Magnetic dipole moment of soft gamma-ray repeaters and anomalous X-ray pulsars described as massive and magnetic white dwarfs

Abstract

Abstract Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are some of the most interesting groups of pulsars that have been intensively studied in recent years. They are understood as neutron stars (NSs) with super-strong magnetic fields, namely B ≳ 1014 G. However, in the last two years two SGRs with low magnetic fields B ∼ (1012–1013) G have been detected. Moreover, three fast and very magnetic white dwarfs (WDs) have also been observed in recent years. Based on these new pulsar discoveries, we compare and contrast the magnetic fields, magnetic dipole moment, characteristic ages, and X-ray steady luminosities of these two SGRs (in the WD model) with the three fast white dwarfs, to conclude that they show strong similarities corroborating an alternative description of several SGRs/AXPs as very massive and magnetic white dwarfs. We show that the values for m obtained for several SGRs and AXPs are in agreement with the observed range 1034 emu ≤ m ≤ 1036 emu of isolated and polar magnetic white dwarfs. This result, together with the fact that for magnetic white dwarfs B ∼ (106–108) G their magnetic dipole moments are almost independent of the star rotation period (104 s ≲ P ≲ 106 s)—a phenomenology not shared by neutron star pulsars—suggests a possible magnetic white dwarf nature for some SGRs/AXPs that have much smaller periods (P ∼ 10 s). Moreover, since for pulsars the dipole radiation power is proportional only to m and to the rotational star frequency, we can explain in the WD model—considering only the different scales of the magnetic dipole moment for WDs and NSs—why the steady luminosity LX for several SGRs/AXPs (and in particular the low-B SGRs) compared to those of X-ray dim isolated neutron stars (XDINs) and high-B pulsars obeys the ratio LXSGRs/AXPs/LXXDINs ∼ mWD/mNS ∼ 103: all these X-ray sources have essentially the same rotational periods (P ∼ 10 s) and the X-ray luminosity is correlated to the spin-down luminosity, which is equal to the dipole radiation power in the dipole model.