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Interpretation 3: At fixed
and fixed
Let's assume that we are interested to detect a given bright line, e.g.,
CO(1-0), at high redshift but the redshift of the source is unknown and/or
their would be a forest of this line at different redshift for the same
line of sight. We can also assume that the parcel of gas is at the same
local velocity (an interesting particular case being when the parcel of gas
is at rest) in the different source frames corresponding to the different
redshift. We thus wish to associate a redshift axis to the set of
brightnesses,
. To do this, we use
 |
(30) |
and, after differentiation,
 |
(31) |
This yields
 |
(32) |
 |
(33) |
The sign in the definition of
ensures that an increase of
implies an increase of
(
). Moreover, the non-linear
character of this axis comes from the fact that the spectral axis is
regularly sampled in frequency unit while the adopted redshift definition
is the optical one. We retrieve a linear axis
 |
(34) |
With current heterodyne detector in millimeter radioastronomy, the last
condition is difficult to satisfy as the radiofrequence bandwidth can cover
a significant fraction of the tune frequency, at least in the 3
band.
The non-linear formula is thus useful in CLASS.
Next: Validity of the radio
Up: Interpreting the spectral axis
Previous: Interpretation 2: At fixed
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2015-03-01