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This is the simplest case, which is currently implemented in CLASS. It is
defined as
 |
(42) |
The radio convention is the result of the first order term of the Taylor
expansion at
of
 |
(43) |
To check the accuracy of the approximation on
, let's use the
next term in this Taylor expansion, i.e.,
 |
(44) |
Differentiating this equation, we obtain the first order correction to the
velocity channel width
 |
(45) |
Let's now assume that we want an accumulated error over
channel to be
less than a given tolerance
. This yields
 |
(46) |
This is the criterion to change from the local universe representation
(using
) to the high redshift universe (using
). If we
want a tolerance of one tenth of channel (i.e.,
), we obtain
-
for
, i.e., 1000
wide
line at 100
resolution (e.g. local galaxies);
-
for
, i.e., 10
wide line
at 0.1
resolution (e.g., a local GMC);
-
for
, i.e., 100
wide
line at 0.1
resolution (e.g., a Galactic outflow).
This does not seem enough.
Next: Solution 2: Special relativity
Up: Going from the frequency
Previous: Going from the frequency
Contents
Gildas manager
2015-03-19