Mass distribution of magnetized quark-nugget dark matter and comparison with observations

Quark nuggets are a candidate for dark matter consistent with the Standard Model. Previous models of quark nuggets have investigated properties arising from their being composed of strange, up, and down quarks and have not included any effects caused by their self-magnetic field. However, Tatsumi found that the core of a magnetar star may be a quark nugget in a ferromagnetic state with core magnetic field B between $10^{ 11}$ T and $10^{ 13}$ T. We apply Tatsumi$'$s result to quark-nugget dark-matter and report results on aggregation of magnetized quark nuggets (MQNs) after formation from the quark-gluon plasma until expansion of the universe freezes out the mass distribution to include $10^{ -24}$ kg to $10^{ 14}$ kg. Aggregation overcomes weak-interaction decay. Computed mass distributions show MQNs are consistent with requirements for dark matter and indicate that geologic detectors (craters in peat bogs) and space-based detectors (satellites measuring radio-frequency emissions after passage through normal matter) should be able to detect MQN dark matter. Null and positive observations narrow the range of a key parameter B to between $10^{ 11}$ T and 3 $10^{ 13}$ T.