Dark Matter Phase-space Distribution Research Articles

A phenomenological model for dark matter phase-space distribution

ABSTRACT Understanding the nature of dark matter is among the top priorities of modern physics. However, due to its inertness, detecting and studying it directly in terrestrial experiments is extremely challenging. Numerical N-body simulations currently represent the best approach for studying the particle properties and phase-space distribution, assuming the collisionless nature of dark matter. These simulations also address the lack of a satisfactory theory for predicting the universal properties of dark matter haloes, including the density profile and velocity distribution. In this work, we propose a new phenomenological model for the dark matter phase-space distribution. This model aims to provide an Navarro–Frenk–White-like density profile, velocity magnitude distribution, and velocity component distributions that align closely with simulation data. Our model is relevant both for theoretical modelling of dark matter distributions, and for underground detector experiments that rely on the dark matter velocity distribution for experimental analysis.

Distinguishing thermal histories of dark matter from structure formation

It is important to understand the implications of current observational constraints and potential signatures on the thermal history of dark matter. In this paper, we build the connection between the present-day velocities and the production mechanism of dark matter and find that the current observation on structure formation can be imposed to constrain the decoupling temperatures and the phase-space distribution of dark matter. We further explore the potential of distinguishing different possible thermal histories of dark matter with hypothetical future observational data. Using the freeze-in/-out scenarios as templates, we find that future precision data may uniquely identify the allowed parameter spaces for freeze-in and freeze-out, or even completely rule out one of the scenarios. This method can be more generally applied to other scenarios.

Forbidden dark matter annihilation into leptons with full collision terms

The standard approach of calculating the relic density of thermally produced dark matter based on the assumption of kinetic equilibrium is known to fail for forbidden dark matter models since only the high momentum tail of the dark matter phase space distribution function contributes significantly to dark matter annihilations. Furthermore, it is known that the computationally less expensive Fokker-Planck approximation for the collision term describing elastic scattering processes between non-relativistic dark matter particles and the Standard Model thermal bath breaks down if both scattering partners are close in mass. This, however, is the defining feature of the forbidden dark matter paradigm. In this paper, we therefore include the full elastic collision term in the full momentum-dependent Boltzmann equation as well as in a set of fluid equations that couple the evolution of the number density and dark matter temperature for a simplified model featuring forbidden dark matter annihilations into muon or tau leptons through a scalar mediator. On the technical side, we perform all angular integrals in the full collision term analytically and take into account the effect of dark matter self-interactions on the relic density. The overall phenomenological outcome is that the updated relic density calculation results in a significant reduction of the experimentally allowed parameter space compared to the traditional approach, which solves only for the abundance. In addition, almost the entire currently viable parameter space can be probed with CMB-S4, next-generation beam-dump experiments or at a future high-luminosity electron-position collider, except for the resonant region where the mediator corresponds to approximately twice the muon or tau mass.

Scalar dark matter production from preheating and structure formation constraints

We investigate the out-of-equilibrium production of scalar dark matter (DM) from the inflaton condensate during inflation and reheating. We assume that this scalar couples only to the inflaton via a direct quartic coupling and is minimally coupled to gravity. We consider all possible production regimes: purely gravitational, weak direct coupling (perturbative), and strong direct coupling (non-perturbative). For each regime, we use different approaches to determine the dark matter phase space distribution and the corresponding relic abundance. For the purely gravitational regime, scalar dark matter quanta are copiously excited during inflation resulting in an infrared (IR) dominated distribution function and a relic abundance which overcloses the universe for a reheating temperature $T_\text{reh}>34 ~\text{GeV}$. A non-vanishing direct coupling induces an effective DM mass and suppresses the large IR modes in favor of ultraviolet (UV) modes and a minimal scalar abundance is generated when the interference between the direct and gravitational couplings is maximal. For large direct couplings, backreaction on the inflaton condensate is accounted for by using the Hartree approximation and lattice simulation techniques. Since scalar DM candidates can behave as non-cold dark matter, we estimate the impact of such species on the matter power spectrum and derive the corresponding constraints from the Lyman-$\alpha$ measurements. We find that they correspond to a lower bound on the DM mass of $\gtrsim 3\times 10^{-4} \, \rm{eV}$ for purely gravitational production, and $\gtrsim 20 \, \rm {eV}$ for direct coupling production. We discuss the implications of these results.

Freeze-in, glaciation, and UV sensitivity from light mediators

Dark matter (DM) freeze-in through a light mediator is an appealing model with excellent detection prospects at current and future experiments. Light mediator freeze-in is UV-insensitive insofar as most DM is produced at late times, and thus the DM abundance does not depend on the unknown early evolution of our universe. However the final DM yield retains a dependence on the initial DM population, which is usually assumed to be exactly zero. We point out that in models with light mediators, the final DM yield will also depend on the initial conditions assumed for the light mediator population. We describe a class of scenarios we call “glaciation” where DM freezing in from the SM encounters a pre-existing thermal bath of mediators, and study the dependence of the final DM yield on the initial temperature of this dark radiation bath. To compute DM scattering rates in this cosmology, we derive for the first time an exact integral expression for the Boltzmann collision term describing interactions between two species at different temperatures. We quantify the dependence of the DM yield on the initial dark temperature and find that it can be sizeable in regions near the traditional (zero initial abundance) freeze-in curve. We generalize the freeze-in curve to a glaciation band, which can extend as much as an order of magnitude below the traditional freeze-in direct detection target, and point out that the DM phase space distribution as well as the yield can be strongly dependent on initial conditions.

Testing the predictions of axisymmetric distribution functions of galactic dark matter with hydrodynamical simulations

Signal predictions for galactic dark matter (DM) searches often rely on assumptions regarding the DM phase-space distribution function (DF) in halos. This applies to both particle (e.g. p-wave suppressed or Sommerfeld-enhanced annihilation, scattering off atoms, etc.) and macroscopic DM candidates (e.g. microlensing of primordial black holes). As experiments and observations improve in precision, better assessing theoretical uncertainties becomes pressing in the prospect of deriving reliable constraints on DM candidates or trustworthy hints for detection. Most reliable predictions of DFs in halos are based on solving the steady-state collisionless Boltzmann equation (e.g. Eddington-like inversions, action-angle methods, etc.) consistently with observational constraints. One can do so starting from maximal symmetries and a minimal set of degrees of freedom, and then increasing complexity. Key issues are then whether adding complexity, which is computationally costy, improves predictions, and if so where to stop. Clues can be obtained by making predictions for zoomed-in hydrodynamical cosmological simulations in which one can access the true (coarse-grained) phase-space information. Here, we test an axisymmetric extension of the Eddington inversion to predict the full DM DF from its density profile and the total gravitational potential of the system. This permits to go beyond spherical symmetry, and is a priori well suited for spiral galaxies. We show that axisymmetry does not necessarily improve over spherical symmetry because the (observationally unconstrained) angular momentum of the DM halo is not generically aligned with the baryonic one. Theoretical errors are similar to those of the Eddington inversion though, at the 10–20% level for velocity-dependent predictions related to particle DM searches in spiral galaxies. We extensively describe the approach and comment on the results.

Dark matter interferometry

The next generation of ultralight dark matter (DM) direct detection experiments, which could confirm sub-eV bosons as the dominant source of DM, will feature multiple detectors operating at various terrestrial locations. As a result of the wave-like nature of ultralight DM, spatially separated detectors will each measure a unique DM phase. When the separation between experiments is comparable to the DM coherence length, the spatially-varying phase contains information beyond that which is accessible at a single detector. We introduce a formalism to extract this information, which performs interferometry directly on the DM wave. In particular, we develop a likelihood-based framework that combines data from multiple experiments to constrain directional information about the DM phase space distribution. We show that the signal in multiple detectors is subject to a daily modulation effect unique to wave-like DM. Leveraging daily modulation, we illustrate that within days of an initial discovery multiple detectors acting in unison could localize directional parameters of the DM velocity distribution such as the direction of the solar velocity to sub-degree accuracy, or the direction of a putative cold DM stream to the sub-arcminute level. We outline how to optimize the locations of multiple detectors with either resonant cavity (such as ADMX or HAYSTAC) or quasistatic (such as ABRACADABRA or DM-Radio) readouts to have maximal sensitivity to the full 3-dimensional DM velocity distribution.

Predicting the dark matter velocity distribution in galactic structures: tests against hydrodynamic cosmological simulations

Reducing theoretical uncertainties in Galactic dark matter (DM) searches is an important challenge as several experiments are now delving into the parameter space relevant to popular (particle or not) candidates. Since many DM signal predictions rely on the knowledge of the DM velocity distribution—direct searches, capture by stars, p-wave-suppressed or Sommerfeld-enhanced annihilation rate, microlensing of primordial black holes, etc—it is necessary to assess the accuracy of our current theoretical handle. Beyond Maxwellian approximations or ad-hoc extrapolations of fits on cosmological simulations, approaches have been proposed to self-consistently derive the DM phase-space distribution only from the detailed mass content of the Galaxy and some symmetry assumptions (e.g. the Eddington inversion and its anisotropic extensions). Although theoretically sound, these methods are still based on simplifying assumptions and their relevance to real galaxies can be questioned. In this paper, we use zoomed-in cosmological simulations to quantify the associated uncertainties. Assuming isotropy, we predict the speed distribution and its moments from the DM and baryonic content measured in simulations, and compare them with the true ones. {Taking as input galactic mass models fitted on full simulation data, we reach a predictivity down to ∼ 10% for some velocity-related observables, significantly better than some Maxwellian models.} This moderate theoretical error is particularly encouraging at a time when stellar surveys like the Gaia mission should allow us to improve constraints on Galactic mass models.

Non-cold dark matter from primordial black hole evaporation

Dark matter coupled solely gravitationally can be produced through the decay of primordial black holes in the early universe. If the dark matter is lighter than the initial black hole temperature, it could be warm enough to be subject to structure formation constraints. In this paper we perform a more precise determination of these constraints. We first evaluate the dark matter phase-space distribution, without relying on the instantaneous decay approximation. We then interface this phase-space distribution with the Boltzmann code to extract the corresponding matter power spectrum, which we find to match closely those of warm dark matter models, albeit with a different dark matter mass. This mapping allows us to extract constraints from Lyman-α data without the need to perform hydrodynamical simulations. We robustly rule out the possibility, consistent with previous analytic estimates, of primordial black holes having come to dominate the energy density of the universe and simultaneously given rise to all the DM through their decay. Consequences and implications for dark radiation and leptogenesis are also briefly discussed.

Observationally inferred dark matter phase-space distribution and direct detection experiments

We present a detailed analysis of the effect of an observationally determined dark matter (DM) velocity distribution function (VDF) of the Milky Way (MW) on DM direct detection rates. We go beyond local kinematic tracers and use rotation curve data up to 200 kpc to construct a MW mass model and self-consistently determine the local phase-space distribution of DM. This approach mitigates any incomplete understanding of local dark matter-visible matter degeneracies that can affect the determination of the VDF. Comparing with the oft used Standard Halo Model (SHM), which assumes an isothermal VDF, we look at how the tail of the empirically determined VDF alters our interpretation of the present direct detection WIMP DM cross section exclusion limits. While previous studies have suggested a very large difference (of more than an order of magnitude) in the bounds at low DM masses, we show that accounting for the detector response at low threshold energies, the difference is still significant although less extreme. The change in the number of signal events, when using the empirically determined DM VDF in contrast to the SHM VDF, is most prominent for low DM masses for which the shape of the recoil energy spectrum depends sensitively on the detector threshold energy as well as detector response near the threshold. We demonstrate that these trends carry over to the respective DM exclusion limits, modulo detailed understanding of the experimental backgrounds. With the unprecedented precision of astrometric data in the GAIA era, use of observationally determined DM phase-space will become a critical and necessary ingredient for DM searches. We provide an accurate fit to the current best observationally determined DM VDF (and self-consistent local DM density) for use in analyzing current DM direct detection data by the experimental community.

Boltzmann-Fokker-Planck formalism for dark matter-baryon scattering

Linear-cosmology observables, such as the Cosmic Microwave Background (CMB), or the large-scale distribution of matter, have long been used as clean probes of dark matter (DM) interactions with baryons. It is standard to model the DM as an ideal fluid with a thermal Maxwell-Boltzmann (MB) velocity distribution, in order to compute the heat and momentum-exchange rates relevant to these probes. This approximation only applies in the limit where DM self-interactions are frequent enough to efficiently redistribute DM velocities. It does not accurately describe weakly self-interacting particles, whose velocity distribution unavoidably departs from MB once they decouple from baryons. This article lays out a new formalism required to accurately model DM-baryon scattering, even when DM self-interactions are negligible. The ideal fluid equations are replaced by the collisional Boltzmann equation for the DM phase-space distribution. The collision operator is approximated by a Fokker-Planck operator, constructed to recover the exact heat and momentum exchange rates, and allowing for an efficient numerical implementation. Numerical solutions to the background evolution are presented, which show that the MB approximation can over-estimate the heat-exchange rate by factors of ~ 2-3, especially for light DM particles. A Boltzmann-Fokker-Planck hierarchy for perturbations is derived. This new formalism allows to explore a wider range of DM models, and will be especially relevant for upcoming ultra-high-sensitivity CMB probes.

On velocity-dependent dark matter annihilations in dwarf satellites

Milky Way dwarf spheroidal satellites are a prime target for Dark Matter (DM) indirect searches. Recently the importance of possible long-range interactions has been recognized, as they can boost the expected DM gamma ray signal by orders of magnitude through an effect commonly known as the Sommerfeld enhancement. However, for such analyses precise modelling of DM phase-space distribution becomes crucial and can introduce large uncertainties in the final result. We provide a pioneering attempt towards a comprehensive investigation of these systematics. First, the DM halo profiles are constrained using Bayesian inference on the available stellar kinematic datasets with a careful treatment of observational and theoretical uncertainties. We consider both cuspy and cored parametric DM density profiles, together with the case of a non-parametric halo modelling directly connected to observable quantities along the line-of-sight. After reconsidering the study case of ergodic systems, the basic ingredient of all previous analyses, we investigate for the first time scenarios where DM particles are allowed to have anisotropic velocity distributions. Referring to a generalized J-factor, sensitive to velocity-dependent effects, an enhancement (suppression) with respect to the isotropic phase-space distributions is obtained for the case of tangentially (radially) biased DM particle orbits. We provide new estimates for J-factors for the eight brightest Milky Way dwarfs also in the limit of velocity-independent DM annihilation, in good agreement with previous results in literature, and derive data-driven lower-bounds based on the non-parametric modelling of the halo density. This work presents a state-of-the-art analysis of the aforementioned effects and falls within the interest of current and future experimental collaborations involved in DM indirect detection programs.

Anatomy of Eddington-like inversion methods in the context of dark matter searches

Irrespective of the dark matter (DM) candidate, several potentially observable signatures derive from the velocity distribution of DM in halos, in particular in the Milky Way (MW) halo. Examples include direct searches for weakly-interacting massive particles (WIMPs), p-wave suppressed or Sommerfeld-enhanced annihilation signals, microlensing events of primordial black holes (PBHs), etc. Most current predictions are based on the Maxwellian approximation which is not only theoretically inconsistent in bounded systems, but also not supported by cosmological simulations. A more consistent method sometimes used in calculations for direct WIMP searches relies on the so-called Eddington inversion method, which relates the DM phase-space distribution function (DF) to its mass density profile and the total gravitational potential of the system. Originally built upon the isotropy assumption, this method can be extended to anisotropic systems. We investigate these inversion methods in the context of Galactic DM searches, motivated by the fact that the MW is a strongly constrained system, and should be even more so with the ongoing Gaia survey. We still draw conclusions that apply to the general case. In particular, we illustrate how neglecting the radial boundary of the DM halo leads to theoretical inconsistencies. We also show that several realistic configurations of the DM halo and the MW baryonic content entail ill-defined DFs, significantly restricting the configuration space over which these inversion methods can apply. We propose consistent solutions to these issues. Finally, we compute several observables inferred from constrained Galactic mass models relevant to DM searches (WIMPs or PBHs), e.g. moments and inverse moments of the DM speed and relative speed distributions.

Revealing the dark matter halo with axion direct detection

The next generation of axion direct detection experiments may rule out or confirm axions as the dominant source of dark matter. We develop a general likelihood-based framework for studying the time-series data at such experiments, with a focus on the role of dark-matter astrophysics, to search for signatures of the QCD axion or axion like particles. We illustrate how in the event of a detection the likelihood framework may be used to extract measures of the local dark matter phase-space distribution, accounting for effects such as annual modulation and gravitational focusing, which is the perturbation to the dark matter phase-space distribution by the gravitational field of the Sun. Moreover, we show how potential dark matter substructure, such as cold dark matter streams or a thick dark disk, could impact the signal. For example, we find that when the bulk dark matter halo is detected at 5$\sigma$ global significance, the unique time-dependent features imprinted by the dark matter component of the Sagittarius stream, even if only a few percent of the local dark matter density, may be detectable at $\sim$2$\sigma$ significance. A co-rotating dark disk, with lag speed $\sim$50 km$/$s, that is $\sim$20$\%$ of the local DM density could dominate the signal, while colder but as-of-yet unknown substructure may be even more important. Our likelihood formalism, and the results derived with it, are generally applicable to any time-series based approach to axion direct detection.

Dark matter in 3D

We discuss the relevance of directional detection experiments in the post-discovery era and propose a method to extract the local dark matter phase space distribution from directional data. The first feature of this method is a parameterization of the dark matter distribution function in terms of integrals of motion, which can be analytically extended to infer properties of the global distribution if certain equilibrium conditions hold. The second feature of our method is a decomposition of the distribution function in moments of a model independent basis, with minimal reliance on the ansatz for its functional form. We illustrate our method using the Via Lactea II N-body simulation as well as an analytical model for the dark matter halo. We conclude that O(1000) events are necessary to measure deviations from the Standard Halo Model and constrain or measure the presence of anisotropies.

Anisotropic dark matter distribution functions and impact on WIMP direct detection

Dark matter N-body simulations suggest that the velocity distribution of dark matter is anisotropic. In this work we employ a mass model for the Milky Way whose parameters are determined from a fit to kinematical data. Then we adopt an ansatz for the dark matter phase space distribution which allows to construct self-consistent halo models which feature a degree of anisotropy as a function of the radius such as suggested by the simulations. The resulting velocity distributions are then used for an analysis of current data from dark matter direct detection experiments. We find that velocity distributions which are radially biased at large galactocentric distances (up to the virial radius) lead to an increased high velocity tail of the local dark matter distribution. This affects the interpretation of data from direct detection experiments, especially for dark matter masses around 10 GeV, since in this region the high velocity tail is sampled. We find that the allowed regions in the dark matter mass-cross section plane as indicated by possible hints for a dark matter signal reported by several experiments as well as conflicting exclusion limits from other experiments shift in a similar way when the halo model is varied. Hence, it is not possible to improve the consistency of the data by referring to anisotropic halo models of the type considered in this work.

PROPERTIES OF GALACTIC DARK MATTER: CONSTRAINTS FROM ASTRONOMICAL OBSERVATIONS

The distributions of normal matter and of dark matter in the Galaxy are coupled to each other as they both move in the common gravitational potential. In order to fully exploit this interplay and to derive the various properties of dark matter relevant to their direct and indirect detection, we have comprehensively reviewed the astronomical observations of the spatial and velocity distributions of the components of normal matter. We then postulate that the phase-space distribution of dark matter follows a lowered-isothermal form and self-consistently solve Poisson's equation to construct several models for the spatial and velocity distributions of dark matter. In this paper, we compute the total gravitational potential of the normal and dark matter components and investigate their consistency with current observations of the rotation curve of the Galaxy and of the spatial and velocity distributions of blue horizontal-branch and blue straggler stars. Even with this demand of consistency, a large number of models with a range of parameters characterizing the dark matter distribution remain. We find the best choice of parameters, within the range of allowed values, for the surface density of the disk 55 M$_\odot$ pc$^{-2}$, are the following: the dark matter density at the Galactic center $\rho_{DM,c}\approx 100-250$ GeV cm$^{-3}$, the local dark matter density $\rho_{DM}(R_0) \approx 0.56-0.72$ GeV cm$^{-3}$, and the root-mean-speed of dark matter particles $< v_{DM}^{2}(R_0)> ^{1/2}\approx490-550$ km s$^{-1}$. We also discuss possible astronomical observations that may further limit the range of the allowed models.

Scientific reach of multiton-scale dark matter direct detection experiments

The next generation of large scale WIMP direct detection experiments have the potential to go beyond the discovery phase and reveal detailed information about both the particle physics and astrophysics of dark matter. We report here on early results arising from the development of a detailed numerical code modeling the proposed DARWIN detector, involving both liquid argon and xenon targets. We incorporate realistic detector physics, particle physics and astrophysical uncertainties and demonstrate to what extent two targets with similar sensitivities can remove various degeneracies and allow a determination of dark matter cross sections and masses while also probing rough aspects of the dark matter phase space distribution. We find that, even assuming dominance of spin-independent scattering, multi-ton scale experiments still have degeneracies that depend sensitively on the dark matter mass, and on the possibility of isospin violation and inelasticity in interactions. We find that these experiments are best able to discriminate dark matter properties for dark matter masses less than around 200 GeV. In addition, and somewhat surprisingly, the use of two targets gives only a small improvement (aside from the advantage of different systematics associated with any claimed signal) in the ability to pin down dark matter parameters when compared with one target of larger exposure.

Optimistic CoGeNT analysis

Inspired by a recently proposed model of millicharged atomic dark matter (MADM), we analyze several classes of light dark matter models with respect to CoGeNT modulated and unmodulated data, and constraints from CDMS, XENON10 and XENON100. After removing the surface contaminated events from the original CoGeNT data set, we find an acceptable fit to all these data (but with the modulating part of the signal making a statistically small contribution), using somewhat relaxed assumptions about the response of the null experiments at low recoil energies, and postulating an unknown modulating background in the CoGeNT data at recoil energies above 1.5 keVee. We compare the fits of MADM---an example of inelastic magnetic dark matter---to those of standard elastically and inelastically scattering light weakly interacting massive particles. The inelastic dark matter model gives the best fit, with MADM close behind. The dark matter interpretation of the DAMA annual modulation cannot be made compatible with these results however. We find that the inclusion of a tidal debris component in the dark matter phase space distribution improves the fits or helps to relieve tension with XENON constraints.

Halo streams in the solar neighborhood

The phase-space structure of our Galaxy holds the key to understand and reconstruct its formation. The Lambda-CDM model predicts a richly structured phase-space distribution of dark matter and (halo) stars, consisting of streams of particles torn from their progenitors during the process of hierarchical merging. While such streams quickly loose their spatial coherence in the process of phase mixing, the individual stars keep their common origin imprinted into their kinematic and chemical properties, allowing the recovery of the Galaxy's individual "building blocks". The field of Galactic Archeology has witnessed a dramatic boost over the last decade, thanks to the increasing quality and size of available data sets. This is especially true for the solar neighborhood, a volume of 1-2 kpc around the sun, where large scale surveys like SDSS/SEGUE continue to reveal the full 6D phase-space information of thousands of halo stars. In this review, I summarize the discoveries of stellar halo streams made so far and give a theoretical overview over the search strategies imployed. This paper is intended as an introduction to researchers new to field, but also as a reference illustrating the achievements made so far. I conclude that disentangling the individual fragments from which the Milky Way was built requires more precise data that will ultimately be delivered by the Gaia mission.