The Effects of Linear Matter Power Spectrum Enhancement on Dark Matter Substructure

TL;DR

This work examines how localized enhancements and cutoffs in the linear matter power spectrum $P(k)$ imprint on Milky Way–like dark matter substructure using high-resolution DM-only zoom-in simulations with Gaussian bumps and optional small-scale cutoffs. The authors demonstrate that the subhalo mass function (SHMF) tracks the shape of $P(k)$, with amplification at scales corresponding to the bump and suppression where the cutoff lies, and that these effects are largely imprinted at infall rather than during tidal evolution. Enhanced $P(k)$ also yields more centrally concentrated subhalo radial distributions and higher subhalo concentrations, indicating measurable signatures in internal structure. These findings provide a benchmark for connecting small-scale $P(k)$ features to substructure, informing semianalytic models, and enabling prospects for reconstructing $P(k)$ from future dwarf-galaxy and lensing data.

Abstract

We present cosmological dark matter (DM)--only zoom-in simulations of a Milky Way analog originating from enhanced linear matter power spectra $P(k)$ relative to the standard cold, collisionless DM (CDM) cosmology. We consider a Gaussian power excess in $P(k)$ followed by a cutoff in select cases; this behavior could arise from early-Universe physics that alters the primordial matter power spectrum or DM physics in the radiation-dominated epoch. We find that enhanced initial conditions (ICs) lead to qualitative differences in substructure relative to CDM. In particular, the subhalo mass function (SHMF) resulting from ICs with both an enhancement and cutoff is amplified at high masses and suppressed at low masses, indicating that DM substructure is sensitive to features in $P(k)$. Critically, the amplitude and shape of the SHMF enhancement depend on the wavenumber of the $P(k)$ excess and the presence or absence of a cutoff on smaller scales. These alterations to the SHMF are mainly imprinted at infall rather than during tidal evolution. Additionally, subhalos are found systematically closer to the host center, and their concentrations are increased in scenarios with $P(k)$ enhancement. Our work thus reveals effects that must be captured to enable $P(k)$ reconstruction using DM substructure.

Figures (9)

• Figure 1: Left: ratio of the linear matter power spectrum in our Bump + Cutoff (solid purple) and WDM (dashed orange) scenarios relative to CDM (black dotted). Models are shown with $k_0=22.8$, $32.1$, and $41.8~\mathrm{Mpc}^{-1}$, corresponding to $k_{\mathrm{hm}}$ for $3$, $4$, and $5~\mathrm{keV}$ WDM, from lightest to darkest shade. Right: examples of Bump + Cutoff (solid purple), Bump (dotted--dashed blue), and Cutoff (dashed red) transfer functions with different values of $k_0$. In both panels, top ticks show halo masses associated with wavenumbers in linear theory Nadler241003635.
• Figure 2: Projected DM density maps for our CDM (top left), Bump + Cutoff (top right), Bump (bottom left), and Cutoff (bottom right) simulations; for all non-CDM models, we show the $k_0=22.8~\mathrm{Mpc}^{-1}$ result. Each visualization is centered on the host, spans $1.5$ times its virial radius, and is created using meshoid (https://github.com/mikegrudic/meshoid).
• Figure 3: Differential SHMFs in CDM (black) and Bump + Cutoff (purple) models with $k_0=22.8$, $32.1$, and $41.8~\mathrm{Mpc}^{-1}$, from lightest to darkest shade. The bottom panel shows the ratio to CDM (Equation \ref{['eq:fsub']}). In both panels, shaded bands show $1\sigma$ Poisson uncertainties.
• Figure 4: Ratio of the differential SHMF relative to CDM (Equation \ref{['eq:fsub']}). Results are shown for Bump + Cutoff (solid purple), Bump (dotted--dashed blue), and Cutoff (dashed red) models with $k_0=22.8$, $32.1$, and $41.8~\mathrm{Mpc}^{-1}$, from lightest to darkest shade. Shaded bands show $1\sigma$ Poisson uncertainties for the Bump results.
• Figure 5: Ratio of the differential SHMF in our models with $P(k)$ enhancement relative to CDM divided by the corresponding ratio for isolated halos (Equation \ref{['eq:fiso']}). Results are shown for Bump + Cutoff (solid purple) and Bump (dotted--dashed blue) models with $k_0=22.8$, $32.1$, and $41.8~\mathrm{Mpc}^{-1}$, from lightest to darkest shade. Shaded bands show $1\sigma$ Poisson uncertainties for the Bump results. The differences in subhalo vs. isolated halo abundances shown here are small compared to the differences in SHMFs relative to CDM that are imprinted by $P(k)$ (see Figure \ref{['fig:sub_ratio']}).