The spin-down problem in the white dwarf of AE Aquarii: numerical study of a turn-over scenario

The white dwarf in AE Aqr is observed to spin down at a steady time rate ~ 5.64*10^{-14} s s^{-1}, while at the same time its UV and X-ray accretion luminosities remain almost unchanged. This is a contradiction, however, since the classicaly estimated spin-down power ~ -10^{34} erg s^{-1} exceeds the accretion luminosity of the primary by a factor ~ 10^2 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 ~ -3*10^{32} erg s^{-1} becomes comparable to the observed luminosities and the spin-down problem is drastically simplified. 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.