Rotation of evolved stars

Among the many problems that beset the theory of rotating stars, the redistribution of angular momentum in stellar interiors during evolution is by far the least understood. As we know, the post-main-sequence evolution of a star is accompanied by a strong contraction of its helium-rich core and by a corresponding expansion of the surrounding envelope. Unless there exists a very efficient transport of angular momentum from the core to the envelope, it is evident that the former has to spin up appreciably while at the same time the latter must spin down. The decrease in surface rotation as a star evolves away from the main sequence has been known for several decades. Unfortunately, to compute the gross changes caused by rotation in evolving stars, we are faced with two largely unresolved questions: Is the total angular momentum J of a star conserved or lost during its post-main-sequence evolution? And is there an effective means to redistribute the specific angular momentum 2 during evolution? The most reliable calculations are those of Endal and Sofia (1979), who have considered different cases of angular momentum redistribution, assuming in all cases conservation of total angular momentum. At the time, their theoretical surface rotation velocities for red-giant models were in agreement with the observed rotation rates for the K giants, so that there was apparently no need to invoke angular momentum losses among these stars.

A different picture emerged, however, when Gray's (1982) Fourier analysis of high signal-to-noise ratio data showed the existence of a discontinuity in rotation for luminosity class III giants.* This sudden drop takes place between spectral types GO III and G3 III. A similar rotational discontinuity was also seen by Gray and Nagar (1985) in a sample of luminosity class IV subgiants. Near GO IV, a sudden drop in rotation was

* This discontinuity, which was initially reported at spectral type G5 III, has been confirmed by Gray (1989) but was found to be near GO III rather than G5III. This change results primarily from improved spectral types.

Fig. 6.11. Projected equatorial velocities as functions of (B — V) color. Triangles refer to values taken from "The Bright Star Catalogue." Source: deMedeiros, J. R., and Mayor, M., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 201, Dordrecht: Kluwer, 1991. (By permission. Copyright 1991 by Kluwer Academic Publishers.)

Fig. 6.11. Projected equatorial velocities as functions of (B — V) color. Triangles refer to values taken from "The Bright Star Catalogue." Source: deMedeiros, J. R., and Mayor, M., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 201, Dordrecht: Kluwer, 1991. (By permission. Copyright 1991 by Kluwer Academic Publishers.)

observed with advancing spectral type, in complete analogy to the drop seen at G0 III in the giants. More recently, a systematic survey of about 2,000 evolved stars was carried out by de Medeiros and Mayor (1991), covering the spectral range from middle F to middle K of luminosity classes IV, III, II, and Ib. Figures 6.11 and 6.12 illustrate the v sin i measurements of their sample of stars as a function of the (B — V) color. The cutoff in the distribution of rotational velocity for each luminosity class is located at F8 IV, G0III, F9II, and near F9 Ib; this corresponds to the (B — V) colors 0.55, 0.70, 0.65, and about 0.70, respectively.

Note the wide range of v sin i values on the left side of the discontinuity for all luminosity classes. This large spread seems to reflect the broad distributions of rotation rates along the main sequence, as illustrated in Figure 6.8. Note also that the spread in v sin i values on the left of the cutoff decreases with increasing luminosity. In fact, the supergiant stars show no sudden decrease in rotation, and there is still a large fraction of slow rotators to the left of the discontinuity. This result strongly suggests that the origin of the rotational discontinuity is not the same for all classes.

As was originally suggested by Gray in the 1980s, the rotational discontinuity for the subgiant and giant stars can be interpreted as a result of a strong magnetic braking due to the deepening of their outer convective envelopes at some point in their evolution. To be specific, since the evolution of these stars carries them from hotter to cooler spectral types, a plot of rotation versus (B — V) color delineates the time sequence of their

Fig. 6.12. Projected equatorial velocities as functions of (B — V) color. Triangles refer to values taken from "The Bright Star Catalogue."Source: de Medeiros, J. R., and Mayor, M., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 201, Dordrecht: Kluwer, 1991. (By permission. Copyright 1991 by Kluwer Academic Publishers.)

Fig. 6.12. Projected equatorial velocities as functions of (B — V) color. Triangles refer to values taken from "The Bright Star Catalogue."Source: de Medeiros, J. R., and Mayor, M., in Angular Momentum Evolution of Young Stars (Catalano, S., and Stauffer, J. R., eds.), p. 201, Dordrecht: Kluwer, 1991. (By permission. Copyright 1991 by Kluwer Academic Publishers.)

rotational changes. As their progenitors evolve off the main sequence, the evolutionary increase in moment of inertia slowly reduces the rotation to the values attained on the left of the discontinuities in Figure 6.11. Sudden changes seen near spectral types G0IV and G0III occur because the evolutionary deepening of the convective envelope has become sufficient to sustain dynamo activity. Thence, a small amount of material escaping from the star's surface is caught in the open field lines of the dynamo-generated magnetic field, so that large amounts of angular momentum can be carried away by the escaping material (see Section 7.2). In short, the star develops an external magnetic brake that rapidly decelerates the rotation of at least its outer convective envelope.

An important piece of evidence in support of Gray's mechanism comes from the work of Simon and Drake (1989), who have shown that subgiant and giant stars undergo a sudden decrease in chromospheric activity at spectral types G0 IV and G0 III, which correspond to the (B — V) colors 0.6 and 0.7, respectively. The fact that in both cases the observed decline in UV emission coincides with the sharp decrease in surface rotation rates strongly suggests that Gray's mechanism is indeed operative in these stars. As they noted, this joint decay in activity and rotation marks a transformation from acoustic heating in the early F-type stars to a magnetically controlled activity in the cooler stars, thus inducing a strong rotational braking action by means of stellar winds. Detailed calculations by Schrijver and Pols (1993) further indicate that the decrease in the observed rotational velocities of subgiants and giants is stronger than expected from the increase in moment of inertia alone, so that loss of angular momentum through magnetically channeled stellar winds must be substantial between the onset of convection and just beyond the upturn onto the giant branch. For the most luminous classes, however, the discontinuity in rotational velocities is probably the result of another evolutionary effect.

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