Galaxy UV-luminosity function and reionization constraints on axion dark matter

TL;DR

This work tests ultralight axion dark matter models against high-redshift galaxy observations and reionization constraints. Using a semi-analytic aMDM framework, the authors compute a scale-dependent halo mass function, perform UV-luminosity function–to–halo abundance matching, and predict reionization histories and CMB optical depths. Comparison with HUDF UVLF and Planck/WMAP τ data rules out m_a ≤ 10^-23 eV as a major DM component (≥50%), while m_a ≈ 10^-22 eV remains viable only under extreme assumptions; m_a ≈ 10^-21 eV is broadly compatible with current data. Future JWST and AdvACT observations could further constrain or distinguish axion DM scenarios in the relevant mass range.

Abstract

If the dark matter (DM) were composed of axions, then structure formation in the Universe would be suppressed below the axion Jeans scale. Using an analytic model for the halo mass function of a mixed DM model with axions and cold dark matter, combined with the abundance-matching technique, we construct the UV-luminosity function. Axions suppress high-$z$ galaxy formation and the UV-luminosity function is truncated at a faintest limiting magnitude. From the UV-luminosity function, we predict the reionization history of the universe and find that axion DM causes reionization to occur at lower redshift. We search for evidence of axions using the Hubble Ultra Deep Field UV-luminosity function in the redshift range $z=6$-$10$, and the optical depth to reionization, $τ$, as measured from cosmic microwave background polarization. All probes we consider consistently exclude $m_a\lesssim 10^{-23}\text{ eV}$ from contributing more than half of the DM, with our strongest constraint ruling this model out at more than $8σ$ significance. In conservative models of reionization a dominant component of DM with $m_a=10^{-22}\text{ eV}$ is in $3σ$ tension with the measured value of $τ$, putting pressure on an axion solution to the cusp-core problem. Tension is reduced to $2σ$ for the axion contributing only half of the DM. A future measurement of the UV-luminosity function in the range $z=10$-$13$ by JWST would provide further evidence for or against $m_a=10^{-22}\text{ eV}$. Probing still higher masses of $m_a=10^{-21}\text{ eV}$ will be possible using future measurements of the kinetic Sunyaev-Zel'dovich effect by Advanced ACTPol to constrain the time and duration of reionization.

Figures (8)

• Figure 1: The mass-dependent critical overdensity for two benchmark models in which some or all of the DM is in the form of ULAs, shown for each redshift in the range $0\leq z \leq 14$. Left-hand panel: $m_a=10^{-22}\text{ eV}$, $\Omega_{\rm a}/\Omega_{\rm d}=0.5$. Right-hand panel: $m_a=10^{-22}\text{ eV}$, $\Omega_{\rm a}/\Omega_{\rm d}=1$.
• Figure 2: Sheth-Tormen mass function for ULAs including scale-dependent growth, shown for each redshift in the range $0\leq z \leq 14$. The result for CDM is shown for reference. Left-hand panel: $m_a=10^{-22}\text{ eV}$, $\Omega_{\rm a}/\Omega_{\rm d}=0.5$. Right-hand panel: $m_a=10^{-22}\text{ eV}$, $\Omega_{\rm a}/\Omega_{\rm d}=1$.
• Figure 3: The DM halo mass--galaxy luminosity relation, $M_{\rm h}(M_{\rm UV})$, for CDM (black) and aMDM models $\{$$m_a = 10^{-21} \text{eV}$, '1' (purple); $m_a = 10^{-22} \text{eV}$, '3' (cyan); $m_a = 10^{-22} \text{eV}$, '1' (blue); $m_a = 10^{-23} \text{eV}$, '1' (green)$\}$ at redshifts $z = 7$ (solid curve), $z = 10$ (dot--dashed), and $z=13$ (dashed). The truncation in the $M_{\rm h}(M_{\rm UV})$ relation for models $m_a = 10^{-22} \text{eV}$, '1' and $m_a = 10^{-23} \text{eV}$, '1' is due to a truncation in the corresponding HMF (as shown in the right-hand panel of Fig. \ref{['fig:hmf_doddy']}). The turnover in the $M_{\rm h}(M_{\rm UV})$ relation in the $m_a = 10^{-22} \text{eV}$, '3' model at $z = 7$ is the result of a turnover (without a complete truncation) in the $m_a = 10^{-22} \text{eV}$, $\Omega_{\rm a}/\Omega_{\rm d}=0.5$ HMF at $z = 7$ (left-hand panel of Fig. \ref{['fig:hmf_doddy']}).
• Figure 4: The cumulative luminosity functions ($z = 6, 7, 8, \text{and }10$) of CDM models '1' (dashed black) and '2' (solid black) and aMDM $m_a=10^{-23}\text{ eV}$ models '3' (large green circle) and '4' (large green triangle), and aMDM $m_a=10^{-22}\text{ eV}$ models '1' (medium blue circle), '2' (medium blue triangle), '3' (small filled blue circle), '4' (small filled blue triangle). The data points on each plot are the cumulative number density of galaxies in HST fields 2014arXiv1403.4295B summed down to the faint-end limit at each redshift. The error bars are $2\sigma$ for $z$ = 6, 7, and 8 ($1\sigma$ for $z$ = 10). The dashed vertical line in each panel is the absolute magnitude faint-end limit JWST will reach at each redshift for a survey down to an apparent magnitude of $\text{AB} = 31.5\text{ mag}$2006NewAR..50..113W. The $m_a=10^{-23}\text{ eV}$ aMDM models truncate prior to reaching the HUDF faint-end limit, and thus this model is ruled out ($>8\sigma$). The truncation magnitude for the $m_a=10^{-22}\text{ eV}$ models scales according to $\Omega_{\rm a}/\Omega_{\rm d}$, but all axion fractions of DM are consistent with HUDF constraints. The $m_a=10^{-21}\text{ eV}$ models are not shown on this plot as they are indistinguishable from CDM over the scales shown. Note: The x-axis and y-axis limits are different in each panel.
• Figure 5: The cumulative luminosity functions ($z = 13$) of CDM models '1' (dashed black) and '2' (solid black) and aMDM $m_a=10^{-21}\text{ eV}$ models '1' (small purple diamond) and '2' (small purple square), and aMDM $m_a=10^{-22}\text{ eV}$ models '1' (medium blue circle), '2' (medium blue triangle), '3' (small filled blue circle), '4' (small filled blue triangle). The $m_a=10^{-23}\text{ eV}$ models are not shown as their maximum cumulative luminosity value fall below the y-axis minimum. The dashed vertical line is the absolute magnitude faint-end limit JWST will reach for a survey down to an apparent magnitude of $\text{AB} = 31.5\text{ mag}$2006NewAR..50..113W. JWST observations with this sensitivity will be able to constrain $m_a=10^{-22}\text{ eV}$ models, but will be unable to distinguish $m_a=10^{-21}\text{ eV}$ models from CDM.