How can redshifted light be detected?

Question

I've been reading about redshifts and it got me really curious. Basically, I want to figure out how we know light is redshifted and what's the original emitted light.

I found the following question here: Link

I understand the answer, but the answer focuses on an assumption that the light we get must have gone through hydrogen. You might say that we got the wavelengths calculated the same way for other elements and one of them will match. But my case is different.

Imagine light came to us and imagine it came to us without scattering in the hydrogen or any other matter during its travel (vacuum).

In that case, we got two different cases:

• case 1: light came to us from an object that didn't move away from us.
• case 2: light came to us from an object that moved away from us.

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• Q1: How do we know that in case 1, it's not redshifted and in case 2, it is?

• Q2: for case 2, how do we determine the original wave?

Answer 1

In a redshift (whether that be caused by relative motion, gravitation or cosmological expansion), all wavelengths are increased by the same factor.

Redshift is determined by identifying features in a redshifted spectrum on the basis of their relative wavelengths (the ratios $\lambda_1/\lambda_2$ etc. remain unchanged) and comparing those wavelengths to the known wavelengths those features would have at rest. The rest wavelengths are known because they can be generated in the laboratory!

If there are no features, then a redshift cannot be measured.

If there is one feature, e.g. an isolated emission line, then there can be ambiguity about the identity of that line and therefore what the redshift is.

Once you get several features then patterns of wavelength ratios can be found and this leads to a unique redshift determination.

It is worth mentioning that all of the above describes determining redshift using spectroscopy, which is the gold standard. Redshifts can also be estimated for galaxies by comparing their brightness in several wavelength bands with template brightness distributions that have varying redshifts applied to them. Often this matching is done using machine-learning techniques that have been trained on samples with spectroscopic redshifts. This is less precise, and can be inaccurate, but allows redshift estimates for galaxies that are too faint, or too numerous, to get spectroscopy.

Answer 2

If something has a perfect blackbody spectrum, with no lines corresponding to absorption by particular elements, then you can't tell. A blackbody that is emitting at 3000K is exactly the same as a blackbody that is emitting at 4000k, but is redshifted.

But such perfect blackbodies don't exist. Every star, galaxy, quasar, nebula (etc) in the universe has a spectrum that has absorption lines (or emission lines)

There's one big exception: the Cosmic Microwave Background. This looks exactly like a massive blackbody, filling the whole sky, at a temperature of 2.8 K. Rob's answer Why is the Cosmic Microwave Background evidence of a hotter, denser early Universe? explains how this can't be real (since a gas of hydrogen and helium is transparent to microwaves, so it must be a plasma of hydrogen filling the universe at a temperature of 3500K, but redshifted to look like 2.8K

So in the case of the CMB we can determine the original wave because we know the nature of the plasma that emitted the light. For literally every other object that is bright enough for us to determine a spectrum for, we can determine redshift by looking at absorption/emmission lines.

Answer 3

I think the answer to the question linked by the OP can be misunderstood. That answer says, "The light emitted by stars passes through various gases, these gases absorb very specific wavelengths of light." This is not referring to clouds of gas between the star and us. Rather, it is talking about to gases in the star between the layer where the light was emitted and the outer limits of the star.

In an old-school spectrogram, they would take the light from a star, send it through a prism or diffraction grating, and use it to expose black and white film. They would just look at the negative, and you would get a dark stripe where the starlight exposed the negative. (They use optics to make it wider than just a line, which the stretched-out image of a star would be.) To be precise, you get a dark stripe except for every frequency where some element in the star's atmosphere absorbs light. That part of the dark stripe is not exposed and you get a line across the width of the stripe. Each element produces a recognizable pattern of lines, and if the star is moving relative to you, those lines will be shifted towards the long or short end of the spectrum.

If there were a nearby cloud of hydrogen absorbing light from a distant galaxy, the absorption lines caused by that cloud would not be shifted. Or, if we did observe them to be shifted, it would tell us about the motion of the cloud, not the distant galaxy.

I think photons from distant galaxies tend to be too low-energy to get absorbed by nearby hydrogen. But it can happen with stars in our galaxy. This site gives an example of a binary star in our galaxy on the other side of an interstellar cloud of hydrogen. Each star had hydrogen lines that were shifted back and forth as the star moved towards and then away from us (as they orbited each other). But there were other hydrogen lines that just stayed in the same place. Those were from the gas cloud.

So, the bottom line is that you are totally correct that using red shift to calculate how fast things are receding would not work if it depended on random intervening gas to generate the absorption spectrum. But it's actually gas associated to the star (or the whole galaxy if it's far enough away to be measured as a unit) that matters.