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Astronomy/How do we really know what stars are?


All we are receiving from the objects we call stars is energy signals (light, gamma rays, etc.).  We have our nearby Sol that we can study "daily", but the likelihood of getting anywhere near another star is very remote.  What proof do we have that that stars are really big balls of thermonuclear activity?  How can we be sure they are not just spots of energy in a distant spherical shell akin to the star light bulbs in "The Truman Show"?


Interesting question- after I had to radically  alter my mental perspective!This perception is in fact quite ancient and was more or less how the Sumerians and others perceived the stars, as "spots of light" on a dome. But this was before the advent of modern physics and an array of highly sophisticated devices, including spectrophotometers, photo-multipliers, interferometers and the like - which enable us not only to discern the chemical composition of distant stars but their level of energy emission.

But instrumentation is only one part of the picture- physical theory had to also advance- and this arrived with the development of self-consistent stellar models, stellar nuclear theory and nucleosynthesis. For example, the amount of energy liberated by a given star depends on the mass: the greater the mass, the more rapid the nuclear transformation to radiant energy, and this affects the stellar lifetime and also the type of reactions in the star's core.

A key quantity in obtaining these stellar energy generation time scales is the energy liberated per (nuclear fusion) chain defined as: W(r) = rE, or W = (rE)/ r which is in ergs/gram for example. (I.e. the total ergs of stellar energy given off per gram of stellar matter available for reaction.)

E is found from specific nuclear fusion reactions, such as p + p -> D2 +e(+) +v, where two protons fuse to yield deuterium, a positron and a neutrino(v). The key quantity is r, defined as the reactions/cm3. Obviously, the greater this value the shorter the energy generation time scale and the smaller the value the longer it will take. It is defined (see, e.g. Astrophysical Concepts, p. 331, by Martin Harwitt:

r = B (r)^2  X1X2/ T^1.5 * exp^-3{2π^4e^4mH (Z1^2)(Z2^2)A'/ h^2kT}^1/3

where B is a proportionality constant, r is the density, h is Planck's constant (e.g. h = 6.62 x 10^-27  erg-sec), k is Boltzmann's constant = 1.38 x 10^-16 erg/K), T is absolute temperature of the reaction, i.e. in K deg, and X1 and X2 are the concentrations associated with atomic numbers Z1, Z2 while A' is the reduced atomic mass, i.e. A' = (A1 A2)/ (A1 + A2).

Then working out 'r' for the proton-proton fusion cycle one can (after a lot of work) obtain the time scales for each chain part and the energy yielded for each, viz. (cf. Harwit, op. cit., p. 336):p + p -> D2 +e(+) +v (1.44 MeV, Time = 14 x 10^9   yrs.)

For the other 'sub'-reactions:

D2 + p -> He3 + y(gamma ray) [5.49 MeV, time = 6 secs)

He3 + He3 -> He4 + 2H1 [12.85 MeV, Time - 6 million years]

Note that the last branch of the cycle already takes 6 million years, i.e. for each fusion to furnish 12.85 Mev (millions of electron volts of energy, were 1 eV = 1.6 x 10^-19   J).

All This is important because it tells us how long a star has on the Main Sequence, and also (using HR diagrams) what the expected luminosity and surface temperature are if it is on the Main Sequence. From this, one can also deduce the radius of the star, e.g.

L = 4π R^2 (T_eff)^4

SO that knowing the effective (surface) temperature, T_eff,and knowing the luminosity L, one can solve algebraically for R.

From such values of R (including from stellar interferometer measurements, more applicable to the nearer stars), we can indeed discern the stars are not tiny little pin points of energy but vast suns in their own right, many (like Antares) much larger than our own and others - e.g. Sirius- much hotter as well as more massive.

This, of course, is only a very brief outline. If you are up to it, you can also check out some of my (related) answers on the astrophysics forum, for example:

to do with using measured stellar radius and other parameters to obtain the flux, 'solar constant':

(Note: The (B- V) indices are obtained from spectrophotometer measurements.)

The way in which we assess the radiation intensity emerging from a plane parallel stellar stmosphere is more technical -  based on the equation of transfer,e.g.

As you can gather, much of what we have and the way we get it is based on highly technical physics, measurements.

But that's what has been needed to show we're not partaking of any cosmic "Truman show"!

A good intermediate level text to get is Jeahn Dufay's 'Astrophysics and the Stars' (Dover) if we you really want to delve into the nitty gritty.

Note: Feel free to Google any unfamiliar terms that appear in this response. Googling such terms saves time in providing a response, making it shorter, and also enables you to expand your own knowledge beyond what's given here.  


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Philip Stahl


I have more than forty years of experience in Astronomy, specifically solar and space physics. My specialties include the physics of solar flares, sunspots, including their effects on Earth and statistics pertaining to sunspot morphology and flare geo-effectiveness.


Astronomy: Worked at university observatory in college, doing astrographic measurements. Developed first ever astronomy curriculum for secondary schools in Caribbean. Gave workshops in astrophysics and astronomical measurements at Harry Bayley Observatory, Barbados. M.Phil. degree in Physics/Solar Physics and more than twenty years as researcher with discovery of SID flares. Developed of first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Develop first ever loop solar flare model using double layers and incorporating cavity resonators.

American Astronomical Society (Solar Physics and Dynamical Astronomy divisions), American Mathematical Society, American Geophysical Union.

Solar Physics (journal), The Journal of the Royal Astronomical Society of Canada, The Proceedings of the Meudon Solar Flare Workshop (1986), The Proceedings of the Caribbean Physics Conference (1985). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'. 'Astronomy and Astrophysics: Notes, Problems and Solutions'.

B.A. Astronomy, M. Phil. Physics

Awards and Honors
American Astronomical Society Studentship Award (1984), Barbados Government Award for Solar Research (1980), Barbados Astronomical Society Award for Service as Journal Editor (1977-91)

Past/Present Clients
Caribbean Examinations Council, Barbados Astronomical Society, Trinidad & Tobago Astronomical Society.

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