Radiative Transfer in Axial Symmetry

Transcription

1 Radiative Transfer in Axial Symmetry Daniela Korčáková Astronomical Institute of the Academy of Sciences, CZ collaborators: T. Nagel, K. Werner, V. Suleymanov, V. Votruba, J. Kubát picture:

2 Outline Description of the method Method applicability limb darkening stellar rotation stellar wind discs

3 description of the method method preview axial symmetry LTE, NLTE hydrogen parallel version (in final test phase) input n e (r, θ), T(r, θ), v(r, θ) χ(r, θ), S(r, θ) output line profile, intensity map Korčáková & Kubát, 2005, A&A 440, 75

4 basic idea solution of the radiative transfer equation in separate planes polar coordinates in every plane combination of the short and long characteristic methods velocity field Lorentz invariance of RTE

5 longitudinal planes whole radiation field rotation axis

6 upper boundary condition radial grid line grid circle zone

7 integration I (B) = I (A) e τ (AB) + τ(ab) 0 S(t)e [ ( τ (AB) t)] dt S(t): bound-bound bound-free free-free Thomson scattering A B τ AB τ BC s AB s BC s CD τ CD C D

8 velocity field d, th v = const. d, th v v v = const. v = const. d, th v = const. d, th+ v = const. d, th+

9 solution in the central region C A B s BC τ τ AB s AB BC

10 lower boundary condition

11 mean intensity rotation axis the grid is defined by global properties advantage better description in outer regions, where the radiation field is strongly anisotropic

12 disadvantage not possible to use an area method HEALPix (Hierarchical Equal Area isolatitude Pixelization) Gorski, Hivon, Banday, Wandelt, Hansen, Reinecke, Bartelmann, 2005, ApJ 622, 759

13 parallelization MPI memory computational time communication formal solution of the radiative transfer equation is splitted into the nodes by lines solution of the NLTE rate equations is distributed to the nodes by frequencies at the given point in final test phase

14 advantages a better description of the global character of the radiation field than by the short characteristic method not so time consuming as the long characteristic method arbitrary velocity field disadvantages high velocity gradients = a finer grid computing time f 2 (f number of frequency points)

15 method applicability limb darkening stellar rotation gravity darkening, differential rotation stellar wind optically thin + optically thick regions polar + equatorial regions Be, B[e] stars,... discs cataclysmic variables, protostellar discs central object + surrounding medium protoplanetary nebulae

16 limb darkening the specific intensity 4e 05 3e 05 2e 05 e x [r/r ] e e e+4 ν 4.564e+4

17

18 stellar rotation rapidly rotating stars gravity darkening differential rotation

19 extended rapidly rotating atmosphere 0.98 relative flux rot grav dif rot+grav dif rot grav+dif rot+grav+dif 4.56e e e e+4 ν

20 stellar wind optically thick atmospheric regions + optically thin wind polar + equatorial region static layers + fast outer region stellar wind + rotation Be, B[e] stars

21 Nv line 242 Å Krtička, Korčáková, Kubát, 2008, ASPC 388, 9 relative flux one component four component λ[å]

22 discs protostellar discs cataclysmic variables = central white dwarf + transition region + disc + hot corona disc optically thick or thin impossible to include a hot spot

23 technique structure, χ and S from AcDc code Nagel et al., 2004, A&A, 428, 09 disc = set of concentric rings consistent solution of: radiative transfer equation hydrostatic equation energy balance equation rate equation equation of charge and particle conservation 2D grid interpolation of S and χ to the new grid Steffen, 990, A&A, 239, 443 Kepler rotation law radiative transfer using the 2.5D code

24 choice of the systems the quiescent phase optically thinner = effects connected with the velocity field better visible SS Cyg Hα Hγ an AM CVn system HeI 4923 Å

25 SS Cyg an intermediate polar M wd (0.8 ± 0.9)M q = M K /M wd ± 0.02 a R wd P i (.36 ± 0.) 0 cm 0.0R days Bitner et al., 2007, ApJ, 662, 564 Wood, 995, LNP, 443, 4 model H + He 8 rings; Ṁ < 0, 0 9 > M yr

26 SS Cyg quiescent phase Hα y [R wd ] log(χ ) r tidal x [R wd ] 4 y [R wd ] 3 2 log(s) x [R wd ] r tidal

27 SS Cyg quiescent phase Hα relative flux i=0 o RTE flux relative flux i=85 o RTE flux 4.55e+4 4.6e+4 ν[hz] 4.55e+4 4.6e+4 ν[hz] relative flux i=70 o RTE flux relative flux i=90 o RTE flux 4.55e+4 4.6e+4 ν[hz] 4.55e+4 4.6e+4 ν[hz]

28 SS Cyg quiescent phase Hγ y [R wd ] log(χ ) r tidal x [R wd ] 4 y [R wd ] 3 2 log(s) x [R wd ] r tidal

29 SS Cyg quiescent phase Hγ 2.04 relative flux i=0 o RTE flux relative flux i=85.0 o RTE flux 6.85e+4 6.9e e+4 ν[hz] 6.85e+4 6.9e e+4 ν[hz] relative flux i=70 o RTE flux relative flux..05 i=90 o RTE flux 6.85e+4 6.9e e+4 ν[hz] e+4 6.9e e+4 ν[hz]

30 an AM CVn star P orb < hour = compact donors nature white dwarf (neutron star) + white dwarf white dwarf (neutron star) + helium core burning star white dwarf (neutron star) + main-sequence star model (GP Com) quiescence phase 9 rings Ṁ 0 M yr HeI 4923Å

31 an AM CVn star HeI 4923Å y [R wd ] log(χ ) x [R 0. wd ] 0.05 y [R wd ] log(s) x [R wd ]

32 an AM CVn star HeI 4923Å relative flux 3 2 i=0 o RTE flux relative flux.3.2. i=89.0 o RTE flux 6.05e+4 6.e+4 6.5e+4 ν[hz] 6.05e+4 6.e+4 6.5e+4 ν[hz] relative flux i=70 o RTE flux 6.05e+4 6.e+4 6.5e+4 ν[hz] relative flux i=90 o RTE flux 6.05e+4 6.e+4 6.5e+4 ν[hz]

33 face-on view rotation velocity field has a negligible influence static disc approximation for the radiative transfer is valid with high accuracy edge-on view important difference v rot [km/s] y [R wd ] x [R wd ] r tidal

34 Where it can play the role? edge-on view opening angle 0 not so small probability self-shielding disc (e.g. V348 Pup) occulting systems some UX UMa or SW Ser systems low luminosity dust is not important in most CVs (in contrast to polars) extended area wind important corona polars, intermediate polars

35 conclusion axial symmetry + wind + rotation = rapidly rotating stars extended stellar atmospheres stellar winds discs