Initial conditions

Fishbone-Moncrief torus (matter variables)

The Fishbone-Moncrief (FM) torus is the ubiquitous initial condition for modelling compact radio sources such as M87* and SgrA*. It is a solution to the relativistic Euler equations in a stationary, axisymmetric background for an isentropic, axisymmetric, purely azimuthal flow. The solutions are parameterized by a constant angular momentum mass density .

iharm sets 'l' by considering its value at the radius of maximum pressure (r_max). The size of the FM torus is completely determined by inner most radius of the torus (r_in) and r_max. The angular momentum mass density determines the specific enthalpy of the fluid h (cf. Equation 3.6). The remaining fluid variables are computed from h using the ideal gas EOS and the isentropic condition. The region outside the torus is initialized to zero enthalpy and density and internal energy are set to their respective flood values.

To maintain a purely azimuthal flow, u^r = u^θ = 0. Equation 3.3 followed by appropriate coordinate transformations yields u^φ. u^t is finally determined from the normalization condition, .

Adding the M in MHD (magnetic field variables)

There is a dichotomy in accretion flows based on the magnetic flux threading the event horizon: SANE (Standard and Normal Evolution) (cf. this) and MAD (Magnetically Arrested Disks) (cf. this paper). Although the state of the disk is determined a posteriori, one can initialize the magnetic fields differently to obtain a SANE or MAD state.

The magnetic vector potential is,

for a SANE and a MAD disk respectively (with all other components set to zero). The magnetic field components are evaluated by taking the curl of A and normalized by (β_act/beta)^1/2 where β_act= and beta is runtime parameter provided in param.dat.