Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.sao.ru/Doc-en/Science/Public/Conf/magstars-2010/p052.pdf Äàòà èçìåíåíèÿ: Thu Aug 11 13:04:17 2011 Äàòà èíäåêñèðîâàíèÿ: Mon Feb 4 15:57:30 2013 Êîäèðîâêà:

Magnetic Stars, 2011, pp. 52 ­ 60

Magnetic Chemically Peculiar Stars with Unsteady Perio ds
Mikul´ Z. asek
1 2 3

1, 2

z , Krti a J.1 , Jan´ J.1 , Zverko J.3 , Zinovsky J.3 , Zv ck ik ´ erina P.1 , Zejda M.

1

Department of Theoretical Physics and Astrophysics, Masaryk University, Brno, Czech Republic Observatory and Planetarium of J. Palisa, VSB -- Technical University, Ostrava, Czech Republic Astronomical Institute, Slovak Academy of Sciences, Tatransk´ Lomnica, Slovak Republic a

Abstract. Photometrically and spectroscopically variable chemically peculiar (CP) stars are the optimum laboratories for testing the rotational evolution of main sequence stars. A vast ma jority of well­studied CP stars have quite steady rotational periods (e. g. SrCrEu star CQ UMa). However, there are several CP stars that exhibit apparent period variations. The origin of the period variations is unclear in many cases. We describe the observed period variations of several individual CP stars, especially V901 Ori, Ori E, HR 7355, CU Vir, SX Ari, and EE Dra. The CP stars with unsteady periods now represent a very diverse group with dissimilar O­C diagrams and time scales. We also discuss the causes of the period changes found and a possible cyclicity or chaoticity of them.

1

Intro duction

Stars originate from a gravitational collapse of dense parts of molecular clouds. Every star, besides its matter, inherits a fraction of the angular momentum of the mother cloud, consequently each star does rotate. Stars spend the prevailing part of their active lifetime as main sequence ob jects. During the whole MS stage the stellar angular momentum is largely conserved. For example, the stellar wind takes away a significant fraction of the total angular momentum only in the case of very massive stars. Besides the angular momentum the rotational period of a main sequence star is also determined by its instant radius, and the inner distribution of its mass and angular momentum. The development of the rotational period will be then gradual on the scale of 107 ­ 109 years. The evolutionary models corresponding to CP stars show that the equatorial rotational velocity remains practically constant during the MS epoch (see e. g. Meynet & Maeder, 2000). How can we test it? Global data on the rotational period of a MS star and its evolution can be derived from the v sin i rotational broadening. However,the method cannot be applied to an individual single star, since we do not know the values of its radius and inclination. To find out the rotational period changes (if any), a much finer instrument is needed. Spotty magnetic chemically peculiar (mCP) stars with a global magnetic field and stable surface structures, whose periods of light, spectral and magnetic filed variations is equal to the rotational one, can serve as the best such instrument. Combining both the present and archive photometric, spectroscopic and spectropolarimetric observations collected during many decades, one can reconstruct the development of the rotation at least of the outer parts of a star with high accuracy.


MAGNETIC CHEMICALLY PECULIAR STARS WITH UNSTEADY PERIODS

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-0.1 0 0.1 0.2 magnitude [mag] 0.3 0.4 0.5 0.6 0.7 0.8 -0.2

u U v B b Hp y+V R
0 0.2 0.4 0.6 rotational phase 0.8 1 1.2

0.03 0.02 0.01 O-Clin [d] 0

-0.01 -0.02 -0.03

CQ UMa

1970

1980

1990

2000

2010

(a)

(b)

Figure 1: (a) CQ UMa light curves in u , U , v , B , b , Hp , V + y and R­bands. Note the disappearance of variations in V + y and the antiphase variations in the R­band. The linear ephemeris: M0 = 2444384.432, P = 2d 4499120(27). (b) The time development of the difference between the . observed (O) and calculated (C) times of the zero phase according to this linear ephemeris depicts the so­called `O­C diagram'. No trend in the diagram indicates that the rotational period of the star is constant over the decades. Careful period analyses of several dozens of mCP stars have been done. They confirmed the expectations that the rotational periods of most of upper MS stars are quite steady. However, a few stars show period changes, the origin of which has not been completely understood yet.

2
2.1

Individual Stars
SrCrEu mCP Star CQ Ursae Ma joris

As an example of the strictly periodic star we mention is CQ UMa = HR 5153 = HD 119213. This "cool" SrCrEu mCP star displays a prominent variation in the Str¨ omgren v ­band with antiphase changes in the red band (see Fig. 1a). We used 1365 individual observations collected in 11 various sources of photometric data that cover a time interval of 42 years (6262 revolutions of the star). The mean period: P = 2d 4499120(27) . can be then derived with the accuracy of 0.23 s. The linear fit in the O­C diagram is depicted in Fig. 1b (the phases of minima are computed for the v ­band). The time derivative of the period is P = (3 ± 7) s/cen (seconds per century) that means the period is stable as for most of other CP stars. However, there are CP stars showing indubitable changes of their periods.

2.2

He­Strong mCP Star V901 Orionis

V901 Ori = HD 37776 is a very young hot star (B2 IV) residing in the emission nebula IC 432, with a complex (quadruple) global magnetic field (Thompson & Landstreet, 1985; Kochukhov et al., 2011). It can be ranked among the He­strong mCP stars, however, the light variations are due to the spots of overabundant Si and He (Krti a et al., 2007). ck


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´ MIKULASEK ET AL.

0.15 0.1 0.05 0 -0.05 -0.1 -0.15 -0.2
P-Pmean [s]

10 8 6 4

lin

[d]

2 0 -2 -4 -6 -8

O-C

V901 Ori
1980 1985 1990 1995 2000 2005 2010

-0.25 1975 1980 1985 1990 1995 2000 2005 2010

-10 1975

(a)

(b)

Figure 2: (a) The nonlinear trend in the O­C diagram of V901 Ori documents an extraordinarily strong increase of the period in the time interval of 1976 ­ 2005. Now (the end of 2010) the period is nearly constant. The O­C values were calculated relatively to the linear ephemeris: M0 = 2445724.669, P = 1d 5386754 published by Adelman (1997b). (b) The dependence of the . difference between the observed and the mean periods (in seconds) on time does not exclude the possibility of cyclic variations of the period. Using photometry and spectroscopy, Mikul´ et al. (2008) proved that the observed period of asek d 5387 has b een gradually changing. The O­C diagram (see Fig. 2a) can b e formally fitted about 1. with a smooth curve either of a 4­th order polynomial or a segment of a cosinusoid. The maximum increase of the period Pmax = 2.10(16) · 10-8 = 66(5) s/cen took place around the year 1989. The mean increase of the period during the recent 35 years is only P = 1.7 · 10-8 = 53 s/cen. The value is now (at the end of 2010) definitely much smaller: P = -8(7) · 10-9 = -25(22) s/cen. of P Ruling out the light­time effect in a binary star, the precession of rotational axis, and the evolutionary changes as possible causes of the period change, we interpret it in terms of braking of the star's rotation (at least of its surface layers) due to the angular momentum loss through events in the stellar magnetosphere (Mikul´ et al., 2008). However, this mechanism is unable to explain asek the possible acceleration of the rotation nowadays.

2.3

Helium­Strong mCP Star Orionis E

The spectrum of a very young star Ori E = HD 37479 is a hybrid of a classical He­strong mCP star and a B emission­line star (Walborn, 1974). The light curves in the optical domain, namely in the u (U )­band, are unusual for the CP stars: the narrow and deep minima cannot be explained in terms of photometric spots on the surface only. A contribution of "eclipses" by magnetospheric "clouds" (Landstreet & Borra, 1978; Townsend et al., 2005) must be allowed. Townsend et al. (2010) discovered recently a smooth rotational braking in a moderate rate = 7.7 s/cen based on their U observations obtained within 2004 ­ 2009, and the u observations P obtained in 1977 by Hesser et al. (1977). Townsend et al. (2010) explained the observed spin­down of the star by the magnetic braking through the line­driven stellar wind.


MAGNETIC CHEMICALLY PECULIAR STARS WITH UNSTEADY PERIODS

55

0.015 HR 7355 0.01

-0.2 0 0.2

0.005
0.4

O-C [d]

0

0.6 0.8

-0.005
1

-0.01

1990

1995

2000

2005

2010

1.2 -0.2

0

0.2

0.4 0.6 0.8 rotational phase

1

1.2

(a)

(b)

Figure 3: (a) The up­to­date O­C diagram of HR 7355 does not indicate any period changes. The open circle: Hipparcos observations, the diamond: ASAS measurements; the square and : observations published by Mikul´ek et al. (2010); : the R measurements of Oksala et al. (2010); : our as unpublished U B V observations. (b) The light curve of HR 7355 represented by normal points. The narrow minima cannot be merely due to photometric spots as it is common in the CP stars.

2.4

Helium­Strong mCP Star HR 7355

The O­C diagram of another He­strong, very rapidly rotating mCP star HR 7355 = HD 180182 (P = 0d 5214) with emission lines is similar to the above discussed stars. This suggest HR 7355 might . be also a spin­down of hot mCP star (Mikul´ et al., 2010). The only puzzling aspect is the rather asek advanced age of the star (20 Myr). However, the recent revision of the ASAS data on HR 7355 (Po jmanski et al., 2010) and the two ´ new extended sets of photometry, obtained recently by Oksala et al. (2010) and our group, ruled out this suspicion reliably. The latest O­C diagram, Fig. 3a, does not indicate any change of the period. The new light curves show the star is an "elder sister" of Ori E with eclipses (as it was proposed in Rivinius et al., 2008), but no braking (now).

2.5

Silicon mCP Star CU Virginis

The famous very fast­rotating silicon mCP star CU Vir = HD 124224 = HR 5313 may show another type of period changes. Amplitudes of the light and spectral variations (He I, Si II, H I, and other) are relatively large. CU Vir is among the most frequently studied mCP stars, consequently, its behaviour is reliably documented. Moreover, CU Vir is a unique main sequence radio pulsar (Trigilio et al., 2008; Ravi et al., 2010). Pyper et al. (1998) discovered an abrupt increase of the period from 0d 5206778 to 0d 52070854 . . that occurred approximately in 1984 and Pyper & Adelman (2004) discussed two possible scenarios of the explanation of the observed O­C diagram, namely a continually changing period or two constant periods. The mean deceleration of the period of CU Vir during the past 60 years is P = 2.4 · 10-9 = -9 = 18 s/cen. Our pho 7.6 s/cen. The estimated maximum increase (near 1984) is Pex = 5.7 · 10 tometric and spectroscopic observations obtained in 2009 ­ 2010 indicate that the period is now


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´ MIKULASEK ET AL.

0.7

-0.1

CU Vir
0.6 0.5

0 0.1 magnitude [mag] 0.2 0.3 0.4 0.5 0.6

0.4 O-Clin [d] 0.3 0.2 0.1 0

0.7
-0.1 1950 1960 1970 1980 1990 2000 2010

0.8 -0.2

0

0.2 0.4 0.6 0.8 corrected rotational phase

1

1.2

(a)

(b)

Figure 4: (a) The O­C diagram of CU Vir for the times of light minima derived from the available photometries (Hardie, 1958; Blanco & Catalano, 1971; Winzer, 1974; Molnar & Wu, 1978; Pyper & Adelman, 1985; Sokolov, 2000; Pyper et al., 1998; Po jmanski et al., 2001) and our new unpublished ´ data according to the ephemeris in Pyper et al. (1998): M0 = 2435178.6417, P = 0d 5206778. The size . of an open circle correspond to the weight of the value, standard accuracy of the value is 0d 0025. . Two or three linear segments can fit the course. Eventually, a more complex smooth function (Pyper et al., 1998; Pyper & Adelman, 2004) can be used. (b) The light curves in u , U , v , B , b , W , Hp and V + y ­bands (arranged from top to bottom) were assembled from 7097 individual photometric observations. Note the gradual change of the shape of the light curves with the effective wavelength of a particular colour band. The points, tightly adjoined the light curves, corrected for the change of period, show that shapes of the individual light curves are constant over the past sixty years. constant. Presently, we are recalculating the whole O­C diagram using all available data, containing phase data. The results will be published in forthcoming papers. The shapes of the light curves of V901 Ori and CU Vir, the prototypes of mCP stars with large period variations are non­variable, thus excluding precession as the cause of observed period changes (for details see Mikul´ et al., 2008). asek

2.6

Silicon mCP Star SX Arietis

SX Ari = 56 Ari = HD 19832 is a fast rotating (P = 0d 728) Si mCP star. Historically, it was the first . mCP star, where the unsteady period was revealed (Musielok, 1998). The behaviour of this star is complex: according to Adelman et al. (2001) the secular rotational braking with a moderate rate of 2 s/cen is superimposed over the cyclic variations of shapes and z amplitudes of light curves (Zinovsky et al., 2000; Shore & Adelman, 1976) with a period of about five ´ years, what could be attributed to the precession of the rotational axis of a magnetically distorted star. On the basis of a precise Four College Photometric Telescope uv by photometry several other mCP stars were revealed with light curves also indicating precession (see the review paper by Pyper & Adelman, 2004): e. g. 108 Aqr (Adelman, 1997b), 20 Eri (Adelman, 2000), V1093 Ori (Pyper & Adel-


MAGNETIC CHEMICALLY PECULIAR STARS WITH UNSTEADY PERIODS

57

0.07 0.06

HD 177410
P = 1.1232524(6) d

0

u v

0.05 0.04

magnitude [mag]

0.05
O-C [d]

B
0.1

0.03 0.02 0.01 0 -0.01

b Hp

0.15

y V

0.2 -0.2 0 0.2 0.4 0.6 0.8 rotational phase 1 1.2
1970 1975 1980 1985 1990 1995 2000 2005 2010

(a)

(b)

Figure 5: (a) Light curves of EE Dra (HD 177410) obtained in the u , v , B , b , Hp , y and V ­bands. Observed changes can be explained through uneven distribution of Si, Fe and other chemical elements (for details see Krti a et al., 2009). (b) O­C diagram constructed from the times of light ck maxima, derived from all the available photometry. The first O­C value corresponds to the discussed observations of Winzer (1974).

man, 2004), MW Vul (Adelman & Young, 2005). As the changes of their periods are marginal (if any), we do not include them among the stars with unsteady rotation.

2.7

Silicon CP Star EE Draconis

The enigmatic EE Dra (HR 7224 = HD 177410) seemed to be a quite ordinary fast­rotating Si CP star. Its rotational period, based on the Winzer (1974), Hipparcos (ESA, 1998) and Adelman (1997a) photometries is P = 1d 1232. This star, however, contrary to the common magnetic CP stars, has . not revealed a magnetic field, which is very likely due to its weakness (Krti a et al., 2009; Shulyak ck et al., 2010). The star exhibits a double­wave light curve (see Fig. 5a) and strong variations of silicon lines. Adelman (2004) reported an unprecedent rise of the amplitude of the light variation from the typical 0.04 to 0.21 mag and an abrupt change of the period from the former 1d 123 to 101 days. He . attributed it to precession. Later, Lehman et al. (2006, 2007) observed the star spectroscopically and confirmed the period 1d 1232. Krti a et al. (2009) then obtained new B V photometry and refined the period to P = . ck d 123524(6). 1. Not only Adelman's (2004) finding indicates an oddity of otherwise seems to be correct, lie out the other ones, as can Does this mean a quick lengthening of the period between between 2003 and 2004 (Adelman, 2004) mean a reaction to this star, Winzer's (1974) data, which be seen on the O­C diagram, Fig. 5b. 1975 and 1990? Do the observations the previous braking?


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Table 1: Summary of CP stars with unsteady periods, P -- the period, -- the spin­down time in Myr, -- the estimated duration of the cycle HD number 19832 37776 37479 124224 177410 name SX Ari V901 Ori Ori E CU Vir EE Dra P [d] 0.728 1.539 1.198 0.521 1.123 P [s/cen] 2 53 8 8 1 P
ex

[s/cen] ­ 66 ­ 18 ­

[Myr] 3 0.25 1.3 0.6 10

[yr] < 250 90 < 200 60 < 500

3

Nature of Perio d Changes of mCP Stars

The known chemically­peculiar stars with unsteady periods represent a relatively diverse group; their O­C diagrams are different, the common properties are rare, if any. It evokes a situation when Edward Pigott (1753 ­ 1825) set up the first catalogue of variable stars: it comprised only several ob jects, but almost each of them represented other type of variability. Similarly, the causes of the period instabilities of mCP stars may be different. The spin­down time (SDT), = P /P , quantitatively represents the rate of the changing period of a star. All the known cases of the period changes are positive (see Table 1) implying braking of rotation, which implies that the process is irreversible. Assuming that the SDT is constant, one can estimate the maximum time­interval of the duration of the process (the rotational period of the star cannot be shorter than the critical one).

3.1

Spin-Down or Cycle?

Except for the extremely young Ori E the SDT values are much shorter than the ages of the stars. Does it mean that the rotational braking sometimes begins long after the star arrives at MS? Why? Why then do not we see a larger percentage of CP stars with extremely long periods? Is it possible to brake the whole star so drastically? Are the abrupt changes of the period of CU Vir reported by Pyper et al. (1998); Pyper & Adelman (2004) astrophysically permitted (the most dramatic case)? The last question was brilliantly discussed by St¸ n (1998), who clearly proved that one epie´ has to abandon the assumption of the necessity of a rigid rotation and to admit that the outer layers, controlled by magnetic field and denser inner parts can rotate differently. This possibility was discussed and developed also in Mikul´ et al. (2008, 2010). asek The nature of CP stars leads us to the speculation about cyclic variations of angular velocity in the outer layers fixed by a global magnetic field of several mCP stars. Let us assume the simple sine course of such angular velocity variation with the period . Then it is useful to introduce a parameter ex with the time dimension, where ex = P 2/|Pex |. Here P is the mean rotational period, Pex is the extremal time derivative of the period (if known). Then the length of the cycle = ex , where is a dimensionless parameter expressing the amplitude of cyclic changes in the O­C diagram in the units of mean rotational period. Only two stars from the set of CP stars with unsteady periods, discussed in the previous section have been observed for so long, that we could estimate their maximum time derivatives of the period Pex : V901 Ori, and CU Vir (see Tab. 1). After an inspection of their O­C diagrams we have accepted to be 0.5 as a first estimate. For V901 Ori and CU Vir with their P = 1d 5387, Pex = 2.1 · 10-8 and . d 521, P = 5.7 · 10-9 we obtain the following estimates of duration of cycles : 90 and 60 ex P = 0. years, respectively.


MAGNETIC CHEMICALLY PECULIAR STARS WITH UNSTEADY PERIODS

59

In the case of other CP stars with changing periods we are forced to manage with the estimate of the instant period derivative P (naturally, |P | |Pex |) we can introduce the similarly defined parameter , = P 2/|P |, by means of which we can estimate the maximum duration of the cycle of a particular star: . The cycle durations for individual discussed CP stars are given in Table 1. It appears that only for CU Vir and V901 Ori the expected cycles are short enough to observe them completely or almost completely, the rotational periods of other stars are changing too slow. We can speculate that the thin outer envelope, dominated by the global magnetic field, frozen in its plasma, performs with respect to the inner part of the rotating star a torsional oscillation along the rotational axis. Assuming that the oscillation period is with an amplitude of A = 2 R, where R is a radius of the star. The maximum mutual equatorial velocity of the oscillating envelope and the core is then v = 4 2 R/, the acceleration in turning points a = 8 R/2 . Numerically for = 75 years, R = 4 R and = 0.5 we get: A = 13 R , v = 25 m/s and a = 7 m/s2 . The torsion force should be connected with alternating protraction and contraction of magnetic field lines. The process of the oscillation excitation is unclear. However, at the moment the speculations are only preliminary, and have to obtain a firmer physical background.

3.2

Where Are the Accelerating mCP Stars?

If we assume the cyclic nature of the period variations, then we should ask: "Do any accelerating mCP stars exist?" "If yes, why do we not see them?" May be, at least one of the stars we discussed is accelerating just now -- the famous V901 Ori -- (see Fig. 2b).
Acknowledgements. This work was supported by the grants: VEGA 2/0074/09, GACR 205/08/0003, MUNI/A/0968/2009, and the APVV pro ject SK­CZ­0032­09.

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