How would you distinguish between gravitational redshift and and redshift due to

Question

How would you distinguish between gravitational redshift and and redshift due to motion receding from the earth?

Explanation / Answer

Redshift is an expression of the shifting of absorption and emission lines in the measured spectrum of an object. To measure redshift (where redshift is expressed as the quantity z) we use z = (observed wavelength - emitted wavelength) / emitted wavelength or 1 + z = observed wavelength / emitted wavelength If z0 then it is redshifted. As has been said above, light-matter interactions such as with dust or scattering result in energy shifts in the radiation field and are generally referred to as "reddening". This means the whole spectrum is moved, rather than the absorption and emission lines shifting within the spectrum, and thus is easy to detect. Once a redshift measurement is made, it then has to be interpreted. This is done using different forms of mathematical transformation, depending on the type of object you are examining. This is the key. Basically, we have to decide what type of redshift(s) an object might have, and then apply the transformations to give us the relevent answers. Redshift alone cannot tell us the story, we have to use our current assumptions about an object to work out the values. If there are 2 mechanisms that may impart redshift on an objects spectrum we have to use other means to work out what proportion is caused by what form of redshift. If z > 0.1 then the redshift is almost totally dominated by cosmological redshift, caused by the expansion of space. Galaxies aren't moving very much, inertially, relative the apparent movement caused by the expansion of space. Galaxies seem to have a tendency to cluster together and move around each other a bit, but this movement is very small when compared to the amount they seem to have moved away from us. There, I said it twice! We know of a few different forms of redshift: Doppler redshift (also known as Doppler-Fizeau effect), Relativistic Doppler Redshift (which is a more complete form of doppler, taking relativity into account), Cosmological redshift and Gravitational redshift. Gravitational red shifts are generally very small, and you only get very large ones from the light emitted near neutron stars or black holes - environments you can independently confirm from other observations. With the exception of the sun, no gravitational red shifts have been detected for ordinary stars, but they ought to be present if we had good enough instruments. Mainly, to distinguish gravitational redshifts from other kinds, you compare the size of the object with its mass to determine how much larger it is than its black hole radius. Objects like nebulae and entire galaxies are trillions of times larger than their BH radius, so the magnitude of the redshift is 1 part in a trillion. Normal stars are only a few hundred thousand times larger than their BH radius, so light from their surfaces is at the limit of being able to detect, spectroscopically, such a gravitational redshift. Neutron stars and white dwarfs are about 10, and 3000 times larger than their BH size so gravitational redshifts are of the order of 1 part in 10 to 1 part in 1000. Cosmological redshifts are only important and easily distinguishable for rather distant galaxies, but can get mixed up with the Doppler shift from the regular spatial motions of galaxies. Cosmological redshifts are only seen unambiguously at distances of billions of light years. At nearer distances, ordinary Doppler shifts from galaxian motion with respect to a local center of mass (galaxy cluster) is comparable to the cosmological effect and you have to disentangle the two contributions very carefully.

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