How Do We Differentiate Between Relativity and Doppler Redshift?

[cannonball]

As I understand it, light will be redshifted when it travels from a large ( gravitationally speaking ) object to us. It will also be redshifted if the object is moving away from us. How do we know how much of the redshift is due to either effect ?

 

[russ_watters]

It is easily calculated from the mass of the object.

 

[Nereid]

As I understand it, light will be redshifted when it travels from a large ( gravitationally speaking ) object to us. It will also be redshifted if the object is moving away from us. How do we know how much of the redshift is due to either effect ?

Welcome to Physics Forums cannonball!

If all one could see of 'an object' were a point of light (or gammas, or IR, or radio waves, etc), then it would be hard to tell. However, the only 'point sources' outside the solar system are stars, and many of them have now been 'resolved' (we can 'see' them as fuzzy blobs, not just points of light). This means that we can understand the 'objects' which show up in images in terms of things like collections of stars, or gas clouds, etc. From this perspective, we can calculate the mass that would be required to produce an observed redshift, and compare it with we think is generating the light that we see. With few exceptions, these 'masses big enough to be responsible for the observed redshifts' are many, many orders of magnitude greater than what other observations suggest is actually there.

 

[marcus]

It is easily calculated from the mass of the object.

hey cannonball
what russ is saying, I think,

is that if you wanted to know the simple formula for calculating (say) the amount the sun's gravity redshifts light coming to us from the surface

then you simply have to ask him

it really is, as he says, easy to calculate
from the radius of the sun and the mass of the sun

the way to find out stuff at PF is to persistently ask

the people here do not automatically launch into lectures (most of them)
instead they depend on new people coming and asking questions

 

[russ_watters]

what russ is saying, I think,

is that if you wanted to know the simple formula for calculating (say) the amount the sun's gravity redshifts light coming to us from the surface

then you simply have to ask him...

the people here do not automatically launch into lectures (most of them)
instead they depend on new people coming and asking questions

Actually, I don't know it offhand - I was hoping someone else would pitch it in if cannonball really wanted it.

I sometimes just post a 'starter answer' to get things rolling (and sometimes a short, sweet answer is all that is wanted/needed.

 

[marcus]

$$\frac{\lambda}{\lambda_0} = \sqrt{\frac{1}{1 - \frac{2GM}{c^2 r}}}$$

 

[marcus]

(1 - 2GM/r c^2)^-1/2

$$\frac{\lambda}{\lambda_0} = \sqrt{\frac{1}{1 - \frac{2GM}{c^2 r}}}$$

there is a simple way to think about it,

there is this important length of 3 km, for the sun
which is the Schw. radius of a black hole with that mass
and it is

3 km = gravitational length for sun = $$\frac{2GM}{c^2}$$

the radius of the sun is 700,000 km

the redshift and some other interesting stuff depends on the ratio:

3 km/700,000 km

the formula just boils down to

$$\frac{\lambda}{\lambda_0} = \sqrt{\frac{1}{1 - \frac{3}{700 000}}}$$

the angle (in radians) that a grazing ray of light is bent by the suns gravity is just twice that same ratio, that is

6/700,000

it is a good ratio to know
and the gravitational length associated with a useful-to-know mass is sometimes
a useful-to-know length

 

[nickdanger]

As I understand it, light will be redshifted when it travels from a large ( gravitationally speaking ) object to us. It will also be redshifted if the object is moving away from us. How do we know how much of the redshift is due to either effect ?

For the sun the calculations are straight forward, but for other galaxies a lot of assumptions have to be made. I am new to this discipline but recently attended a lecture. They put a 'lensing tomography" map together setting galaxies in probable distance 'bands' by their redshift. They have to assume an amount of dark energy (71% of universe) is weak lensing, producing the redshift. They also have to assume the cold, dark matter model to begin with, so that foreground galaxies whose distance we know (and the amount of their associated dark energy which produces the weak lensing) are producing most of the redshift of galaxies further away. Now treating the bands as we would treat aperatures of a lense system, there is a certain 'distance aperature' value (which I don't understand) for each band that can be put into ratios to verify the weak lensing from dark energy and thereby properly space the bands of the tomography map.

Anyway, sorry if I am mistating any of this method I am mostly writing this expecting you experts to correct it. I am just trying to repeat from my notes from a colloquium (U. Penn, B. Jain). But it seems there are a lot of assumptions. The upshot of the talk is that the new astronomical scan projects will give us much more information to know if this method is even close to correct.

Also, review the thread on "Big bang is wrong". It posts an article saying that most of the redshift (even known redshift from the sun) is due to compton effect from electrons in the atmosphere around stars and not the doppler effect of receding galaxies as presumed by Hubble.

 

[marcus]

... sorry if I am mistating any of this method I am mostly writing this expecting you experts to correct it. I am just trying to repeat from my notes from a colloquium (U. Penn, B. Jain)...

It's great to get a report from a colloquium like that.
BTW I can see how the 'dark matter' included in clusters of galaxies
(and thought to constitute some 23 percent of universe overall)
could participate in lensing because the distribution of dark matter
is presumed to be bunched, but cannot see how 'dark energy' (the
estimated 73 percent overall) would contribute since it is generally
supposed to be more or less uniformly spread out----like a vacuum energy: so and so much per cubic meter----and not to clump together under the influence of gravity. But in some sense that is just a quibble about terminology, much of it recently minted.

Best not to count on folks expertise on any given topic, or that people will necessarily correct errors, this is an unabashedly relaxed board for much of the time. It's great to have someone posting here who goes to cosmology talks at U. Penn!
I am hoping for more such. Will try to comment or respond simply so as not to be purely on the receiving end.

 

[Labguy]

Here is a handy link: http://www.kingsu.ab.ca/~brian/astro/course/lectures/winter/chp13.htm that shows the formula for simple "Doppler redshift" and also corrections that need to be made for relativistic redshift. The site also has some handy redshift calculators you can click on and plug in different numbers to see the results. I think the charts there use 75 km/sec/mpc as Ho, but recent WMAP data has narrowed that a bit to be fairly certain at Ho = 71.