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Matteo Cantiello edited Magnetic WD.tex
about 9 years ago
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It is therefore worth looking at other potential mechanisms.
\subsubsection{Red Clump Dynamo}
Even if a low-mass star reaches the clump with little or no magnetic fields in its core, it could still generate a strong magnetic field. This is because He is burning in a convective core, where dynamo action could be at work. The turnover timescale in the convective He-burning core is about 10-20d, while the asteroseismic inferred rotation rates are in the range 30...250 d. This means that Rossby numbers ($Ro$) are in general larger than 1; however for some He-burning cores $Ro$ could be close to 1, potentially allowing for an efficient $\alpha\omega-$dynamo. The core magnetic field in that case could reach the equipartition value, on the order $10^6-10^7$ G. Note that this field would be probably confined to the convective core and do not affect the g-mode cavity, so it would not be probed by the dipole modes.
At the end of the core He-burning phase, when convection disappears the generated magnetic flux could end up in a stable configuration. Since the Ohmic timescale is way longer than the remaining lifetime of the star (this is actually true during any evolutionary phase for stars of mass above $1\mso$) this dynamo-generated magnetic field could survive till the white dwarf stage. Assuming conservation of magnetic flux, the change in radius of a factor of 10 implies a factor of 100 in B, resulting in a maximum magnetic field of B=$10^8-10^9$ G for the WD. Fields higher than $10^6$ G are indeed observed in 8-16\% of WD
\citep{Liebert_2003,Kawka_2007}; \citep{Liebert_2003,Kawka_2007}, the most magnetic WDs
have having B$\approx10^9$ G.
A stable magnetic configuration requires a certain degree of interlocking between the toroidal and poloidal components of the magnetic field \cite{Braithwaite_2006}. The magnetic helicity is probably the important quantity determining if an initial configuration of the field can evolve into a stable equilibrium. However, being convection an inherently stochastic process (and helicity conserved only in ideal MHD) it is not obvious how to build a predictive theory. In absence of such theory, observations provide some guidance: Since the number of magnetic main sequence stars with radiative envelopes (OB and A) is roughly speaking 10\%, it is tempting to imagine that this broadly represents the chance of a convectively generated magnetic flux to land a stable magnetic configuration when convection disappears. Here we are implicitly assuming this chance is more or less the same for both a convective core and a fully convective star, even though this might not be the case.
%To estimate how many stars could do this, one has to look at the distribution of core rotation rates at the clump (how many stars with P<50d or so?). Then one can take a fractio of 10% of this number. My impression is that overall one would get something like <1% for the He-core dynamo channel
\subsubsection{Binary channels}