this is for holding javascript data
Matteo Cantiello edited Magnetic WD.tex
about 9 years ago
Commit id: 46a72b75573b8d9953caa64136eccbd1d645a7bb
deletions | additions
diff --git a/Magnetic WD.tex b/Magnetic WD.tex
index 8be9a6f..446c2f7 100644
--- a/Magnetic WD.tex
+++ b/Magnetic WD.tex
...
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}; the most magnetic WDs have 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}
% Add discussion on binary incidence and other avenues for the generatation of WD f