[Paper Review] WMAP Microwave Emission Interpreted as Dark Matter Annihilation in the Inner Galaxy

Douglas P. Finkbeiner|ArXiv.org|Sep 2, 2004

Dark Matter and Cosmic Phenomena2 references20 citations

TL;DR

This paper proposes that the excess microwave emission observed by WMAP in the inner Galaxy is produced by synchrotron radiation from ultra-relativistic electron-positron pairs generated by 100 GeV dark matter particle annihilation. The inferred electron energy distribution, consistent with inverse-Compton scattering of starlight, matches the observed microwave spectrum and is compatible with a dark matter annihilation cross section of $2 \times 10^{-26}\ \mathrm{cm^3\ s^{-1}}$ and an $r^{-1}$-profile dark matter distribution truncated in the inner Galaxy.

ABSTRACT

Excess microwave emission observed in the inner Galaxy (inner ~1 kpc) is consistent with synchrotron emission from highly relativistic electron-positron pairs produced by dark matter particle annihilation. More conventional sources for this emission, such as free-free (thermal bremsstrahlung), thermal dust, spinning dust, and the softer Galactic synchrotron traced by low-frequency surveys, have been ruled out. The total power observed in the range 23 < nu < 61 GHz is between 10^{36} and 5x10^{36} erg/s, depending on the method of extrapolation to the Galactic center, where bright foreground emission obscures the signal. The inferred electron energy distribution is diffusion hardened, and is in qualitative agreement with the energy distribution required to explain the gamma ray excess in the inner Galaxy at 1-30 GeV as inverse-Compton scattered starlight. We investigate the possibility that this population of electrons is produced by dark matter annihilation of 100 GeV particles, with cross section =2x10^{-26} cm^3/s, and an 1/r dark matter mass profile truncated in the inner Galaxy, and find this scenario to be consistent with current data.

Motivation & Objective

• To explain the unexplained excess microwave emission in the inner Galaxy (23–61 GHz) observed by WMAP.
• To rule out conventional astrophysical sources such as free-free emission, thermal dust, spinning dust, and standard synchrotron radiation.
• To investigate whether the observed emission can be attributed to dark matter annihilation producing relativistic electron-positron pairs.
• To test the consistency of the dark matter annihilation hypothesis with observed electron energy spectra and microwave luminosity.
• To constrain the dark matter particle mass, annihilation cross section, and spatial distribution using multi-wavelength data and theoretical modeling.

Proposed method

• Modeling the electron energy distribution using a Fokker-Planck equation that includes diffusion, energy losses from synchrotron and inverse Compton scattering, and spatial transport.
• Using an analytic solution for the simplest case and numerical solutions for variable diffusion and energy loss parameters.
• Applying the NFW dark matter density profile with a core radius $r_s = 20$ kpc and a solar neighborhood density of $6.5 \times 10^{-25}\ \mathrm{g\ cm^{-3}}$.
• Defining the annihilation rate per volume as $\Gamma(r) = \left(\rho_{\text{NFW}}(r)/m_\chi\right)^2 \langle\sigma_A v\rangle$, assuming Majorana fermion annihilation.
• Computing the electron number density per energy via convolution of the annihilation rate with a Green's function that accounts for spatial diffusion and energy loss.
• Integrating the resulting electron distribution to predict microwave synchrotron emission and comparing with WMAP data.

Experimental results

Research questions

• RQ1 Can the observed microwave excess in the inner Galaxy be explained by synchrotron emission from relativistic electrons produced by dark matter annihilation?
• RQ2 Are conventional astrophysical foregrounds—free-free, thermal dust, spinning dust, and standard synchrotron—sufficient to explain the observed microwave emission?
• RQ3 What dark matter particle mass and annihilation cross section are consistent with the observed microwave luminosity and spectral shape?
• RQ4 How does the electron energy distribution, shaped by diffusion and energy losses, match the requirements for inverse-Compton scattering of starlight and CMB photons?
• RQ5 Is a truncated $r^{-1}$ dark matter profile in the inner Galaxy consistent with the observed emission and current constraints?

Key findings

• The total microwave luminosity in the inner Galaxy (23–61 GHz) is estimated at $1 \times 10^{36}$ to $5 \times 10^{36}\ \mathrm{erg\ s^{-1}}$, depending on extrapolation to the Galactic center.
• The inferred electron energy distribution is diffusion-hardened and matches the energy spectrum required to produce the observed inverse-Compton scattered photons in the 1–30 GeV range.
• A dark matter particle mass of 100 GeV with an annihilation cross section of $\langle\sigma_A v\rangle = 2 \times 10^{-26}\ \mathrm{cm^3\ s^{-1}}$ is consistent with the observed microwave emission.
• The model assumes a truncated $r^{-1}$ dark matter density profile in the inner Galaxy, which helps avoid overproduction of synchrotron emission near the Galactic center.
• The total annihilation rate in the Galaxy is calculated to be $4.6 \times 10^{38}\ \mathrm{s^{-1}}$, with $4 \times 10^{38}\ \mathrm{s^{-1}}$ contributing to the electron population responsible for the microwave emission.
• The absence of a strong signal in other galaxies may stem from insufficient resolution to disentangle emission components, suggesting that the inner Galaxy signal is uniquely resolvable due to WMAP's precision.