[Paper Review] WIMP matter power spectra and small scale power generation

Céline Bœhm, H. Mathis+2 more|arXiv (Cornell University)|Sep 24, 2003

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper investigates weakly interacting massive particles (WIMPs) with non-negligible self-interactions that induce collisional damping, leading to a damped linear matter power spectrum on scales of ~10³ M⊙. Despite this damping, numerical simulations show that non-linear matter power spectra at low redshift (z ≤ 1) become indistinguishable from standard cold dark matter (CDM) due to small-scale power regeneration, implying lensing measurements alone cannot robustly distinguish such collisional WIMPs from conventional CDM candidates.

ABSTRACT

Dark Matter (DM) is generally assumed to be massive, cold and collisionless from the structure formation point of view. A more correct statement however is that DM indeed experiences collisional damping, but on a scale which is supposed to be too small to be relevant for structure formation. The aim of this paper is to present a Cold (although ``collisional'') Dark Matter particle whose matter power spectrum is damped and see whether it is distinguishable from standard candidates. To achieve this purpose, we calculate the collisional damping and free-streaming scales of neutralinos and non conventional candidates (say light particles heavier than ~1 MeV but lighter than O(10) GeV). The latter can be considered as Cold Dark Matter (CDM) particles in the sense that they become non relativistic before their thermal decoupling epoch. Unlike neutralinos, however, their linear matter power spectrum can be damped on scales of ~ 10^3 Msol due to their interactions. Since these scales are of cosmological interest for structure formation, we perform a series of numerical simulations to obtain the corresponding non linear matter power spectra P(k)_{nl} at the present epoch. We show that because of small scale regeneration, they all resemble each other at low redshifts, i.e. become very similar to a typical CDM matter power spectrum on all but the smallest scales. Therefore, even if lensing measurements at redshift below unity were to yield a P(k)_{nl} consistent with CDM models, this would not constitute a sufficiently robust evidence in favour of the neutralino to rule out alternative DM candidates.

Motivation & Objective

• To assess the impact of self-interactions on the matter power spectrum for light WIMP-like dark matter candidates with masses >1 MeV and <10 GeV.
• To determine whether such collisional WIMPs can be distinguished from standard cold dark matter (CDM) via non-linear matter power spectra.
• To investigate the role of small-scale power regeneration in making non-CDM power spectra resemble CDM at low redshift.
• To evaluate the robustness of lensing measurements in constraining alternative dark matter candidates with damped linear power spectra.

Proposed method

• Calculate collisional damping and free-streaming scales for conventional (e.g., neutralinos) and non-conventional light WIMP candidates (1 MeV – 10 GeV) that achieve correct relic density via annihilation.
• Perform numerical N-body simulations to compute non-linear matter power spectra P(k)nl at z = 0 and z = 10 for models with cut-offs at 10⁶, 10⁷, 10⁸, and 10⁹ h⁻¹ M⊙.
• Compare the resulting P(k)nl spectra across different dark matter models, including standard CDM and warm dark matter (WDM) with varying masses.
• Analyze the halo mass function at z = 0 and z = 10 to quantify differences in structure formation efficiency across models.
• Use the time evolution of P(k)nl to assess the viability of weak lensing measurements as a discriminator of dark matter models.
• Evaluate the sensitivity of the results to simulation dynamic range and redshift, focusing on scales below 100 kpc/h.

Experimental results

Research questions

• RQ1 Can WIMP candidates with non-negligible self-interactions produce a damped linear matter power spectrum on cosmologically relevant scales (~10³ M⊙)?
• RQ2 To what extent does small-scale power regeneration erase the imprint of initial damping in the non-linear matter power spectrum at low redshift?
• RQ3 Can weak lensing measurements at z < 1 distinguish between standard CDM and collisional WIMP models with damped linear spectra?
• RQ4 How do halo mass functions differ between CDM and light WIMP models with varying cut-off scales at high (z = 10) and low (z = 0) redshift?
• RQ5 Are structural parameters or reionization signatures more effective than P(k)nl in discriminating between alternative dark matter candidates?

Key findings

• The non-linear matter power spectrum P(k)nl for collisional WIMP models with a cut-off at ~10³ M⊙ becomes indistinguishable from standard CDM at redshifts z ≤ 1 due to small-scale power regeneration.
• Even with a cut-off at 10⁹ h⁻¹ M⊙, the simulated P(k)nl for collisional WIMPs closely matches the CDM spectrum at z < 1, limiting the discriminative power of lensing surveys.
• At z = 10, the 0.6 keV WDM model shows a deficit of haloes by a factor of ~40 compared to CDM, indicating early suppression of structure formation.
• The halo mass function in the 0.6 keV WDM model is significantly suppressed at low masses (M < 10⁸.⁵ h⁻¹ M⊙) at z = 10, but recovers at higher masses.
• Lensing measurements probing scales down to 70 h⁻¹ kpc may begin to probe the critical region for a 10⁹ h⁻¹ M⊙ cut-off, but current surveys at 200 h⁻¹ kpc are insufficient to distinguish such models.
• Other signatures such as halo structural parameters or reionization history may offer better discrimination, but are weakened by uncertainties in baryonic physics.