# How to calculate the redshift of a line in a bunch of line spectra?

If in a spectra, there are many lines, mixed with gravitational redshift and non-redshift lines. For example, in this paper, they identify lines both redshifted and no-redshifted. Then how can i distinguish those redshifted from those do not?

• Red-shift is not selective for frequency. Either the whole spectrum of a source is red-shifted, or nothing at all. The only type of lines which are NOT red-shifted are the absorption lines from Earth's atmosphere - and those can actually work nicely as calibration lines (though professionally you might want to use a iodine cell for more precision). For a rotating source you additionally have line-broadening. You might want to refine your question; what exactly gives you a problem in calculating red-shift when you have a line at wavelength $\lambda_z$ instead of $\lambda_r$. Jul 27 '20 at 13:25
• For a spectra, the lines can be rediated from different part of a source, so the lines can be both redshifted or no-redshifted. So i want to know the method to distinguish them.
– Chen
Jul 27 '20 at 14:17

While @planetmaker's comment is true if the lines come from the same source, you can have lines emerging from different physical processes which still appear to come from the same location.

An example is absorption (or more rarely emission) lines from galactic winds, which are typically blueshifted with respect to the "systemic" redshift, i.e. the "average" redshift of the galaxy. You can also have strong emission from an object — e.g. a supernova — that has a large peculiar velocity inside a galaxy.

In general, to distinguish lines with different redshifts, you need to have an idea of where you expect the lines to be (well, the same is true even if you just want to identify spectra where all lines are redshifted uniformly). In this case, the authors know which lines may be expected from the neutron star, namely highly ionized iron and oxygen lines, but the absorption features are then redshifted with respect to the rest of the spectrum.

For instance, the O VII Ly$$\alpha$$ line has a rest wavelength of 19 Å, but is seen at ~25.6 Å, i.e. a factor 1.35 higher, so its redshift is $$z = 0.35$$.

• Then how can they know for example 13.45A is highly ionized and redshifted Fe, not less ionized and un-redshifted Ne? Even if neay the neutron star both ionize degree and redshift are large, how can they identity them in such dense lines, just by experience or there are any criterion to do that?
– Chen
Jul 27 '20 at 15:03
• You have to look at your object as a whole and use knowledge about chemical composition and involved processes. In this case: iron is abundant in / around neutron stars as it is the end of the fusion line while neon is not. Add knowledge about energies involved you can calculate relative strength of emission or absorption lines. You cannot do this by looking a single line - you have to make use of the whole spectrum. Each element has its typical emission or absorption spectrum and it has to make consistently sense for all lines. Jul 27 '20 at 18:25
• Chen, @planetmaker is right. And if you think that sounds like a mess, given the large number of lines with different energies, I absolutely agree, but experienced observers have an amazing overview of all possible lines and, in particular, their relative strengths, given the values of temperature, density, pressure, and ionization field. You probably wouldn't see a study like this based on one line, but when several lines yield the same redshift and their relative strengths have sensible values, you can have a high confidence in the result.
– pela
Jul 27 '20 at 19:15
• Thank you pela and planetmaker. Now i see that redshift calculation is absolutely more depend on the experience of the observer to the spectrum and the related physical meaning of the source. So maybe i need to read more about these articles. Anyway, thank you so much for your explanation. :-)
– Chen
Jul 28 '20 at 3:07