Are ultracompact minihalos really ultracompact?

Ultracompact minihalos (UCMHs) have emerged as a valuable probe of the primordial power spectrum of density fluctuations at small scales. UCMHs are expected to form at early times in regions with ${\delta\rho/\rho \gtrsim 10^{-3}}$, and they are theorized to possess an extremely compact ${\rho\propto r^{-9/4}}$ radial density profile, which enhances their observable signatures. Nonobservation of UCMHs can thus constrain the primordial power spectrum. Using $N$-body simulations to study the collapse of extreme density peaks at ${z \simeq 1000}$, we show that UCMHs forming under realistic conditions do not develop the ${\rho\propto r^{-9/4}}$ profile and instead develop either ${\rho\propto r^{-3/2}}$ or ${\rho\propto r^{-1}}$ inner density profiles depending on the shape of the power spectrum. We also demonstrate via idealized simulations that self-similarity---the absence of a scale length---is necessary to produce a halo with the ${\rho\propto r^{-9/4}}$ profile, and we argue that this implies such halos cannot form from a Gaussian primordial density field. Prior constraints derived from UCMH nonobservation must be reworked in light of this discovery. Although the shallower density profile reduces UCMH visibility, our findings reduce their signal by as little as $\mathcal O(10^{-2})$ while allowing later-forming halos to be considered, which suggests that new constraints could be significantly stronger.