Ap stars with variable rotation periods

1. Ap starswith variablerotation periods Magnetic chemically peculiar stars with variable rotation periods Zdeněk Mikulášek, Jiří Krtička, Greg W. Henry, Jan Janík, JurajZverko, Jozef Žižňovský, and Miloslav Zejda Putting A stars into a context. Evolution, environment, related stars. June 5, 2013 Moscow, Russia

2. Introduction • mCP stars – the most suitable test beds for studying the rotational evolution in tepid (B2 to F6) MS stars. • Abnormal surface chemical composition concentrated into large persistent spots - for decades or centuries. As the star rotates, periodic variations in the brightness, spectrum, and magnetic field are observed. • Combination of present + archival observations of mCP stars + method → period evolution with unprecedented accuracy. • The changes of period cannot be observed directly – they must be derived from shifts of (light, spectroscopic) phase curves obtained in the past. • Mikulášek et al. 2008 developed the method and applied it to V901 Ori. Then it was many times improved and tested on mCPs and other types of variables. • It is based on LSM, uses models of phase curves and models of period P(t). • We process always all available data with phase information (of all kind). • Solution: all model parameters + estimation of their uncertainty

3. Estimations of uncertainties of period and time derivatives • Selection of mCP stars apt for period analyzes: P ↓, s ↓, A↑, Δ ↑ → we are obliged to use all observations. • V901 Ori: τd ~10 Myr. τMS ~ 30 Myr. One of the fastest evolving mCP stars - the method is not able to detect changes due to their MS evolution. • The rotational periods would be stable.

4. SrCrEu mCP star CQ Ursae Majoris • The example of a ‘constant’ star: CQ UMa = HR5153 = HD 119213 – ‘cool’ SrCrEu mCP star with prominent variations in v and antiphase changes in red. • The photometric observations cover 42 years – 1365 individual observations from 11 sources. P=2.4499120(27) – accuracy of 0.23 s! Error of one measurement 0.005 mag! • A linear fit – O-C diagram (phases of v minima). Ṗ = (3 ± 7) s/cen • However, there are also ‘inconstant’ stars…

5. He-strong mCP star V901 Orionis • V901 Ori= HD 37776– a very young hot star (B2IV) 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 He strong mCPs, however the light variations are due to spots of overabundant Si (Krtička et al., 2007) • Using 3500 measurements (photometry + spectroscopy) we found gradual changes of the observed period that can be very well fitted by a parabola (O-C diagram – cubic parabola). • Spin-down time 1/100 of the τMS • 2009 – deceleration switched to the acceleration. Period variations cannot be explained by evolution + AM loss

6. He-strong mCP star σ Orionis E • σ Ori E = HD 37479 – a hybrid of a classical He-strong CP star and a Be one with strong stellar wind. • The light curves in optical domain are unusual – deep minima namely in u (U) cannot by explained only with spots on the surface – we need ‘eclipses’ with an circumstellar matter around. • Townsend et al. (2010) have quite recently discovered a smooth rotational braking in the rate Ṗ = 7.7 s/century from their own U (2004-9) and Hessers u observations (1977). • They explained it by magnetic braking through strong stellar wind.

7. Silicon mCP star CU Virginis • Other type of period changes shows the famous fast-rotating (0.521 d) Si mCP star CU Vir = HD 124224 = HR 5313, the first stellar radiopulsar. • Strong variations: light, spectral lines of He I, Si II, H I, and other. Krtička et al. 2012 partly explained light variability in UV and optical regions. • Pyper et al. 1988, 2004 + our observations 2009-10: O-C diagram documents two period jumps in 1984 and 1998 – the period suddenly arose by several seconds. • The amplitude of the light variations is relatively large – the behaviour of the star is reliably documented. The light curves of CU Vir isnon-variable. • Mikulášek et al. 2011 – period changes monotonic – prediction of switch of deceleration to acceleration. Cyclic-like O-C and P(t). • Pyper et al. 2013 – new period study – a lot of precise photometric data FCAPT data published. Present study – local extrema 1969, 2004. Short-time oscillations confirmed. • Biquadratic parabola for P(t), other period models were also discussed.

8. Search for other mCP with variable periods • Only three mCPs are known to have variations in their periods. • Very disparate members of the zoo, minimum common properties: • CU Vir - Si star, MS radiopulsar, • V901 Ori, He-strong, hot star with entangled magnetic field, • σ Ori - hybrid of Be star and He-strong star with very strong magnetized stellar wind causing the observed slow rotation braking. • Common: short rotational period - may be the selection effect (δ ~ P2). • Common: hot stars - more massive and absolutely younger mCP stars. • The conclusions done on sample of three star are … • Motivation for deep period analyses of short-periodic SrCrRE or moderately cool mCP with large amplitude in v. • All studied moderately cool mCP star - stable, with one exception BS Cir.

9. BS Cir – brand new animalfor our zoo • BS Cir = HD 125630 = HIP 70346, P = 2.20 d, SrCrEu mCPstar, strong antiphase light variations in y and v. • Parameters: Teff = 8800(500) K, L = 40(2) LS, M = 2.3(2) MS,age = 500 Myr, Bp several kG. • Data: 13 756 photometric measurements (10 data sets 1975-2013, s~0.016 mag) – one of the best monitored mCP stars. • Light curves in 9 filters 350-1100 nm - disparate shapes. • Succeful model of LCs: two different photometric spots centred to φ = 0.00 and 0.47, (S and N poles). • P = 2.2042849(6) d , dP/dt = 5.7(4) x 10-9 = 0.181(13) s/yr (13 σ) The spin-down time 1.05(8) Myr 0.2% of MS age.

10. How to explain monotonic changes in observed periods of CU Vir, V901 Ori, and BS Cir? Are the observed variations of the periods caused by unsteady rotation? Possible changes inobservedperiods mCP stars • A few mCPs may display variations in the LC shapes – Shore and Adelman (1976) - precession of magnetically distorted star. It should cause also marginal cyclic period variations. • Mikulášek, Krtička et al. 2008, the phase variations amplitude < than observed (BS Cir 6%, V901 Ori 16%, CU Vir 62%) + no LC shape changes → precession is not able match observed changes. • LiTE – period changes due to variable RV – orbital motion in the system of at least two bodies (spectroscopically invisible companion). Changes in period = changes in RV. • V901 Ori – we should observe increase 1972-2009 in RV of 43 km/s. No RV changes. Hypothetical companion should a massive BH. • CU Vir - we should observe variations of RV with an amplitude of 23 km/s. No RV changes. Hypothetical companion should a BH of 10 Mʘ • BS Cir – we should observe RV increase of 10.5 km/s, RV is constant. Precession, light-time effect – no significant role. Other explanation please…

11. Evolutionary changes in the rotation of MS stars • Main sequence – the longest stage of a stellar career. • Assumption: a tepid MS star rotates as a solid body + mass and angular momentum are constant. • MS rotational period then evolves only due to gradual change of moment of inertia J. • MS evolutionary models → J(t) ~ R(t), and R(t)= R0 exp(t/τMS). • τMS > 30 Myrfor all mCPs, τd < 25 Myr even for the best monitored CP star: τMS >τd →mCPperiod analysis is unable to detect evolutionary changes.

12. Angular momentum loss via stellar winds • Each stellar wind decreases mass + namely AM→ rotational braking. • Standard stellar wind – is entering in the outer space from the surface. • According to Krtička 2013 stellar winds Ṁ = 0 for Teff < 15 kK. • For Teff = 23kK, Ṁ = 10-11 Mʘ/yr. τSW = P/Ṗ = 850Myr >> τMS = 30 Myr. → No detectable braking via standard stellar wind. • Magnetized stellar wind escapes the extended corotating magnetosphere (ud-Doula et al. 2009 + Krtička 2013) – AM loss much efficient. • In extreme situation of σ Ori E, τMW = P/Ṗ ~ 1.3 Myr with very strong magnetic field (Bp> 5 kG) – the rotation braking due to AM loss via MSWmay be detectable. Otherwise not - field of V901 is too complex. Partial conclusions • All three mechanisms → braking Ṗ > 0, with constant rate: d2P/dt2 = 0. • We can explain only the observed rotational braking in the case of σ Ori E, in CU Vir and V901 Ori bad time scales + d2P/dt2 ≠ 0, cold CS Vir – no wind.

13. Nature of rotation variations in some mCP stars • The discovery of the moderately cool BS Cir as the mCP star with variable rotation shows that such stars may occur across all mCP types and may be all tepid MS stars. • Consequently, we shall “abandon the apparently false 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.” Stępień (1998). • We offer now an alternative concept of the structure of surface layers dominated the dominant role by global magnetic field. It contribute to immobilization of outer parts of mCPs in vertical direction and also prevents the spot structures against their dissolving in the horizontal directions. • Magnetic field could do it only there where its energy is larger than the energy dissipative motions. Simple calculations show that in A, B photosheres even very weak magnetic field is enough. • See an example of EE Dra and ε UMa.

14. ‘Non-magnetic’ CP stars = stars with weak (= unmeasurable) magnetic field = ‘weather’ changes in structures Hg/Mn stars (Heidi Korhonen) • Assuming magnetic field of tepid MS stars is fossil one → all photospheres should be in some extent controlled by magnetic field → transient spot structures on even ‘normal’ (non-CP) tepid MS stars are allowed. • The depth of magnetic field dominance (~ the thickness and endurance of spot structures) strongly depends on the strength of magnetic field. CU Vir – the mass of magnetically controlled layer 2x10-9 Mʘ - three Charons. • Such ‘eggshell’ fastened by magnetic field may behave as the solid body. Even negligibly weak interaction with the outer environment or the interior is able to accelerate or decelerate this layer very effectively. • All these considerations and speculations are the challenge for theoreticians dealing with the structure of upper MS stars. • Thank you for your kind attention.