Variability in Black Hole Accretion: Dependence on Rotational and Magnetic Energy Balance

Most general relativistic magnetohydrodynamic simulations of black hole (BH) hot accretion flows are initialized with small rotating tori and produce stable jets with only small fluctuations. However, recent studies using larger scale Bondi-like initial conditions have reported intermittent jet activity and loss of coherent rotation. To investigate the differences, we modify the standard torus setup across four BH spins: $a_*=0$, $0.5$, $0.9$, $-0.9$. First, we increase the torus size significantly (pressure maximum at 500 gravitational radii), allowing long simulations ($2.8\times10^5$ gravitational times) without gas depletion. These runs reproduce the weak variability seen in smaller tori, indicating that a larger dynamic range alone does not cause strong fluctuations. We observe moderate suppression of the accretion rate by factors of $\sim 1.6, ~2.5$ for BH spins $a_*=0.5,~0.9$, respectively, compared to $a_*=0$. Also, the density profile scales as $ρ(r)\propto r^{-1.1}$ for prograde BHs. Next, we considerably strengthen the initial magnetic field in the large torus by setting the plasma-$β\approx 1$. This induces strong variability in the evolution. The jet efficiency in the $a_*=0.9$ model, for instance, now varies by over 3 orders of magnitude, and gas rotation reverses directions. Combining these results with prior studies, we propose that a key parameter is the ratio $R$ between the rotational and magnetic energies in the initial state. Strong variability appears later in models with a larger value of $R$. The implication is that all simulations, and by extension all hot accretion flows in Nature, will ultimately develop intermittent jets if evolved long enough.