Abstract
This chapter steps finally away from the sun and towards the stars, the idea being to apply the physical insight gained so far to see how much of stellar magnetism can be understood in terms of dynamo action. Dynamo action in the convective core of massive main-sequence stars is first considered and shown viable. For intermediate-mass main-sequence stars the fossil field hypothesis will carry the day, although possible dynamo alternatives are also briefly discussed. The extension of the solar dynamo models investigated in Chap. 3 to other solar-type stars will first take us through an important detour in first having to understand rotational evolution in response to angular momentum loss in a magnetized wind. Dynamo action in fully convective stars comes next, and the chapter closes with an overview of the situation for pre- and post-main-sequence stars and compact objects, leading finally to the magnetic fields of galaxies and beyond.
ELWOOD: It’s 106 miles to Chicago, we’ve got a full tank of gas, half a pack of cigarettes, it’s dark and we’re wearing sunglasses. JAKE: Hit it!
Dan Ackroyd and John Belushi
The Blues Brothers (1980)
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Notes
- 1.
The content of this section is based on the paper by Charbonneau and MacGregor (2001) given in the bibliography.
- 2.
The \(\alpha ^2\) form of the mean-field dynamo equations also admits growing solutions that are non-axisymmetric even though the \(\alpha \)-effect profile exhibits axisymmetry with respect to the rotation axis. Growth rates for non-axisymmetric modes are often comparable to those of their axisymmetric counterparts. Motivated largely by the challenge posed by planetary magnetic fields, \(\alpha ^2\) models can and have been constructed where non-axisymmetric modes are the fastest growing, and dominate in the moderately supercritical nonlinear regime. For complex enough spatial profiles of \(\alpha \), i.e., including multiple sign changes in each hemisphere, it is also possible to produce \(\alpha ^2\) dynamo solutions undergoing cyclic polarity reversals.
- 3.
The content of this section is based primarily on the paper by Brun et al. (2005) given in the bibliography.
- 4.
Note however that the above relation was calibrated in a relatively narrow range of parameters: \(2\le u_0\le 30\,\)m s\(^{-1}\), \(0.03\le s_0\le 1\,\)m s\(^{-1}\), \(2\times 10^6\le \eta _0\le 5\times 10^7\,\)m\(^2\) s\(^{-1}\), and is only expected to hold in the so-called advection-dominated regime; see the paper by Dikpati & Charbonneau (1999) cited in the bibliography of Chap. 3.
- 5.
The content of this section is based primarily on the paper by Dobler et al. (2006).
References
The following conference proceedings gives an excellent sampling of the current state-of-the-art in the observation of stellar magnetic fields: Neiner, C., & Zahn, J.-P., eds.: 2009, Stellar Magnetism, EAS Publications Series, 39
The first three chapters therein, authored by John Landstreet (pps. 1–53), provide an outstanding overview of the subject, in just a little over 50 pages. The linear \(\alpha ^2\) and \(\alpha ^2\Omega \) models for core dynamo action in massive stars presented in Sect 5.1 are taken pretty directly from Charbonneau, P., & MacGregor, K.B.: 2001, Magnetic fields in massive stars. I. Dynamo models, Astrophys. J., 559, 1094–1107
This paper also adresses the effects of thermally-driven meridional circulation in the radiative envelope, including its deleterious effect on core dynamo action. The difficulty in bringing the magnetic fields produced by core dynamo action to the surface of a star with a thick radiative envelope was cogently demonstrated a while ago already by Levy, E.H., & Rose, W.K.: 1974, Production of magnetic fields in the interiors of stars and several effects on stellar evolution, Astrophys. J., 193, 419–427
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The discussion of core dynamo action in massive stars (Sect. 5.1.2) is based on the following paper: Brun, A.S., Browning, M.K., & Toomre, J.: 2005, Simulations of core convection in rotating A-type stars: magnetic dynamo action, Astrophys. J., 629, 461–481
from which Figure 5.4 was taken. For calculations of buoyantly rising thin flux tubes in the radiative envelope of massive stars, see MacGregor, K.B., & Cassinelli, J.P.: 2003, Magnetic fields in massive stars. II. The buoyant rise of magnetic flux tubes through the radiative interior, Astrophys. J., 586, 480–494
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On the stability of large-scale magnetic field in stellar radiative interiors, start with: Pitts, E., & Tayler, R.J.: 1985, The adiabatic stability of stars containing magnetic fields. IV-The influence of rotation, Mon. Not. Roy. Astron. Soc., 216, 139–154
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and for consequences on the structural, rotational and chemical evolution of massive stars: Maeder, A., & Meynet, G.: 2003, Stellar evolution with rotation and magnetic fields. I. The relative importance of rotational and magnetic effects, Astron. & Astrophys., 411, 543–552
Maeder, A., & Meynet, G.: 2005, Stellar evolution with rotation and magnetic fields. III. The interplay of circulation and dynamo, Astron. & Astrophys., 440, 1041–1049
The potential observational consequences of iron opacity-driven outer convection zones in massive stars (including a brief discussion of the possibility of dynamo action) are discussed in Cantiello, M., Langer, N., Brott, I., et al.: 2009, Sub-surface convection zones in hot massive stars and their observable consequences, Astron. & Astrophys., 499, 279–290
Observations of solar-like activity in late-type stars is the subject of the following two recent online review articles: Berdyugina, S.V.: 2005, Starspots: a key to the stellar dynamo, Living Reviews in Solar Physics, 2, 8, http://solarphysics.livingreviews.org/Articles/lrsp-2005-8/
Hall, J. C.: 2008, Stellar chromospheric activity, Living Reviews in Solar Physics, 5, 2, http://solarphysics.livingreviews.org/Articles/lrsp-2008-2/
Figure 5.7 was taken from the following paper, still today one of the more cogent exposition of the Mt. Wilson CaII project and data: Baliunas, S.L., Donahue, R.A., Soon, W.H., et al.: 1995, Chromospheric variations in main-sequence stars, Astrophys. J., 438, 269–287
Figures 5.8 and 5.9 were taken from, respectively Kraft, R.P.: 1967, Studies of stellar rotation. V. The dependence of rotation on age among solar-type stars, Astrophys. J., 150, L183–L188
Skumanich, A.: 1972, Time scales for Ca II emission decay, rotational braking, and Lithium depletion, Astrophys. J., 171, 565–567
On the confrontation of such observations with various types of dynamo models, start with Noyes, R.W., Weiss, N.O., & Vaughan, A.H.: 1984, The relation between stellar rotation rate and activity cycle periods, Astrophys. J., 287, 769–773
Saar, S.H., & Brandenburg, A.: 1999, Time evolution of the magnetic activity cycle period. II. Results for an expanded stellar sample, Astrophys. J., 524, 295–310
Moss, D.: 2004, Dynamo models and the flip-flop phenomenon in late-type stars, Mon. Not. Roy. Astron. Soc., 352, L17–L20
Jouve, L., Brown, B. P., & Brun, A. S.: 2010, Exploring the P\(_{cyc}\) vs. P\(_{rot}\) relation with flux transport dynamo models of solar-like stars, Astron. & Astrophys., 509, A32
On the Weber-Davis MHD wind model, see Weber, E.J., & Davis, Jr., L.: 1967, The angular momentum of the solar wind, Astrophys. J., 148, 217–227
Belcher, J.W., & MacGregor, K.B.: 1976, Magnetic acceleration of winds from solar-type stars, Astrophys. J., 210, 498–507
as well as Keppens, R., & Goedbloed, J.P.: 1999, Numerical simulations of stellar winds: polytropic models, Astron. & Astrophys., 343, 251–260
for a geometrically more realistic version. The idea that magnetized outflows can lead to stellar angular momentum loss can be traced to Schatzman, E.: 1962, A theory of the role of magnetic activity during star formation, Annales d’Astrophysique, 25, 18–29
In this context, another important pioneering paper is Mestel, L.: 1968, Magnetic braking by a stellar wind-I, Mon. Not. Roy. Astron. Soc., 138, 359–391
The theoretical derivation of Skumanich’s square root relation in the context of \(\alpha \Omega \) dynamo theory is due to Durney, B.: 1972, Evidence for changes in the angular velocity of the surface regions of the sun and stars-comments, in Solar Wind, Sonett, C.P., Coleman, P.J., & Wilcox, J.M., eds., NASA Special Publication, 308, NASA, 282–286
There is a huge technical literature available on the observation, evolution and consequences of stellar rotation. The following conference proceedings volume should make a good starting point to those interested in digging further into the various ramifications of this topic: Maeder, A., & Eenens, P., eds.: 2004, Stellar rotation, IAU Symposium, 215, Astronomical Society of the Pacific
The discussion of dynamo action in fully convective stars (Sect. 5.4) is based primarily on the following paper: Dobler, W., Stix, M., & Brandenburg, A.: 2006, Magnetic field generation in fully convective rotating spheres, Astrophys. J., 638, 336–347
but on this topic do not miss: Durney, B.R., De Young, D.S., & Roxburgh, I.W.: 1993, On the generation of the large-scale and turbulent magnetic fields in solar-type stars, Solar Phys., 145, 207–225
Browning, M.K.: 2008, Simulations of dynamo action in fully convective stars, Astrophys. J., 676, 1262–1280
On magnetic field detection in white dwarfs and hot subdwarfs, see Liebert, J., Bergeron, P., & Holberg, J.B.: 2003, The true incidence of magnetism among field white dwarfs, Astron. J., 125, 348–353
Kawka, A., Vennes, S., Schmidt, G.D., Wickramasinghe, D.T., & Koch, R.: 2007, Spectropolarimetric survey of Hydrogen-rich white dwarf stars, Astrophys. J., 654, 499–520
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I found the following online article a good starting point to learn about galactic magnetic fields: Beck, R.: 2007, Galactic magnetic fields, Scholarpedia, 2, 2411, http://www.scholarpedia.org/article/Galactic_Magnetic_Fields
On galactic dynamo models, as well as alternatives explanatsions for galactic magnetic fields, the following review article provides an excellent entry point into the technical literature: Kulsrud, R.M., & Zweibel, E.G.: 2008, On the origin of cosmic magnetic fields, Rep. Prog. Phys., 71, 046901
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Charbonneau, P. (2013). Stellar Dynamos. In: Steiner, O. (eds) Solar and Stellar Dynamos. Saas-Fee Advanced Courses, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32093-4_5
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