Multi-copy Axion Transfer Function and Observational Implications of Effective de Broglie Scales

TL;DR

This work addresses how a multi-copy axion dark matter sector, natural in the String Axiverse, alters structure formation and halo-scale phenomenology compared to single-copy models. It develops a linear perturbation framework based on the Schrödinger–Poisson equations for multiple axion fields, yielding an effective mass $m_{ ext{eff}}$ with $m_{ ext{eff}}^{-2}= \sum_i w_i m_i^{-2}$ that governs large-scale suppression, and provides a practical multi-copy transfer-function prescription that interpolates between decoupled copies and collective behavior. In the non-linear regime, the authors extend the framework to halos by defining an effective lensing mass $m_{ ext{eff}}'$ with $1/m_{ ext{eff}}' = \sum_i (\Sigma_i/\Sigma_{tot})^2 (1/m_i)$, predicting radially varying wave interference and observable signatures in JWST lensing and stellar heating, e.g., $m_{ ext{eff}}'$ compatible with transients spreads near critical curves. The results offer a coherent set of observational tests—through spatial variations in $m_{ ext{eff}}'$ and transferred LSS suppression—that could validate or constrain a multi-copy ψDM scenario within current and upcoming surveys.

Abstract

Ultra-light axions are viable fuzzy/wave-like dark matter ($ψ$DM) candidates generically predicted by the String Axiverse paradigm with multiple particle copies, whereas most of the discussions/constraints on $ψ$DM from astronomical observations to date are based on the assumption of a single particle copy. Here, we aim to complete this gap by exploring the generic multi-axion scenario motivated in the String Axiverse context, and investigate its astronomical implications in both the linear and nonlinear regimes. In the linear regime, with linear density perturbation analysis, we provide a simplified prescription for obtaining multi-copy axion transfer functions and also identify an "equivalence" among all axion copies owing to the mutual coupling to the gravitational potential. As a result of this 'equivalence', we argue the suppression to LSS is governed by an effective mass $m_{eff}^{-2}=\sum_i w_i m_i^{-2}$, with $\{ w_i\}$ being fractional contributions of different copies to the full cosmic dark matter density. In non-linear regime within galaxy halos, we show that similar notions of effective mass, with expressions provided, to govern the collective wave interference and hence determine the net stellar heating rates and the substructure-induced spread of JWST transients near critical curves. Distinctive to the multi-copy scenario, the effective mass within galaxy halos is generically anticipated to be radially decreasing following the stronger concentration of heavier copies to the galactic center. Such a spatial variation leads to radially increasing spreading scales for micro-lensed transients at different radial positions, a signature that may be tested with future JWST lensing observations.

Figures (1)

• Figure 1: Example transfer functions (solid lines) for each axion copy at redshift $z=127$. The three copies have masses $1, 5$ and $20\times10^{-22}$ eV, accounting for $15\%, 25\%$ and $60\%$ of the total dark matter density $\overline{\rho_{\text{tot}}}$, respectively. The transfer functions $\hat{T}_i$ and $\hat{T}_{\text{tot}}$ for a single-copy axion Universe are computed using Eq. \ref{['transfer_2']}. We have also indicated the scale of $\tilde{k}$ using a red vertical dotted line, it is seen that at $k\gg \tilde{k}$ axion copies asymptote to their respective single-copy Universe transfer functions (dashed lines of same respective color).