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Register a new userBayesian Reconstruction of the Velocity Distribution of Weakly Interacting Massive Particles from Direct Dark Matter Detection Data
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Chung-Lin Shan
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In this paper, we extended our earlier work on the reconstruction of the (time-averaged) one-dimensional velocity distribution of Galactic Weakly Interacting Massive Particles (WIMPs) and introduce the Bayesian fitting procedure to the theoretically predicted velocity distribution functions. In this reconstruction process, the (rough) velocity distribution reconstructed by using raw data from direct Dark Matter detection experiments directly, i.e. measured recoil energies, with one or more different target materials, has been used as reconstructed-input information. By assuming a fitting velocity distribution function and scanning the parameter space based on the Bayesian analysis, the astronomical characteristic parameters, e.g. the Solar and Earths Galactic velocities, will be pinned down as the output results. Our Monte-Carlo simulations show that this Bayesian scanning procedure could reconstruct the true (input) WIMP velocity distribution function pretty precisely with negligible systematic deviations of the reconstructed characteristic Solar and Earths velocities and 1 sigma statistical uncertainties of <~ 20 km/s. Moreover, for the use of an improper fitting velocity distribution function, our reconstruction process could still offer useful information about the shape of the velocity distribution. In addition, by comparing these estimates to theoretical predictions, one could distinguish different (basic) functional forms of the theoretically predicted one-dimensional WIMP velocity distribution function with 2 sigma to 4 sigma confidence levels.
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In this paper, as a preparation of developing data analysis procedures for using 3-dimensional information offered by directional Dark Matter (DM) detection experiments, we study the patterns of the angular distribution of the Monte Carlo-generated 3-D velocity of halo Weakly Interacting Massive Particles (WIMPs) as well as apply the Bayesian fitting technique to reconstruct the radial distribution of the 3-D WIMP velocity. Besides the diurnal modulation of the angular WIMP velocity distribution, the so-called directionality of DM signals proposed in literature, we will also demonstrate possible annual modulations of both of the angular and the radial distributions of the 3-D WIMP velocity. Our Bayesian reconstruction results of (the annual modulation of) the radial WIMP velocity distribution will also be discussed in detail. For readers reference, the angular distribution patterns of the 3-D WIMP velocity in the laboratory (location)-dependent reference frames of several underground laboratories are given in the Appendix.
In this paper, as the third part of the third step of our study on developing data analysis procedures for using 3-dimensional information offered by directional direct Dark Matter detection experiments in the future, we introduce a 3-dimensional effective velocity distribution of halo Weakly Interacting Massive Particles (WIMPs), which, instead of the theoretically prediction of the entire Galactic Dark Matter particles, describes the actual velocity distribution of WIMPs scattering off (specified) target nuclei in an underground detector. Its target and WIMP-mass dependences as well as (annual modulations of) its anisotropy in the Equatorial/laboratory and even the Galactic coordinate systems will be demonstrated and discussed in detail. For readers reference, all simulation plots presented in this paper (and more) can be found in animation on our online (interactive) demonstration webpage (http://www.tir.tw/phys/hep/dm/amidas-2d/).
In this paper, we investigate the modification of our expressions developed for the model-independent data analysis procedure of the reconstruction of the (time-averaged) one-dimensional velocity distribution of Galactic Weakly Interacting Massive Particles (WIMPs) with a non-negligible experimental threshold energy. Our numerical simulations show that, for a minimal reconstructable velocity of as high as O(200) km/s, our model-independent modification of the estimator for the normalization constant could provide precise reconstructed velocity distribution points to match the true WIMP velocity distribution with a <~ 10% bias.
Weakly Interacting Massive Particles (WIMPs) are one of the leading candidates for Dark Matter. Currently, the most promising method to detect WIMPs is the direct detection of the recoil energy deposited in a low-background laboratory detector due to elastic WIMP-nucleus scattering. So far the usual procedure has been to predict the event rate of direct detection of WIMPs based on some model(s) of the Galactic halo from cosmology and of WIMPs from elementary particle physics. The aim of this work is to invert this process. In this thesis I present methods which allow to reconstruct (the moments of) the WIMP velocity distribution function as well as to determine the WIMP mass from the recoil energy spectrum as well as from experimental data directly. The reconstruction of the velocity distribution function has been further extended to take into account the annual modulation of the event rate. Moreover, the reconstruction of the amplitude of the annual modulation of the velocity distribution and an alternative, better way for confirming the annual modulation of the event rate have been discussed. On the other hand, the determination of the WIMP mass by combining two (or more) experiments with different detector materials has been developed. All formulae and expressions given here are not only independent of the model of Galactic halo but also of that of WIMPs. This means that we need neither the as yet unknown WIMP density near the Earth nor the WIMP-nucleus cross section. The only information which we need is the measured recoil energies and their measuring times.
The velocity distribution function of dark matter particles is expected to show significant departures from a Maxwell-Boltzmann distribution. This can have profound effects on the predicted dark matter - nucleon scattering rates in direct detection experiments, especially for dark matter models in which the scattering is sensitive to the high velocity tail of the distribution, such as inelastic dark matter (iDM) or light (few GeV) dark matter (LDM), and for experiments that require high energy recoil events, such as many directionally sensitive experiments. Here we determine the velocity distribution functions from two of the highest resolution numerical simulations of Galactic dark matter structure (Via Lactea II and GHALO), and study the effects for these scenarios. For directional detection, we find that the observed departures from Maxwell-Boltzmann increase the contrast of the signal and change the typical direction of incoming DM particles. For iDM, the expected signals at direct detection experiments are changed dramatically: the annual modulation can be enhanced by more than a factor two, and the relative rates of DAMA compared to CDMS can change by an order of magnitude, while those compared to CRESST can change by a factor of two. The spectrum of the signal can also change dramatically, with many features arising due to substructure. For LDM the spectral effects are smaller, but changes do arise that improve the compatibility with existing experiments. We find that the phase of the modulation can depend upon energy, which would help discriminate against background should it be found.
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