Energy Injection And Absorption In The Cosmic Dark Ages

TL;DR

This work provides a detailed mapping from energy injection histories to energy deposition histories for photons and electrons during the cosmic dark ages, enabling immediate CMB based constraints on arbitrary electromagnetic injection spectra and redshift dependence. By computing deposition histories on a dense grid of initial energies and injection redshifts and packaging them as T^{ijk} tables, the authors derive an effective deposition efficiency f(z) and assess the impact of structure formation on deposition. The framework supports updated constraints on late-decaying species and oscillating asymmetric DM, and it demonstrates the utility of principal component methods to translate deposition histories into CMB limits. The results, publicly available online, offer a practical tool for rapid evaluation of DM models and other new physics scenarios affecting the ionization history and CMB.

Abstract

Dark matter annihilation or de-excitation, decay of metastable species, or other new physics may inject energetic electrons and photons into the photon-baryon fluid during and after recombination. As such particles cool, they partition their energy into a large number of efficiently ionizing electrons and photons, which in turn modify the ionization history. Recent work has provided a simple method for constraining arbitrary energy deposition histories using the cosmic microwave background (CMB); in this note, we present results describing the energy deposition histories for photons and electrons as a function of initial energy and injection redshift. With these results, the CMB bounds on any process injecting some arbitrary spectrum of electrons, positrons and/or photons with arbitrary redshift dependence can be immediately computed.

Figures (10)

• Figure 1: Fraction of initial energy deposited by $1+z_\mathrm{final}=10$, by a particle or pair injected at a redshift $z$. The different panels show the results for different species. Left panel: electron + positron pair (note "energy" on the $x$-axis refers to the kinetic energy of the electron or positron individually, not the pair -- we assume the electrons and positrons have the same spectrum -- but the plotted values give the fraction of the pair's total (mass + kinetic) energy that is absorbed), center panel: photon, right panel: electron (in this case, as there is no way to liberate the electron's mass energy, we plot the fraction of kinetic energy which is absorbed). The energy axis on the right panel is truncated because the behavior is uninteresting at lower energies; when the electron's kinetic energy is small compared to its mass energy, the deposition fraction $\approx 1$.
• Figure 2: Effective efficiency (i.e. the ratio of the energy deposition history to the energy injection history) for (top) annihilating DM and (bottom) decaying DM, for electron-positron pairs (left-hand panels) and photons (right-hand panels), as a function of redshift-of-deposition and initial energy of the photon/electron/positron.
• Figure 3: Left panel: The $f(z)$ curves derived in Slatyer:2009yq for 41 models of interest (solid black lines), and the recovered $f(z)$ curves using the results presented in this paper (red diamonds), between $z=10$ and $z=1500$. Right panel: The percentile difference between the two curves, between $z=10$ and $z=1500$.
• Figure 4: The ratio of the energy deposited, from the halos + the smooth component, to the energy injected from the smooth component, as a function of injection energy and redshift-of-deposition, for (left panel) $e^+ e^-$ pairs, (right panel) photons.
• Figure 5: The ratio of the energy deposited, from the halos + the smooth component, to the energy injected from the smooth component, as a function of redshift-of-deposition, for three different electron injection energies (assuming they are injected as a pair with a positron of the same energy), as well as the on-the-spot curve where the deposited energy at every redshift is equal to the injected energy (from halos + smooth component). Dotted lines show the result of simply multiplying the $f(z)$ derived for the smooth component by the enhancement factor from the halos, rather than correctly inserting the enhancement factor inside the integral in Eq. \ref{['eq:effectivef']}.