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Probably this is a extremely basic question, but after a lot of time searching about it without results (in all the sites/publications i've found they only use this term but there is no specific definition)i came here with the hope of get an answer to my question: in the context of chemical abundance in stars, what is a differential abundance?

I already know what is a chemical abundance, the question is simply about the implication of the "differential" word.

Specifically, my doubt emerged when i was reading this publication. In the second paragraph of the section 3.2 "Stellar Parameters" is the first encounter with this concept:

We adopted the same line list as in Ramírez et al. (2014). The EW measurements were used to obtain elemental abundances with the abfind driver of MOOG (Sneden 1973), using Kurucz model atmospheres (Castelli & Kurucz 2004). Then, line-by-line differential abundances were obtained.

The stellar parameters $(T_\text{eff}, \log g, {\rm[Fe/H]}, v_t)$ of HIP 68468 were determined by imposing a differential spectroscopic equilibrium of iron lines relative to the Sun (e.g. Meléndez et al. 2014a), using as initial parameters the values given in Ramírez et al. (2014). The solar values were kept fixed at $(T_\text{eff}, \log g, v_t) = \rm (5777\,K, 4.44\,dex, 1.0\,km\,s^{-1})$. Our solution for HIP 68468 gives consistent differential abundances for neutral and ionised species of different elements, and also for atomic and molecular lines, as discussed in more detail in the next section.

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If the line emission is optically thin, then the measured line flux is proportional to the abundance $F_{\nu} \sim n$ of a species along the line of sight (if it's only one species).

The problem here is that $F_{\nu}$ needs to be measured relative to a baseline. If that fails, e.e. when the stellar signal is too noisy, one doesn't know what this should be. But a measurment at two different wavelengths $\nu$ and $\nu'$ that lie reasonably close together, can at least yield a difference in abundances $F_{\nu}-F_{\nu'} \approx n-n'$ relative to this unknown base level.
This allows then to construct an atmospheric model, up to the unknown base level, which one can try to fix with other physical arguments.

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