Modeling of sgB[e] circumstellar disks urst 1 , Achim Feldmeier 2 , - PowerPoint PPT Presentation

Modeling of sgB[e] circumstellar disks urst 1 , Achim Feldmeier 2 , and Jiˇ cka 1 Petr Kurf¨ r´ ı Krtiˇ 1 Department of Theoretical Physics and Astrophysics, Masaryk University, Brno, Czech Republic 2 Institut f¨ ur Physik und Astronomie, Universit¨ at Potsdam, Potsdam-Golm, Germany The B[e] Phenomenon: Forty Years of Studies Praha, June 27, 2016

Main stellar types associated with outflowing disks Be phenomenon - “a non-sg B-type star with Balmer spectral lines in emission”

Main stellar types associated with outflowing disks Be phenomenon - “a non-sg B-type star with Balmer spectral lines in emission” B[e] phenomenon: • B-type stars with forbidden optical emission lines ( Conti 1976 ) • Different populations with different mechanisms responsible for feeding CE with gas ( Lamers+ 1998 , Miroshnichenko 2007 ) • sgB[e]: B supergiants with relative luminosity log( L ⋆ / L ⊙ ) � 4 . 0 • HAeB[e] or pre-main sequence stars: very young stars - evidence of CM inflow rather than outflow • cPNB[e]: compact planetary nebula stars - low mass stars - evolving into planetary nebula ( Ciatti+ 1974 ) • SymB[e]: symbiotic stars - interacting binaries with a hot compact object and a cool giant - surrounded by a nebula • unclB[e]: unclassified stars - do not fit to any of the previous classes

Main stellar types associated with outflowing disks Be phenomenon - “a non-sg B-type star with Balmer spectral lines in emission” B[e] phenomenon: • B-type stars with forbidden optical emission lines ( Conti 1976 ) • Different populations with different mechanisms responsible for feeding CE with gas ( Lamers+ 1998 , Miroshnichenko 2007 ) • sgB[e]: B supergiants with relative luminosity log( L ⋆ / L ⊙ ) � 4 . 0 • HAeB[e] or pre-main sequence stars: very young stars - evidence of CM inflow rather than outflow • cPNB[e]: compact planetary nebula stars - low mass stars - evolving into planetary nebula ( Ciatti+ 1974 ) • SymB[e]: symbiotic stars - interacting binaries with a hot compact object and a cool giant - surrounded by a nebula • unclB[e]: unclassified stars - do not fit to any of the previous classes • Disk formation mechanisms still under debate - viscous disk × outlowing disk-forming wind? ( Kraus+ 2007 , 2010 )

Basic hydrodynamics Basic (magneto)hydrodynamics in conservative form: • Continuity equation (mass conservation law) ∂ρ ∂ t + � ∇ · ( ρ� V ) = 0 • Equation of motion (conservation of momentum, angular momentum) ∂ ( ρ� V ) ∇ Φ + 1 + � ∇ · ( ρ� V � V ) = − � ∇ p − ρ� µ ( � ∇ × � B ) × � B (+ � f visc .... ) ∂ t • Energy equation ρǫ + ρ V 2 2 + B 2 � � ∂ E ∂ t + � ∇ · ( E � V ) = − � ∇ · ( p � V ) .... , E = 2 µ • Induction equation ∂� B � � ∂ t = � V × � � ∇ × B • Equations of state E − ρ V 2 2 − B 2 � � p = ρ a 2 p = ( γ − 1) , 2 µ

Basic hydrodynamics Determining equations of viscous disk structure ∞ � • Integrated disk column (surface) density Σ = ρ d z −∞ • Shear viscous stress σ R φ ≈ η dV φ dR ≈ ν Σ dV φ dR ≈ α a λ Σ dV φ dR , η = f ρλ V turb • Kinematic viscosity ν , viscosity parameter α ( Shakura & Sunyaev 1972 ) ν = η/ρ ∼ λ V turb ≈ α a λ, α = V turb / a • Parameterization of temperature and viscosity: � p � n � R eq � R eq T = T ( R eq ) , α = α ( R eq ) R R • The full second order φ component of viscosity ( ∂/∂φ = 0 , ∂/∂ z = 0): � � σ R φ = − 1 ∂ α a 2 R 3 Σ ∂ ln V φ − α a 2 R 2 Σ R 2 ∂ R ∂ R

1-D hydrodynamic modeling of circumstellar viscous disks • Time-dependent 1-D hydrodynamic calculations using own MHD code ( Kurf¨ urst, Feldmeier & Krtiˇ cka 2014 ) • In the models we recognize the wave that converges the initial state to the final stationary state Left panel: disk of classical Be star, Right panel: disk of sgB[e] star, M =14.5 M ⊙ , R =5.8 R ⊙ , T eff = 30 kK M =40 M ⊙ , R =75 R ⊙ , T eff = 20 kK Video otevˇ rete kliknut´ ım na Video otevˇ rete kliknut´ ım na n´ asleduj´ ıc´ ı n´ asleduj´ ıc´ ı odkaz : odkaz : Be evolution.mp4 B[e] evolution.mp4 � • In supersonic region - a shock wave with propagation speed D = a Σ 1 / Σ 0 • The shock propagation time t dyn ≈ R / D = 0 . 3 R / a - the disk evolution time � R R eq V φ d R / ( α a 2 ) • Corresponding disk viscous time t visc =

1-D hydrodynamic modeling of circumstellar viscous disks B0 star sgB[e] star T eff = 30 kK T eff = 20 kK 10 2 . . 10 2 . . J / J ( R eq ) log g ≈ 2 . 1 J / J ( R star ) log g ≈ 0 . 4 V φ / V K 1 V φ / V K 1 V crit ≈ 560 km/s V crit ≈ 250 km/s 10 -2 V R / a V R / a 10 -2 10 -4 Σ / Σ ( R eq ) 10 -4 Σ / Σ ( R star ) 10 -6 10 -6 10 -8 n = 0.0 n = 0.0 10 -8 n = 0.2 10 -10 n = 0.2 n = -0.1 n = -0.1 10 -12 10 -10 10 2 10 3 10 4 10 5 10 2 10 3 10 4 1 10 1 10 . . . . 10 2 . . J / J ( R eq ) J / J ( R eq ) 10 2 J / J ( R star ) V φ / V K V φ / V K 1 V φ / V K 1 10 -2 V R / a V R / a 10 -2 V R / a 10 -4 10 -4 10 -6 Σ / Σ ( R eq ) Σ / Σ ( R eq ) Σ / Σ ( R star ) 10 -6 10 -8 n = 0.0 n = 0.0 n = 0.0 10 -8 n = 0.2 10 -10 n = 0.2 n = 0.2 n = -0.1 n = -0.1 n = -0.1 10 -12 10 -10 10 2 10 3 10 4 10 5 10 2 10 3 10 4 1 10 1 10 R / R eq R / R star • Upper panels: T = 0 . 6 T eff , lower panels: T ∼ 0 . 6 T eff R − 0 . 4 • α ( R ⋆ ) = 0 . 025 ( Penna+ 2012 ), α ∼ R − n • Sonic point radius dependence on T profile, in sgB[e] disk significantly lower

1-D calculations of disk magnetorotational instability • Powerful shearing instability ( Balbus & Hawley 2003 ) - main source of anomalous viscosity in Be star disks (cf. talk of J. Krtiˇ cka) • Is it true also in sgB[e] disks? (cf. Kraus+ 2007 ) • MS B3 star, T eff = 20 kK, T = 0 . 6 T eff , α ≈ 0 . 1 (1 − R / 390 R eq ) (Krtiˇ cka+ 2015 ) 10 2 . . 10 2 V φ / a J / J ( R eq ) 10 . . V φ / a J / J ( R eq ) 10 i ω / Ω 1 i ω / Ω 1 10 -1 N R / Ω R crit V R / a N R / Ω 10 -1 ρ 0 / ρ 0 ( R eq ) R crit V R / a 10 -2 ρ 0 / ρ 0 ( R eq ) 10 -2 10 -3 α = α ( R eq ) 10 -3 α ≈ α ( R eq )[1-R/390 R eq ] α = α ( R eq ) 10 -4 α ≈ α ( R eq )[1-R/390 R eq ] 1 10 100 1000 10 -4 R / R eq 1 10 100 1000 R / R eq • Left panel: inner boundary viscosity α ( R eq ) = 0 . 025, right panel: α ( R eq = 0 . 1) • Magnetorotational instability calculated in the disk midplane ( N z = 0) • In Keplerian region MRI frequency ω = 3 / 4 i Ω • The radius where MRI instability vanishes increases with decreasing viscosity

1-D hydrodynamic modeling of circumstellar viscous disks • Models with very low constant initial density • B-type star, T eff = 25 000 K, V eq ≈ 300 km s − 1 • Σ ini is of a very low constant value throughout the entire isothermal disk with constant viscosity α = 0 . 025 • Snapshots of evolved radial profiles of the disk Σ and V R in two different times 10 6 10 6 t = 25 yrs t = 160 yrs 10 4 10 4 V R (m s -1 ) V R (m s -1 ) 10 2 10 2 1 1 10 -2 10 -2 10 -4 10 -4 Σ (arbitrary units) Σ (arbitrary units) 10 -6 10 -6 10 -8 10 -8 10 -10 10 -10 10 2 10 3 10 4 10 5 10 6 10 2 10 3 10 4 10 5 10 6 1 10 1 10 R / R eq R / R eq • Rarefaction wave propagates radially with time ( cf. Kurf¨ urst+ 2014 ) • The gas is moved to the edge of the unperturbed ISM • Density bumps at the edge of ISM - bow shocks ?

1-D hydrodynamic modeling of circumstellar viscous disks • B[e] CE - disks or rings? (courtesy from G. Maravelias) • Multiple rings are traced by emission of [OI], [CaII] and CO

1-D hydrodynamic modeling of circumstellar viscous disks • B[e] CE - disks or rings? (courtesy from G. Maravelias) • Multiple rings are traced by emission of [OI], [CaII] and CO • Models with subcritically rotating star � GM ⋆ R eq • Model with stellar radial pulsations: V φ ( R eq )( t ) = R eq + ( δ R eq ) sin ω t 10 8 • ω corresponds to P ≥ 0 . 25 d (6 hours) and Σ (kg m -2 ) 10 6 δ R eq = 0 . 1 R eq t 0 + 1.5 h 10 4 t 0 + 4.5 h V R (m s -1 ) • Pulsations in Σ and V R up to 2-3 stellar radii, t 0 + 7.5 h 10 2 otherwise they rapidly decrease 1 • Three different times of Σ and V R waves 10 -2 1 1.2 1.4 1.6 1.8 2.0 R / R eq

1-D hydrodynamic modeling of circumstellar viscous disks • B[e] CE - disks or rings? (courtesy from G. Maravelias) • Models with subcritically rotating star • The model with sgB[e] star parameters: V φ ( R ⋆ ) = 90% of V crit , α ≥ 0 . 5 • The material may fall inwards and increase the angular momentum of the inner disk Video otevˇ rete kliknut´ ım na ı odkaz : • May these waves explain the rings? n´ asleduj´ ıc´ subcritical.mp4 • Probably not since no significant radial motion is detected (priv. comm. with G. Marvelias) • Black line denotes the density in case of V crit

2-D hydrodynamic modeling Time-dependent 2-D calculations • Calculation of vertical hydrodynamic and thermal structure of the disk • Vertical hydrostatic equilibrium in the thin disk ( z ≪ R ): − z 2 � � ρ ≈ ρ 0 exp , where ρ 0 is the disk midplane density 2 H 2 √ • Vertical scale height: H = aR / V φ , Σ ≈ 2 πρ 0 H . • Vertical thermal equilibrium: 3 κ p dT dz = ∇ T dp F z dz , ∇ = d ln T / d ln p , ∇ rad = p 16 σ T 4 g z • Including convection ∇ rad > ∇ ad and satisfying the condition F z = 0 at z = 0, we obtain the vertical temperature distribution (Lee+ 1991 )