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Magnetic Fields in Non-Convective Regions of Stars

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Magnetic Fields in Non-Convective Regions of Stars Magnetic fields in non-convective regions of stars Jonathan Braithwaite Argelander Institut f¨urAstronomie Universit¨atBonn, Auf dem H¨ugel71, 53121 Bonn email: [email protected] http://www.astro.uni-bonn.de/~jonathan Henk C. Spruit Max Planck Institut f¨urAstrophysik Karl-Schwarzschild-Str. 1, 85741 Garching email: [email protected] http://www.mpa-garching.mpg.de/~henk (arXiv version 7 April 2017) 1 Introduction We review the current state of knowl- edge of magnetic fields inside stars, con- Interest in magnetic fields in the interiors of centrating on recent developments con- stars, in spite of a lack of immediate observ- cerning magnetic fields in stably strati- ability, is rapidly increasing. It is sparked by fied (zones of) stars, leaving out convec- progress in spectropolarimetric observations of tive dynamo theories and observations of surface magnetic fields as well as by asteroseis- convective envelopes. We include the ob- mology and numerical magnetohydrodynamic servational properties of A, B and O-type simulations. main-sequence stars, which have radiative An important incentive also comes from devel- envelopes, and the fossil field model which opments in stellar evolution theory. Discrepan- is normally invoked to explain the strong cies between results and steadily improving ob- fields sometimes seen in these stars. Ob- servations has led to a newly perceived need for servations seem to show that Ap-type sta- evolution models ‘with magnetic fields’. At the ble fields are excluded in stars with con- same time the demand for results from stellar vective envelopes. Most stars contain both evolution have increased for application outside radiative and convective zones, and there stellar physics itself. An example is the need for are potentially important effects arising predictable colors of stellar populations in cal- from the interaction of magnetic fields at culations of galaxy evolution. the boundaries between them. Related to Key questions concern the rate of mixing this, we discuss whether the Sun could of the products of nuclear burning, since stel- arXiv:1510.03198v4 [astro-ph.SR] 7 Apr 2017 harbour a magnetic field in its core. Re- lar evolution is sensitive to the distribution of cent developments regarding the various these products inside the star. The heavier nu- convective and radiative layers near the clei are normally produced later and deeper in- surfaces of early-type stars and their ob- side the star. Outside of convective zones, these servational effects are examined. We look nuclei reside stably in the gravitational poten- at possible dynamo mechanisms that run tial. Even weak mixing mechanisms in radia- on differential rotation rather than con- tive zones, operating on long evolutionary time vection. Finally we turn to neutron stars scales, can nevertheless change the distribution with a discussion of the possible origins enough to affect critical stages in the evolu- for their magnetic fields. tion of stars. Possible mechanisms include hy- 1 drodynamic processes like extension of convec- and CoRoT satellites. These data now provide tive regions into nominally stable zones (‘over- stringent tests for theories of angular momentum shooting’), shear instabilities due to differential transport in stars (Sections 5.5, 5.4). rotation, and large-scale circulations. Assump- Possible internal magnetic fields come in two tions about the effectiveness of such processes distinct kinds. One kind is time-dependent mag- are made and tuned to minimise discrepancies netic fields created and maintained by some kind between computed evolution tracks and observa- of dynamo process, running from some source of tions. The presence of magnetic fields adds new free energy. Dynamos in convective zones have mechanisms, some of which could compete with been studied and reviewed extensively before; or suppress purely hydrodynamic processes. they are not covered in this review except for As well as mixing chemical elements1, mag- a discussion of subsurface convection in O stars netohydrodynamic processes in radiative zones (Section 6.5). Another obvious source of free en- should damp the differential rotation that is pro- ergy is differential rotation, and this could pro- duced by the evolution of a star. An indirect duce a self-sustained small-scale magnetic field observational clue has been the rotation rate in a radiative zone. This would be the candidate of the end products of stellar evolution (Sec- for transport of angular momentum and chemi- tion 5.5). As the core of an evolving star con- cal elements described above. tracts it tends to spin up. However, it is evi- The other kind of internal magnetic field is dent from the slow rotation of stellar remnants fossil fields, remnants of the star formation pro- that angular momentum is transferred outwards cess that have somehow survived in a stable con- to the envelope, and in many cases stellar rem- figuration. The theory of such fields is discussed nants rotate much slower than can be explained in Section 3. even with the known hydrodynamic processes. A subset of intermediate-mass stars display Maxwell stresses are more effective in transport- strong magnetic fields, the chemically pecular ing angular momentum than hydrodynamic pro- Ap and Bp stars; and some more massive stars cesses (they can even transport angular momen- display similar fields. These are thought to be tum across a vacuum). This leads to the study of such fossil fields. They used to be interpreted dynamo processes driven by differential rotation in terms of configurations resembling simple in stably stratified environments (Section 5.4). dipoles. With the improved observations of the Note that there is a difference regarding the past decade a much larger range of configura- mixing of chemical elements. In purely hydrody- tions is found; this is reviewed in Section 2. namic processes, the transport of angular mo- Theory indicates that only a small fraction of mentum and chemical elements are directly re- all imaginable magnetic equilibria in a star can lated to each other, but this is not the case be stable as observed. Comparing these the- for magnetohydrodynamic processes. For a given oretically allowed configurations with the sur- rate of angular momentum transport, mixing by face fields actually observed in individual stars magnetohydrodynamic processes is less effective gives clues about the internal structure of the than in the case of hydrodynamic processes. fields. Together with statistical information on Until recently, the Sun was the only star for observed field strengths and configurations, this which direct measurements of internal rotation holds the promise of telling us something about were available, made possible by helioseismol- the conditions under which the magnetic fields ogy. For all other stars the only source of in- formed. formation on angular momentum transport in- Though stably stratified throughout most of side stars was the rotation of their end products. their interior, Ap stars still contain a small con- This has changed dramatically with the astero- vective core. This raises the question to what seismic detection of rotation-sensitive oscillation extent convection interacts with the fossil field, modes in giants and subgiant stars by the Kepler or whether a fossil field is compatible at all with the presence of a convective zone somewhere in 1 The term ‘chemical elements’ is used anomalously in astrophysics (including this review) to mean atomic the star. A related question is whether stars with species. convective envelopes like the Sun might have fos- 2 sil fields hidden in their stably stratified interi- Also worth a look are the books by Choudhuri ors. These questions are addressed in Section 6. (1998) and Kulsrud (2005), which have a greater Also thought to be of fossil nature are the emphasis on plasma effects, i.e. not using the sin- magnetic fields in neutron stars. As in upper- gle fluid approximation. main-sequence stars, there is a puzzlingly enor- mous range in field strengths, spanning five or- ders of magnitude. There are two obvious ways to explain this range: either it is inherited from the progenitor stars, in which case one still needs to explain the range in birth magnetic proper- ties of main-sequence stars, or it is produced during the birth of the neutron star. It is pos- sible that it is produced from the conversion of energy from differential rotation into magnetic, and that the same physics is at work during the birth of main-sequence stars. These issues are addressed in Section 7.1. This review is organised as follows. In the next section, we look at observations of mag- Figure 1: Measured magnetic fields in a sample of netic stars, with some focus on peculiarities that Ap stars in which either no magnetic field had yet may hold clues on the origin of their fields. been detected or in which there had been an ambigu- Among the main-sequence star these are the ous or borderline detection. In this study the detec- Ap/Bp stars and the apparently non-magnetic tion limit is only a few gauss; every star in the sam- intermediate-mass stars, next are the massive ple is found to have a magnetic field much stronger stars, and the magnetic white dwarfs then are than this. The dashed line represents the cutoff at discussed very briefly. Section 3 is a review of 300 G. This result confirms convincingly that all the theory of static ‘fossil’ magnetic fields in ra- Ap-type chemically peculiar stars have strong mag- diative zones, and in Section 4 we examine var- netic fields. In contrast, other A stars have never been found to have any magnetic field above a few ious scenarios which could explain where these gauss; there is a clear bimodality. From Auri`ereet fossil fields come from. In Sections 5 and 6 re- al. (2007). spectively we look at the interaction of mag- netic fields with differential rotation and with convection.
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