Giant Primeval Magnetic Dipoles

Macroscopic magnetic dipoles are considered as cosmic dark matter. Permanent magnetism in relativistic field structures can involve some form of superconductivity, one example being current-carrying string loops (`springs') with vanishing net tension. We derive the cross section for free classical dipoles to collide, finding it depends weakly on orientation when mutual precession is rapid. The collision rate of `spring' loops with tension ${\cal T} \sim 10^{-8}c^4/G$ in galactic halos approaches the measured rate of fast radio bursts (FRBs) if the loops comprise most of the dark matter. A large superconducting dipole (LSD) with mass $\sim 10^{20}$ g and size $\sim 1$ mm will form a $\sim 100$ km magnetosphere moving through interstellar plasma. Although hydromagnetic drag is generally weak, it is strong enough to capture some LSDs into long-lived rings orbiting supermassive black holes (SMBHs) that form by the direct collapse of massive gas clouds. Repeated collisions near young SMBHs could dominate the global collision rate, thereby broadening the dipole mass spectrum. Colliding LSDs produce tiny, hot electromagnetic explosions. The accompanying paper shows that these explosions couple effectively to propagating low-frequency electromagnetic modes, with output peaking at 0.01-1 THz. We describe several constraints on, and predictions of, LSDs as cosmic dark matter. The shock formed by an infalling LSD triggers self-sustained thermonuclear burning in a C/O (ONeMg) white dwarf (WD) of mass $\gtrsim 1\,M_\odot$ ($1.3\,M_\odot$). The spark is generally located well off the center of the WD. The rate of LSD-induced explosions matches the observed rate of Type Ia supernovae.