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Going from the frequency to the velocity axis

The velocity scale is only meaningful locally (i.e., at small values of $(\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}})\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{}}}}$) around a given rest frequency, \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}. It is thus legitimate to use a linear relation between the frequency and the velocity axis. There are 3 possibilities depending on the approximation used to defined the systemic velocity. We stress that all these possibilities are equivalent for observations of the high redshift universe because, in this case, \ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} and thus \ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} are zero valued.



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Gildas manager 2015-03-01