Power-law relations between tracers of baryonic mass and rotational velocities of disk galaxies, so-called Tully-Fisher relations (TFRs), offer a wealth of applications in galaxy evolution and cosmology. However, measurements of rotational velocities require galaxy inclinations, which are difficult to measure, thus limiting the range of TFR studies. This work introduces a maximum likelihood estimation (MLE) method for recovering the TFR in galaxy samples with limited or no information on inclinations. The robustness and accuracy of this method is demonstrated using virtual and real galaxy samples. Intriguingly, the MLE reliably recovers the TFR of all test samples, even without using any inclination measurements - that is, assuming a sin(i)-distribution for galaxy inclinations. Explicitly, this inclination-free MLE recovers the three TFR parameters (zero-point, slope, scatter) with statistical errors only about 1.5-times larger than the best estimates based on perfectly known galaxy inclinations with zero uncertainty. Thus, given realistic uncertainties, the inclination-free MLE is highly competitive. If inclination measurements have mean errors larger than 10 degrees, it is better not to use any inclinations, than to consider the inclination measurements to be exact. The inclination-free MLE opens interesting perspectives for future HI surveys by the SKA and its pathfinders.
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