The impact of the slow solutions in the winds of massive stars

Transcription

1 The impact of the slow solutions in the winds of massive stars Departamento de Física y Astronomía, Universidad de Valparaiso, Chile Collaborators: Lydia Cidale, Anahi Granada et al. Univ. Nac. de La Plata, Argentina Diego Rial, Univ. de Buenos Aires, Argentina Alfredo Santíllan, UNAM, Mexico Ignacio Araya,

2 History Late 60: first UV spectral observations

3 History

4 History

5 Theory Only known Theory: Parker s Model for the Solar Wind (Parker, E.N.: 1960, ApJ 132, 821) For O stars => Teff = 10 7 K But at this Temperature C IV - N V - Si IV Don t Exist Destroyed by collisional ionization

6 Radiation Driven Winds Lucy & Solomon (1970, ApJ, 159, 870): Wind driven by resonance lines Obtained only mass loss rates of about 1/100th of the observed values Castor, Abbott & Klein (1975, ApJ, 195, 157) Wind driven by an ensemble of lines (scattering) They obtained a qualitative agreement with the observational values

7 Radiation Driven Winds Lucy & Solomon (1970, ApJ, 159, 870): Wind driven by resonance lines Obtained only mass loss rates of about 1/100th of the observed values Castor, Abbott & Klein (1975, ApJ, 195, 157) Wind driven by an ensemble of lines (scattering) They obtained a qualitative agreement with the observational values The Standard Model (m-cak)

8 1D - Hydrodynamics Assumptions: Stationary - Low viscosity - Spherical symmetry - No Mag. Fields. From Mass and Momentum Conservation laws:

9 1D - Hydrodynamics Assumptions: Stationary - Low viscosity - Spherical symmetry - No Mag. Fields. From Mass and Momentum Conservation laws:

10 Line Force: Very Simplified Version Contribution by one line i at frequency ν i

11 Line Force: Very Simplified Version Contribution by one line i at frequency ν i

12 Line Force: Very Simplified Version Contribution by one line i at frequency ν i dm = 4πr 2 ρdr

13 Line Force: Very Simplified Version Contribution by one line i at frequency ν i

14 Line Force: Very Simplified Version Contribution by one line i at frequency ν i total photon momentum rate provided by the star

15 Line Force: Very Simplified Version Contribution by one line i at frequency ν i total photon momentum rate provided by the star fraction absorbed by one spectral line in an outer shell of thickness dr

16 Line Force: Very Simplified Version Contribution by one line i at frequency ν i optical thickness total photon momentum rate provided by the star fraction absorbed by one spectral line in an outer shell of thickness dr

17 Line Force: Very Simplified Version Contribution by one line i at frequency ν i optical thickness total photon momentum rate provided by the star fraction absorbed by one spectral line in an outer shell of thickness dr

18 Line Force: Very Simplified Version Contribution by one line i at frequency ν i optical thickness total photon momentum rate provided by the star fraction absorbed by one spectral line in an outer shell of thickness dr dm = 4π r 2 ρdr

19 Line Force: Very Simplified Version Contribution by one line i at frequency ν i optical thickness total photon momentum rate provided by the star fraction absorbed by one spectral line in an outer shell of thickness dr dv/dr dm = 4π r 2 ρdr

20 Line Force: Super Simplified Version Contribution by one line i at frequency ν i Dependence on the Velocity gradient FORCE MULTIPLIER

21 Line Force Contribution from an ensemble of lines Currently: 4.2 Mega lines, 150 ionization stages (H Zn),

22 Line Force Logarithmic plot of line-strength distribution function for an O-type wind at 40,000 K and corresponding power-law fit (Puls et al. 2000, A&AS 141)

23 Line Force Mass-loss Ensemble of lines Logarithmic plot of line-strength distribution function for an O-type wind at 40,000 K and corresponding power-law fit (Puls et al. 2000, A&AS 141)

24 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986)

25 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986)

26 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986) Eigenvalue (Mass-loss)

27 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986) Eigenvalue (Mass-loss) Ensemble of lines

28 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986) Eigenvalue (Mass-loss) Ensemble of lines Changes in Ionization

29 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986) Eigenvalue (Mass-loss) Ensemble of lines Correction Factor Changes in Ionization

30 CAK & m-cak Models Castor, Abbott & Klein (1975), Abbott (1982), Friend & Abbott (1986), Pauldrach et al. (1986) Eigenvalue (Mass-loss) Ensemble of lines Correction Factor Changes in Ionization

31 Radiation Driven Wind Hydrodynamics

32 Radiation Driven Wind Hydrodynamics Mass Conservation

33 Radiation Driven Wind Hydrodynamics Mass Conservation

34 Radiation Driven Wind Hydrodynamics Mass Conservation Inertia Gas Pressure Gravity Line Force

35 First Topological Analysis Non-Rotating Solution Schema

36 Singularity Condition First Topological Analysis Non-Rotating Solution Schema

37 First Topological Analysis Non-Rotating Solution Schema Singularity Condition Regularity Condition

38 CAK Model CAK Theory: Qualitatively acceptable agreement with the observational values Theory weak assumption: Point Star approximation

39 m-cak Model modified-cak Theory: Finite Disk Correction Factor Friend & Abbott ApJ, 311,701,1986 Pauldrach, Puls & Kudritzki A&A, 164,86, 1986

40 m-cak Model m-cak: better agreement with observations

41 Radiation Driven Wind Hydrodynamics The effect of Rotation in 1D models Pauldrach et al. A&A, 164,86, 1986 Friend & Abbott ApJ, 311,701,1986

42 Radiation Driven Wind Hydrodynamics The effect of Rotation in 1D models? Pauldrach et al. A&A, 164,86, 1986 Friend & Abbott ApJ, 311,701,1986

43 Radiation Driven Wind Hydrodynamics The effect of Rotation in 1D models Friend & Abbott ApJ, 311,701,1986

44 Radiation Driven Wind Hydrodynamics with Rotation: Revisited Mass Conservation

45 Radiation Driven Wind Hydrodynamics with Rotation: Revisited Mass Conservation

46 Radiation Driven Wind Hydrodynamics with Rotation: Revisited Mass Conservation Inertia Gas Pressure Gravity Centrifugal force Line Force

47 Changing of variables Equation of Motion

48 Changing of variables Equation of Motion

49 Changing of variables Equation of Motion

50 Changing of variables Equation of Motion

51 Changing of variables Equation of Motion

52 Changing of variables Equation of Motion

53 with the influence of the ROTATION

54 with the influence of the ROTATION

55 with the influence of the ROTATION

56 with the influence of the ROTATION At the Singular Point: us,ys,zs,c

57 Without any Approximation!

58 Without any Approximation!

59 Without any Approximation! and

60 R(u, Z) = 0 singular point location

61 R(u, Z) = 0 singular point location

62 R(u, Z) = 0 singular point location

63 R(u, Z) = 0 singular point location

64

65

66

67

68 CAK family of singular points

69 CAK family of singular points

70 CAK family of singular points

71 CAK family of singular points

72 CAK family of singular points NEW family of singular points

73 CAK family of singular points NEW family of singular points

74 Rotating CAK and m-cak solutions CAK y m-cak (Slow solution) with different! cak!=0.70 cak!=0.80 cak!=0.99 m-cak!=0.70 m-cak!=0.80 m-cak!= v u

75 Rotating CAK and m-cak solutions CAK y m-cak (Slow solution) with different! cak!=0.70 cak!=0.80 cak!=0.99 m-cak!=0.70 m-cak!=0.80 m-cak!=0.99 Slow Solution is the analytical prolongation of the CAK solution 250 v u

76 Rotating Radiation Driven Winds Applications of the Slow solution Rotation: B[e] Supergiants

77 Rotating Radiation Driven Winds Applications of the Slow solution Rotation: B[e] Supergiants

78 Rotating Radiation Driven Winds B[e]-Supergiant star from Zickgraf 1986

79 Bistability Proposed by Lamers & Pauldrach (1991) Vink et al. (1999) Theoreticaly showed: Bistability Jump T=25,000K due to Recombination of Fe IV to Fe III

80 Bistability Jump Observational determination of the Bistability Jump Lamers, Snow & Lindholm, ApJ, 455, 269, 1995

81 Bistability Jump

82 Bistability Jump

83 B[e] Supergiant Wind m-cak Bistability line force parameters (T eff =25,000K): one set for polar latitudes and other set for equatorial latitudes Fast (polar) and Slow (equatorial) solutions (m-cak) Rotation parameter Ω

84 B[e] Supergiant Wind Stellar Parameters Line-Force Parameters form Pelupessy et al. (2000) form Pelupessy et al. (2000) form Zickgraf (1998)

85 B[e] Supergiant m-cak Wind

86 B[e] Supergiant m-cak Wind density contrast Observational values

87 B[e] Supergiant m-cak Wind 2D Wind

88 B[e] Supergiant m-cak Wind 2D Wind

89 B Supergiant m-cak Wind Disk Aperture Angle HD Ω = 0.75 Ω = 0.85 Ω = 0.95

90 Rotating Radiation Driven Winds Applications of the Slow solution Rotation: Be Stars

91 Rotating Radiation Driven Winds Rotating Stars OBJECTS Be-Star from Lamers & Pauldrach 1991

92 Be Star Wind Stellar Parameters Line-Force Parameters

93 Be Star Wind Von Zeippel Effect - Gravity Darkening Rotational Velocity

94 Be Star Wind Oblate Disk Correction Factor

95 Be Star Wind Oblate Disk Correction Factor 2.5 fd R r

96 Be Star Wind Oblate Disk Correction Factor Velocity field V km s 1000 V km s R r R r

97 Be Star Wind Oblate Disk Correction Factor Density contrast Α=0.4 Ρe Ρp 10 2 Α=0.4 Α=0.45 Α= Ρe Ρp 10 2 Α=0.45 Α= r R r R 1

98 Applications of the Slow solution Changes in ionization: (OB)A Supergiants

99 Wind Momentum Luminosity Relationship A Supergiants NGC3621

100 Wind Momentum Luminosity Relationship Hα dependence on the mass loss rate O5 Ia A3 Ia

101 Wind Momentum Luminosity Relationship Radiative Transport models do not use velocity (density) profile from CAK Hydrodynamic. Instead: beta-profile

102 Wind Momentum Luminosity Relationship OB Supergiants

103 Wind Momentum Luminosity Relationship A-Supergiant Models Achmad, Lamers & Pasquini, A&A 320,196, 1997

104 Wind Momentum Luminosity Relationship A-Supergiant Models Achmad, Lamers & Pasquini, A&A 320,196, 1997 Discrepancy

105 Wind Momentum Luminosity Relationship

106 Wind Momentum Luminosity Relationship

107 Wind Momentum Luminosity Relationship

108 Rotating Radiation Driven Winds Time dependent Hydrodynamic

109 Rotating Radiation Driven Winds Time dependent Hydrodynamic

110 Time dependent Hydrodynamic ZEUS-3D CAK model time radius

111 Time dependent Hydrodynamic ZEUS-3D m-cak model Fast Solutions

112 Time dependent Hydrodynamic ZEUS-3D m-cak model Slow Solutions

113 Conclusions Slow wind solutions may solve some of the problems from massive stars hydrodynamic: Winds from B[e] Supergiants (outflowing disk) Winds from BA Supergiants (WML relationship) Classical Be Stars (Gravity Darkening) Future Work Time dependent Calculations (bifurcation, oscillation, clumping?) 2D-calculations Observations (constrains to theory) Magnetic Fields

114 F I N