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Magnetic braking of the 1 Ori C main component
Y.Balega, V.Leushin, and G.Weigelt
Special Astrophysical Observatory, Nizhnij Arkhyz Max-Planck-Institute for Radioastronomy, Bonn 2010


1 Ori C

­ the youngest and the nearest high-mass star P = 11.26 yrs T = 2002.57 e = 0.592 a = 43.6 mas i = 99 = 26.5 = 23.6 km/s M1 + M2 = 39M0 + 8M O5.5 + B2 dist = 410 ± 20 pc (S.Kraus et al. 2009)
0

Fig.1


· Max-Planck-Institute for Radioastronomy, Bonn , VLBI ESO,


COMPONENTS PARAMETERS FROM INTERFEROMETRY · Following S.Kraus et al. (2009): Comp. 1 - Teff = (37000 - 40000 K) log L1/L = (5.21 ­ 5.29) M1= (34.0 - 39.0) M Comp. 2 - T
eff

= (30000 - 33000 K) log L2/L = (4.68 ­ 4.76) M2= (8.0 ­ 15.5) M

· Large spread of fundamental parameters complicates the analysis of the spectrum


LIST OF THE SPECTRA
· · · · · · · · · 3-5.03.2000. Wade et al. (A&A, 451,195), Ph=0.78. Vr (1-2) Va=-25.0 km/s. 32 -7 57 18 km/s 17-18.12.2008. 2 m tel. at Peak Terskol., Ph=0.57 (R=45000) t29010 23:26 Va = -1.9 km/s. 27 13 29 15 t29011 00:14 t29012 01:04 t29013 01:16 5-6.12. 2009. 6 m BTA telescope, Ph=0.655. znvvo2830 2455171.424 s/n2370 Va=4.12km/s 28 5 24 1 znvvo3334 2455171.463 1610 28 5 24 1 27.01.2010. 6 m BTA telescope, Ph=0.666. hd37022nnorm 2455224.3 Va=-18.7 km/s 29 2 48 20 27.02.2010. 6 m BTA telescope, Ph=0.674. nHD37022145 2455255.2 Va=-25.4 km/s 30 2 55 27 BTA spectra SNR/px 2000


MODEL ATMOSPHERES
· Spectrum analysis was made for the model atmospheres

1OriC 1 : Teff = 39000 K, log L/L R = 10.7, log g = 3.91 1OriC 2 : Teff = 31900 K, log L/L R = 7.2, log g = 3.92
·

= 5.41 , M = 34.0, = 4.68, M = 15.5,

For these parameters we used Vt = 15 km/s and the solar chemistry: H = 1.00, He = 0.089 ­ by mass logN(H)=12.00, logN(He) = 10.95 ­ by number of atoms logN for the remaining elements: 8.52, N 8.01, O 8.89, Ne 8.05, Mg 7.54, Si 7.51, Fe 7.63


ROTATION VELOCITY FOR 1ORI C1

· v sini for the primary star was defined in the range 24 to 140 km/s (Vitrichenko, 2003; Simon-Dias et al., 2006). The rotation of the secondary has never been measured before. From our spectrums: v sini = 35 km/s (the equatorial value is v1rot = 35.4 km/s) for the primary. The rotation period of 1 OriC1 is 15d.422 (Stahl et al., 2008), which gives the equatorial velocity 33 km/s for the radius R1 = 10 R . Using i=105o , we obtain v sini = 32 km/s.


BEST MODEL FIT

1OriC 1
· Mass, M · Luminosity, log L · Radius, R · Teff, K · log g · Equatorial rotation velocity, km/s · Magnetic field, G · The time of life, yrs 35.8 5.20 10.0 37000 4.01 5.4 500-1500 150 000

1OriC 2
10.0 4.69 8.2 30000 3.60 96.2 moves to MS


1 OriC RADIAL VELOCITIES

Primary ­ black, secondary ­ red)


OIII ABSORPTION PROFILES

· HI, HeI, HeII, CII - CIV, NII - NIV, OII ­ OIV, NeII, SiIII ­ SiIV MgII ion absorption lines are observed in the spectrum between 3000 and 9000 AA. All H and He lines are contaminated by emission components, therefore the atmospheric parameters of the two stars were defined from the weak profiles of C, N, O, Ne, Si, and Mg lines.


OBSERVED (red) AND SYNTHETIC (black) PROFILES FOR OIII LINES IN THE SPECTRUM

Orbital phase 0.55. Corresponding Vr1 =26 km/s Vr2=14 km/s (relative to the Sun) and Vr1=5.5 km/s Vr2=-7.5 km/s (relative to the Earth)


OIII PROFILES FOR TWO COMPONENTS SEPARATELY

The primary star rotation velocity corresponds to Vsin i = 35 km/s


· Rotation velocity for 1 OriC2 was estimated from the width of atmospheric triplet Si III 4552.62, 4567.84, 4574.76 AA formed mainly in the atmosphere of the secondary. · The BTA spectra give: = 2.97, 3.15, 2.79 A. From the width of the lines we obtain v sini = 98.7 km/s. The lower limit is v2rot = 95 km/s.


Si III TRIPLET ABSORPTION (v sin i 95 km/s for 1 Ori C 2)


LINE PARAMETERS FOR THE SYNTHETIC SPECTRUM CALCULATION NEAR Si III TRIPLET

Ion FeIII NII SiIII CaIII NeII SiIII OIII OII OII FeIII

, A 4548.99 4552.94 4552.62 4553.29 4553.40 4554.00 4555.38 4557.73 4557.91 4558.85

, eV log gf 20.88 23.48 19.02 45.06 34.83 28.12 46.92 31.37 46.92 55.11 -1.66 0.33 0.18 0.05 -0.80 -0.16 -0.41 -0.32 -0.89 -0.53

Ion NeI VIII SiIII NeII OIII NeII SiIII VIII NeII NeII

, A 4565.55 4567.59 4567.84 4569.06 4569.26 4574.42 4574.76 4574.92 4575.72 4576.32

, eV 34.82 20.18 19.02 34.93 45.99 34.84 19.02 20.18 36.18 37.48

log gf 1.59 0.95 -0.04 0.14 0.07 -1.16 -0.51 -0.27 -1.64 -1.71


OBSERVED (red) AND SYNTHETIC (black) SPECTRA IN THE REGION 4550-4578 AA

SNR=2000. Orb. phase = 0.653, 0.691. Corresponding radial velocities: Vr1=29 km/s and Vr2=3 km/s (relative to the Sun), or Vr1= 45 km/s and Vr2= 19 km/s (relative to the Earth).


RADIAL VELOCITIES FROM He II AND Si III LINES

· We used the spectra from Wade et al (2006) to estimate the radial velocities of the components for the orbital phase 0.78. The primary component HeII 4541 "stable" lines were compared with the Si III triplet lines 4552.62, 4567.84, 4574.76 AA. Our orbit gives radial velocities Vr 1 = + 32 km/s and Vr 2 = -7 km/s for this phase, which is in good agreement with the observations.


RADIAL VELOCITIES OF THE COMPONENTS FROM He II and Si III lines


MAGNETIC BRAKING ?
Magnetic braking due to the momentum carried away by the electromagnetic radiation from the rotating magnetic field gives the following period change (Longair 1994):

& 8 2 R 4 B 2 P 0 = 3 2 P 3c MP
here B0 is the surface magnetic field. For 1 OriC1 parameters with B0 = 1 - 1.5 kG (Wade et al. 2006), it gives
P/P ~ 2 X 10
-13

yr-1 - a negligible effect.


The upper estimate for the magnetic energy of 1 OriC1 is:
E
magn

= H 2 / 8 4 / 3R 3 = 1.72 10 40 В 2.75 10 41 erg

which is a very small part of its rotational energy:
E = 0 .2 M 1
2 1

rot 1

R

2 1

= 1 .9449 10 47 erg .


· Both components of 1 OriC were formed as a result of fragmentation of a non-magnetic (or weakly magnetic) cloud. We assume that 1 OriC2 has constant rotation velocity Vrot2. Then, the primary star 1 OriC1 after the formation had

V

0 rot1

R1 0 10.70 = Vrot 2 = 96.2 = 129.64km / s. R2 7.94
E0 =2,61 в1048erg rot1

· Its original rotation energy was

· The rate of the energy dissipation for the age 150 000 yrs is 0.51·1036 erg/s for the total luminosity of the star 7.46·1038 erg/s.


SCENARIO
Fast rotating magnetic star generates a toroidal component Bt of the magnetic field. There is a continuous outflow of gas from 1 Ori C 1 in the form of magnetically confined wind. The magnetic field lines force the highly conducting gas to corotate with the star. Even a moderate rate of mass loss leads to a disproportionately large rate of loss of angular momentum (Mestel 1999). Angular momentum dissipation for a simple monopole magnetic field is (Weber & Davis 1967):

RA is the Alfven radius.


Ud-Doula et al. (2009) modified the momentum loss equation for the case of dipolar magnetic field:

where the wind confining parameter is

Spin-down time for a magnetic dipole star (strong-confinement limit) is:


· 1 OriC . . , , , . , , .