Suppressing Linear Power on Dwarf Galaxy Halo Scales

TL;DR

This study investigates whether a suppression of the primordial power spectrum on small scales, as motivated by the dwarf-halo paucity in the Local Group, can be constrained by structure formation. Using two sets of N-body simulations in a LCDM cosmology and parametric filtering of the initial power spectrum with break scales $k_0$, the authors analyze halo abundance, non-linear power regeneration, and Ly-$\alpha$ forest statistics. They find that non-linear gravitational evolution regenerates small-scale power, diminishing the discriminating power of several probes such as Ly-$\alpha$ forest flux, while halo counts remain closely tied to the linear power spectrum; to achieve a factor of $\gtrsim 5$ reduction in $M\sim 10^{10} M_\odot$ halos requires fairly extreme power suppression. Consequently, the most promising observational constraints may come from the abundance of damped Ly-$\alpha$ systems or the timing of reionization, though accurate theoretical predictions for these observables remain challenging. The work highlights the importance of non-linear regeneration in interpreting small-scale power and its implications for testing inflationary scenarios that modify $P(k)$ on small scales.

Abstract

Recently is has been suggested that the dearth of small halos around the Milky Way arises due to a modification of the primordial power spectrum of fluctuations from inflation. Such modifications would be expected to alter the formation of structure from bottom-up to top-down on scales near where the short-scale power has been suppressed. Using cosmological simulations we study the effects of such a modification of the initial power spectrum. While the halo multiplicity function depends primarily on the linear theory power spectrum, most other probes of power are more sensitive to the non-linear power spectrum. Collapse of large-scale structures as they go non-linear regenerates a ``tail'' in the power spectrum, masking small-scale modifications to the primordial power spectrum except at very high-z. Even the small-scale (k>2h/Mpc) clustering of the Ly-alpha forest is affected by this process, so that CDM models with sufficient power suppression to reduce the number of 10^10 Msun halos by a factor of about 5 give similar Ly-alpha forest power spectrum results. We conclude that other observations that depend more directly on the number density of collapsed objects, such as the number of damped Ly-alpha systems, or the redshift of reionization may provide the most sensitive tests of these models.

Figures (9)

• Figure 1: Slices though the particle distribution in the TreePM simulations of our 4 models at $z=3$. From left to right, the panels show the models with filter scale $k_0=2\;h\;{\rm Mpc}^{-1}$, $k_0=5\;h\;{\rm Mpc}^{-1}$ (top row), $k_0=10\;h\;{\rm Mpc}^{-1}$, and fiducial $\Lambda$CDM (bottom row). The box side-length in each case is $25\;h^{-1}{\rm Mpc}$ and the slice thickness $0.25\;h^{-1}{\rm Mpc}$.
• Figure 2: The linear and non-linear power spectrum at $z=3$. We show the mean from 3 runs of our TreePM simulations for each of 4 models: our fiducial $\Lambda$CDM model (triangles), one filtered at $k_0=10h{\rm Mpc}^{-1}$ (open squares), $k_0=5h{\rm Mpc}^{-1}$ (open circles), and $k_0=2h{\rm Mpc}^{-1}$ (three pointed stars). The solid line shows the prediction of Peacock & Dodds (PD96) for the fiducial model (the theory is not applicable to the filtered models) and the dotted lines are the linear theory input spectra. While the N-body simulations have the same random phases and so are directly comparable, comparison with the analytic models requires error bars. We show the $1\sigma$ error on the mean of the fiducial model computed from our 3 realizations. The errors on the other models are similar.
• Figure 3: The non-linear power spectra as a function of redshift for our fiducial model (solid symbols) and one filtered model with $k_0=5h\,{\rm Mpc}^{-1}$ (open symbols). The symbols represent the mean of 3 runs of our PM simulations, the error bars show the $1\sigma$ error on the mean estimated from our 3 realizations at $z=0$. (However recall that for each model the simulations have the same random phases.) The spectra are scaled by $(4a)^{-2}$ to reduce the effect of linear evolution and highlight the non-linear growth.
• Figure 4: The redshift space non-linear power spectra as a function of redshift for our fiducial model (solid symbols) and one filtered model with $k_0=5h\,{\rm Mpc}^{-1}$ (open symbols). The symbols represent the mean of 3 runs of our PM simulations. The spectra are scaled by $(4a)^{-2}$ to reduce the effect of linear evolution and highlight the non-linear growth.
• Figure 5: (top): The 1D power spectrum of the flux measured from our simulations of the 4 models (lines), all with $T_0=10^4$K. The observational results, also at $z=3$, of McDonald et al. (1999) are shown as points. (bottom): The 1D power spectrum of the flux for the fiducial model with 3 different values of $T_0$.