Wind emission of OB supergiants and the influence of clumping
aa r X i v : . [ a s t r o - ph ] A ug Wind emission of OB supergiants and the influence of clumping
Clumping in Hot Star WindsW.-R. Hamann, A. Feldmeier & L. Oskinova, eds.Potsdam: Univ.-Verl., 2007URN: http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13981
Wind emission of OB supergiantsand the influence of clumping
M. Kraus , J. Kub´at & J. Krtiˇcka Astronomick´y ´ustav, Akademie vˇed ˇCesk´e republiky, Ondˇrejov, Czech Republic ´Ustav teoretick´e fyziky a astrofyziky PˇrF MU, Brno, Czech Republic The influence of the wind to the total continuum of OB supergiants is discussed. For windvelocity distributions with β > .
0, the wind can have strong influence to the total continuumemission, even at optical wavelengths. Comparing the continuum emission of clumped andunclumped winds, especially for stars with high β values, delivers flux differences of up to 30%with maximum in the near-IR. Continuum observations at these wavelengths are therefore anideal tool to discriminate between clumped and unclumped winds of OB supergiants. The spectra of hot stars show often excess emissionat IR and radio wavelengths that can be ascribed tofree-free and free-bound (ff-fb) emission from theirwind zones (see e.g. Panagia & Felli 1975).Waters & Lamers (1984) have investigated this ex-cess emission for λ ≥ µ m and winds with a β -lawvelocity distribution of varying β , pointing alreadyto the sensitivity of the wind emission to the chosenvelocity distribution.Over the last few years, two major effects have be-come obvious that both strongly influence the windcontinuum emission: (i) the winds of hot stars seemto be clumped, and (ii) many OB supergiants havewinds with 1 . ≤ β ≤ . β values is discussed, andlater on the effects of clumping are studied. The calculation of the continuum emission of a typ-ical OB supergiant is performed in three steps: (i)we first calculate the stellar emission of the super-giant with no stellar wind, (ii) then we calculatethe emission of the wind with the stellar parameters( R ∗ , T eff ) as boundary conditions, (iii) and finallywe combine the two continuum sources whereby thestellar emission still has to pass through the ab-sorbing wind. To simulate a typical OB supergiantwe adopt the following set of stellar parameters: T eff = 28 000 K, R ∗ = 27 . R ⊙ , log L ∗ /L ⊙ = 5 . g = 3 .
1. With these parameters we com-pute the stellar continuum emission with the code ofKub´at (2003), suitable for the calculation of NLTEspherically-symmetric model atmospheres. Table 1: Range of β values found for OB supergiantsin the Galaxy (Markova et al. 2004 = Ma;Crowther et al. 2006 = Cr; Kudritzki etal. 1999 = Ku) and the Magellanic Clouds(Evans et al. 2004 = Ev; Trundle & Lennon2005 = TL; Trundle et al. 2004 = Tr).Sp. Type β Ref.O4 – O9.7 0.7 – 1.25 MaO9.5 – B3 1.2 – 3.0 CrB0 – B3 1.0 – 3.0 KuO8.5 – B0.5 1.0 - 3.5 EvB0.5 – B2.5 1.0 - 3.0 TLB0.5 – B5 1.0 - 3.0 TrThe spherically symmetric wind is assumed to befully ionized, isothermal, and in LTE. This reducesthe problem to a pure 1D treatment of the simpli-fied radiation transfer (e.g. Panagia & Felli 1975).The electron temperature is fixed at 20 000 K, andthe density distribution in the wind follows from theequation of mass continuity, relating the density atany point in the wind to the mass loss rate and thewind velocity.The velocity of hot star winds can be approxi-mated with a β -law v ( r ) = v + ( v ∞ − v ) (cid:18) − R ∗ r (cid:19) β (1)where β describes the steepness of the velocity in-crease at the base of the wind, and v defines thevelocity on the stellar surface. A more detailed de-scription of the calculations will be given elsewhere.
1. Kraus, J. Kub´at & J. Krtiˇcka
The range in β found for galactic and MagellanicCloud OB supergiants is listed in Table 1. Increas-ing β means that the wind is accelerated more slowly.Consequently, the density in these regions is en-hanced because n e ( r ) ∼ ˙ M /v ( r ). These densitypeaks close to the stellar surface with respect to thewind density with β = 1 . M = 5 × − M ⊙ yr − , v ∞ = 1550 km s − , andwe calculate the continuum emission for β = 1 , β the wind creates a near-IRexcess, absorbs more of the stellar emission, and con-tributes to the total emission even at optical wave-lengths.Figure 1: Pronounced density peaks close to the sur-face (compared to the density for β = 1)that grow with increasing β . Hillier et al. (2003) introduced a formalism to ac-count for the presence of wind clumping, and in ourcalculations we use their filling factor defined by f ( r ) = f ∞ + (1 − f ∞ ) e − v ( r ) /v cl (2)and setting f ∞ = 0 . , v cl = 30 km s − , and v ( R ∗ ) = v thermal . Since f depends on the velocity distribu-tion, this filling factor is a function of radius as well,constructed such that it quickly reaches its termi-nal value (top panel of Fig. 3). This way of clump-ing introduction requests, however, that in order tomaintain the same radio flux, the mass loss rate has to be decreased, i.e. ˙ M cl = √ f ∞ ˙ M smooth , while theabsorption coefficient of the ff-fb processes increases, < κ > cl = f ( r ) − κ smooth , due to its density squareddependence. Our clumped models automatically ac-count for this mass loss reduction.At those positions in the wind where f ( r ) = f ∞ there is no difference between the clumped and theunclumped wind. However, in those regions where f ( r ) = f ∞ , which are also the regions where β hasits strongest influence, the wind opacity is sensitiveto the clumping. But while β enhances the density,clumping (for the same input ˙ M smooth ) reduces thedensity again. A wind with high β and clumping willtherefore have a different opacity in the innermostwind region than a wind with low β and clumping,and the clumped wind will have a different opacitythan the smooth wind. This is shown in the lowerpanel of Fig. 3 where we plotted the opacity ratioof the clumped with respect to the smooth wind fordifferent values of β . The higher β , the strongerthe effect. In Fig. 4 we compare the continuum of aclumped with an unclumped wind for β = 3 . β . Shown arethe stellar emission having passed throughthe absorbing wind (dotted), the ff-fbemission from the wind (dashed) and thetotal continuum (solid). Figure 3: Top: Filling factor for different values of β .Bottom: Opacity ratio between clumpedwind model and unclumped wind model.It is obvious that the clumped model generatesless wind emission for λ < µ m. For a better visu-alization we calculated the flux ratios between un-clumped and clumped models (Fig. 5). They showa maximum of up to 30% at near-IR wavelengths.Continuum observations at these wavelengths aretherefore an ideal tool to discriminate whether thewinds of OB stars with β > . β =3 .
0. The clumped model produces lesswind emission for λ < µ m, resulting ina lower total near-IR flux. For OB supergiants with high β values the ff andespecially the fb emission can strongly influence thetotal continuum, even at optical wavelengths.Clumping, introduced by the filling factor ap-proach, also influences the wind opacity and there- fore the continuum emission. Whether the wind ofan OB supergiant is clumped or not can be checkedbased on continuum observations in the optical andnear-IR region. Especially winds with high β arefound to have fluxes that differ by about 30% (seeFig. 5). The optical and near-IR continuum aretherefore ideal to discriminate between clumped andunclumped winds.Figure 5: Continuum flux ratio between the un-clumped and clumped wind models. Theratio increases with β having a maximumin the near-IR. Acknowledgements
M.K. acknowledges financialsupport from GA AV grant number KJB 300030701.
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