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Context. Within the Λ cold dark matter (ΛCDM) cosmology, dark matter haloes are expected to deviate from spherical symmetry. The particular shape of a galactic halo reflects the environment and mass assembly history of its host, as well as the nature of dark matter. Constraining halo shapes at large galactocentric distances is challenging because of the low density of luminous tracers. The well-studied massive early-type galaxy NGC 5128, also known as Centaurus A (Cen A), has a large number of radial velocity measurements for globular clusters (GCs) and planetary nebulae (PNe) extending over a vast area of its extended low-surface-brightness stellar halo. Aims. In this work, we aim to determine the deviation from spherical symmetry of the dark matter halo of Cen A at 5 Re using its GCs as kinematic tracers of the gravitational potential. Methods. We investigated the largest photometric catalogue of GC candidates in order to accurately characterise the spatial distribution of the relaxed population of GCs. To investigate the presence of non-relaxed structures in the kinematic catalogue of GCs, we used the relaxed point-symmetric velocity field as determined by the host's PNe population. We used anisotropic Jeans modelling under axisymmetric assumptions together with the Gaussian likelihood and GCs as discrete tracers. The gravitational potential is generated by flattened stellar and dark matter distributions. We leveraged the different orbital properties of the blue and red GCs – such as rotation and velocity anisotropy – to model both populations separately. By minimising χ2, we iteratively find the best-fit parameters. Results. We find that the discrete kinematics of the GCs are consistent with being drawn from an underlying relaxed velocity field determined from PNe. The best-fit parameters of the gravitational potential recovered from the blue and red GCs separately agree well and we use them to compute the final results: M200 = 1.86−0.691.61 × 1012 M⊙, M⋆/LB = 2.98−0.78+0.96, and the flattening qDM = 1.45−0.53+0.78. Both GC populations show mild rotation, with red having a slightly stronger rotational signature and radially biased orbits, and blue GCs preferring negative velocity anisotropy. Conclusions. An oblate or a spherical dark matter halo of NGC 5128 is strongly disfavoured by our modelling. [ABSTRACT FROM AUTHOR]

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