Accurate halo mass functions from the simplest excursion set theory

Excursion set theory is a powerful and widely used tool for describing the distribution of dark matter haloes, but it is normally applied with simplifying approximations. We use numerical sampling methods to study the mass functions predicted by the theory without approximations. With a spherical top-hat window and a constant $\delta=1.5$ threshold, the theory accurately predicts mass functions with the $M_{200}$ mass definition, both unconditional and conditional, in simulations of a range of matter-dominated cosmologies. For $\Lambda$CDM at the present epoch, predictions lie between the $M_\mathrm{200m}$ and $M_\mathrm{200c}$ mass functions. In contrast, with the same window function, a nonconstant threshold based on ellipsoidal collapse predicts uniformly too few haloes. This work indicates a new way to simply and accurately evaluate halo mass functions, clustering bias, and assembly histories for a range of cosmologies. We provide a simple fitting function that accurately represents the predictions of the theory for a wide range of parameters.Comment: 16 pages, 14 figures. Accepted by MNRAS; includes more estimates of statistical uncertaint

Can prompt cusps of WIMP dark matter be detected as individual gamma-ray sources?

Prompt $\rho\propto r^{-1.5}$ density cusps are the densest and most abundant dark matter systems. If the dark matter is a weakly interacting massive particle (WIMP), recent studies have shown that prompt cusps dominate the aggregate dark matter annihilation rate. This article explores whether individual prompt cusps could be detected as gamma-ray sources. At the Fermi telescope's point-source sensitivity, WIMPs with the canonical annihilation cross section could form detectable prompt cusps if the particle mass is of order 10 GeV. These objects could be 10-100 pc away and weigh under a solar mass; they would subtend around 0.1 degrees on the sky. For GeV-scale dark matter particles with below-canonical cross sections, searches for individual prompt cusps can be more sensitive than searches for the annihilation signals from galactic dark matter halos.Comment: 8 pages, 5 figures; accepted by Physical Review

Massive prompt cusps: A new signature of warm dark matter

Every dark matter halo and subhalo is expected to have a prompt $\rho\propto r^{-1.5}$ central density cusp, which is a relic of its condensation out of the smooth mass distribution of the early universe. The sizes of these prompt cusps are linked to the scales of the peaks in the initial density field from which they formed. In warm dark matter (WDM) models, the smoothing scale set by free streaming of the dark matter can result in prompt cusps with masses of order $10^7$ M$_\odot$. We show that WDM models with particle masses ranging from 2 to 6 keV predict prompt cusps that could detectably alter the observed kinematics of Local Group dwarf galaxies. Thus, prompt cusps present a viable new probe of WDM. A prompt cusp's properties are highly sensitive to when it formed, so prospects can be improved with a better understanding of when the haloes of the Local Group dwarfs originally formed. Tidal stripping can also affect prompt cusps, so constraints on satellite galaxy orbits can further tighten WDM inferences.Comment: 5 pages, 6 figures; accepted by MNRAS Letters. Includes more detail on the sampling of prompt cusp

Simulations of Gravitational Heating Due to Early Matter Domination

In cosmologies with an early matter-dominated era (EMDE) prior to Big Bang nucleosynthesis, the boosted growth of small-scale matter perturbations during the EMDE leads to microhalo formation long before halos would otherwise begin to form. For a range of models, halos can even form during the EMDE itself. These halos would dissipate at the end of the EMDE, releasing their gravitationally heated dark matter and thereby imprinting a free-streaming cut-off on the matter power spectrum. We conduct the first cosmological $N$-body simulations of the formation and evaporation of halos during and after an EMDE. We show that in these scenarios, the free-streaming cut-off after the EMDE can be predicted accurately from the linear matter power spectrum. Although the free streaming can erase much of the EMDE-driven boost to density perturbations, we use our findings to show that the (re-)formation of halos after the EMDE nevertheless proceeds before redshift $\sim 1000$. Early-forming microhalos are a key observational signature of an EMDE, and our prescription for the impact of gravitational heating will allow studies of the observational status and prospects of EMDE scenarios to cover a much wider range of parameters.Comment: 33 pages, 16 figures. Comments welcom

Lensing constraints on ultradense dark matter halos

Cosmological observations precisely measure primordial variations in the density of the Universe at megaparsec and larger scales, but much smaller scales remain poorly constrained. However, sufficiently large initial perturbations at small scales can lead to an abundance of ultradense dark matter minihalos that form during the radiation epoch and survive into the late-time Universe. Because of their early formation, these objects can be compact enough to produce detectable microlensing signatures. We investigate whether the EROS, OGLE, and HSC surveys can probe these halos by fully accounting for finite source size and extended lens effects. We find that current data may already constrain the amplitudes of primordial curvature perturbations in a new region of parameter space, but this conclusion is strongly sensitive to yet undetermined details about the internal structures of these ultradense halos. Under optimistic assumptions, current and future HSC data would constrain a power spectrum that features an enhancement at scales $k \sim 10^7/{\rm Mpc}$, and an amplitude as low as $\mathcal{P}_\zeta\simeq 10^{-4}$ may be accessible. This is a particularly interesting regime because it connects to primordial black hole formation in a portion of the LIGO/Virgo/Kagra mass range and the production of scalar-induced gravitational waves in the nanohertz frequency range reachable by pulsar timing arrays. These prospects motivate further study of the ultradense halo formation scenario to clarify their internal structures.Comment: 17 pages, 10 figures. v2: matching published versio

Inner cusps of the first dark matter haloes: Formation and survival in a cosmological context

We use very high resolution cosmological zoom simulations to follow the early evolution of twelve first-generation haloes formed from gaussian initial conditions with scale-free power spectra truncated on small scales by a gaussian. Initial collapse occurs with a diverse range of sheet- or filament-like caustic morphologies, but in almost all cases it gives rise to a numerically converged density cusp with $\rho = Ar^{-3/2}$ and total mass comparable to that of the corresponding peak in the initial linear density field. The constant $A$ can be estimated to within about 10 per cent from the properties of this peak. This outcome agrees with earlier work on the first haloes in cold and warm dark matter universes. Within central cusps, the velocity dispersion is close to isotropic, and equidensity surfaces tend to align with those of the main body of the halo at larger radii. As haloes grow, their cusps are often (but not always) overlaid with additional material at intermediate radii to produce profiles more similar to the Einasto or NFW forms typical of more massive haloes. Nevertheless, to the extent that we can resolve them, cusps survive at the smallest radii. Major mergers can disturb them, but the effect is quite weak in the cases that we study. The cusps extend down to the resolution limits of our simulations, which are typically a factor of several larger than the cores that would be produced by phase-space conservation if the initial power spectrum cutoff arises from free streaming.Comment: 23 pages, 28 figures; to be submitted to MNRA