Probing axion dark matter with 21 cm fluctuations from minihalos

If the symmetry breaking inducing the axion occurs after the inflation, the large axion isocurvature perturbations can arise due to a different axion amplitude in each causally disconnected patch. This causes the enhancement of the small-scale density fluctuations which can significantly affect the evolution of structure formation. The epoch of the small halo formation becomes earlier and we estimate the abundance of those minihalos which can host the neutral hydrogen atoms to result in the 21 cm fluctuation signals. We find that the future radio telescopes, such as the Square Kilometer Array, can put the axion mass bound of order $m_a\gtrsim {10}^{-13}\mathrm{eV}$ for the simple temperature-independent axion mass model, and the bound can be extended to of order $m_a\gtrsim {10}^{-8}\mathrm{eV}$ for a temperature-dependent axion mass.

Figure 1

The halo mass functions $dn/dlnM$ (${\mathrm{Mpc}}^{-3})$ as a function of the halo mass $M[M_{\odot }]$ for the adiabatic plus axon isocurvature perturbations ($k_{\mathrm{osc}}=5000/\mathrm{Mpc}$) and those for the adiabatic perturbations alone.

Figure 2

The mass fraction of isolated collapsed halos $df(M)/d\log M$ using the Press-Schechter formalism. The mass fractions for the adiabatic perturbations alone at $z=100$, 50 are too small to be shown in this figure.

Figure 3

The 21 cm angular power spectra at $z=10$, $C_l(z=10)$ and the cross power spectra $C_l^{\mathrm{cross}}(z_1,z_2)$ between the redshift bins $z=z_1$ and $z=z_2$ [two examples of $(z_1,z_2)=(10,10.1)$ and (10, 10.5) are shown]. The absolute values $|C_l|$ are shown in this log plot. The cross power spectrum amplitudes decrease for the redshift binds with a larger redshift difference.

Figure 4

$\overline{\mathrm{\Delta }{T}_b}(z)(\mathrm{mK})$ and $\overline{b}(z)$ for the adiabatic plus axion isocurvature perturbations $(k_{\mathrm{osc}}=5\times {10}^3/\mathrm{Mpc})$ and for no axion (only adiabatic perturbations) scenarios.

Figure 5

$1\sigma$ error $\sigma (k_{\mathrm{osc}})/k_{\mathrm{osc}}(\%)$ as a function of a fiducial value $k_{\mathrm{osc}}(/\mathrm{Mpc})$.

Figure 6

Marginalized $1\sigma$ confidence ellipses for ${\mathrm{\Omega }}_{\mathrm{CDM}}{h}^2$ and $k_{\mathrm{osc}}(/\mathrm{Mpc})$. The fiducial values are $(k_{\mathrm{osc}},{\mathrm{\Omega }}_{\mathrm{CDM}}{h}^2)=(500/\mathrm{Mpc},0.11933)$ and (5000/Mpc, 0.11933).

Figure 7

The halo mass functions as a function of a halo mass. The vertical lines represent the minimal and maximal minihalo masses of our interest at $z=10$ [given by Eqs. (3) and (4)].

Figure 8

The comoving horizon scale $k_{\mathrm{osc}}=R(T_{\mathrm{osc}})H(T_{\mathrm{osc}})$ when the axion oscillation starts as a function of $m_{a0}$. $n$ represents the temperature dependence of the axion mass. The horizontal line indicates the maximum $k_{\mathrm{osc}}=1.2\times {10}^5/\mathrm{Mpc}$ below which $k_{\mathrm{osc}}$ can be measured by the 21 cm signals within $1\sigma$ confidence level.

Figure 9

$1\sigma$ error $\sigma (k_{\mathrm{osc}})/k_{\mathrm{osc}}(\%)$ as a function of a fiducial value $k_{\mathrm{osc}}(/\mathrm{Mpc})$. ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{CDM}}=0.1$.

Figure 10

The axion decay constant $f_a$ for ${\mathrm{\Omega }}_a/{\mathrm{\Omega }}_{\mathrm{CDM}}=1$ as a function of the zero temperature axion mass $m_{a0}$.