GNU Astronomy Utilities

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2.2.6 Cosmological coverage

Having found the angular coverage of the dataset in Angular coverage on the sky, we can now use Gnuastro to answer a more physically motivated question: “How large is this area at different redshifts?”. To get a feeling of the tangential area that this field covers at redshift 2, you can use Gnuastro’s CosmicCalcular program (CosmicCalculator). In particular, you need the tangential distance covered by 1 arc-second as raw output. Combined with the field’s area that was measured before, we can calculate the tangential distance in Mega Parsecs squared (\(Mpc^2\)).

## If your system language uses ',' (not '.') as decimal separator.
$ export LANG=C

## Print general cosmological properties at redshift 2 (for example).
$ astcosmiccal -z2

## When given a "Specific calculation" option, CosmicCalculator
## will just print that particular calculation. To see all such
## calculations, add a `--help' token to the previous command
## (under the same title). Note that with `--help', no processing
## is done, so you can always simply append it to remember
## something without modifying the command you want to run.
$ astcosmiccal -z2 --help

## Only print the "Tangential dist. covered by 1arcsec at z (kpc)".
## in units of kpc/arc-seconds.
$ astcosmiccal -z2 --arcsectandist

## But its easier to use the short version of this option (which
## can be appended to other short options.
$ astcosmiccal -sz2

## Convert this distance to kpc^2/arcmin^2 and save in `k'.
$ k=$(astcosmiccal -sz2 | awk '{print ($1*60)^2}')

## Re-calculate the area of the dataset in arcmin^2.
$ n=$(aststatistics flat-ir/xdf-f160w.fits --number)
$ r=$(astfits flat-ir/xdf-f160w.fits -h1 | grep CDELT1   \
              | awk '{print $3}')
$ a=$(echo $n $r | awk '{print $1 * ($2*60)^2 }')

## Multiply `k' and `a' and divide by 10^6 for value in Mpc^2.
$ echo $k $a | awk '{print $1 * $2 / 1e6}'

At redshift 2, this field therefore covers approximately 1.07 \(Mpc^2\). If you would like to see how this tangential area changes with redshift, you can use a shell loop like below.

$ for z in 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0; do        \
    k=$(astcosmiccal -sz$z);                                  \
    echo $z $k $a | awk '{print $1, ($2*60)^2 * $3 / 1e6}';   \

Fortunately, the shell has a useful tool/program to print a sequence of numbers that is nicely called seq. You can use it instead of typing all the different redshifts in this example. For example the loop below will calculate and print the tangential coverage of this field across a larger range of redshifts (0.1 to 5) and with finer increments of 0.1.

## If your system language uses ',' (not '.') as decimal separator.
$ export LANG=C

## The loop over the redshifts
$ for z in $(seq 0.1 0.1 5); do                                  \
    k=$(astcosmiccal -z$z --arcsectandist);                      \
    echo $z $k $a | awk '{print $1, ($2*60)^2 * $3 / 1e6}';   \

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