A Model For Halo Formation With Axion Mixed Dark Matter

TL;DR

The paper investigates ultra-light axion–like particles as dark matter to resolve three dwarf-galaxy problems of ΛCDM. It develops a mixed dark matter framework (aMDM) with a scalar DM component of mass $m_a$ and fraction $\Omega_a/\Omega_d$, derives scale-dependent transfer functions and Jeans scales, and computes the halo mass function and halo density profiles under both single- and two-component DM. It finds that pure ULAs with $m_a\sim 10^{-22}$ eV can create kpc-scale cores but risk tension with high-redshift and Lyman-α constraints; including a modest CDM fraction or choosing $m_a\gtrsim 10^{-21}$ eV yields substantial cores while preserving sufficient halo formation and lowering $v_{\max}$ of dwarfs. Overall, ULAs offer a viable path to alleviating MSP, CCP, and MFP without the Catch-22 of WDM, albeit requiring careful treatment of non-linear physics, baryons, and hydrodynamical simulations to confirm observational viability.

Abstract

There are several issues to do with dwarf galaxy predictions in the standard $Λ$CDM cosmology that have suscitated much recent debate about the possible modification of the nature of dark matter as providing a solution. We explore a novel solution involving ultra-light axions that can potentially resolve the missing satellites problem, the cusp-core problem, and the `too big to fail' problem. We discuss approximations to non-linear structure formation in dark matter models containing a component of ultra-light axions across four orders of magnitude in mass, $10^{-24}\text{ eV}\lesssim m_a \lesssim 10^{-20}\text{ eV}$, a range too heavy to be well constrained by linear cosmological probes such as the CMB and matter power spectrum, and too light/non-interacting for other astrophysical or terrestrial axion searches. We find that an axion of mass $m_a\approx 10^{-21}\text{ eV}$ contributing approximately $85\%$ of the total dark matter can introduce a significant kpc scale core in a typical Milky Way satellite galaxy in sharp contrast to a thermal relic with a transfer function cut off at the same scale, while still allowing such galaxies to form in significant number. Therefore ultra-light axions do not suffer from the \emph{Catch 22} that applies to using a warm dark matter as a solution to the small scale problems of cold dark matter. Our model simultaneously allows formation of enough high redshift galaxies to allow reconciliation with observational constraints, and also reduces the maximum circular velocities of massive dwarfs so that baryonic feedback may more plausibly resolve the predicted overproduction of massive MWG dwarf satellites.

Figures (14)

• Figure 1: The transfer function, Eq. (\ref{['eqn:transfer_ax']}) for aMDM with $m_a=10^{-22}\text{ eV}$ and varying axion fractions to total DM. For comparison, we also plot the FCDM transfer function of hu2000 and the WDM transfer function (Eq. (\ref{['eqn:tk_wdm']})) with $m_W\approx 0.84 \text{ keV}$ chosen to match the transfer function half mode, $k_m$ (Eq. (\ref{['eqn:km_def']})). With this choice and $\Omega_a/\Omega_d=1$ the axion transfer function at $k_m$ is much steeper than its WDM counterpart.
• Figure 2: The characteristic mass associated to the half-mode, $k_m$, of the transfer function as a function of axion mass, $M_m(m_a)$, found from Eqs. (\ref{['eqn:km_def']}) and (\ref{['eqn:suppress_mass']}). It is well fit by a power law $M_m\propto m_a^{-\gamma}$ with $\gamma \approx 1.35$. We also show the mass associated to the Jeans scale of Eq. (\ref{['eqn:hu_jeans_def']}), which is lower by two to three orders of magnitude.
• Figure 3: Thermal relic warm dark matter mass in keV chosen to give the same transfer function half-mode, $k_m$ (Eq. (\ref{['eqn:km_def']})), as a ULA, as a function of ULA mass in eV. We also show the Lyman-$\alpha$ forest constraints $m_W>0.55\text{ keV}$ of viel2005 corresponding to $m_a>5\times10^{-23}\text{ eV}$, consistent with amendola2005.
• Figure 4: Variance $\sigma(M)$ for $\Lambda$CDM, and aMDM with various $\Omega_a h^2$ at fixed total $\Omega_d h^2=0.112$ and axion mass $m_a=10^{-22}\text{ eV}$.
• Figure 5: The mass dependent critical density from scale-dependent growth, Eq. (\ref{['eqn:g_def']}), is given by $\delta_c(M)=\mathcal{G}(M)\delta_\text{EdS}$. We show $\mathcal{G}(M)$ for aMDM with various $\Omega_c/\Omega_d$ at fixed total $\Omega_d h^2=0.112$ and axion mass $m_a=10^{-22}\text{ eV}$. The spikes at low fraction are due to BAO distortions and numerical instability defining scale-dependent growth via a ratio.