Predictions of the effect of clumping on the wind properties of O-type stars

Abstract

Aims. Both empirical evidence and theoretical findings indicate that the stellar winds of massive early-type stars are inhomogeneous, i.e., porous and clumpy. For relatively dense winds, empirically derived mass-loss rates might be reconciled with predictions if these empirical rates are corrected for clumping. The predictions, however, do not account for structure in the wind. To allow for a consistent comparison, we investigate and quantify the effect of clumpiness and porosity of the outflow on the predicted wind energy and the maximal effect on the mass-loss rate of O-type stars. Methods. Combining non-LTE model atmospheres and a Monte Carlo method to compute the transfer of momentum from the photons to the gas, the effect of clumping and porosity on the energy transferred from the radiation field to the wind is computed in outflows in which the clumping and porosity stratification is parameterized by heuristic prescriptions. Results. The impact of structure in the outflow on the wind energy is complex and is a function of stellar temperature, the density of gas in the clumps, and the physical scale of the clumps. If the medium is already clumped in the photosphere, the emergent radiation field will be softer, slightly increasing the wind energy of relatively cool O stars (30 000 K) but slightly decreasing it for relatively hot O stars (40 000 K). More important is that as a result of recombination of the gas in a clumped wind the line force increases. However, because of porosity the line force decreases, simply because photons may travel in-between the clumps, avoiding interactions with the gas. If the changes in the wind energy only affect the mass-loss rate and not the terminal velocity of the flow, we find that the combined effect of clumpiness and porosity is a small reduction in the mass-loss rate if the clumps are smaller than 1/100th the local density scale height H ρ . In this case, empirical mass-loss determinations based on Hα fitting and theory match for stars with dense winds (Ṁ > ∼ 10 −7 M yr −1 ) if the overdensity of gas in the clumps, relative to the case of a smooth wind, is modest. For clumps larger than 1/10th H ρ , the predicted mass-loss rates exhibit almost the same dependence on clumpiness as do empirical rates. We show that this implies that empirical and predicted mass-loss rates can no longer be matched. Very high overdensities of gas in clumps of such large size may cause the predictedṀ to decrease by a factor of from 10 to 100. This type of structure is likely not to be the cause of the "weak-wind problem" in early-type stars, unless a mechanism can be identified that causes extreme structure to develop in winds for whichṀ < ∼ 10 −7 M yr −1 (weak winds) that is not active in denser winds.

Mass loss from inhomogeneous hot star winds

“…These analytic scalings are qualitatively consistent with the numerical simulations by Muijres et al (2011), who modeled the effects of clumping and porosity in velocity space by using a smooth wind velocity law and assigning clump length scales 5 l, and found general trends of higher mass-loss rates from the shifted ionization balance and lower rates from the inclusion of velocity porosity. A detailed comparison is not possible, however, since their Monte-Carlo models only predict the total wind kinetic energyṀ 2 ∞ , and so cannot separate between a change in terminal wind speed and a change in mass-loss rate.…”

“…In O stars with δ ≈ 0.1 (e.g., Pauldrach et al 1986), the latter results in an upward corrected rate by approximately 25%, assuming a typical volume filling factor f vol ≈ 0.1. Physically, this results from the increased amount of recombination in such clumped models, which drives the ionization balance toward lower ion stages with more efficient driving lines (see also Muijres et al 2011). …”

Predictions for mass-loss rates and terminal wind velocities of massive O-type stars

“…The reason for the over-predicted ∞ values is unclear. Possible explanations (for part of the problem) include, i) overestimated corrections for the effect of turbulence (see above); ii) a clumped and porous outer wind, hampering the acceleration of the flow in this part of the outflow from reaching as high a terminal velocity as predicted here and in (modified) CAK (see Muijres et al 2011); or iii) a systematic over-estimate of stellar masses. A systematic discrepancy between masses of galactic stars derived from comparing their positions in the Hertzsprung-Russell diagram to evolutionary tracks and masses calculated from the spectroscopically determined gravity was reported by e.g.…”

Grids of stellar models with rotation

“…In that case we keep to the Vink et al (2001) prescription until the WR prescription becomes higher. These mass-loss rates account for some clumping effects (Muijres et al 2011) and are a factor of 2-3 lower than the rates used in the standard 1992 grid. -When, for massive stars (>15 M ) in the RSG phase, some points in the most external layers of the stellar envelope exceed the Eddington luminosity of the star (L Edd = 4πcGM/κ, with κ being the opacity), we artificially increase the massloss rate of the star (computed according to the prescription described above) by a factor of 3 so that the time-averaged mass-loss rate during the RSG phase for 20 and 25 M stars is of the order of the mass-loss rates estimated by van Loon et al (2005) for RSGs.…”