Be Stars Modeling

Daniela Korcakova & Jirı Kubat

Astronomical Institute Academy of Sciences of the Czech Republic

Outline

nature of Be stars

theoretical description - what we need?, what we have?hydrodynamicradiative transfer

conclusion

Outline

nature of Be stars

theoretical description - what we need?, what we have?hydrodynamicradiative transfer

conclusion

Outline

nature of Be stars

theoretical description - what we need?, what we have?hydrodynamicradiative transfer

conclusion

nature of Be stars

I Be stars are “nonsupergiant B-type stars whose spectra have,or had at one time, one or more Balmer lines in emission.”(Collins, 1987)

I first observation – Secchi in 1866 – γ Cas

1

2

3

4

6300 6400 6500 6600 6700

rela

tive

flux

λ [Å]

Hα

I first systematic study of Be stars - Merrill (1913)

I may be emission lines of ionized metals (He, FeII, MgII, . . . )

nature of Be stars

I Struve’s model (Slettebak, 1988)

nature of Be stars

I infrared excess from free-free and free-bound emission ina disk-like structure (Gehrz at al., 1974)

I Balmer discontinuities

I polarizationI intrinsic linear polarization up to 2% of continuum (Bjorkman,

2000)I polarimetric position angles =⇒ an axisymmetric equatorial

structureI no rate of polarization in lines (Shorlin et al., 2002) =⇒ mag.

field up to 103Gauss

I photometric variability

nature of Be stars

I spectroscopic variabilityI short term variability

I hoursI non-radial pulsations (Baade, 1984)

I medium term variabilityI from days to hundreds daysI binarity ( Krız & Harmanec, 1975)

I long term variabilityI from years to decadesI the elongated disk model with apsidal motion (Hirata &

Kogure, 1984)I one-armed oscillations (Okazaki, 1991)

nature of Be stars

I UVI resonance lines SiIII, SiIV, CIV =⇒ v∞ ∼ 1000km/s, P Cygni

profile (Snow, 1981)I discrete absorption components

I rotationI rapid rotation (close to the critical limit) ⇐= absorption

photospheric linesI possible extremely differential rotation (Balona, 1975)I Keplerian rotating disk (Meilland et al., 2007)

I stellar windI structured windI radiatively driven wind (CAK theory, Castor, Abbott & Klein,

1975 )

nature of Be stars

model requirements

I star + surrounding media = disk-like structure

I rapid rotation

I wind

theoretical description - what we need?, what we have?

ideal case =

hydrodynamic +

radiative transfer =

fantasy for today

hydrodynamic - what we need?, what we have?

need a hydrodynamic model, which:

I describes a photosphere together with wind region = problemmomentum equation:

vr

dv

dr= g rad − g −

1

ρ

d

dr(ρa2)

g rad is radiative acceleration, g gravitation acceleration, ρdensity, a isothermal speed of soundequation of mass continuity:

d

dr(r2ρvr ) = 0

M 6= 0 =⇒ vr 6= 0 in all the atmosphere =⇒ we are not ableto go sufficiently close to the static photosphere +

hydrodynamic - what we need?, what we have?

need a hydrodynamic model, which:

hydrostatic models fail in the region with nonzero velocitygradient =⇒ a gap between photosphere and wind region

photospherestellar

wind region

hic suntleones

I rotation =⇒ 2.5D model

I clumping =⇒ 3D model

hydrodynamic - what we need?, what we have?

need a hydrodynamic model, which:

hydrostatic models fail in the region with nonzero velocitygradient =⇒ a gap between photosphere and wind region

photospherestellar

wind region

hic suntleones

I rotation =⇒ 2.5D model

I clumping =⇒ 3D model

hydrodynamics =⇒ radiative transfer

the grid problem

The grid for the description of matter (density, velocity, ...) isusually not suitable for the description of radiation.

I radiationI the grid defined by optical depthI five (seven) points per decade of optical depthI frequency dependent

I velocityI Sobolev condition

“You cannot choose thebest grid until you knowthe answer.” (Auer)

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

need a radiative transfer model, which:

I geometryI rotation + wind characteristics =⇒ 2D modelI inclusion of clumping =⇒ 3D modelI plane parallel atmosphere – unusable

I describe a photosphere together with wind region =deep optically thick photosphere −→ very optically thin windandstatic media −→ high velocity gradient

I rotation −→ velocity gradient + stellar shape changes +gravity darkening

I inclusion of velocityI Sobolev approximation (Sobolev, 1957) – fast, not valid in

small velocity gradientI other methods – slow

I NLTE

radiative transfer - what we need?, what we have?

appropriate multidimensional methods for the sol. of the RTE:

I short characteristics (Mihalas, Auer, Mihalas, 1978, Kunasz &Auer, 1988)

I the bestI multidimensional, accurate, fast, stableI both optically thick, optically thin mediaI possible to use for velocity fields

I not ideal – do not describe the global character of radiationfield so well =⇒ some modifications of short characteristics

other multidimensional methods for the solution of the RTE:

I long characteristic methods (Cannon, 1970)

I finite volume method (Adam, 1990)

I discontinuous finite element method (Dykema et al., 1996)

I Monte Carlo (Boisse, 1990)

I diffusion limit (Mihalas & Mihalas, 1999)

radiative transfer - what we need?, what we have?

multidimensional radiative transfer models for Be stars:

1969 Marlborough cylindrical symmetry,hydrodynamics + radiative transfer

1974 Krız axial symmetry, improvementof Sobolev approximation

1975 Kuan & Kuhi Sobolev approximation1979 Krız axial symmetry, hydrodynamics +

radiative transfer1980 Hamann Sobolev appr. in expanding atmospheres1986 Rybicki & Hummel Sobolev approximation in thin disk1988 Hanuschik opticaly thin1990 Hubeny disk = a set of plane-parallel atmospheres1994 Hillier axial symmetry, continuum,

polarization

radiative transfer - what we need?, what we have?

multidimensional radiative transfer models for Be stars:

1994 Hummel 3D, velocity,star – boundary condition

1994 Stee & Araujo axial symmetry, Sobolev ap.1997 Hummel & Hanuschik 3D, oscilations2000 Busche & Hillier axial symmetry, static2003 Folini & Walder 3D2004 Budaj & Richards 3D, velocity, optically thin,

star – boundary condition2005 Korcakova & Kubat axial symmetry, velocity2006 Carciofi & Bjorkman, J. E. 3D Monte Carlo2006 Georgiev, Hillier, Zsargo axial symmetry, velocity2006 Lobel & Blomme 3D, velocity

conclusion

Even if a lot of work has been done, only several questions havebeen answered. There is still a lot of questions in Be stars

I How the stellar wind originate?

I How the disk-like structure originate?

I What about a multicomponent nature of the wind?

I What about cooling and heating of the wind?

I Is there any clumping? Wow it originates?

I What about oscillations? Why the observed pulsational modeschange with time?

I . . .

references

review papers:

Auer, L.,2003, ASPC 288, p. 405 – 417

Marlborough, J. M., 1976 IAUS 70, p. 335 – 370

Poeckert, R., 1982, IAUS 98, p. 453 – 481

Porter, J. & Rivinius, T., 2003, PASP 115, p. 1153 – 1170

Slettebak, A., 1979, SSSRv 23, p. 541 – 580

Slettebak, A., 1988, PASP 100, p. 770 – 784

Sokolovicova, J., 2005, Diploma thesis