# How the mass loss rate by stellar wind is calculated for massive stars?

I have been searching for some examples about the different rates at which massive stars lose their mass by stellar wind, but I haven't been able to get anything other for the sun.

To be more specific, I want to find a example for a known star with mass between 20-40 solar masses.

• The title and text seem to be asking for very different things. Could you clarify? – dmckee --- ex-moderator kitten Jan 12 '14 at 16:48
• @dmckee sure, what I need to know is: at what rate does a star with initial mass of 20-40 solar masses lose its mass by stellar wind. – Abanob Ebrahim Jan 12 '14 at 16:55
• That depends enormously on what part of the star's lifetime you are talking about. I believe that at that mass is pulses toward the end of it's life, too. – dmckee --- ex-moderator kitten Jan 12 '14 at 17:18
• I am fairly certain mass-loss rate also depends on metallicity. – Kyle Kanos Jan 12 '14 at 17:40
• So are there any examples of known stars available ? – Abanob Ebrahim Jan 12 '14 at 17:53

Just for some context, mass loss rates are one of the larger uncertainties in our current understanding of stars. They're particularly important in the case of massive stars, like your 20-40 solar mass range. As far as I know, there aren't any first-principles calculations around. In stellar modelling, we usually use fits to observations. Here's a brief list of the relevant papers for certain phases of evolution:

As far as I know, these are "streaming" rates. i.e. continuous loss from the surface. There are times in a star's life (e.g. the thermally-pulsing asymptotic giant branch) where there can be substantial episodic mass loss.

Part of the work my research group does involves calculating mass-loss rates for hot, massive main sequence and post-main sequence O stars ($$\gtrsim20M_{\odot}$$), so I'll say a little bit about our methods.

The radiation-driven winds in these stars produce shocks through a phenomenon known as the line-driving instability. The shock heating in turn leads to x-ray emission, which is also influenced by absorption within the wind itself; this absorption is the key to how we determine the mass-loss rate of the star. The resulting spectrum has a number of key lines in the $$5Å<\lambda<25Å$$ range, which we typically fit with several free parameters: elemental abundances (we typically let O, N and C vary), the radius at which emission begins, and a parameter called $$\Sigma_*$$ defined by

$$\Sigma_*=\frac{\dot{M}}{4\pi R_*v_{\infty}}$$

where $$R_*$$ is the stellar radius and $$v_{\infty}$$ is the speed of the wind as $$r\to\infty$$. ($$\Sigma_*$$ is proportional to optical depth $$\tau_*=\kappa \Sigma_*$$, which is what affects absorption at different points in the wind.) $$R_*$$ and $$v_{\infty}$$ are typically already known, so once $$\Sigma_*$$ is fit, we get an easy expression for $$\dot{M}$$. Cohen et al. 2014 goes into the basic methodology in more detail than I've provided here, but this is essentially how we do it (they use $$\tau_*$$ instead of $$\Sigma_*$$).

Warrick cited Vink et al. 2001 as one of the major works on theoretical mass-loss rates for these stars (if not the key work!), and it certainly is. That said, over the past decade and a half there have been a number of indications that those predictions are inconsistent with observations, well beyond uncertainties. Vink et al.'s models predict mass-loss rates for many of these stars of $$\sim1$$-$$2\times10^{-6}M_{\odot}\text{ yr}^{-1}$$, while various diagnostics (involving not just x-ray but also UV and optical measurements) shift that downwards by a factor of 2-3 (Puls et al. 2006). $$\zeta$$ Ori is an example I like to quote, with $$\dot{M}_{\text{theory}}=1.2\times10^{-6}M_{\odot}\text{ yr}^{-1}$$ and, in sharp contrast, $$\dot{M}_{\text{obs}}=3.4\pm0.6\times10^{-7}M_{\odot}\text{ yr}^{-1}$$. The cause of the discrepancy is still unknown.