Radiation from matter-antimatter annihilation in the quark nugget model of dark matter

We revisit the properties of positron cloud in quark nugget (QN) model of dark matter (DM). In this model, dark matter particles are represented by compact composite objects composed of a large number of quarks or antiquarks with total baryon number $B\sim {10}^{24}$. These particles have a very small number density in our galaxy which makes them “dark” to all DM detection experiments and cosmological observations. In this scenario, antiquark nuggets play special role because they may manifest themselves in annihilation with visible matter. We study electron-positron annihilation in collisions of free electrons, hydrogen and helium gases with the positron cloud of antiquark nuggets. We show that a strong electric field of antiquark nuggets destroys positronium, hydrogen and helium atoms and prevents electrons from penetrating deeply in positron cloud, thus reducing the probability of the electron-positron annihilation by nearly five orders of magnitude. Therefore, electron annihilation in the positron cloud of QNs cannot explain the observed by SPI/INTEGRAL detector photons with energy 511 keV in the center of our galaxy. These photons may be explained by a different mechanism in which QN captures protons which annihilate with antiquarks in the quark core or transform to neutrons thus reducing the QN core charge and increasing QN temperature. As a result QN loses positrons to space which annihilate with electrons there. Even more positrons are produced from charged pions resulting from the proton annihilation. Another manifestation may be emission of photons from ${\pi }^0$ decays.

Figure 1

Numerical solutions of the Thomas-Fermi equation (4) in the vicinity of the quark core. The abscissa $z=r-R_0$ is the distance from the surface of the QN core referred to as “altitude.” The three solutions ${\mu }_{50}$, ${\mu }_{25}$ and ${\mu }_{10}$ (from top to bottom) correspond to the boundary conditions with the values of the chemical potential $\mu =50$, 25 and 10 MeV at the boundary of the core.

Figure 2

Strength of the electric field in the vicinity of the quark core as a function of the distance $z=r-R_0$ from the boundary. The three graphs correspond to three different solutions for the chemical potential with boundary conditions $\mu (R_0)=50$, 25 and 10 MeV from top to bottom, respectively.

Figure 3

Chemical potential $\mu$ (top curve) and screened chemical potential $\frac{2}{3}\mu$ (bottom curve) in the positron cloud. Dashed horizontal line represents the kinetic energy of electron incident from infinity with the initial velocity $v={10}^{-3}c$. The point $z_0$ is the turning point for the electron in the electric field of the quark nugget.

Figure 4

Strength of the (radial component of) electric field near the boundary of antiquark core. Dashed line (top) corresponds to the electric field $E=1.7\mathrm{V}/a_B$ which may ionize the hydrogen atom. Dotted line (bottom) stands for the electric field $E=0.4\mathrm{V}/a_B$ ionizing the positronium.

Figure 5

Electric field near the core of quark nugget. Points $z_1$ and $z_2$ represent the altitudes where the helium atom loses its electrons.