[Paper Review] Effect of realistic astrophysical inputs on the phase and shape of the WIMP annual modulation signal

Anne M. Green|arXiv (Cornell University)|Apr 24, 2003

Dark Matter and Cosmic Phenomena50 references75 citations

TL;DR

This paper investigates how realistic astrophysical inputs—particularly Earth's orbital motion and non-standard WIMP velocity distributions—affect the phase and shape of the annual modulation signal in direct WIMP detection. It demonstrates that simplified models of Earth's motion can introduce phase errors of up to 10 days and amplitude errors of tens of percent, while anisotropic velocity distributions can shift the signal phase by up to 20 days and alter the signal shape significantly, challenging the assumption of sinusoidal modulation in WIMP searches.

ABSTRACT

The orbit of the Earth about the Sun produces an annual modulation in the WIMP direct detection rate. If the local WIMP velocity distribution is isotropic then the modulation is roughly sinusoidal with maximum in June, however if the velocity distribution is anisotropic the phase and shape of the signal can change. Motivated by conflicting claims about the effect of uncertainties in the local velocity distribution on the interpretation of the DAMA annual modulation signal (and the possibility that the form of the modulation could be used to probe the structure of the Milky Way halo), we study the dependence of the annual modulation on various astrophysical inputs. We first examine the approximations used for the Earth's motion about the Sun and the Sun's velocity with respect to the Galactic rest frame. We find that overly simplistic assumptions lead to errors of up to ten days in the phase and up to tens of per-cent in the shape of the signal, even if the velocity distribution is isotropic. Crucially, if the components of the Earth's velocity perpendicular to the motion of the Sun are neglected, then the change in the phase which occurs for anisotropic velocity distributions is missed. We then examine how the annual modulation signal varies for physically and observationally well-motivated velocity distributions. We find that the phase of the signal changes by up to 20 days and the mean value and amplitude change by up to tens of per-cent.

Motivation & Objective

• To assess the impact of realistic astrophysical inputs on the phase and shape of the WIMP annual modulation signal.
• To challenge the common assumption of sinusoidal modulation in WIMP direct detection experiments.
• To quantify errors introduced by oversimplified models of Earth's motion and velocity distribution.
• To evaluate how non-standard halo models affect the interpretation of the DAMA signal.

Proposed method

• Modeling Earth's velocity relative to the Galactic rest frame using precise orbital mechanics, including ecliptic and Galactic coordinate transformations.
• Using a time-dependent Galilean transformation to compute the WIMP velocity distribution in the detector frame.
• Applying the differential event rate formula involving the WIMP speed distribution, minimum recoil velocity, and form factors.
• Testing various physically motivated velocity distributions, including isotropic and anisotropic models.
• Comparing signal phase and amplitude under different assumptions about Earth's motion and local halo kinematics.
• Using numerical integration to compute the modulation signal and assess deviations from sinusoidal behavior.

Experimental results

Research questions

• RQ1 How do inaccuracies in modeling Earth's orbital motion affect the phase and amplitude of the WIMP annual modulation signal?
• RQ2 To what extent does anisotropy in the local WIMP velocity distribution alter the phase and shape of the annual modulation?
• RQ3 Can the annual modulation signal deviate significantly from a sinusoidal form under realistic astrophysical conditions?
• RQ4 How do uncertainties in the Sun's velocity and local circular velocity affect the interpretation of the DAMA signal?
• RQ5 What are the implications of non-sinusoidal modulation for WIMP mass and cross-section constraints?

Key findings

• Oversimplified models of Earth's motion can introduce phase errors of up to 10 days and amplitude errors of up to tens of percent, even for isotropic velocity distributions.
• Neglecting the perpendicular components of Earth's velocity leads to a complete failure to detect phase shifts induced by anisotropic WIMP velocity distributions.
• Anisotropic velocity distributions can shift the signal phase by up to 20 days compared to the standard model.
• The mean event rate and modulation amplitude can change by up to tens of percent due to realistic halo models.
• The annual modulation signal can deviate significantly from a sinusoidal form, especially under non-standard halo assumptions.
• These effects can lead to incorrect constraints on WIMP mass and cross-section if not properly accounted for in data analysis.