Neutrinos as galactic dark matter in the Ursa Major galaxy group?

We present the analysis of 23 published rotation curves of disc galaxies belonging to the Ursa Major group of galaxies, with kinematics free of irregularities. The rotation curves are analysed in the context of modified Newtonian dynamics (MOND). We add an extra component to the rotation curve fits, in addition to the stellar and gaseous discs: a speculative halo of constant density made of, for example, neutrinos, which would solve the bulk of the problem currently faced by MOND on rich galaxy cluster scales. We find that this additional unseen mass density is poorly constrained (as expected a priori, given that a neutrino halo never dominates the kinematics), but we also find that the best-fitting value is non-zero: rho = 3.8 x 10(-27) g cm(-3), and that a zero density is marginally excluded with 87 per cent confidence; also, the 95 per cent confidence upper limit for the density is rho = 9.6 x 10(-27) g cm(-3). These limits are slightly above the expectations from the Tremaine-Gunn phase-space constraints on ordinary eV neutrinos, but in accordance with the maximum density expected for one or two species of 5 eV sterile neutrinos.