The stellar bar - dark matter halo connection in the TNG50 simulations

Stellar bars in disk galaxies grow as stars in near circular orbits lose angular momentum to their environments, including their Dark Matter (DM) halo, and transform into elongated bar orbits. This angular momentum exchange during galaxy evolution hints at a connection between bar properties and the DM halo spin $\lambda$, the dimensionless form of DM angular momentum. We investigate the connection between halo spin $\lambda$ and galaxy properties in the presence/absence of stellar bars, using the cosmological magneto-hydrodynamic TNG50 simulations at multiple redshifts ($0<z_r<1$). We determine the bar strength (or bar amplitude, $A_2/A_0$), using Fourier decomposition of the face-on stellar density distribution. We determine the halo spin for barred and unbarred galaxies ($0<A_2/A_0<0.7$) in the centre of the DM halo, close to the galaxy's stellar disk. At $z_r=0$, there is an anti-correlation between halo spin and bar strength. Strongly barred galaxies ($A_2/A_0>0.4$) reside in DM halos with low spin and low specific angular momentum at their centers. In contrast, unbarred/weakly barred galaxies ($A_2/A_0<0.2$) exist in halos with higher central spin and higher specific angular momentum. The anti-correlation is due to the barred galaxies' higher DM mass and lower angular momentum than the unbarred galaxies at $z_r=0$, as a result of galaxy evolution. At high redshifts ($z_r=1$), all galaxies have higher halo spin compared to those at lower redshifts ($z_r=0$), with a weak anti-correlation for galaxies having $A_2/A_0> 0.2$. The formation of a DM bar in strongly barred systems highlights how angular momentum transfer to the halo can influence its central spin.