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Magnetic stars, 2007, pp. 143147

Model magnetic fields of CP stars with long rotation periods
Yu. V. Glagolevskij1 , E. Gerth
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Special Astrophysical Observatory of the Russian AS, Nizhnij Arkhyz 369167, Russia Ewald Gerth, D-14471 Potsdam, Germany, (retired, formerly Astrophysical Institute Potsdam)

Abstract. The formerly adopted hyp othesis of loss of rotational momentumum in the presence of magnetic fields seems to b e contradicted by some recently investigated magnetic CP stars. Key words: Magnetic stars mo dels rotation long p erio ds

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The problem of slow rotation of CP stars

Considering the statistics of stellar rotational p erio ds there are some difficulties to explain the slow rotation of CP stars. Rather probable prove the hyp otheses: 1. The loss of the rotation momentum to ok place under the influence of the magnetic field just b efore the "pre-main sequence"-phase of evolution. 2. The small rotation momentum was taken from protostellar clouds. The only prop erty of CP stars is in favor of the hyp othesis of deceleration -- the smaller the mass the greater the difference b etween their average velo city v sini and normal stars (Fig. 1).

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The influence of the initial rotation on the star formation

On the other hand, there is another prop erty -- the lower the velo city of CP stars the greater their prop ortions among normal stars (Fig. 2). The latter prop erty supp orts the hyp othesis that the lower the initial rotation velo city of a star when it forms, the greater the probability it will b ecome a chemically p eculiar one. It has turned out that this prop erty is common to chemically p eculiar stars -- with or without magnetic field. Glagolevskij and Chuntonov (2003) suggested that the cause of the slow rotation of CP stars should b e searched for at the very initial stages of formation, which is also the reason for division into CP magnetic, CP nonmagnetic and normal stars, b ecause Ae/Be Herbig stars do not p ossess any magnetic field of sufficient strength.

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The deceleration of CP stars

In accordance with a statement suggested by Stё n (2000), the closeness of the dip ole and rotaepie ґ tional axes (small angles b etween them) must b e a serious condition for deceleration of CP stars. It is only in this case that conditions arise, under which the loss of the moment of rotation is effective. To clear this up, we investigate in the present pap er magnetic configurations of several slow rotating CP stars (P > 25d ) for which phase relationships of variation of the effective B e and the
Poster representation available at www.ewald-gerth.de/118pos.pdf.

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Figure 1: Average values of the rotation velo city v sini for normal stars with different temp eratures (circles) and chemically p eculiar stars (asterisks). mean surface Bs magnetic fields are known. For the mo deling we used the metho ds of "magnetic charges" that we have develop ed (Gerth et al. 1997, Gerth & Glagolevskij 2000, Glagolevskij & Gerth 2004).

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Mo deling of some slowly rotating magnetic stars

Table 1 presents the summary of our results of mo deling slow rotators, which shows that they have no predominant orientation of the magnetic dip ole with resp ect to the rotational axis, that is, there is no domination of small angles as predicted by Stё n (2000). epie ґ It turned out that the magnetic field structure in two of the investigated stars is b est describ ed by the central dip ole mo del, four of them show a noticeable displacement of the dip ole from the center by r along the dip ole axis (in units of the star's radius). The displacement can b e b oth towards the p ositive and negative charges, i.e. the magnetic field is asymmetric ab out the magnetic equator. The physics of this phenomenon is not clear yet. The angles b etween the rotational axis and the dip ole axis proved to b e considerable in all cases, apart from HD2435. It is known from literature data that the quantity of the photometric variability V of the investigated stars is rather large, although in the case of small the variability must b e practically imp erceptible.

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Slowing down by magnetic fields?

One more argument against the magnetic deceleration is that the relationship b etween the average surface magnetic field of slow rotators and the rotation p erio d proves to b e opp osite to the exp ected one (Fig. 3). Nevertheless, the "slowest" star Equ has a rather weak magnetic field. "Magnetic braking" would b e the interaction b etween magnetic moment of the rotating star and surrounding interstellar magnetic field. It is not improbable that the magnetic field has played an imp ortant role only in diminishing the moment of rotation of protostellar clouds.

MODEL MAGNETIC FIELDS OF CP STARS...

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Figure 2: Relative numb er of CP stars with different rotation velo cities with a magnetic field (circles) and without a field (asterisks).

Table 1: Results of mo deling magnetic fields of CP stars with long rotation p erio ds: i is the inclination of the star, is the angle b etween the dip ole axis and axis of rotation, r is the value of the dip ole shift from the star center (partial radius), B p is the magnetic field at the p oles Star HD 2453 12288 9996 201601 116458 126515 187474 200311 P [days] 547 35 8000 3800 4600 12300 5000 8600 Average: i 14 24 89 34 75 22 86 30 80 66 10 85.5 12 86 24 86

r 0.00 0.00 0.00 0.00 0.07 0.24 0.10 0.08

Bp [Gauss] ±6560 ±13400 ±8100 ±6210 +9510 6220 45800 +11100 + 6300 11600 +18520 11420

Reference Glagolevskij, Gerth, 2004 Glagolevskij, Gerth, 2004 our last results Glagolevskij, Gerth, 2006 Glagolevskij, 2005a Glagolevskij, 2005a Glagolevskij, 2005b Glagolevskij, Gerth, 2004

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56

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Figure 3: Dep endence of the average surface magnetic field of CP stars on their p erio d of rotation. In case of "magnetic" braking the p erio d would b e the longer the stronger the magnetic field is.

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Asymmetry of the dip ole magnetic field

It can b e seen from the Table that in some cases the dip ole is shifted along the axis by a considerable value up to r = 0.24 of the radius of the star, which seems to b e quite noteworthy. It is not clear yet to what extent the magnetic field configuration of CP stars is asymmetric in reality and to what degree the field measurements are distorted by the influence of inhomogeneous distribution of chemical elements. In the stars considered the average angle of the diverging axes is = 56 , which corresp onds approximately to the mean value that must b e the case for an arbitrary orientation of the magnetic dip oles.

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Conclusions
1. The fact that the axes of rotation and of the dip ole are not parallel is one of the indications that the deceleration at the "pre-main sequence" stages is absent. This verifies the hyp othesis of initial slow rotation of CP stars as a result of the small moment of rotation for protostellar clouds. 2. The absence of sufficiently strong magnetic fields in Ae/Be Herbig stars (see Glagolevskij & Chuntonov 2003, Glagolevskij & Gerth 2006) also p oses difficulties for the hyp othesis of "magnetic" deceleration at "pre-main sequence" stages of evolution. 3. The known considerable photometric variability of the investigated CP stars is another argument against the closeness of the axes. 4. The axes of the magnetic field dip oles in slow rotators are oriented randomly with resp ect to the rotational axes, as b eing in the case of fast rotators. 5. The inverse relationship Bs (P ) to the rotational velo city at some stars contradicts the assumption that the magnetic field is involved in the deceleration.

MODEL MAGNETIC FIELDS OF CP STARS...

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6. The same relation b etween the relative numb er of chemically p eculiar stars and nonmagnetic stars is inconsistent with the assumption that the magnetic field is involved in the deceleration. 7. The loss of the moment of rotation with the magnetic field involved could hardly o ccur at "pre-main sequence" evolutionary stages, the slow rotation is most likely due to its origin from protostellar clouds.

References
Glagolevskij Yu.V., Chuntonov G.A., 2003, Bull. Spec. Astrophys. Obs., 55, 38 Stё n K., 2000, A&A, 353, 227 epieґ Gerth E., Glagolevskij Yu.V., Scholz G., 1997, in: Proc. Intern. Conf. "Stellar Magnetic Fields", eds.: Yu.V. Glagolevskij and I.I. Romanyuk, 1318 May 1996, Nizhnij Arkhyz, 67 Gerth E., Glagolevskij Yu.V., 2000, in: Proc. Intern. Conf. "Magnetic fields of chemically peculiar and related stars", eds.: Yu. V. Glagolevskij, I.I. Romanyuk, Nizhnij Arkhyz 2427 Sep. 1999, 151 Glagolevskij Yu.V., Gerth E., 2004, Bull. Spec. Astrophys. Obs., 58, 1 Glagolevskij Yu.V., 2005a, Astron. Zhurnal, 82, 1119 Glagolevskij Yu.V., 2005b, Astrofizika, 48, 575 Glagolevskij Yu.V., Gerth E., 2006, Astrofizika, 49, 252

Pap ers and p osters of the authors are available from the homepage: www.ewald-gerth.de