How do we find the exact temperature of a star/galaxy?

[Yashbhatt]

This is a very basic question, but I am a little confused. As far as I know, the temperature of a star is analyzed based on the color of the light it emits. So, if a star is moving away from us, then the light emitted by it will be redshifted(or if it is stationary with respect to us and the light undergoes gravitational redshift), then how do we know the exact temperature of that star or any other object because it is possible that we observe red light but actually the star might be emitting yellow light.

 

[Bandersnatch]

Well, all you need to do is calculate redshift before calculating temperature.

 

[Yashbhatt]

But how do you do it? If the object is traveling uniformly with respect to us, then we wouldn't know if it is actual spectrum or the redshifted spectrum.

 

[Bandersnatch]

What you do, is you look at the stellar spectrum and identify the characteristic absorption lines. A stationary element(e.g., a hydrogen atom) always produces the same set of spectral lines associated with the discrete energy levels of its electrons.

By comparing the lines to lines produced by atoms in laboratory, you can find out the redshift.

More here:
http://en.wikipedia.org/wiki/Astronomical_spectroscopy
and about spectral lines:
http://en.wikipedia.org/wiki/Atomic_structure#Energy_levels
here you can see the spectral lines of a hydrogen atom:
http://en.wikipedia.org/wiki/Hydrogen_spectral_series

 

[Drakkith]

But how do you do it? If the object is traveling uniformly with respect to us, then we wouldn't know if it is actual spectrum or the redshifted spectrum.

As Bandersnatch said, we use emission and absorption lines of known elements to calculate the amount of redshift or blueshift an object has. Then we can correct for it and calculate the correct temperature.

 

[Yashbhatt]

Suppose we have redshifted spectra of hydrogen. Then, can't we say that the star contains some material which emits light similar to hydrogen but slightly at the red end?

 

[D H]

There is no such material. Astronomers don't look at just one spectral line; one line by itself supplies no information. Several lines do supply information. There is no substance that mimics the spectra of hydrogen.

 

[Yashbhatt]

I found thishttps://ca.answers.yahoo.com/question/index?qid=20140111123552AA01t4e. See the third answer on that page. Is that what you are trying to say?

 

[Mordred]

not a very good site to look at lol. All right think of it this way, when a new star is being studied. The first question you need to answer is how far the star is from us. So you determine its redshift, then you need to determine its motion, to isolate redshift due to motion, as well as any potential gravitational redshift. This will isolate the cosmological redshift which is due to expansion. Keep in mind you need to confirm that distance by other means other than redshift, often done by types of parallex or using nearby standard candles. Then you measure the stars Luminosity. There is a relation of a stars luminosity to its temperature, however you also need its spectrum analysis to determine the stars composition to correctly determine the stars temperature, both these measurements are affected by the redshift. All forms of redshift can influence these measurements.

Luminosity is often measured in flux where flux is

$$f=\frac{L}{4\pi r^2}$$

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a difference of 100 flux.

there is also a luminosity to distance relation

$$d^2=\frac{L}{4\pi b}$$

b is the stars apparent brightness.

Other luminosity relations include, luminosity to mass
http://en.wikipedia.org/wiki/Mass–luminosity_relation

but there is also a luminosity to radius to temperature relation. This is primarily the surface temperature of the star, and is an approximation only, knowing the stars composition and volume (Density) can refine the temperature analysis by using the ideal gas laws, however those calculations can get intense. The luminosity to radius to temperature relation is as follows (at least the one I'm familiar with, been a while)

$$L=R^2*T^4$$

here is a good article covering distance measurement according to the cosmic distance ladder, as no one method is suitable to confirm redshift at various distance scales.

http://terrytao.files.wordpress.com/2009/09/cosmic-distance-ladder1.pdf

here is a technical detail concerning the various influences on measurements of the intergalactic medium including stars.
"physics of the intergalactic medium" Highly technical but it covers the various measurement methods and possible errors in those measurements as understood today
http://web.physics.ucsb.edu/~phys233/w2014/errata_p1.pdf

Keep in mind the method I described is only an approximation, The physics of the intergalactic medium is far more accurate and refined to temperature vs a stars composition

 

[Mordred]

Forgot to add, in order to determine a stars exact temperature, you need to know the

Stars mass, composition (spectrum analysis), distance, influence of redshift upon measurements, density, volume, how each element absorbs temperature, viscosity, turbulence influences, understanding of nuclear fusion. All these details including any I missed is covered in the physics of the IGM article. However essentially the calculations involve careful applications of the ideal gas laws. Needless to say we never get exact, we only get better and better approximations, that depend on our degree of detail and understanding

 

[Drakkith]

Spectral lines are unique to every element. They are like fingerprints. No two elements are the same. It's important to understand that we know why and how these lines are created, so we are certain that there is no material that will emit that specific pattern of lines other than one specific element.

 

[Yashbhatt]

How do we find the mass of the star? Universal Gravitational law?

 

[Drakkith]

How do we find the mass of the star? Universal Gravitational law?

Sometimes. If the star is part of a multi-star system, especially binary systems where we can see both stars, it is easy to find the mass by observing the orbital period of the stars around their common barycenter.

 

[Yashbhatt]

And what about the other times?