5 Equipartition

In stellar atmospheres, a magnetic field is a source of magnetic pressure, P = B2∕8 π. 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 (1990Jump To The Next Citation Point) estimate scaling relations of equipartition magnetic fields in field stars, and Johns-Krull (2007Jump To The Next Citation Point) 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 (2007Jump To The Next Citation Point) 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 (2007Jump To The Next Citation Point) 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 (2007Jump To The Next Citation Point) also provide evidence that fields in these young stars may be of fossil origin and not generated by a dynamo, although Chabrier and Küker (2006Jump To The Next Citation Point) 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.

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