The photosphere of a star is a layer from which of order half the photons can escape to infinity. It is often called the surface of a star for convenience. In fact, stars have no sharp surface: they just extend outward morphing into stellar winds.
The photosphere itself is NOT a sharp surface, but has a thickness defined in some way and the whole stellar atmosphere extends from a bit below the photosphere to well above: in fact, it is the thing that morphs into stellar winds.
For a cartoon of the solar atmosphere which an example of stellar atmospheres, see the figure below (local link / general link: sun_outer_layers_cartoon.html).
For characterizing stellar atmospheres,
we would like to have an average atmosphere temperature.
There are actually 4 kinds of average atmosphere temperature that can be mentioned.
If stars radiated exactly like a blackbody radiators from sharply defined surface (which would necessarily be a sharply defined photosphere), then the four kinds of the average atmosphere temperature would be exactly the blackbody radiator temperature. Since stars are only blackbody radiators to 1st order, the four kinds of average atmosphere temperature will NOT be equal in general, but they will usually be rather close to equal in some sense.
We explicate the four kinds of average atmosphere temperature in the subsections below.
A stellar atmosphere model inner boundary temperature is a basic parameter of stellar atmosphere and is obtained by fitting the stellar atmosphere model to observations of the star or star type you are modeling.
So the model inner boundary temperature is a model-dependent result and NOT a direct NOR an indirect observable.
We can explicate stellar atmosphere modeling a bit.
The simplest model of a stellar atmosphere is specified as follows:
The atmosphere model gives you among other things a temperature PROFILE for the stellar atmospheres that varies to 1st order only with radius.
Of course, atmosphere model fitted free parameters, temperature PROFILE, and other model results are only accurate insofar as your model fits the observations AND is sufficiently realistic to capture actual stellar atmosphere behavior.
More complex models can be developed for greater realism which means they give more accurate model results. But more complex models are harder to calculate.
An example of an stellar atmosphere model is the model of the Sun's atmosphere shown in the figure below (local link / general link: sun_atmosphere_model.html).
The effective temperature
is explicated in
the figure below
(local link /
general link: solar_spectrum_graph.html).
If we apply
Wien's law
to a stellar spectrum,
we obtain
a characteristic or sort of average
photospheric temperature
which we call the
Wien's-law
temperature.
Wien's law
is described in the figure below
(local link /
general link: wien_law.html).
For example,
Sun's
flux peak is
at ∼ 0.475 μ
(Solar Spectral Irradiance Handbook of Chemistry and Physics
82nd Edition Boca Raton, FL: CRC Press 2001.),
and so by Wien's law
we get T_W = (2897.7729 μ*K)/(0.475 μ) = 6100 K.
A general definition of
color temperature is:
The B-V color index
is the difference of the
B
and
V
magnitudes
which is roughly speaking the
ratio of
yellow
to blue
light.
The UBVRI passband system
is illustrated in the figure below
(local link /
general link: photometry_ubvri.html).
Because of the problem of
extinction
and other reasons, it usually better to determine temperature from
spectroscopy
and stellar atmosphere modeling
rather than
photometry if
one has
spectroscopy
available.
Answer 4 is a secondary definition.
One often says something like "the spectroscopy of
star X shows ...".
The accuracy of the fit depends on the physical realism of the model.
A crude model that gives a good fit is NOT usually very accurate.
A very realistic model that gives a good fit should give a
high accuracy photospheric temperature
as well as all the other details of the
stellar atmosphere.
But highly realistic
stellar atmosphere models are
demanding to create.
However, whole online catalogues of advanced
stellar atmosphere models
have been created and are always being improved.
Nowadays, one's computer searches the catalogues
and finds a match to your observations.
So it's all become rather easy.
However, even advanced models are NOT perfect.
A detailed model of the
Sun's atmosphere is illustrated in
the figure below.
Atmosphere models for the Sun
are particularly demanding if one wants to understand all of the
Sun's atmosphere.
We just know so much about the
Sun's atmosphere
that a complete model incorporating all we know is challenging to build.
UNDER RECONSTRUCTION BELOW
The color temperature
of a light source
is the temperature of
an ideal blackbody radiators
that radiates light
of a color comparable to
that of the light source
(Wikipedia: Color temperature).
In astronomy, we usually use
a more specific definition replacing
"color comparable to"
by "B-V color index equal to"
(Wikipedia:
Color temperature: Color temperature in astronomy).
Question:
Spectroscopy is:
Spectroscopy is done using
spectroscopes.
A spectroscope is illustrated in
the figure below
(local link /
general link: spectroscope.html).
Answer 3 and 4 are right, but answer 3 is the primary definition.
The process of determining the photospheric temperature
is to model the stellar atmosphere
and adjust the model atmosphere to get to fit to an observed spectrum.
File: Star file:
star_modeling_temperature.html.