The Magnetic Filling in MAD Simulations and its Impact on the Jet in M87

Abstract

Magnetically arrested accretion disks (MADs) in black hole jet launching simulations are very successful in modelling low-luminosity active galactic nuclei (AGN) like M87*. The Fishbone-Moncrief torus is well established for this purpose in numerical astrophysics. The extent of the magnetic vector potential inside the torus that we coin the filling factor has not been studied before in the case of MAD simulations. We employ five 3D general relativistic magneto-hydrodynamics (GRMHD) simulations initialized with large-scale tori, that are immersed in weak, poloidal magnetic fields. To study the impact of the spatial extent of the initial magnetic field, hence the magnetic energy content in the torus, we scale it with the filling factor w.r.t. the poloidal geometric area of the mass density distribution. A common choice of the filling factor is complimented and investigated in terms of altered energetics and angular momentum transport. Further, we investigate the polarized, radiative imprints of synchrotron emission on M87 at 86 GHz, comparing them with VLBI observations. Our simulations show that elevated filling factors significantly increase the electromagnetic energy contributions and outward angular momentum transport in the jet, due to the initially increased magnetic energy-content in the torus. High magnetic fillings exhibit increased linear polarization fractions, agreeing with the observed 15$\%$ in M87*. We find the jet morphology more prone to disk-vertical flux tubes generated by MAD events. We show, that GRMHD simulations bracket the jet width measurements at the jet base in M87*. Increased magnetic filling of the torus produces jets that are noticeably brighter downstream compared to our reference models, hence, we find high fillings well suited for extended GRMHD jet models of other low-luminosity AGN, as well.

Figures (21)

• Figure 1: Invariant magnetic field strength $b$, the spatial magnetic field components $B^r$ and $B^\theta$, and four-vector-potential component $A_\phi$ over the polar angle at the initialization step ($t=0\,\rm{M}$). Colors correspond to simulations K.60 (orange), K.80 (green), K.90 (blue), K.95 (magenta) and K.99 (red). In the middle row the solid lines show $B^r$ and the dashed lines $B^\theta$. We choose polar slices at radii around the inner edge of the torus at $r_{\rm{in}}=20\,\rm{M}$ and at the pressure maximum in the tori at $r=50\,\rm{M}$. Note that going from left to right colums, i.e. radially outwards, the simulations with higher filling factors show increased magnetic field strengths and extended magnetic field, both radially and in the polar-angle, especially at the inner edge of the torus.
• Figure 2: Mass accretion rates $\dot{M}$, magnetic flux through the event horizon of the BH $\phi_\mathrm{BH}$ and the MAD-parameter $\Psi=\phi_\mathrm{BH}/\sqrt{\dot{M}}$ for the simulations K.80, K.90 and K.99 over time.
• Figure 3: Temporal evolution of the total energy flux (solid lines) and EM energy flux (dashed lines) measured at $r=10\, \unit{M}$ in the jet for simulations K.60 (orange), K.80 (green), K.90 (blue), K.95 (magenta) and K.99 (red). The horizontal lines show the average of the total energy fluxes for each run over the shown time interval.
• Figure 4: Time averaged total energy fluxes (dash-dotted lines), EM energy fluxes (solid lines) and kinetic energy fluxes (dashed lines) in the time interval $(25000-30000)\,M$ for varying BH separations along the jet for simulations K.60 (orange), K.80 (green), K.90 (blue), K.95 (magenta) and K.99 (red). The vertical dotted lines indicate the radii at which the kinetic and EM energy fluxes are in equipartition.
• Figure 5: Jet efficiencies for simulations K.60 (orange), K.80 (green), K.90 (blue), K.95 (magenta) and K.99 (red), where the dashed horizontal lines show the time averaged efficiencies and the correlation corrected $2\sigma_{\rm{corr}}$ error-band over the shown interval (listed in Tab. \ref{['tab: Outflow Efficiencies of Jet']}).