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

Abstract

Context. Mass loss from massive stars forms an important aspect of the evolution of massive stars, as well as for the enrichment of the surrounding interstellar medium. Aims. Our goal is to predict accurate mass-loss rates and terminal wind velocities. These quantities can be compared to empirical values, thereby testing radiation-driven wind models. One specific topical issue is that of the so-called "weak-wind problem", where empirically derived mass-loss rates and (modified) wind momenta fall orders of magnitude short of predicted values. Methods. We employ an established Monte Carlo model and a recently suggested new line acceleration formalism to solve the wind dynamics more consistently. Results. We provide a new grid of mass-loss rates and terminal wind velocities of O-type stars, and compare the values to empirical results. Our models fail to provide mass-loss rates for main-sequence stars below a luminosity of log(L/L ) = 5.2, where we appear to run into a fundamental limit. At luminosities below this critical value there is insufficient momentum transferred to the wind in the region below the sonic point in order to kick-start the acceleration of the flow. This problem occurs at almost the exact location of the onset of the weak-wind problem. For O dwarfs, the boundary between being able to start a wind, and failing to do so, is at spectral type O6/O6.5. The direct cause of this failure for O6.5 stars is a combination of the lower luminosity and a lack of Fe v lines at the base of the wind. This might indicate that -in addition to radiation pressure -another mechanism is required to provide the necessary driving to initiate the wind acceleration. Conclusions. For stars more luminous than 10 5.2 L , our new mass-loss rates are in excellent agreement with the mass-loss prescription by Vink et al. (2000, A&A, 362, 295) using our terminal wind velocities as input to this recipe. This implies that the main assumption entering the method of the Vink et al. prescriptions -i.e. that the momentum equation is not explicitly solved for -does not compromise the reliability of the Vink et al. results for this part of parameter space. Finally, our new models predict terminal velocities that are typically 35 and 45 percent larger than observed values. Such over-predictions are similar to those from (modified) CAK-theory.

The 2.35 year itch of Cygnus OB2 #9

“…Finally, we note that Muijres et al (2012) provide improved mass-loss rate estimates compared to the Vink et al (2001) recipe. The revised mass-loss rates of the primary and secondary are a factor ∼2 lower, and the terminal velocities a factor ∼1.4 higher than the ones listed in Table 3.…”

Mass-loss predictions for evolved very metal-poor massive stars

“…To determine mass-loss rates, we use an iterative method, as developed by Müller & Vink (2008) and Muijres et al (2012), in which isa-wind model atmospheres (de Koter et al 1993) are used to describe the model atmosphere and mc-wind models (de Koter et al 1997;Vink et al 1999) to treat the wind dynamics. The latter uses a Monte Carlo approach based on the method developed by Abbott & Lucy (1985).…”

“…The procedure followed is based on the method described by Müller & Vink (2008) and Muijres et al (2012), that improve on the treatment developed by de Koter et al (1997) and Vink et al (1999), and applied by Vink et al (e.g., 2000Vink et al (e.g., , 2001) Actually, the Müller & Vink and Muijres et al studies present two approaches to deal with the equation of motion. In one solution, referred to as best-β method, the velocity law is assumed to be a β-law (Lamers & Rogerson 1978).…”

“…In the other solution the fit function to the line force is used to numerically solve the equation of motion, referred to as the hydrodynamical method. Both methods are compared in Muijres et al (2012), where it is found that the derived mass-loss rates do not differ more than about 25 percent and that the terminal wind velocities agree within 20 percent.…”

Long term variability of Cygnus X-1

“…These high velocity winds that can reach terminal velocities ∞ > 2000 km s −1 (e.g., Muijres et al 2012) are perturbed and clumpy (Owocki et al 1988;Feldmeier et al 1997;Puls et al 2006;Oskinova et al 2012; with over 90% of the wind mass concentrated in less than ∼10% of the wind volume (Sako et al 1999;Rahoui et al 2011, for Vela X-1 and Cyg X-1, respectively). Binary systems consisting of an O/B-type giant and a compact object offer us the unique chance to investigate these winds by using the X-ray source as a test probe.…”