deletions | additions       diff --git a/WH_YIS_THIS_PARA_WIDER__.tex b/WH_YIS_THIS_PARA_WIDER__.tex  index cc9a65e..3fdc0ad 100644  --- a/WH_YIS_THIS_PARA_WIDER__.tex  +++ b/WH_YIS_THIS_PARA_WIDER__.tex 
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%[WH YIS THIS PARA WIDER THAN THE REST IN THE VIEW MODE?] In Fig. 4, 4  we show the observed \numax\ and inferred mass of all the stars superimposed on a contour plot of minimum magnetic field strengths required for mode suppression (Fuller et al. 2015). \citep{Fuller15}.  For stars with suppressed modes (filled red  circles), the underlying color colour  provides a lower bound to thecore  field strength. strength at the hydrogen-burning shell.  For stars without suppressed modes (open black  circles), the underlying color colour  represents an upper limit to the field at the hydrogen-burning shell; above or below the shell the field could potentially be larger. Hence, normal and dipole-suppressed stars that fall in the same regions of Fig. 4 may have core field strengths that are only slightly different. However, we expect that the dipole-suppressed stars on average exhibit stronger core fields than their normalstar  counter parts.Considering first the low-mass stars ($< 1.1$\msol), we see from Figure 4 that magnetic fields above $\approx 10 \, {\rm kG}$ are not present at the hydrogen-burning shell when the stars are near the red giant luminosity bump (\numax\ $\approx 50 \, \mu{\rm Hz}$).  Assuming magnetic flux conservation from the main-sequence phase, this suggests that magnetic fields above $\approx 1 \, {\rm kG}$ do not exist within the cores of Sun-like stars (Fuller et al. 2015). This does not rule out strong horizontal fields near the radiative-convective boundary because these fields are outside the core and cannot cause mode suppression when the star evolves into a red giant.  %For stars with suppressed modes we derive the lower limit of how  %strong the field in the core [at least] needs to be for suppression to  %be observed.  Turning to higher masses, we see that for a given \numax\, stars above 1.4\msol\ require increasingly strong magnetic fields to suppress their dipole modes. From Figure 4, there is no clear upper limit to the field strengths attainable in red giant cores, given that suppressed stars are common even when field strengths $ B> 1 \, {\rm MG}$ are required for suppression. However, the hint of a decline in the occurrence of dipole-suppressed stars above 2\msol\ seen in Fig. 3 suggests there may be a mass above which dynamo-generated magnetic fields can no longer cause oscillation mode suppression in intermediate-mass stars.  %Such a cutoff might be caused by the different core structure of stars more massive than 2\msol, which evolve through the red giant phase much faster than stars of lower mass.   The high occurrence rate of dipole mode suppression demonstrates that core-dynamo-generated fields can remain through the red giant phase, more than $10^8 \, {\rm yr}$ after the dynamo shuts off at the end of hydrogen-core burning. Therefore, dynamo-generated fields are frequently able to settle into long-lived stable configurations \citep{Braithwaite_2004,Braithwaite_2006,Duez_2010}, a result that was not certain from magnetohydrodynamical simulations. The occurrence rate of these long-lived core fields is much larger than the occurrence rate of strong fields observed at the surfaces of magnetic A stars, which may have been generated by a pre-hydrogen-core burning dynamo during star formation (e.g., \citealt{Moss_2004}). We conclude that fields generated during hydrogen-core burning are able to settle into stable equilibrium configurations much more commonly (greater than $60\%$ of the time) than fields generated during star formation (less than $10\%$ of the time).