5 Equipartition
In stellar atmospheres, a magnetic field is a source of magnetic pressure, 
. In hydrostatic
equilibrium, this pressure must be balanced by the gas pressure so that magnetic flux is limited by the total
gas pressure. Such stability considerations lead to the expectation that stellar magnetic fields in general are
limited by atmospheric structure (e.g., Spruit and Zweibel, 1979). Saar and Linsky (1985) and Saar (1990
)
estimate scaling relations of equipartition magnetic fields in field stars, and Johns-Krull (2007) provides a
detailed comparison between magnetic fields in pre-main sequence stars and corresponding equipartition
field strengths.
The values of equipartition fields and, therefore, the expected maximum field strengths in main sequence
stars are obviously a function of surface temperature and gravity. They turn out to be of the order of
1 – 2 kG for spectral type G, 2 – 3 kG for spectral type K, and 3.5 – 4.0 kG for spectral type early- to
mid-M (Saar, 1990). From a first glance, this is in remarkable agreement with the maximum average field
strengths observed in M dwarfs. However, the average field of a star with flux tubes satisfying equipartition
would probably be much lower than the maximum field because the gas pressure available to balance
magnetic pressure must be available in some non-magnetic regions (in other words, f cannot be
1).
As discussed above, we have no conclusive information about maximum field strengths in hotter, sun-like
stars. We can, therefore, not exclude that maximum field strengths in sun-like stars are significantly lower
than 
4 kG. Even if the local field strengths in M dwarfs are probably above our estimate of
equipartition field strengths, there still may be a scaling of maximum field strengths with gas pressure, and
only the absolute value of the limiting field differs somewhat from our approximations. Again, infrared
observations of Zeeman splitting are required in active sun-like stars to shed light on this fundamental
question.
Equipartition field strengths are predicted to be much lower than 4 kG in pre-main sequence stars.
Johns-Krull (2007) has found a significant mismatch between observed field strengths and predictions from
equipartition. Average magnetic fields in pre-main sequence stars appear to have typical values of
2.5 kG, but predicted field strengths for the young stars of the sample in Johns-Krull (2007) are
between 0.5 and 3 kG, and the observed field values do not show a correlation with equipartition
estimates. Therefore, at least in pre-main sequence stars, magnetic fields exist with magnetic
pressure dominating gas pressure. Such stars probably have no field-free regions on their surface.
Johns-Krull (2007) also provide evidence that fields in these young stars may be of fossil origin and
not generated by a dynamo, although Chabrier and Küker (2006) estimate survival times
for fossil fields in fully convective stars well below 1000 yr. Assuming that such fields survive
much longer, a tentative conclusion consistent with observations is that dynamo generated
fields are in agreement with pressure balance, while fossil fields can exceed this boundary. An
alternative conclusion from the available data, however, is that the limit for stellar average fields is
simply on the order of 3 – 4 kG in all stars, and pressure balance has a minor effect on the
generated field strength. A physical motivation for such a minimalistic approach, however, is
missing.
