Anne M. Green

The First wimpy halos

Dark matter direct and indirect detection signals depend crucially on the dark matter distribution. While the formation of large scale structure is independent of the nature of the cold dark matter (CDM), the fate of inhomogeneities on subgalactic scales, and hence the present day CDM distribution on these scales, depends on the microphysics of the CDM particles. We study the density contrast of weakly interacting massive particles (WIMPs) on subgalactic scales. We calculate the damping of the primordial power spectrum due to collisional damping and free streaming of WIMPy CDM and show that free streaming leads to a CDM power spectrum with a sharp cut-off at about 10(-6) M-circle dot. We also calculate the transfer function for the growth of the inhomogeneities in the linear regime, taking into account the suppression in the growth of the CDM density contrast after matter-radiation equality due to baryons and show that our analytic results are in good agreement with numerical calculations. Combining the transfer function with the damping of the primordial fluctuations we produce a WMAP normalized primordial CDM power spectrum, which can serve as an input for high resolution CDM simulations. We find that the smallest inhomogeneities typically have comoving radius of about 1 pc and enter the nonlinear regime at a red-shift of 60 +/- 20. We study the effect of scale dependence of the primordial power spectrum on these numbers and also use the spherical collapse model to make simple estimates of the properties of the first generation of WIMP halos to form. We find that the very first WIMPy halos may have a significant impact on indirect dark matter searches.

The power spectrum of SUSY-CDM on subgalactic scales

ABSTRACT The formation of large scale structure is independent of the nature of the cold darkmatter (CDM), however the fate of very small scale inhomogeneities depends on themicro-physics of the CDM particles. We investigate the matter power spectrum forscales that enter the Hubble radius well before matter-radiation equality, and followits evolution until the time when the first inhomogeneities become non-linear. Ourfocus lies on weakly interacting massive particles (WIMPs), and as a concrete exam-ple we analyze the case when the lightest supersymmetric particle is a bino. We showthat collisional damping and free-streaming of WIMPs lead to a matter power spec-trum with a sharp cut-off at about 10 −6 M ⊙ and a maximum close to that cut-off. Wealso calculate the transfer function for the growth of the inhomogeneities in the lin-ear regime. These three effects (collisional damping, free-streaming and gravitationalgrowth) are combined to provide a WMAP normalized primordial CDM power spec-trum, which could serve as an input for high resolution CDM simulations. The smallestinhomogeneities typically enter the non-linear regime at a redshift of about 60.Key words: cosmology: theory – dark matter – early Universe

Generalised constraints on the curvature perturbation from primordial black holes

Primordial black holes (PBHs) can form in the early Universe via the collapse of large density perturbations. There are tight constraints on the abundance of PBHs formed due to their gravitational effects and the consequences of their evaporation. These abundance constraints can be used to constrain the primordial power spectrum, and hence models of inflation, on scales far smaller than those probed by cosmological observations. We compile, and where relevant update, the constraints on the abundance of PBHs before calculating the constraints on the curvature perturbation, taking into account the growth of density perturbations prior to horizon entry. We consider two simple parameterizations of the curvature perturbation spectrum on the scale of interest: constant and power-law. The constraints from PBHs on the amplitude of the power spectrum are typically in the range 10 −2 10 −1 with some scale dependence.

Directional statistics for realistic weakly interacting massive particle direct detection experiments

The direction dependence of the event rate in WIMP direct detection experiments provides a powerful tool for distinguishing WIMP events from potential backgrounds. We use a variety of (non-parametric) statistical tests to examine the number of events required to distinguish a WIMP signal from an isotropic background when the uncertainty in the reconstruction of the nuclear recoil direction is included in the calculation of the expected signal. We consider a range of models for the Milky Way halo, and also study rotational symmetry tests aimed at detecting non-sphericity/isotropy of the Milky Way halo. Finally we examine ways of detecting tidal streams of WIMPs. We find that if the senses of the recoils are known then of order ten events will be sufficient to distinguish a WIMP signal from an isotropic background for all of the halo models considered, with the uncertainties in reconstructing the recoil direction only mildly increasing the required number of events. If the senses of the recoils are not known the number of events required is an order of magnitude larger, with a large variation between halo models, and the recoil resolution is now an important factor. The rotational symmetry tests require of order a thousand events to distinguish between spherical and significantly triaxial halos, however a deviation of the peak recoil direction from the direction of the solar motion due to a tidal stream could be detected with of order a hundred events, regardless of whether the sense of the recoils is known.

Astrophysical uncertainties on direct detection experiments

Direct detection experiments are poised to detect dark matter in the form of weakly interacting massive particles (WIMPs). The signals expected in these experiments depend on the ultra-local WIMP density and velocity distribution. Firstly we review methods for modelling the dark matter distribution. We then discuss observational determinations of the local dark matter density, circular speed and escape speed and the results of numerical simulations of Milky Way-like dark matter halos. In each case we highlight the uncertainties and assumptions made. We then overview the resulting uncertainties in the signals expected in direct detection experiments, specifically the energy, time and direction dependence of the event rate. Finally we conclude by discussing techniques for handling the astrophysical uncertainties when interpreting data from direct detection experiments.

Direct detection of WIMPs.

If the Milky Way’s DM halo is composed of WIMPs, then the WIMP flux on the Earth is of the order of 105(100 GeV/mχ)cm−2 s−1. This flux is suf- ficiently large that, even though the WIMPs are weakly interacting, a small but potentially measurable fraction will elastically scatter off nuclei. Direct detection experiments aim to detect WIMPs via the nuclear recoils, caused by WIMP elastic scattering, in dedicated low background detectors [988]. More specifically they aim to measure the rate, R, and energies, ER, of the nuclear recoils (and in directional experiments the directions as well). In this chapter we overview the theoretical calculation of the direct detection event rate and the potential direct detection signals. Section 17.2 outlines the calculation of the event rate, including the spin-independent and spin-dependent contributions and the hadronic matrix elements. Section 17.3 discusses the astrophysical input into the event rate calculation, including the local WIMP velocity distribution and density. In Section 17.4 we describe the direction detection signals, specifically the energy, time and direction dependence of the event rate. Finally in Section 17.5 we discuss the predicted ranges for the WIMP mass and cross-sections in various particle physics models.

Dependence of direct detection signals on the WIMP velocity distribution

The signals expected in WIMP direct detection experiments depend on the ultra-local dark matter distribution. Observations probe the local density, circular speed and escape speed, while simulations find velocity distributions that deviate significantly from the standard Maxwellian distribution. We calculate the energy, time and direction dependence of the event rate for a range of velocity distributions motivated by recent observations and simulations, and also investigate the uncertainty in the determination of WIMP parameters. The dominant uncertainties are the systematic error in the local circular speed and whether or not the MW has a high density dark disc. In both cases there are substantial changes in the mean differential event rate and the annual modulation signal, and hence exclusion limits and determinations of the WIMP mass. The uncertainty in the shape of the halo velocity distribution is less important, however it leads to a ~ 5% systematic error in the WIMP mass. The detailed direction dependence of the event rate is sensitive to the velocity distribution. However the numbers of events required to detect anisotropy and confirm the median recoil direction do not change substantially.

Effect of halo modeling on weakly interacting massive particle exclusion limits

WIMP direct detection experiments are just reaching the sensitivity required to detect galactic dark matter in the form of neutralinos. Data from these experiments are usually analysed under the simplifying assumption that the Milky Way halo is an isothermal sphere with maxwellian velocity distribution. Observations and numerical simulations indicate that galaxy halos are in fact triaxial and anisotropic. Furthermore, in the cold dark matter paradigm galactic halos form via the merger of smaller subhalos, and at least some residual substructure survives. We examine the effect of halo modelling on WIMP exclusion limits, taking into account the detector response. Triaxial and anisotropic halo models, with parameters motivated by observations and numerical simulations, lead to significant changes which are different for different experiments, while if the local WIMP distribution is dominated by small scale clumps then the exclusion limits are changed dramatically.

Determining the weakly interacting massive particles mass using direct detection experiments

We study the accuracy with which the WIMP mass could be determined by a superCDMS-like direct detection experiment, given optimistic assumptions about the detector set-up and WIMP properties. We consider WIMPs with an interaction cross-section of \sigma_{\rm p} = 10^{-7} {\rm pb} (just below current exclusion limits) and assume, initially, that the local WIMP velocity distribution and density are known and that the experiment has negligible background. For light WIMPs (mass significantly less than that of the target nuclei) small variations in the WIMP mass lead to significant changes in the energy spectrum. Conversely for heavy WIMPs the energy spectrum depends only weakly on the WIMP mass. Consequently it will be far easier to measure the WIMP mass if it is light than if it is heavy. With exposures of {\cal E}= 3 \times 10^{3}, 3 \times 10^{4} and 3 \times 10^{5} {\rm kg day} (corresponding, roughly, to the three proposed phases of SuperCDMS) it will be possible, given the optimistic assumptions mentioned above, to measure the mass of a light WIMP with an accuracy of roughly 25%, 15% and 2.5 % respectively. These numbers increase with increasing WIMP mass, and for heavy WIMPs, m_{\chi} > {\cal O}(500 {\rm GeV}), even with a large exposure it will only be possible to place a lower limit on the mass. Finally we discuss the validity of the various assumptions made, and the consequences if these assumptions are not valid. In particular if the local WIMP distribution is composed of a number of discrete streams it will not be possible to determine the WIMP mass.

A review of the discovery reach of directional Dark Matter detection

Cosmological observations indicate that most of the matter in the Universe is Dark Matter. Dark Matter in the form of Weakly Interacting Massive Particles (WIMPs) can be detected directly, via its elastic scattering off target nuclei. Most current direct detection experiments only measure the energy of the recoiling nuclei. However, directional detection experiments are sensitive to the direction of the nuclear recoil as well. Due to the Sun’s motion with respect to the Galactic rest frame, the directional recoil rate has a dipole feature, peaking around the direction of the Solar motion. This provides a powerful tool for demonstrating the Galactic origin of nuclear recoils and hence unambiguously detecting Dark Matter. Furthermore, the directional recoil distribution depends on the WIMP mass, scattering cross section and local velocity distribution. Therefore, with a large number of recoil events it will be possible to study the physics of Dark Matter in terms of particle and astrophysical properties. We review the potential of directional detectors for detecting and characterizing WIMPs.