Abstract
We explore the possibility that soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are powered by highly magnetized white dwarfs (B-WDs). We take a sample of SGRs and AXPs and provide the possible parameter space in mass, radius, and surface magnetic field based on their observed properties (period and its derivative) and the assumption that these sources obey the mass-radius relation derived for the B-WDs. The radius and magnetic field of B-WDs are adequate to explain energies in SGRs/AXPs as the rotationally powered energy. In addition, B-WDs also adequately explain the perplexing radio transient GCRT J1745-3009 as a white dwarf pulsar. Note that the radius and magnetic fields of B-WDs are neither extreme (unlike of highly magnetized neutron stars) nor ordinary (unlike of magnetized white dwarfs, yet following the Chandrasekhar's mass-radius relation (C-WDs)). In order to explain SGRs/AXPs, while the highly magnetized neutron stars require an extra, observationally not well established yet, source of energy, the C-WDs predict large ultra-violet luminosity which is observationally constrained from a strict upper limit. Finally, we provide a set of basic differences between the magnetar and B-WD hypotheses for SGRs/AXPs.