The multi-wavelength Tully-Fisher relation in the TNG50 cosmological simulation

The Tully-Fisher relation (TFR) is one of the most important and widely used empirical correlations in extragalactic astronomy. Apart from its importance as a secondary distance indicator, the TFR relation serves as a test for galaxy evolution models, because it connects the baryonic and dark matter components of galaxies. We aim at simulating the multi-wavelength TFR relation from UV to mid-infrared wavelengths for the TNG50 cosmological simulation at $z = 0$, and at comparing the results with observational TFR studies. We want to compare the wavelength dependence of the slope and scatter with the observed values, and search for secondary parameters that reduce the scatter in the TFR. We select a large sample of simulated late-type, disc-dominated galaxies from the TNG50 simulation. For each galaxy, we use the SKIRT radiative transfer code to generate realistic synthetic global fluxes in 12 UV to mid-infrared broadbands and synthetic integrated HI line profiles. We use bivariate linear regression to determine the TFR in each band, and we search for a second TFR parameter by correlating the residuals with different physical parameters. Our TNG50 TFR reproduces the characteristic behaviour of the observed TFR in many studies: the TFR becomes steeper and tighter as we move from UV/optical to infrared wavelengths. The slope changes from $-7.46 \pm 0.14~{\text{mag}}~{\text{dex}}^{-1}$ in the NUV band to $-9.66 \pm 0.09~{\text{mag}}~{\text{dex}}^{-1}$ in the IRAC [4.5] band. Quantitatively, our slopes are well within the spread of different observational results. The ${\textit{u}} - {\textit{r}}$ colour or the sSFR can significantly reduce the scatter in the UV and optical bands. Using ${\textit{u}} - {\textit{r}}$ colour as second parameter, the modified TFR has a roughly constant intrinsic tightness of over the entire UV to MIR range. The combination of the TNG50...