A Fresh Approach to Forecasting in Astroparticle Physics and Dark Matter Searches

We present a toolbox of new techniques and concepts for the efficient forecasting of experimental sensitivities. These are applicable to a large range of scenarios in (astro-)particle physics, and based on the Fisher information formalism. Fisher information provides an answer to the question what is the maximum extractable information from a given observation?. It is a common tool for the forecasting of experimental sensitivities in many branches of science, but rarely used in astroparticle physics or searches for particle dark matter. After briefly reviewing the Fisher information matrix of general Poisson likelihoods, we propose very compact expressions for estimating expected exclusion and discovery limits (equivalent counts method). We demonstrate by comparison with Monte Carlo results that they remain surprisingly accurate even deep in the Poisson regime. We show how correlated background systematics can be efficiently accounted for by a treatment based on Gaussian random fields. Finally, we introduce the novel concept of Fisher information flux. It can be thought of as a generalization of the commonly used signal-to-noise ratio, while accounting for the non-local properties and saturation effects of background and instrumental uncertainties. It is a powerful and flexible tool ready to be used as core concept for informed strategy development in astroparticle physics and searches for particle dark matter.Comment: 33 pages, 12 figure

Convergence Acceleration via Combined Nonlinear-Condensation Transformations

A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating series. In the second step, the convergence of the transformed series is accelerated with the help of suitable nonlinear sequence transformations that are known to be particularly powerful for alternating series. Some theoretical aspects of our approach are discussed. The efficiency, numerical stability, and wide applicability of the combined nonlinear-condensation transformation is illustrated by a number of examples. We discuss the evaluation of special functions close to or on the boundary of the circle of convergence, even in the vicinity of singularities. We also consider a series of products of spherical Bessel functions, which serves as a model for partial wave expansions occurring in quantum electrodynamic bound state calculations.Comment: 24 pages, LaTeX, 12 tables (accepted for publication in Comput. Phys. Comm.

Bayesian Model Comparison and Analysis of the Galactic Disk Population of Gamma-Ray Millisecond Pulsars

Pulsed emission from almost one hundred millisecond pulsars (MSPs) has been detected in $\gamma$-rays by the Fermi Large-Area Telescope. The global properties of this population remain relatively unconstrained despite many attempts to model their spatial and luminosity distributions. We perform here a self-consistent Bayesian analysis of both the spatial distribution and luminosity function simultaneously. Distance uncertainties, arising from errors in the parallax measurement or Galactic electron-density model, are marginalized over. We provide a public Python package for calculating distance uncertainties to pulsars derived using the dispersion measure by accounting for the uncertainties in Galactic electron-density model YMW16. Finally, we use multiple parameterizations for the MSP population and perform Bayesian model comparison, finding that a broken power law luminosity function with Lorimer spatial profile are preferred over multiple other parameterizations used in the past. The best-fit spatial distribution and number of $\gamma$-ray MSPs is consistent with results for the radio population of MSPs.Comment: 13 pages, 8 figures, 3 tables + Appendix. Public code and source list available from http://github.com/tedwards2412/MSPDis

CMB bounds on dark matter annihilation: Nucleon energy-losses after recombination

We consider the propagation and energy losses of protons and anti-protons produced by dark matter annihilation at redshifts 100<z<~2000. In the case of dark matter annihilations into quarks, gluons and weak gauge bosons, protons and anti-protons carry about 20% of the energy injected into e^\pm and \gamma's, but their interactions are normally neglected when deriving cosmic microwave background bounds from altered recombination histories. Here, we follow numerically the energy-loss history of typical protons/antiprotons in the cosmological medium. We show that about half of their energy is channeled into photons and e^\pm, and we present a simple prescription to estimate the corresponding strengthening of the cosmic microwave background bounds on the dark matter annihilation cross section.Comment: 5 pages, 2 figures. References added. Matches version published in PR

A Unique Multi-Messenger Signal of QCD Axion Dark Matter

We propose a multi-messenger probe of QCD axion Dark Matter based on observations of black hole-neutron star binary inspirals. It is suggested that a dense Dark Matter spike may grow around intermediate mass black holes ($10^{3}-10^{5} \mathrm{\,M_{\odot}}$). The presence of such a spike produces two unique effects: a distinct phase shift in the gravitational wave strain during the inspiral and an enhancement of the radio emission due to the resonant axion-photon conversion occurring in the neutron star magnetosphere throughout the inspiral and merger. Remarkably, the observation of the gravitational wave signal can be used to infer the Dark Matter density and, consequently, to predict the radio emission. We study the projected reach of the LISA interferometer and next-generation radio telescopes such as the Square Kilometre Array. Given a sufficiently nearby system, such observations will potentially allow for the detection of QCD axion Dark Matter in the mass range $10^{-7}\,\mathrm{eV}$ to $10^{-5}\,\mathrm{eV}$.Comment: 5 pages, 3 figures. Appendix added with additional figures. Updated to published versio

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic