The ΛCDM model strongly suggests the existence of dark matter (DM), a non-baryonic component crucial for the evolution of the universe and galaxy formation. Despite its gravitational effects, the particle properties of DM remain unknown. Two main search methods exist: direct detection (searching for DM-nucleon scattering in terrestrial detectors) and indirect detection (observing DM-induced cosmic rays from various galaxies). Direct detection experiments have excluded many DM candidates above GeV, while indirect detection, based on X-ray and γ-ray observations, has eliminated many candidates above keV. Recent indirect detection studies have started exploring lighter DM candidates (below keV) leveraging advanced detectors. For example, axion-like particle (ALP) DM around 2.7-5.3 eV has been constrained using MUSE optical spectrograph data from the Leo T dSph. Other studies have used VIMOS data from galaxy clusters to constrain DM in the 4.5-7.7 eV range. These detectors offer excellent arcsecond-level angular resolution. More recently, it was suggested that infrared spectrographs like WIRCam and NIRSpec could not only constrain but also discover DM by exploiting the suppression of sky background noise due to excellent spectral resolution. The possibility of using the Infrared Camera and Spectrograph (IRCS) at the Subaru telescope was mentioned, but a detailed analysis was lacking. This spectrograph's high angular and spectral resolution (O(0.01-0.1) arcsec) makes it a potentially valuable DM detector. This paper details an investigation into indirect DM detection using detectors with small fields of view and high angular resolution, highlighting the importance of using the differential D-factor for searching DM in dSphs.

Several studies have explored indirect dark matter detection using high-resolution instruments. The work by Bacon et al. (2017) and Regis et al. (2021) used the MUSE spectrograph to constrain axion-like particle (ALP) dark matter in the Leo T dwarf spheroidal galaxy. Grin et al. (2007) utilized VIMOS data from galaxy clusters to place constraints on DM in a different mass range. These studies demonstrate the potential of high angular resolution instruments in constraining DM properties. More recent work has pointed towards the potential of infrared spectrographs with high energy resolution for DM detection, exploiting their ability to suppress sky background noise. This approach relies on the characteristic line-like spectrum produced by DM decay into two particles, including a photon. The IRCS instrument on the Subaru telescope, with its high angular and spectral resolution, has been suggested as a promising candidate for this kind of DM search but lacked a detailed investigation, addressed in the current paper.

The authors consider the decay of dark matter particles (ϕ) with a decay width Γϕ into Standard Model particles, focusing on the flux of photons (γ) from the decay. The differential flux is decomposed into extragalactic and galactic components, with the latter focusing on the contribution from dSphs. Neglecting photon scattering, the galactic component can be expressed in terms of the DM energy density distribution (ρiϕ), the photon spectrum from a single DM decay (∂²Nϕ,i/∂Eγ∂Ω), and geometric factors. The photon spectrum depends on the DM model, velocity distribution (fi), and the rest-frame spectrum (Frest). In dSphs, the velocity dispersion is small (<10 km/s), and the Doppler shift distortion on the spectrum is negligible (<10⁻⁴ × mϕ/2) given the detectors' high energy resolution (R = O(10⁴)). The analysis simplifies to an expression involving a differential D-factor (∂ΩD), defined as the integral of the DM density along the line of sight: ∂ΩD ≡ ∫ dsρiϕ(s, Ω). The differential D-factor is calculated using mass density profiles estimated from non-spherical mass models based on axisymmetric Jeans equations, which helps to mitigate the degeneracy between DM density and stellar velocity anisotropy. The authors utilize data from Hayashi et al. (2020, 2022) and adopt the Hernquist profile for DM density. The uncertainty in the differential D-factor stems mainly from the degeneracy between the dark matter halo shape and stellar velocity anisotropy and data limitations for ultra-faint dwarfs. The differential D-factor offers several advantages: it allows for optimal data integration, considering detector efficiency; it helps distinguish DM signal from noise by correlating the photon angular distribution with the DM distribution; and it serves as a good approximation when the field of view is small. The differential D-factor distributions are calculated for various dSphs, including Draco and Ursa Major II. The typical angular distance between stars (dstars) is also estimated to assess the benefit of high angular resolution. For a concrete example, the authors consider the decay of an ALP into two photons, using the relevant Lagrangian and decay rate. They focus on the parameter region (mϕ ∼ eV, gϕγγ ∼ 10⁻¹¹ - 10⁻¹⁰ GeV⁻¹) motivated by several observational implications (alleviating the tension in horizontal-branch star cooling, explaining the cosmic infrared background anisotropy, and explaining a bump in the cosmic γ-ray spectrum). Theoretical motivations for eV-range DM, including hot DM, Bose enhancement, and the ALP miracle scenario, are discussed. The authors then propose searching for ALP DM in Draco and Ursa Major II using the IRCS on the Subaru telescope. Sky noise (zodiacal light and stellar light) is considered, and it is shown that the stellar densities are sparse enough to avoid visible stars in the central regions of the dSphs. The differential D-factor is used to calculate sensitivity reaches for different IRCS bands (zJ, J, H, K, L, M) using an exposure time calculator.

The authors find that using the differential D-factor significantly enhances the predicted dark matter signal compared to conventional methods. For Draco and Ursa Major II, they observe an O(10) enhancement in the signal flux at r ∼ arcsec, with considerably different uncertainties. The high values of the differential D-factor indicate these dSphs are promising targets for detecting eV-scale DM. The analysis shows that O(1) hours of observation with IRCS can explore ALP DM in the 1-2 eV range, potentially surpassing stellar cooling bounds within a few nights for the H and K bands. This improved sensitivity is a direct result of the use of the differential D-factor and the high angular resolution of IRCS. The study also provides a novel strategy for distinguishing DM signal from noise by correlating the angular distribution of detected photons with the expected DM distribution. This approach is most effective with detectors having large fields of view and high angular resolution. The sensitivity reaches for different IRCS bands are detailed in the paper, demonstrating the potential for detecting DM signals in this mass range.

The results address the research question by demonstrating the significantly increased sensitivity achievable by using the differential D-factor and high-angular-resolution detectors. The findings demonstrate the feasibility of using the IRCS on the Subaru Telescope to probe the eV-mass range for dark matter, a region previously less accessible. The O(10) enhancement of signal rate from using the differential D-factor compared to conventional averages significantly improves the prospect of discovering light dark matter. The study highlights the crucial importance of considering the spatial distribution of DM within the target galaxy when using detectors with limited fields of view and high angular resolution. The improved sensitivity pushes the reach of the experiment beyond previously established bounds, particularly relevant in the context of axion-like particle dark matter models. The ability to potentially surpass stellar cooling bounds within a few nights of observation represents a substantial advancement in the search for light dark matter.

This paper presents a strong case for using high-angular-resolution detectors like the Subaru-IRCS for indirect detection of decaying dark matter, particularly in the eV mass range. The novel use of the differential D-factor significantly improves detection sensitivity, revealing the potential for surpassing existing bounds on axion-like particle dark matter within a reasonable observation time. The findings highlight the importance of incorporating the detailed spatial distribution of dark matter and utilizing high-resolution instruments for future DM searches. Future research could involve actual observations of Draco and Ursa Major II using IRCS, validating the theoretical predictions and exploring the potential for other similar instruments to search for dark matter.

The main limitation is the reliance on theoretical models for DM density profiles. The uncertainty in the differential D-factor is partially influenced by the degeneracy between DM halo shape and stellar velocity anisotropy. Additionally, the analysis simplifies the treatment of sky background noise. The star density estimates, especially at larger angular distances, might be subject to uncertainties, The calculations assume a single DM component, but this can be extended to multiple components.