... study

Appendices A to D are only available in electronic form at http://www.edpsciences.org

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... extensions

This is in no way contradictory with the assumption that all lines of sight considered are parallel. The cloud is supposed to be infinite, but only a small fraction of it is observed and supposed to be representative of the whole.

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... nonzero

The case v₀=0 is only special in the way the calculations are performed, as the end result amounts to setting v₀ to zero in the general formulæ. This is shown in Appendix B.

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... support

If any continuum emission is present, it should first be removed.

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... terms

In these integrated fluctuation terms, we chose to denote the position $\vec{X}$ on the plane of the sky as a subindex, rather than as an argument, to allow for concise equations in the subsequent developments.

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... field

It should be stressed that no hypothesis is made on the strength of velocity fluctuations, so that scaling them to the mean velocity v₀ is merely a convenient way to symmetrize expressions, and should not be given too much importance. We are aware, however, that the sound speed would be a much more physically meaningful velocity scale, and it will be used as such when the mean velocity is zero (see Appendix B).

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... by

We chose to write  $B_{\rho ,\rho }$ instead of using the more consistent notation  $A_{\delta\rho}$ for the autocorrelation function of the density fluctuations, because, in the following developments, higher order and multipoint correlation functions of mixed fields arise for which the  $A_\mathcal{F}$ notation would have become cumbersome.

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