined within a galacto-centric user defined distance (defaults to 20 kpc), and zero elsewhere. If you have any questions please contact us.



Spiral Symmetric Models

Templates

  • ASS_A:
    F ass_a model NORM PITCH SCALE1 SCALE2 SCALE3 SCALE4 ZCUT
  • ASS_S:
    F ass_s model NORM PITCH SCALE1 SCALE2 SCALE3 SCALE4 ZCUT
  • BSS_A:
    F bss_a model NORM PITCH SCALE1 SCALE2 SCALE3 SCALE4 ZCUT
  • BSS_S:
    F bss_s model NORM PITCH SCALE1 SCALE2 SCALE3 SCALE4 ZCUT

Units and descriptions

  • 'model' - select either 'stanev' or 'hmr'. Descriptions of these fields can be found in: Stanev. Astropart. Journ. 479:290, 1997 (arXiv:astro-ph/9607086) Harari, Mollerach, Roulet. JHEP 9908:022, 1999 (arXiv:astro-ph/9906309)
  • NORM - [microGauss], the total magnitude of the spiral field at the position of the Sun for *SS_* models. While value of (1) will produce a dipole field with components Bx=By=0, Bz=(1 microGauss).
  • PITCH - [degrees], looking from the Galactic North Pole, the pitch angle is positive if the clockwise tangent to the spiral is outside the circle with radius R
  • SCALE1 - [kpc], Galactocentric distance of the location of maximum field strength in the direction (0,0)
  • SCALE2 - [kpc], scale length for tanh attenuation factor in the Galactic disk (not used for stanev field, but an entry here is required anyway)
  • SCALE3 - [kpc], scale length for exponential decay along z-direction
  • SCALE4 - [kpc], scale length for exponential decay along z-direction
  • ZCUT - [kpc], distance in z-direction where exponential decay scale length changes from SCALE3 to SCALE4 (not used for hmr field, but an entry here is required anyway)

Note:SCALE2 is not used for 'stanev' fields. ZCUT is not used for 'hmr' fields. Simply set these values to (1) in these cases.

Internal Coordinate System

System-A coordinates (x,y,z) are converted into Field coordinates (x',y',z') by the following transformation:
x' = (-x) + R_sun
y' = (-y)
z' = z

The Field coordinate system then uses the following quantities calculated from (x',y',z'):
r = sqrt( x'^2 + y'^2)
theta = arctan(y' / x')

Model 'type'

There are 2 types of SS models included by default:

  • Stanev, described in Astrophys. J. 479:290 (1997), also (arXiv:astro-ph/9607086)
  • HMR, described in JHEP 9908 (1999) 022, also (arXiv:astro-ph/9906309)

Important Note: Stanev considers a *SS_A field, HMR consider a *SS_S field.
CRT uses the convention that a *SS_S field preserves field direction upon crossing the galactic disk.

Stanev Model

Uses the field equations are generalized below.
B(r,theta,z) = B(r,theta) * f(z)
B(r,theta) = (3 * R_sun / r) * cos[theta - beta*LOGE[r / r1] ]

Where:
f(z) = exp[ - abs(z) / r3 ] if abs(z) <= zc
f(z) = exp[ - abs(z) / r4 ] if abs(z) > zc
PITCH = p
SCALE{X} = r{X}
beta = 1/tan(p)
ZCUT = z_c
LOGE = natural logarithm function
In the ASS model, the cosine term is replaced by its absolute value.
For values of r < 4kpc:
B( {r<4kpc} ,theta) = B( 4kpc , theta)

Note: Stanev used this formulation for 2 field arrangements:

  • BSS_S where the field direction is preserved upon disk crossing
  • ASS_A where field direction changes

In CRT, the user has the BSS_{A/S} and ASS_{A/S} available.

HMR Model

Uses the field equations are generalized below.
B(r,theta,z) = B(r,theta) * f(z)
B(r,theta) = (3 * R_sun / r) * {tanh(r/r2)}^3 * cos[theta - beta*LOGE[r / r1] ]

Where:
f(z) = f(z) = exp[ 0.5* { 1/cosh(z/r3) + 1/cosh(z/r4)} ]
PITCH = p
SCALE{X} = r{X}
beta = 1/tan(p)
ZCUT = z_c
LOGE = natural logarithm function
In ASS models, the cosine term is replaced by its squared value.

Additionally, the disk field reversal in *SS_A models is calculated by:
B_A(r,theta,z) = B_S(r,theta,z) * tanh(r / r5)
 Where r5= 20 parsecs.
The value of 20 parsecs is hard-coded into CRT.


Dipole Model

Template

F dipole NORM

Units and descriptions

NORM - [microGauss], Where a value of (1) will produce a dipole field with components Bx=By=0, Bz=(1 microGauss).

Internal Coordinate System

The magnitudes for each component are given below. 'theta' and 'phi' refer to the zenith and azimuthal angles in the spherical coordinate centered on the galaxy. The user specifies the total field strength at the Sun's position.

Functional Form

Bx = -3 * sin(theta)cos(theta)cos(phi) / (r^3)
By = -3 * sin(theta)cos(theta)sin(phi) / (r^3)
Bz = (1 - 3*{cos(theta)}^2) / (r^3)


Uniform Model

Template

F uniform BX BY BZ

Units and descriptions

B{XYZ} - [microGauss], field strength in the {xyz} direction.


Simple Random Model

Template

F simprand NORM corrlen sigmalen sigmanorm

Units and descriptions

The simple random model implement is CRT starts by randomly picking a direction. The size of the cell is then chosen by selecting from a gaussian distribution with mean correlen and sigma sigmalen. The field strength is chosen by selecting from a gaussian distribution with mean NORM and sigma sigmanorm.

  • NORM - [microGauss], nominal field strength.
  • corrlen - [kpc], nominal cell size.
  • sigmalen - [kpc], sigma of a gaussian defining the variation of cell to cell size.
  • sigmanorm - [microGauss], sigma of a gaussian defining the variation of cell to cell field strength.

Ring Model

Template

F ring NORM INNEREDGE OUTEREDGE SCALE5

Units and descriptions

The magnetic field is nonzero for a defined radial range in the Galactic plane. The field experiences exponential decay perpendicular to the plane.

  • NORM - [microGauss], Normalization of field strength.
  • INNEREDGE - [kpc], inner edge of annulus of nonzero field magnitude
  • OUTEREDGE - [kpc], outer edge of annulus
  • SCALE5 - [kpc], scale length for exponential decay along z-direction

Functional Form

Bx = norm*sin(fieldPhi(x,y))*exp(-fabs(z)/scaleHeight)
By = norm*cos(fieldPhi(x,y))*exp(-fabs(z)/scaleHeight)
Bz = 0


Toroidal Model

Template

F toroidal TORRAD SCALE6 LORWIDTH BMAX

Units and descriptions

A simple toroidal magnetic model taken from Prouza, Smida. Astronomy and Astrophysics, v.410, p.1-10 (2003), also (arXiv:astro-ph/0307.165). The field has constant magnitude within a disk oriented parallel to the Galactic plane, and has exponential decay beyond the disk radius out to the maximum extent Rmax. There are 4 parameters: maximum value of toroidal field Bmax, radius of circle for toroidal field R, scale height for decay perpendicular to Galactic plane H, half-width of Lorentzian distribution P.

  • TORRAD - [kpc], radius of circle for constant field magnitude
  • SCALE6 - [kpc], scale height above Galactic plane
  • LORWIDTH - [kpc], half-width of Lorentzian distribution
  • SCALE5 - [kpc], scale length for exponential decay along z-direction

Functional Form

Bx = -B_t sin(phi)
By = B_t cos(phi)
Bz = 0

Where:
B_t = Bmax * (1+((z-H)/P)^2)^-1 for rho < R
B_t = Bmax * exp(-rho/R) * (1+((z-H)/P)^2)^-1 for rho >= R