Ap starsAp stars  with with

variablevariable  rotation periodsrotation periods

Zdeněk Mikulášek, Zdeněk Mikulášek,

Jiří Krtička, Jiří Krtička, Greg Greg W. W. Henry, Henry, Jan Janík, Jan Janík,

JurajJuraj  Zverko, Jozef ŽižňovskýZverko, Jozef Žižňovský, and Miloslav Zejda, and Miloslav Zejda

Putting A stars into a context. Evolution, environment, related stars. June 5, 2013 Moscow, RussiaPutting A stars into a context. Evolution, environment, related stars. June 5, 2013 Moscow, Russia

Magnetic chemicallMagnetic chemicallyy peculiar stars peculiar stars

withwith variable rotation periods variable rotation periods

IntroductionIntroduction

mCP stars – the most suitable test beds for studying the rotational mCP stars – the most suitable test beds for studying the rotational

evolution in evolution in tepidtepid (B2 to F6) MS stars. (B2 to F6) MS stars.

Abnormal surface chemical composition concentrated into large persistent Abnormal surface chemical composition concentrated into large persistent

spots - for decades or centuries. As the star rotates, periodic variations in the spots - for decades or centuries. As the star rotates, periodic variations in the

brightness, spectrum, and magnetic field are observed. brightness, spectrum, and magnetic field are observed.

Combination of present + archival observations of mCP stars + method Combination of present + archival observations of mCP stars + method → →

period evolution with unprecedented accuracy.period evolution with unprecedented accuracy.

The changes of period cannot be observed directly – they must be derived The changes of period cannot be observed directly – they must be derived

from shifts of (light, spectroscopic) phase curves obtained in the past. from shifts of (light, spectroscopic) phase curves obtained in the past.

MikulMikulášek et al.ášek et al. 2008 developed the method and applied it to V901 Ori. Then it 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.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 It is based on LSM, uses models of phase curves and models of period PP((tt).).

We process always all available data with phase information (of all kind). We process always all available data with phase information (of all kind).

Solution: all model parameters + estimation of their uncertainty Solution: all model parameters + estimation of their uncertainty

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.

SrCrEu mCP star CQ Ursae Majoris

The example of a ‘constant’ star: CQ UMa = HR 5153 =

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…

He-strong mCP star V901 Orionis

V901 OriV901 Ori = HD 37776 – 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 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

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 brakingrotational braking in the rate ṖṖ = 7.7 s/century = 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.

Silicon mCP star CU Virginis

Other type of period changes shows the famous fast-rotating (0.521 d) Si mCP star

CU VirCU 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 two

period jumpsperiod 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 is non-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.

Search for other mCP with variable periodsSearch 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:

1.1. CU Vir - Si star, MS radiopulsarCU Vir - Si star, MS radiopulsar,,

2.2. V901 Ori, He-strong, hot star with entangled magnetic field, V901 Ori, He-strong, hot star with entangled magnetic field,

3.3. σ Oriσ Ori - hybrid of Be star and He-strong star with very strong magnetized stellar wind causing the observed slow rotation braking.

CommonCommon: short rotational period - may be the selection effect (δ ~ P2).

CommonCommon: 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 CirBS Cir.

BS Cir – brand new BS Cir – brand new animalanimal forfor our zoo our zoo

BS Cir = HD 125630 = HIP 70346, BS Cir = HD 125630 = HIP 70346, PP = 2.20 d, SrCrEu mCPstar, = 2.20 d, SrCrEu mCPstar,

strong antiphase light variations in strong antiphase light variations in yy and and vv..

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).

PP = 2.2042849(6) d , d = 2.2042849(6) d , dPP/d/dtt = 5.7(4) x 10 = 5.7(4) x 10-9 -9 = 0.181(13) s/yr (13 = 0.181(13) s/yr (13 σσ))

The spin-down time 1.05(8) Myr 0.2% of MS age.The spin-down time 1.05(8) Myr 0.2% of MS age.

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 in observedobserved periods 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…Other explanation please…

Evolutionary changes in the rotation of MS stars

Main sequence – the longest stage of a stellar career. Main sequence – the longest stage of a stellar career.

Assumption: a tepid MS star rotates as a solid bodyAssumption: a tepid MS star rotates as a solid body + mass and angular + mass and angular

momentum are constantmomentum are constant.

MS rotational period then evolves only due to gradual change of moment MS rotational period then evolves only due to gradual change of moment

of inertia of inertia JJ. .

MS evolutionary models MS evolutionary models → → JJ((tt) ~ ) ~ RR((tt)) , and , and RR((tt)) = = RR00 exp( exp(tt//ττMSMS).).

τMS > 30 Myr for all mCPs, τd < 25 Myr even for the best monitored CP

star: τMS > τd → mCP period analysis is unableunable to detect evolutionary

changes.

τRR

PP

eRR

R

Rαα

PP

JL

Pπ

ω;LM τ/t 120

020

2

00

Angular momentum loss via stellar winds Each stellar wind decreases mass + namely AM → rotational braking.

Standard stellar windStandard 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 = 850 Myr >> τMS = 30 Myr. → No

detectable braking via standard stellar wind.

Magnetized stellar windMagnetized 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 MSW may be

detectable. Otherwise not - field of V901 is too complex.

Partial conclusions1.1. All three mechanisms → braking All three mechanisms → braking Ṗ Ṗ > 0, with constant rate: d> 0, with constant rate: d22P/P/ddtt2 2 = 0.= 0.

2.2. We can explain only the observed rotational braking in the case of σ Ori E, in We can explain only the observed rotational braking in the case of σ Ori E, in CU Vir and V901 Ori bad time scales + dCU Vir and V901 Ori bad time scales + d22P/P/ddtt2 2 ≠ 0, cold CS Vir – no wind.≠ 0, cold CS Vir – no wind.

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 abandon the apparently false assumption of the

necessity of a necessity of a rigid rotationrigid rotation and to admit that the and to admit that the outer layersouter layers controlled by controlled by

magnetic field and denser inner parts can rotate differently.” 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.

‘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.Thank you for your kind attention.