A Cuspy Dark Matter Halo

The cusp-core problem is one of the main challenges of the cold dark matter paradigm on small scales; the density of a dark matter halo is predicted to rise rapidly toward the center as rho(r) proportional to r(alpha) with alpha between -1 and -1.5, while such a cuspy profile has not been clearly observed. We have carried out the spatially resolved mapping of gas dynamics toward a nearby ultradiffuse galaxy (UDG), AGC 242019. The derived rotation curve of dark matter is well fitted by the cuspy profile as described by the Navarro-Frenk-White model, while the cored profiles including both the pseudo-isothermal and Burkert models are excluded. The halo has alpha = -(0.90 0.08) at the innermost radius of 0.67 kpc, M-halo = (3.5 1.2) x 10(10) M, and a small concentration of 2.0 0.36. The UDG AGC 242019 challenges alternatives of cold dark matter by constraining the particle mass of fuzzy dark matter to be 3.3 x 10(-22) eV, the cross section of self-interacting dark matter to be <1.63 cm(2) g(-1), and the particle mass of warm dark matter to be >0.23 keV, all of which are in tension with other constraints. The modified Newtonian dynamics is also inconsistent with a shallow radial acceleration relationship of AGC 242019. For the feedback scenario that transforms a cusp to a core, AGC 242019 disagrees with the stellar-to-halo mass ratio dependent model but agrees with the star formation threshold dependent model. As a UDG, AGC 242019 is in a dwarf-sized halo with weak stellar feedback, late formation time, normal baryonic spin, and low star formation efficiency (SFR/gas).