tokens: ; Boylan-Kolchin etal. 2012 ), and rotation curves (van der Marel Kallivayalil 2014 ). 2.4 Likelihood from <italic>V</italic><sub>max</sub> distributions Here, we summarize the statistical method for comparing the observational and simulated V max distributions. It is identical to that of Jiang van den Bosch ( 2015 ) except where noted below. The goal is to determine the probability that the Milky Way satellite V max function can be drawn from the distribution of simulated functions. We will establish the statistical scatter between the simulated V max functions, and calculate the mean deviation between the measured Milky Way V max function and the simulated systems. The size of the measured V max function deviation relative to the size of the scatter will tell us about how readily the Milky Way V max function is realized in each of our models. The first step is to define the variation within the set of V max for a given halo mass-dark matter modelgalaxy formation model combination. The n most massive satellites of the i th simulated halo are selected, and their values of V max are sorted into descending order. The V max distribution is then { V i , 1 , V i , 2 , V i , 3 V i , n }; here we have omitted the max subscript for clarity. We can define the difference between this i th halo distribution with respect to the j th halo distribution thus: and if there are N realizations of the model in question, the mean Q for the i th distribution, , is Similarly, if we substitute the i th simulated V max distribution to instead be { V MW, 1 , V MW, 2 , V MW, 3 V MW, n }, i.e. the observed V max distribution of the Milky Way satellites, then we obtain Q MW : The probability that a V max function with Q MW could be drawn from the parent distribution is then P ( Q MW ), where P is the cumulative distribution of . We expand on the method described above to describe how we select satellites. The luminosities calculated for the satellites enable us to take account of the fact that the brightest satellites, for which the velocity dispersions have been measured with the highest precision, need not necessarily reside in the most massive haloes. Therefore, we consider two options for selecting our top n satellites to be matched to observations: (i) select the n brightest V -band satellites and (ii) select the n highest V max satellites. We compare the results from these two approaches in Section 3.1.3 . 2.5 Sterile neutrino matter power spectra In addition to CDM, we consider keV-scale, resonantly produced sterile neutrino dark matter. The latter constitutes part of a larger particle physics model called the neutrino minimal standard model (MSM), which explains neutrino oscillations and baryogenesis in addition to yielding a dark matter candidate, see Boyarsky, Ruchayskiy Shaposhnikov ( 2009 ) for a review. The keV sterile neutrino behaves like WDM, in that it free streams out of small perturbations in the early Universe. The resulting matter power spectrum
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