Diffusion in magnetic fields G. Alecian (CNRS, Observatoire de Paris)
Ap magnetic Magnetic Ap star Also: -Ambipolar diffusion (Babel & Michaud, 1991) -Effect on models (LeBlanc, Michaud & Babel, 1994) G.Alecian, IAU 224 2
Ion diffusion velocity without magnetic field Microscopic diffusion velocity of an ion (Z i ) : m p m p V Di ≈ D ip − A i − Z i − 1 rad +… kT g + A i kT g i 2 gravity Radiative acceleration G.Alecian, IAU 224 3
The effect of horizontal magnetic fields on the diffusion velocity • Correcting factor in the direction orthogonal to magnetic lines t i is the « collision » time − 1 ( ) 2 t i 2 f slow , i = 1 + ω i ω i / 2 π is the cyclotron frequency ω i = ZeH 0 < f slow , i ≤ 1 m i c • The corrected average diffusion velocity (approximated) for horizontal field ∑ N i f slow , i V Di i V D ≈ ∑ N i i G.Alecian, IAU 224 4
Some typical results • Silicon : Vauclair, Hardorp & Peterson (1979) have shown the consequence of the ions trapping by the magnetic field Fig4a of Alecian & Vauclair (1981) Similar studies for: - Oblique rotator model (Michaud, Megessier & Charland, 1981) - Ga in Ap stars (Alecian & Artru, 1987) - Ca, Sc, Ti, Mn, Cr, Sr in 53 Camelopardalis (Babel & Michaud, 1991) - Al in Ap stars (Hui Bon Hoa, Alecian & Artru, 1996) G.Alecian, IAU 224 5
Oblique magnetic lines Alecian & Vauclair, 1981 : 1 sin 2 θ V H , Zi = V i f slow , i + f slow , i and, an horizontal component! V H , Xi = f slow , i V i sin2 θ 2 G.Alecian, IAU 224 6
Horizontal diffusion ! • Mégessier, 1984 (Si distribution on Bp and Ap stars with dipolar field and applying the previous formulae) However, the time scale for the appearance of significant inhomogeneities through horizontal diffusion onto the stellar surface is about 10 7 y ! This implies that magnetic structures should be stable over a long period. Moreover, time scales are much shorter for vertical diffusion, which remains dominant in the stratification process Therefore, abundance patches are more likely formed through the V z component (by inhomogeneous vertical diffusion according to the local field angle). G.Alecian, IAU 224 7
Radiative accelerations, with and without magnetic field n i , k ∞ rad = ∑ ∫ ( ) d ν g i φ ν , n i σ k , m n i Am p c k , m > k 0 n i , k rad = ∑ ν ∫ ∫ ( ) Ω d Ω d ν g i e . I (magnetic) n i Am p c k , m > k Ω G.Alecian, IAU 224 8
The CARAT code • Polarized radiation transfer in LTE (Alecian & Stift, 2004) – VALD data base, Kurucz ATLAS9 models, plane-parallel – Magnetic field up to 60 000 Gauss, any angle – Detailed opacities up to 5 mA of resolution – radiative accelerations for 329 ions – parallel computing G.Alecian, IAU 224 9
Effet du champ sur g rad 6.0 6 (b) (a) 0T CARAT β = 60° 0T BM 1.5T CARAT 1.5T CARAT without M-O Raie du Mg II 5 5.5 1.5T BM log g v (SrII): CARAT CARAT without M-O 4 BM 5.0 log g v (SrII) log g (SrII) 3 4.5 2 4.0 log g h (SrII): 1 BM CARAT without M-O (-x) CARAT (+x) 3.5 -6 -4 -2 0 2 CARAT (-x) log τ 5000 0 -6 -4 -2 0 2 log τ 5000 SrII λ 4077 T eff =8500K G.Alecian, IAU 224 10
6.0 5.5 Blends Cr 5.0 4.5 Effect of Blends 4.0 5.0 4.8 Fe 4.6 log g rad 4.4 4.2 4.0 3.8 6 Ag 5 4 0T, with blends 4T, with blends 3 0T, alone 4T, alone 2 -6 -4 -2 0 2 log τ 5000 G.Alecian, IAU 224 11
Zeeman amplification log(amplification) 0.4 4T vs 0T, 0° Zn Ca Mg Fe T eff = 12 000K Ni 0.3 S Hg Ga Mn P Ge Co Cu 0.2 Pr In Cr Ti Sc ε O Cl B Ir 0.1 Cd Sn Zr C Al Si 0.0 Be Au Os Ag -0.1 Bi -0.2 -6 -4 -2 0 2 log τ 5000 G.Alecian, IAU 224 12
Preliminary results (complete computation with CARAT) Al T eff =12000K G.Alecian, IAU 224 13
Preliminary results (2) Al comparing fluxes G.Alecian, IAU 224 14
Future developments • Stratification at equilibrium (already in progress for zero field case, see LeBlanc et al.) – Self-consistent models – NLTE • 2D stratifications (modelling oblique rotators) • + all potentially important processes (ambipolar diffusion, hydrodynamics,…) • Connection to internal structure • Far in the future: time-dependent stratifications (LTE,…) G.Alecian, IAU 224 15
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