Probing small-scale dark matter clumping with the large-scale 21-cm power spectrum

Abstract

The 21-cm line of hydrogen is the most promising probe of the Dark Ages and Cosmic Dawn. We combine hydrodynamical simulations with a large-scale grid in order to calculate the effect of non-linear structure formation on the large-scale 21-cm power spectrum, focusing on redshifts $z=20-40$. As the clumping effect arises from small-scale density fluctuations, it offers a unique opportunity to probe the standard cold dark matter model in a new regime and thus potentially investigate the properties of dark matter. To this end, we also study a warm dark matter $-$ like model with a Gaussian cutoff on a scale of 50 kpc. We find that clumping has a significant impact on the large-scale 21-cm power spectrum. For example, for the Dark Ages case at $z=30$ and wavenumber $k=0.05$ Mpc$^{-1}$, small-scale clustering enhances the 21-cm power spectrum by $13\%$. Once Lyman-$α$ coupling kicks in due to the first stars, the 21-cm signal strengthens, and the effect of clumping grows; it suppresses the observable power spectrum at $z=20$ by a factor of two, while the cutoff model has less than half the clumping impact. The clumping effect is significantly higher than the sensitivity of the planned Square Kilometre Array (SKA) AA$^\star$ configuration, by up to a factor of 20 for standard cold dark matter, though detection will require separation from foregrounds and from astrophysical contributions to the 21-cm power spectrum.

Figures (5)

• Figure 1: Top panels: The 21-cm power spectrum as a function of $k$, for the CDM model (solid), WDM-like model with $k_{\rm{cut}} = 100 \ h\ \rm{Mpc}^{-1}$ (dotted) and Large-scale fluctuations only (dashed). We consider the Dark Ages, as well as the Lyman-$\alpha$ coupling cases of Moderate coupling and Saturated coupling, each at $z = 20, 30$ or 40. Bottom panels: The difference "Diff" in $\Delta^2$ due to clumping (i.e., between a given model and the case of Large-scale fluctuations only), as a function of $k$. Panels with coupling show $|\rm{Diff}|$; those panels also show the $z=20$ sensitivity for SKA AA$^\star$ (solid grey line and the corresponding shaded area) and SKA AA4 (dot-dashed grey line). We note that the precise output redshifts that we used from the numerical simulations are 19.46, 30.00 and 39.89 (which we loosely refer to as 20, 30, and 40).
• Figure 2: Top panels: The 21-cm power spectrum as a function of $z$ at $k = 0.05$, 0.1 and 0.5 Mpc$^{-1}$. We show the same models and cases as in Fig. \ref{['fig:21cmPS_vs_k_3cases']}: CDM (solid), WDM-like (dotted), and Large-scale (dashed), for Dark ages, Moderate coupling and Saturated coupling. Bottom panels: The difference "Diff" in $\Delta^2$ due to clumping. Panels with coupling show $|-\rm{Diff}|$, and also show the $k= 0.05$ Mpc$^{-1}$ sensitivity for SKA AA$^\star$ (solid grey line and the corresponding shaded area) and SKA AA4 (dot-dashed grey line).
• Figure 3: Top panels: 21-cm power spectrum as a function of $k$ for the CDM (solid) and Large-scale fluctuation (long-dashed) cases (repeated from the top panels of Fig. \ref{['fig:21cmPS_vs_k_3cases']}, but shown here only down to $k= 0.02$ Mpc$^{-1}$), along with the No $v_{\rm{bc}}$ (short-dashed), $v_{\rm{bc}}$ effect (dot - dashed, shown in absolute value), and $v_{\rm{bc}}$ only (dotted) cases (see text). Results are shown for the Dark Ages at $z = 30$, and for Moderate coupling and Saturated coupling at $z = 20$. The panels with coupling show the $z= 20$ sensitivity for SKA AA$^\star$ (solid grey line and corresponding shaded area) and SKA AA4 (dot-dashed grey line). We note that the precise output redshifts that we used from the numerical simulations are 19.46 and 30.00 (which we loosely refer to as 20 and 30). The $v_{\rm{bc}}$ effect is positive in the coupling cases, and for the Dark Ages case it is positive in the $k$ range [0.026, 0.028] and negative otherwise. Bottom panels: 21-cm power spectrum as a function of $z$ for the CDM and Large-scale fluctuation cases (repeated from the top panels of Fig. \ref{['fig:21cmPS_vs_z_3cases']}), as well as the No $v_{\rm{bc}}$, $v_{\rm{bc}}$ effect, and $v_{\rm{bc}}$ only cases. We consider the Dark ages, Moderate coupling, and Saturated coupling, all at $k = 0.05$ Mpc$^{-1}$. The panels with coupling show the $k= 0.05$ Mpc$^{-1}$ sensitivity for SKA AA$^\star$ and SKA AA4. The styles of the cases and sensitivities are the same as in the top panels. The $v_{\rm{bc}}$ effect is positive in the coupling cases, and for the Dark Ages case it is positive in the $z$ ranges [20.17, 25.19] and [43.88, 75], and negative otherwise. Note: In this figure, all cases were calculated with a $256^3$ large-scale grid, unlike the previous two figures, which used $512^3$.
• Figure 4: Testing convergence with respect to the size of our large-scale grid. We show the 21-cm power spectrum of CDM as a function of $k$ at $z=20$, 30 and 40, for three box sizes: 1536, 768 and 384 Mpc on a side, corresponding to $512^3, 256^3$ and $128^3$ pixels, respectively. The curves go down to $k = 0.01$, 0.02, and 0.04 Mpc$^{-1}$, respectively. We note that the precise output redshifts that we used from the numerical simulations are 19.46, 30.00 and 39.89 (which we loosely refer to as 20, 30, and 40).
• Figure 5: Examples of the dependence of $T_{\rm{21}}$ on $\delta$ and $V_{\rm{bc}}$ (each in units of its cosmic standard deviation, see section \ref{['s:sim']}). The points show the outputs of the hydrodynamical simulations, and the curves show our interpolation. We show the case with clumping (solid curves) or without, i.e., uniform simulation boxes without small-scale fluctuations (dashed curves); the latter case is independent of $V_{\rm{bc}}$ and the values are shown as $V_{\rm{bc}}=1$.