Earth-lens telescope for distant axion-like particle sources with stimulated backward reflection

TL;DR

The paper introduces an Earth-lens telescope design that uses Earth's gravity to concentrate a unidirectional ALP flux and employs stimulated backward reflection (SBR) to detect ALP decays into photon pairs. It provides a numerically grounded treatment of the focal-region structure by simulating ALP geodesics in and around the Earth and quantifies the signal-collection efficiency via a curved-trajectory acceptance model. A detailed sensitivity projection for the ALP–photon coupling $g/M$ is produced, revealing potentially competitive reach in the eV mass range (e.g., $g/M \sim \mathcal{O}(10^{-22})~\mathrm{GeV^{-1}}$) for S1-like fluxes. The results support the feasibility of a space-based ALP observatory capable of probing distant sources beyond $\mathcal{O}(10)\,\mathrm{kpc}$, contingent on sufficiently large $g/M$ and practical realization of the inducing-field system in space.

Abstract

We propose a novel telescope concept based on Earth's gravitational lensing effect, optimized for the detection of distant dark matter sources, particularly axion-like particles (ALPs). When a unidirectional flux of dark matter passes through Earth at sufficiently high velocity, gravitational lensing can concentrate the flux at a distant focal region in space. Our method combines this lensing effect with stimulated backward reflection (SBR), arising from ALP decays that are induced by directing a coherent electromagnetic beam toward the focal point. The aim of this work is to numerically analyze the structure of the focal region and to develop a framework for estimating the sensitivity to ALP-photon coupling via this mechanism. Numerical calculations show that, assuming an average ALP velocity of 520,km/s -- as suggested by the observed stellar stream S1 -- the focal region extends from $9 \times 10^9$,m to $1.4 \times 10^{10}$,m, with peak density near $9.6 \times 10^9$,m. For a conservative point-like ALP source located approximately 8,kpc from the solar system, based on the S1 stream, the estimated sensitivity in the eV mass range reaches $g/M = \mathcal{O}(10^{-22}),\mathrm{GeV}^{-1}$. This concept thus opens a path toward a general-purpose, space-based ALP observatory that could, in principle, detect more distant sources -- well beyond $\mathcal{O}(10),\mathrm{kpc}$ -- provided that ALP-photon coupling is sufficiently strong, that is, $M \ll M_\mathrm{Planck}$.

Figures (11)

• Figure 1: Search geometry of an axion-like particle (ALP) lensing object using the Stimulated Backward Reflection (SBR) method from a space probe (yellow). The blue circle denotes the Earth, while the blue lines indicate the trajectories of individual ALPs incident from the left. The black triangular structure with trailing tails illustrates the concentrated distribution of dark matter at the focal region. The localized ALP flux is probed by a spherical wave of a coherent electromagnetic field to induce decay of the ALPs. $L_0$ denotes the emission point of the inducing field, and $L_1$ represents the effective terminal point beyond which the field strength becomes negligible. The total probing distance, $L_1 - L_0$, extends to approximately $10^9$ m.
• Figure 2: Geometry of a particle trajectory, the initial position, the initial velocity, and the impact parameter. The ALP trajectory is shown with the red curve. The initial position is located at a distance of $-1000R_E$ from the Earth’s center along the incident axis $z$, and the vertical offset by the impact parameter $b$. The initial velocity is $v_0=520$ km/s, directed parallel to the incident axis.
• Figure 3: Deflection of particle trajectories. Red curves correspond to trajectories with $b > 0$, while blue curves represent those with $b < 0$. The focal points are distributed in the range $9.2 \times 10^9 \lesssim z \lesssim 1.4 \times 10^{10}$ for the incident velocity of $v_0=520$ km/s.
• Figure 4: Normalized density profile on the x-z plane of the lensing object when a unidirectional dark matter flux is incident along the z-axis with the velocity of 520 km/s.
• Figure 5: Geometry of the inducing field emission point, interaction point, and signal photon trajectory. The red arrow indicates the wavevector of the inducing field. The blue arrow and dashed line represent the emission direction of the signal photon and the path to the detector plane, respectively. The black dot and arrow denote the ALP and its velocity direction, respectively. Subscripts: “$a$” for the ALP, “$i$” for the inducing field, “$s$” for the signal photon. The angles $\theta^\prime_a$ and $\theta^\prime_s$ represent the relative angles with respect to the wavevector of the inducing field.