Observed Fields and Limits

Magnetic fields are present in most kinds of stars, but with different intensities. T Tauri stars show magnetic fields in the range of 1-2.5 kG [225], brown dwarfs, M and K dwarfs also show such strong fields and evidences of large spots. The average poloidal field in the Sun is of the order of 1 G; however, there are fine structures with field intensities reaching locally a few kG. The field in solar-type stars originates from the convective dynamo in the envelope, which produces time-dependent fields responsible for the observed magnetic activity cycles. In fully convective stars (M < 0.4 M0), a different, possibly more turbulent, dynamo may be present.

Fields reaching several tens of kG are observed in Ap stars, which have globally organized fields, generally dipolar with an axis inclined with respect to the rotation axis. These fields are stable over decades, they are likely of fossil origin with some further evolution [63]. At the opposite, Am and HgMn stars show no evidence of magnetic fields [521].

Searches for magnetic fields in OB-type stars show in general no evidence of fields at the level of ^100 G [392]. There are, however, a few exceptions, such as d Ori C, an O7-type star with a field of 1-2 kG [166], and ( Ori (B2IIIe) with an oblique poloidal field of 530 G [438]. Weak poloidal fields of a few 102 G have also been found in some B stars [242]. The origin of these fields, fossil or dynamo created, is still uncertain. It is unlikely that, if built in the convective core, the field can be advected by meridional circulation to the surface [116]. Thus, there must be either a dynamo process, different from the solar dynamo, or some transport mechanism.

Let us consider a straight flux tube of magnetic field of intensity B perpendicular to the stellar surface. If Pext and Pint are, respectively, the pressures outside and inside the tube, the lateral pressure equilibrium or magnetostatic balance (13.12) implies

The hydrostatic equilibrium for an atmosphere of given gravity g and constant opacity k leads to the following estimate of the pressure at an optical depth t = 2/3, P(t = 2/3) = (2/3) g/K (see Eq. 24.18). Since P^t should be positive, the maximum possible field Beq for magnetic equilibrium is [503],

This expression gives the order of magnitude of the equilibrium field intensities. These are indicated in Table 13.1 for stars of various spectral types.

This applies to local field tubes as present in stars with an external convective zone. The observed field intensities are of the above order of magnitude; however, they are often up to a factor of 2 larger than the values in Table 13.1. The discrepancies seem to be due to the fact that the theoretical models for deriving the field intensities use the same gaseous pressure inside and outside the intense field tubes [503]. For an O star with log g = 4^0 and electron scattering opacity, the equilibrium field would be about 200 G. The occurrence of convective envelopes in very luminous O stars (Sect. 5.5.1), especially if they rotate fast, could explain the presence of magnetic fields in some OB stars. It is clear that large-scale dipolar fields, as in Ap stars, are not following the above condition (13.21), since they are global stellar fields.

Table 13.1 The equilibrium field for stars of various spectral types. The stars are on the ZAMS, except the Sun

Spectral type Field (kG)

M0

2.8

KO

1.5

Sun

1.3

G0

1.0

F2

0.6

0 0

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