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Velocity Density The effect of clumping on predictions of the mass-loss rate of early-type stars Lianne Muijres 1 , Jiri Krticka 2 , Alex de Koter 1 , Jorick Vink 3 , Joachim Puls 4 , Ines Brott 5 , Norbert Langer 5

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The effect of clumping on predictions of the mass-loss rate of early-type stars

Lianne Muijres1, Jiri Krticka2, Alex de Koter1, Jorick Vink3, Joachim Puls4, Ines Brott5, Norbert Langer5

1) Universiteit van Amsterdam, 2) Masaryk University, 3) Armagh Observatory , 4) Universitäts-Sternwarte München, 5) Universiteit Utrecht

  • Why study mass loss?
  • Through the course of their evolution, massive stars lose mass through radiation driven stellar winds, rotational shedding and possibly other eruptive mechanisms.
  • The total mass lost can be up to 90% of their initial mass. This has an important effect on the course of their evolution, the type of supernova explosion they will experience and the nature of the compact object left behind.
  • Therefore, it is important to study physical effects that occur in winds to determine their effect on the mass-loss rate.
  • Density and velocity perturbations might occur in stellar winds; we are studying the effect of these perturbations on the mass-loss rates in order to modify the current mass-loss predictions (e.g., Vink et al. 2000, 2005) for these effects.

Fig.1: Hubble image of Wolf-Rayet star WR 124; providing an observational motivation for studying density inhomogeneities in stellar winds.


  • Instability of radiation driven stellar winds
  • Winds of massive stars are driven by radiation line pressure. The general properties (density and velocity structure) are given by CAK-theory (Castor et al. 1975) and corresponding improvements (Friend & Abbott 1986, Pauldrach et al. 1986).
  • Mechanism is intrinsically unstable (Lucy & Solomon. 1970, Owocki & Rybicki 1984).
  • Therefore, the wind is predicted to be highly structured (i.e., clumpy),
  • whereas the (average) mass-loss rate should remain unchanged wrt. its corresponding stationary value (as predicted by the modified CAK-theory). See Fig. 2 for time-dependent hydrodynamic simulations (from Owocki 1994).
  • The effect of the perturbation on the ionization structure of the gas is not taken into account, this (amongst other effects) needs to be further investigated.

Fig.2: Time snap shot of line driven instability; density and velocity pattern are shown. The blue dotted and red dotted line show the stationary, smooth (from modified CAK-theory) density and velocity (resp.) profile of the wind (Owocki, 1994).

Handling clumping

Up to now, we assumed a smooth flow in our mass-loss predictions (de Koter et al. 1997, Vink et al. 2000). To deal with inhomogeneities in the flow, we introduced clumps described by a constant volume filling factor (fv). This means that each volume element is only filled for a fraction fv , and that the density in this part is enhanced by a factor 1/fv. The rest of the volume, i.e. the inter-clump matter, is assumed to be void (see Fig. 2). We calculated the ionization structure of the clumpy wind and then computed the mass-loss rate. We looked at optically thin clumps for continuum processes, but the clumps might be optically thick in lines. Line absorption is treated purely locally, within the Sobolev approximation.

We also investigated the case in which only the ionization is affected by the presence of clumps, but the effects of a clumpy medium on the effectiveness of the line driving is ignored.

  • Preliminary Results:
  • Effect on the mass-loss rates
  • Optically thin clumps: we find a drop of mass-loss rate with decreasing volume filling factor (See Fig. 3). We looked at three stars with different luminosity and found that with decreasing luminosity the effect of clumping on the mass-loss rate becomes stronger.
  • Our way of introducing clumping allows for many photons to escape without interacting. This prevents momentum and energy transfer from radiation field to gas. Therefore the mass-loss rate drops. There are some effect that we didn’t take into account yet. These effects may counteract this drop of the mass-loss rate (see future work).
  • Allowing for changes in the ionization-/excitation-structure alone (i.e. keeping line acceleration unmodified except for ionization/excitation effects) leads to an increase of mass-loss rate (See Fig. 4). The ionization structure changes in such a way that line absorption becomes more effective (clumping leads to increased recombination, and lower ions have more lines than higher ones). Thus, the mass-loss rate increases.

dM/dt ~ f0.74

dM/dt ~ f0.81

dM/dt ~ f1.06

Fig.4: The effect of the changed ionization structure on the mass-loss rate of a star of 20 Msun and 2.09∙105 Lsun. The mass-loss rate increases with decreasing volume filling factor.

Fig.3: The effect of clumping on the mass-loss rate for three stars of M = 20 Msun , Teff= 30000 K with different luminosities. The red circles belong to a star with L = 5.01∙105 Lsun, the green circles to L = 2.09∙105 Lsun, and the blue triangles to L = 7.94∙104 Lsun. With decreasing volume filling factor the mass-loss rate drops.

  • References
  • Castor et al., ApJ 195, 1975
  • De Koter et al., ApJ 477, 1997
  • Friend & Abbott, ApJ 311, 1986
  • Lucy & Solomon., ApJ 159, 1970
  • Owocki & Rybicki, ApJ 284, 1984
  • Owocki, Ap&SS 221, 1994
  • Pauldrach et al., A&A 164, 1986
  • Vink et al., A&A 362, 2000
  • Vink et al., A&A 442, 2005
  • Future work
  • Our study of clumping is not yet complete. Some effects still need to be studied :
  • clumps smaller than the line absorption region
  • a velocity dispersion in the clump
  • porosity effects
  • a radially dependent clumping factor
  • the dependence of clumping on metallicity (-> First Stars)