User:BSVulturis/sandbox

Note to stale draft editors: I haven't yet abandoned this, just got too busy in my real-life day job to make progress for a few months. (Yes, I worked on model stellar atmospheres once Long Ago, and taught the subject a couple of times.) Leave me a note on my talk page if you get a hankerin'. BSVulturis (talk) 02:11, 17 April 2019 (UTC)

The stellar atmosphere is the outer region of the volume of a star, lying above the stellar core, radiation zone and convection zone, being the layers from which the star's radiation can escape to interstellar space. The bottom of the atmosphere is defined to be the place in the star where the matter becomes tenuous enough that outward-going radiation can reach space without further interaction with the matter of the star. The atmosphere includes the photosphere, chromosphere, transition region, and corona, though not all stars are thought to have all of these. The last three can only be observed directly for the Sun, but can be detected spectroscopically for many stars similar to the Sun and cooler. Consequently, often a discussion of stellar atmospheres in general, or for atmospheres of specific stars other than the Sun, treats only the stellar photosphere.

Overview
Much of the understanding of stellar atmospheres is an extended analogy of the solar atmosphere. Only for the Sun can detailed atmospheric structure be observed directly and measured. For other stars the spectrum can be measured and often indicators of the parts of the atmosphere other than the photosphere detected. Generally, however, discussion of stellar atmospheres in general is usually restricted to mean treatments of the stellar photosphere.

The study of the atmospheres of stars is usually divided into two or three bins. Hot stars, by which is meant stars of spectral type A and earlier, are divided from cool stars (those of types F, G, K) because energy transport by convection is important in the cooler stars. There is no convection zone immediately below the atmospheres of the hot stars, and the higher radiative energy fluxes means that stellar winds and non-LTE effects are important in these stars, and many hot stars also rotate rapidly enough that the atmosphere structure varies appreciably with latitude. In the cooler stars, for all but the youngest stars rotation is not directly important to atmosphere structure, and energy transport is predominantly convective immediately below the atmosphere. When this is the case, convection gives rise to "activity" -- starspots and other magnetically-linked features -- in the photosphere, as well much of the observed transient phenomena in the chromosphere, the transition region, and the corona. In stars of type M, in the giants the stellar radii become large enough that the atmospheres may no longer be geometrically thin, while in dwarfs the magnetically-linked activity (flares) may dominate the radiation output from the star for brief intervals of time.

Grey atmosphere models
Early work on understanding the radiative transfer of energy and how it affects the structure of the atmospheres of the Sun and stars occurred early in the 20th Century. The simplest physical model of a stellar atmosphere is the grey atmosphere, which assumes that the opacity is independent of wavelength (so that the matter is "grey" in the sense of a neutral color"). This model can represent only the photosphere; the higher, more tenuous portions of the atmosphere cannot be represented with the approximations inherent to the grey atmosphere.  The atmosphere itself is assumed to have a vertical depth much smaller than the stellar radius, to have no important bulk motions, to be homogeneous in the horizontal directions, and that the populations of atomic (and ionic and molecular) states in the gas are given by the local temperature and the Boltzmann and Saha equations.  With these assumptions the problem is reduced to one dimension, the vertical height.  At every level in the atmosphere radiative equilibrium is assumed (that is, the net amount of radiative energy coming from below is equal to the net amount exiting upward), and that hydrostatic equilibrium holds, so that at every point the gas pressure is equal to the weight of the column of matter above it. The stellar effective temperature then sets the flux of energy through the atmosphere, the acceleration of gravity appropriate for the star blah blah,

The approximations going into the gray atmosphere are too simple to be realistic, but the similarity of the gray model to the gross observed structure of the Sun's photosphere is enough to be encouraging: the geometric depth is about right when the important opacity sources are identified and the appropriate Rosseland mean value is used, and the continuum limb darkening computed from the model is similar to that observed. One also can compute profiles for absorption lines in the model (assuming the constant continuous opacity, but allowing the line opacity to vary strongly with wavelength, computing the population of line absorbers at each depth in the atmosphere, and solving the radiative transfer over a number of wavelengths that adequately samples the line profile); the result obtains results qualitatively similar to many observed spectral lines in the solar spectrum.

The success of the gray model stems from the dominance of the bound-free opacity of the negative hydrogen ion in the solar atmosphere over the visible part of the spectrum, the wavelength interval in which most of the solar luminosity emerges.

Beyond the grey model
The next level of sophistication in stellar atmosphere models is to include explicit wavelength dependence in the opacity sources, use the Boltzmann and Saha equations to compute the number densities of the opacity sources as functions of depth, and solve the radiation transfer for many wavelengths, and integrate over wavelength to get the correct total radiation flux. This represents the state of the art in the 1970s....

The presence of chromosphere and corona can be determined from the presence of emission lines in the star's spectrum, most easily in the ultraviolet.

Through the photosphere, the temperature and matter density decrease steadily outward. Black-body radiation is released at each point with the thermal spectrum characterized by the temperature at that point. Radiation is absorbed at each point depending on the density of various opacity sources and the cross-section for absorption for each source.


 * The photosphere, which is the atmosphere's lowest layer, is normally its only visible part. Most of the light escaping from the surface of the star stems from this region and passes through the higher layers. The Sun's photosphere has a temperature in the 5,770 K to 5,780 K range. The minimum temperature point in the atmosphere lies at the top of the photosphere and defines the boundary between it and the chromosphere.  Starspots, cool regions of disrupted magnetic field lie on the photosphere.
 * Above the photosphere lies the chromosphere. This part of the atmosphere first cools down and then starts to heat up to about 10 times the temperature of the photosphere.
 * Above the chromosphere lies the transition region; in the Sun, the temperature increases rapidly in a distance of only around 100 km.
 * The outermost part of the stellar atmosphere is the corona, a tenuous plasma which has a temperature above one million Kelvin. While all stars on the main sequence feature transition regions and coronae, not all evolved stars do so. It seems that only some giants, and very few supergiants, possess coronae. An unresolved problem in stellar astrophysics is how the corona can be heated to such high temperatures. The answer lies in magnetic fields, but the exact mechanism remains unclear.

During a total solar eclipse, the photosphere of the Sun is obscured, revealing its atmosphere's other layers. Observed during eclipse, the sun's chromosphere appears (briefly) as a thin pinkish arc, and its corona is seen as a tufted halo. The same phenomenon in eclipsing binaries can make the chromosphere of giant stars visible.