tokens: drive heat conduction in the disc. Fig. 6 shows that, even in 3D, the heat flux is negligible in regions in which P saturates. From our EMHD simulation, we thus deduce that the average impact of the non-ideal effects in the compact, SANE disc studied here might be close to what one would obtain by setting P 0.25 b 2 and q 0. We also note that our results critically depend on the treatment of the mirror instability in the EMHD model. We assume that when driven above the threshold of the mirror instability, P saturates at nearly exactly the instability threshold P mirror , through an increase in the effective collision rate in the plasma. Our results are only physical if this approximation captures the global behaviour of the plasma on length-scales much larger than the Larmor radius. While current particle-in-cell simulations broadly support this model (Kunz etal. 2016 ), comparisons of the EMHD model with more detailed local simulations of a plasma at the mirror instability threshold will be required to test this assumption. 4.4 Stress tensor and angular momentum transport In previous sections, we showed that the pressure anisotropy in the EMHD simulations of SANE discs is, in a time-averaged sense, P b 2 /4. In Section 2 , we also argued that the associated shear stress, , is effectively of the same form as the magnetic shear stress, . As far as the shear stress is concerned, the pressure anisotropy P and the magnetic energy density b 2 are interchangeable. Additionally, for 1, the magnetic energy density and isotropic magnetic pressure do not play a particularly important role in the dynamics of the accretion flow. Accordingly, we may expect similar steady-state accretion flows to be reached in EMHD and IMHD if . Our simulations appear consistent with this interpretation of the impact of the pressure anisotropy: in the SANE configuration, we find similar density and temperature profiles for the EMHD and IMHD models, but with a weaker magnetic field in the EMHD model, e.g. the plasma parameter satisfies EMHD (1.21.4) IMHD . We can have a more direct look at the component of the stress-energy tensor responsible for angular momentum transport in the disc, . We show radial profiles of (averaged over time and azimuthal angle, integrated over the polar angle and normalized by the gas pressure) in Fig. 10 . The first notable result is that the total stress is nearly identical for the IMHD and EMHD simulations. However, in the IMHD model, the entirety of the stress is due to the magnetic field. In the EMHD model, outside the ISCO of the black hole, (7075)percent of the r component of the stress is due to the magnetic field and (2530)percent to the pressure anisotropy. While this fraction of the stress due to the pressure anisotropy is slightly larger than one might have expected based on the simplistic model of a constant ratio P b 2 1 4, the properties of the stress tensor are broadly consistent with the view that in EMHD the pressure anisotropy
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