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?
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 &quot;systemic&quot; redshift, i.e. the &quot;average&quot; 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 $z = 0.35$.