Shapes of dark matter haloes with discrete globular cluster dynamics: The example of NGC 5128 (Centaurus A)
Within the $Λ$CDM cosmology, dark matter haloes are expected to deviate from spherical symmetry. Constraining the halo shapes at large galactocentric distances is challenging due to the low density of luminous tracers. The well-studied early-type galaxy NGC 5128 (Centaurus A - CenA), has a large number of radial velocities for globular clusters (GCs) and planetary nebulae (PNe) of its extended stellar halo. In this work, we aim to determine the deviation from spherical symmetry of the dark matter halo of CenA at 5 $R_{\rm e}$ using its GCs as kinematic tracers. We used the largest photometric catalogue of GC candidates to accurately characterise the spatial distribution of the relaxed population and investigated the presence of non-relaxed structures in the kinematic catalogue of GCs using 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 different orbital properties of the blue and red GCs to model them separately. We find that 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 the joint results are: $M_{200} = 1.86^{1.61}_{-0.69}\times 10^{12}$ M$_\odot$, $M_\star/L_{\rm B} = 2.98^{+0.96}_{-0.78}$ and the flattening $q_{\rm DM} = 1.45^{+0.78}_{-0.53}$. 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. An oblate or a spherical dark matter halo of CenA is strongly disfavoured by our modelling.