The Spin-down Problem in the White Dwarf of Ae Aquarii: Numerical Study of a Turn-over Scenario

The white dwarf (i.e., the primary) in the AE Aqr binary star system is observed to spin down at a steady time rate Ṗnow = 5.64 × 10−14 s s−1, while at the same time its UV (LUV ) and X-ray (LX) accretion luminosities seem to remain almost unchanged. This is a contradiction, however, since the classically estimated spin-down power due to decrease of rotational kinetic energy T , Ṫ ∼ −1034 erg s−1, exceeds the accretion luminosity of the primary by a factor ∼> 102 and, as a dominating power, should lead either to observable luminosity changes or to other detectable effects. This so-called “spin-down problem” can be relaxed under the assumption that the primary is now in a phase of rapidly decreasing its differential rotation under constant angular momentum, undergoing a nonaxisymmetric transition — i.e., turning over its magnetic symmetry axis with respect to its angular momentum axis and eventually becoming a perpendicular rotator — from a “differential rotation state” (DRS) to a “rigid rotation state” (RRS) on a relatively short “nonaxisymmetric DRS-to-RRS transition timescale”. If so, then the estimated spin-down power, −Ṫ ∼< 4 × 1032 erg s−1, becomes comparable to the observed luminosities and the spin-down problem is drastically simplified. In this paper, we present a detailed numerical study of such a “turn-over scenario”, which study mainly points out the fact that an observed large spin-down time rate does not always imply a large spin-down power. Subject headings: stars: individual (AE Aqr) — stars: magnetic fields — stars: rotation and spin-down — stars: white dwarfs