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The faintness of satellite systems in galaxy groups has contributed to the widely discussed missing satellite and too big to fail issues. Using techniques based on Tremaine & Richstone (1977), we show that there is no problem with the luminosity function computed from modern codes per se, but that the gap between first and second brightest systems is too big {it given} the luminosity function, that the same large gap is found in modern, large scale baryonic $Lambda$CDM simulations such as EAGLE and IllustrisTNG, is even greater in dark matter only simulations, and finally, that this is most likely due to gravitationally induced merging caused by classical dynamical friction. Quantitatively the gap is larger in the computed simulations than in the randomized ones by $1.79 pm 1.04$, $1.51 pm 0.93$, $3.43 pm 1.44$ and $3.33 pm 1.35$ magnitudes in the EAGLE, IllustrisTNG, and dark matter only simulations of EAGLE and IllustrisTNG respectively. Furthermore the anomalous gaps in the simulated systems are even larger than in the real data by over half a magnitude and are still larger in the dark matter only simulations. Briefly stated, $Lambda$CDM does not have a problem with an absence of too big to fail galaxies. Statistically significant large gaps between first and second brightest galaxies are to be expected.
We use the Arecibo legacy fast ALFA (ALFALFA) 21cm survey to measure the number density of galaxies as a function of their rotational velocity, $V_mathrm{rot,HI}$ (as inferred from the width of their 21cm emission line). Based on the measured velocit
We use a semi-analytical model for the substructure of dark matter haloes to assess the too-big-to-fail (TBTF) problem. The model accurately reproduces the average subhalo mass and velocity functions, as well as their halo-to-halo variance, in N-body
N-body dark matter simulations of structure formation in the $Lambda$CDM model predict a population of subhalos within Galactic halos that have higher central densities than inferred for satellites of the Milky Way, a tension known as the `too big to
Recent studies have established that extreme dwarf galaxies --whether satellites or field objects-- suffer from the so called too big to fail (TBTF) problem. Put simply, the TBTF problem consists of the fact that it is difficult to explain both the m
We study the problem of fairly allocating a divisible resource, also known as cake cutting, with an additional requirement that the shares that different agents receive should be sufficiently separated from one another. This captures, for example, co