Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gamma-rays from ultracompact minihalos: potential constraints on the primordial curvature perturbation

Amandeep S. Josan, Anne M. Green

TL;DR

This paper investigates using gamma-ray emissions from ultracompact minihalos (UCMHs) to constrain the primordial curvature perturbation on small scales. It models UCMH formation, their density profiles, and the gamma-ray flux from WIMP annihilation, deriving how Fermi detections or non-detections translate into bounds on the UCMH halo fraction $f_{\\rm UCMH}$ and, subsequently, on the power spectrum $\\mathcal{P_R}(k)$ across scales $k$ from about $10^{1}$ to $10^{8} \, {\\rm Mpc}^{-1}$. The study finds that a Fermi detection would yield a lower bound on $f_{\\rm UCMH}$ and thus a lower limit on $\\mathcal{P_R}$, while non-detection would produce upper limits on $f_{\\rm UCMH}$ and tighter constraints on $\\mathcal{P_R}$, with typical bounds around $\\mathcal{P_R} \lesssim 10^{-6}$ on relevant scales. These results can surpass constraints from primordial black hole formation but hinge on assuming WIMPs and minimal disruption of UCMHs during Milky Way formation, highlighting a promising cross-check for inflationary models that generate enhanced small-scale power.

Abstract

Ultracompact minihalos (UCMHs) are dense dark matter structures which can form from large density perturbations shortly after matter-radiation equality. If dark matter is in the form of Weakly Interacting Massive Particles (WIMPs), then UCMHs may be detected via their gamma-ray emission. We investigate how the {\em{Fermi}} satellite could constrain the abundance of UCMHs and place limits on the power spectrum of the primordial curvature perturbation. Detection by {\em Fermi} would put a lower limit on the UCMH halo fraction. The smallest detectable halo fraction, $f_{\rm UCMH} \gtrsim 10^{-7}$, is for $M_{\rm UCMH} \sim 10^{3} M_{\odot}$. If gamma-ray emission from UCMHs is not detected, an upper limit can be placed on the halo fraction. The bound is tightest, $f_{\rm UCMH} \lesssim 10^{-5}$, for $M_{\rm UCMH} \sim 10^{5} M_{\odot}$. The resulting upper limit on the power spectrum of the primordial curvature perturbation in the event of non-detection is in the range $\mathcal{P_R} \lesssim 10^{-6.5}- 10^{-6}$ on scales $k \sim 10^{1}-10^{6} \, {\rm Mpc}^{-1}$. This is substantially tighter than the existing constraints from primordial black hole formation on these scales, however it assumes that dark matter is in the form of WIMPs and UCMHs are not disrupted during the formation of the Milky Way halo.

Gamma-rays from ultracompact minihalos: potential constraints on the primordial curvature perturbation

TL;DR

This paper investigates using gamma-ray emissions from ultracompact minihalos (UCMHs) to constrain the primordial curvature perturbation on small scales. It models UCMH formation, their density profiles, and the gamma-ray flux from WIMP annihilation, deriving how Fermi detections or non-detections translate into bounds on the UCMH halo fraction and, subsequently, on the power spectrum across scales from about to . The study finds that a Fermi detection would yield a lower bound on and thus a lower limit on , while non-detection would produce upper limits on and tighter constraints on , with typical bounds around on relevant scales. These results can surpass constraints from primordial black hole formation but hinge on assuming WIMPs and minimal disruption of UCMHs during Milky Way formation, highlighting a promising cross-check for inflationary models that generate enhanced small-scale power.

Abstract

Ultracompact minihalos (UCMHs) are dense dark matter structures which can form from large density perturbations shortly after matter-radiation equality. If dark matter is in the form of Weakly Interacting Massive Particles (WIMPs), then UCMHs may be detected via their gamma-ray emission. We investigate how the {\em{Fermi}} satellite could constrain the abundance of UCMHs and place limits on the power spectrum of the primordial curvature perturbation. Detection by {\em Fermi} would put a lower limit on the UCMH halo fraction. The smallest detectable halo fraction, , is for . If gamma-ray emission from UCMHs is not detected, an upper limit can be placed on the halo fraction. The bound is tightest, , for . The resulting upper limit on the power spectrum of the primordial curvature perturbation in the event of non-detection is in the range on scales . This is substantially tighter than the existing constraints from primordial black hole formation on these scales, however it assumes that dark matter is in the form of WIMPs and UCMHs are not disrupted during the formation of the Milky Way halo.

Paper Structure

This paper contains 4 sections, 21 equations, 2 figures.

Table of Contents

  1. Introduction
  2. UCMH formation and gamma-ray emission
  3. Constraints on the primordial curvature perturbation
  4. Conclusions

Figures (2)

  • Figure 1: Constraints on the UCMH halo fraction, $f_{\rm UCMH}$, as a function of present day UCMH mass, $M_{\rm UCMH}(z=0)$. The solid line shows the lower bound on the halo fraction which would result from the detection of gamma-rays from an UCMH by Fermi. The dotted line shows the upper limit on the halo fraction if gamma-rays from UCMHs are not detected, assuming DM is in the form of WIMPs.
  • Figure 2: Limits on the power spectrum of the primordial curvature perturbation as a function of comoving wavenumber (in units of ${\rm{Mpc}}^{-1}$). The solid line shows the potential lower bound on the power spectrum resulting from the detection of gamma-rays from an UCMH by Fermi at threshold sensitivity. The dotted line shows the upper limit on the power spectrum obtained if gamma-rays from UCMHs are not detected by Fermi, assuming DM is in the form of WIMPs and UCMHs are not disrupted during structure formation.