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The dearth of dwarf galaxies in the local universe is hard to reconcile withthe large number of low mass haloes expected within the concordance$\Lambda$CDM paradigm. In this paper we perform a systematic evaluation of theuncertainties affecting the measurement of DM halo abundance using galaxykinematics. Using a large sample of dwarf galaxies with spatially resolvedkinematic data we derive a correction to obtain the observed abundance ofgalaxies as a function of their halo maximum circular velocity from theline-of-sight velocity function in the Local Volume. This estimate provides adirect means of comparing the predictions of theoretical models and simulations(including nonstandard cosmologies and novel galaxy formation physics) to theobservational constraints. The new "galactic $V_{max}$" function is steeperthan the line-of-sight velocity function but still shallower than thetheoretical CDM expectation, showing that some unaccounted physical process isnecessary to reduce the abundance of galaxies and/or drastically modify theirdensity profiles compared to CDM haloes. Using this new galactic $V_{max}$function, we investigate the viability of baryonic solutions such asfeedback-powered outflows and photoevaporation of gas from an ionisingradiation background. At the 3-$\sigma$ confidence level neither energeticfeedback nor photoevaporation are effective enough to reconcile thedisagreement. In the case of maximum baryonic effects, the theoretical estimatestill deviates significantly from the observations for $V_{max} < 60$ km/s. CDMpredicts at least 1.8 times more galaxies with $V_{max} = 50$ km/s and 2.5times more than observed at $30$ km/s. Recent hydrodynamic simulations seem toresolve the discrepancy but disagree with the properties of observed galaxieswith resolved kinematics. (abridged)

Another baryon miracle? Testing solutions to the "missing dwarfs" problem