Lecture #12a-- Stellar winds


1) Three types of winds
Most normal stars have winds, because they either have envelope convection zones that combine with rotation to produce magnetic dynamos and its resulting activity and high-temperature coronae, or they have high luminosity that can radiatively drive winds. The high-temperature winds are gas-pressure driven, and the high-luminosity stars produce winds driven by radiation pressure. The radiatively driven winds come in two flavors-- the cool evolved-star version, where the low temperatures allow dust formation and that provides the opacity to be radiatively driven, and the hot-star version, which takes advantage of high metal-ion opacity in the UV. The radiatively driven versions allow much higher mass-loss rates, because they supply much more energy capable of lifting the mass out of the stellar gravitational potential well. Indeed, radiatively driven winds from the hottest stars like Wolf-Rayet stars, and from cool AGB stars, often drive a billion times higher mass-loss rates than the Sun has with its gas pressure-driven wind.

2) Gas pressure-driven winds from cool stars
For gas pressure to drive a wind, it is necessary for the proton thermal speed to approach the escape speed of the star. For main-sequence stars, the escape speed is always in the range 500 - 1000 km/s (the Sun is about 600 km/s). For the protons to achieve speeds approaching that level requires temperatures of many millions of K. This is only possible because main-sequence stars have atmospheres with very short scale heights, so the density of their atmospheres drops precipitously. When the densities are so low, even a small amount of mechanical heating from magnetic activity suffices to raise the T past the thermal instability at about 200,000 K, and it then quickly rises to temperatures where convection is highly efficient at moving that heat out of the hot corona. By sheer coincidence, the T required to move the heat out by conduction is high enough to get a significant escape of protons and their electron cohorts, and create a wind. This type of wind does not have any particular importance to the ISM, however.

3) Radiation-driven winds from cool evolved stars
When a normal star evolves into a red giant for the second time, it becomes an asymptotic giant branch (AGB) star. These are very bloated and cool stars, and tend to be pulsationally unstable due to the kappa mechanism in the hydrogen ionization zone.

(Aside on the kappa mechanism-- this is a stellar interiors topic, but is explained so badly in so many places that I'll set the record straight here. Stellar atmospheres are marginally stable to adiabatic oscillations, because compression causes pressure increases. This is the cause of sound waves, and "acoustic mode" oscillations can get trapped in stellar envelopes (as in the 5-minute oscillations of the Sun). But these have to be constantly driven, and never achieve large pulsational amplitudes, because over time they gradually damp away and need to be replaced by newly excited modes. But if there is some input of heat during the compressed portion of the cycle, and removal of heat during the expanded portion, then work is done just as in an internal combustion engine, and instead of damping, this work will drive the pulsations to very large amplitude over many cycles. What adds heat is if the opacity increases when compressed, for this can trap radiative heat. Normally, when gas is compressed, its temperature and density rise, and these effects are having a fight to control the ionization changes. The temperature sensitivity of the ionization of the metals that are responsible for the opacity is rather strong, so the temperature effect normally wins, and compression causes metal ionization which usually reduces opacity, so no kappa mechanism. But if hydrogen or helium are partially ionized, their ionization is extremely temperature sensitive, and so tiny increases in T caused by the compression will induce significant increases in free electron density, over and above what compression alone would do, and this allows the density effect to win over the temperature effect and cause metal recombination. That normally increases the opacity, which yields the kappa mechanism. There is actually another rather different form of the kappaa mechanism wherein some narrow T regimes a metal, particularly iron, can have its opacity increase when it is more ionized, rather than the usual result of decreasing opacity, and this causes a kappa mechanism by itself-- because the T sensitivity of the ionization is now able to increase opacity upon compression, and the more subtle importance of rising electron density is not required as in the normal kappa mechanism in H and He partial ionization zones.)

Back to pulsating AGB stars. A classic example is a Mira variable, which has significant mass-loss rate (indeed Mira is herself a symbiotic star, which means she has a white dwarf companion that she is passing mass to). Such stars cool even further when they expand, and the T gets low enough to allow dust to form. Even though the Eddington parameter (the ratio of the radiative force on free electrons to the force of gravity, which is a benchmark for the strength of radiative forces in driving winds) is still rather low (though not nearly as low as the 10^-5 value it has for our Sun), the dust grains have a much higher cross section per gram than do free electrons, so the radiative force can exceed gravity and drive a wind. The star is so bloated that its potential well is not very deep, and its luminosity is high, so a significant mass-loss rate can be achieved without too high of an efficiency of conversion of radiative energy into wind energy. Mass-loss rates of up to 10^-4 solar masses per year can be achieved, which clearly has an important evolutionary effect on the star in a short time, and is responsible for planetary nebulae such stars generate (though binarity might be required to condition the PN into a geometry that makes it visible). This PN is rich with carbonaceous dust, with importance to the carbon content of the ISM-- which in turn affects its radiative cooling and formation of organic molecules like PAHs, and is of course also relevant to life on planets that may ultimately form.

4) Hot-star winds
Hot stars are both highly luminous (since the blackbody flux depends on surface T like T^4) and also emit a significant fraction of the starlight in the UV range, where metal opacities are quite high (hydrogen and helium are usually too highly ionized at radiation temperatures where their lines would be important). The Eddington parameter of hot stars is often as high as 0.5 or so, so even small opacity enhancements by the metal ions is sufficient to allow the radiative force to exceed gravity and drive a wind. The escape speeds from main-sequence hot stars can approach 1000 km/s, which means that winds from such stars will also be quite fast, perhaps up to 1% of the speed of light. This mitigates the usual problem with line opacity-- lines are very strong but also very narrow in frequency space, so radiative flux tends to flow out at frequencies between the lines, "missing" the line opacity. But in winds accelerating to 1% of the speed of light, each line sweeps out a region in frequency space of order 1% of the blackbody continuum, so it takes merely 100 strong lines in the wind to completely blanket the UV spectrum of the star. This prevents the flux from escaping betweeen the lines, and can allow for fairly efficient conversion of the stellar luminosity into wind energy, particularly for the densest winds-- those of Wolf-Rayet stars and the hottest O stars. Thus we see that these winds have a kind of "bootstrap" quality-- they cannot exist unless the lines are broad enough to intercept a significant amount of the starlight, and the lines are only broad enough to do that if the wind exists! This means the line opacity in effect "turns on" in the wind, which allows the static envelope of the star to remain static, and the "Eddington limit" is only exceeded in the moving wind, not the stationary envelope. A star with no wind would have no reason to have a wind, except that the potential for such a line-driven wind would be there, and nature seems to find a way to actualize that potential-- hot stars invariably do have strong winds, and the hottest main-sequence stars have strong enough winds that their mass-loss rates speed up their evolution as the star literally oblates a significant fraction of its own mass during its main-sequence lifetime. Since these winds are fast and massive, they contribute a lot of kinetic energy to the ISM, and can even rival the kinetic energy that is ejected in their eventual supernova. The wind material can also be enriched in CNO elements, for winds from more evolved hot stars like Wolf-Rayet stars. Finally, such winds can also create wind-blown bubbles in the ISM, which are a kind of slowly generated analog to SN remnants.