[bug #65254] Non-flat cases of angular diameter distance

[Boud Roukema]

URL:
  <https://savannah.gnu.org/bugs/?65254>

                 Summary: Non-flat cases of angular diameter distance
                   Group: GNU Astronomy Utilities
               Submitter: boud
               Submitted: Sun 04 Feb 2024 04:26:25 PM UTC
                Category: None
                Severity: 3 - Normal
              Item Group: Output not reasonable
                  Status: None
                 Privacy: Public
             Assigned to: None
             Open/Closed: Open
         Discussion Lock: Any


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Follow-up Comments:


-------------------------------------------------------
Date: Sun 04 Feb 2024 04:26:25 PM UTC By: Boud Roukema <boud>
PROBLEM: Gnuastro 0.22.1-bc3d calculates the comoving one-radian arclength (=
the "areal radius" = the "proper motion distance"), and the corresponding
physical-units one-radian arclength that is usually called the "angular
diameter distance", and other parameters deriving from this, on the assumption
that the FLRW model is flat. This is incorrect for non-flat models. This
implies that:
* --angulardiamdist
* --luminositydist
* --arcsectandist
* --distancemodulus
are all wrong in the non-flat cases. This error was mentioned earlier in bug
#65195 [1].)

TASK: Introduce a function equivalent to *cosm_get_pm_dist* in cosmdist 0.3.12
(GPL-2+) [2] to calculate the comoving one-radian arclength based on the
radial comoving distance (currently called 'proper_distance' in gnuastro,
which is acceptable) and the cosmology curvature parameter. Then functions
such as *gal_cosmology_angular_distance* will need to be corrected.

CHECK:
These checks are for cosmdist 0.3.12 and gnuastro 0.22.1-bc3d, showing that
only the flat case (olambda+omatter+oradiation = 1) for astcosmiccal is
currently correct; the non-flat cases are wrong.

*Comoving tangential one-radian arclength*:

$ for OmLam0 in 0.0 0.1 0.8 0.9; do echo 9 | ./cosmdist --tangential -r 0 -m
0.9 -l ${OmLam0} ; done
6219.73  
6105.05  
4981.32  
4758.45
$ for OmLam0 in 0.0 0.1 0.8 0.9; do ./bin/cosmiccal/astcosmiccal
--arcsectandist --oradiation=0.0 --omatter=0.9 --olambda=${OmLam0} --H0=70
--redshift=9 --quiet; done |awk '{print $1*3600*180/3.141593/1000.0
*(1.0+9.0)}' # convert 1 arcsec to 1 radian; convert physical to comoving
units
6019.57
6105.05
6851.35
6986.83


*Angular diameter distance:*

$ for OmLam0 in 0.0 0.1 0.8 0.9; do echo 9 | ./cosmdist --angular-diameter -r
0 -m 0.9 -l ${OmLam0} ; done
621.97  
610.51  
498.13  
475.85  
$ for OmLam0 in 0.0 0.1 0.8 0.9; do ./bin/cosmiccal/astcosmiccal
--angulardiamdist --oradiation=0.0 --omatter=0.9 --olambda=${OmLam0} --H0=70
--redshift=9 --quiet; done 
601.956856
610.505315
685.134960
698.682594


*Luminosity distance:*

$ for OmLam0 in 0.0 0.1 0.8 0.9; do echo 9 | ./cosmdist --luminosity -r 0 -m
0.9 -l ${OmLam0} ; done
62197.34  
61050.53  
49813.16  
47584.52  
$ for OmLam0 in 0.0 0.1 0.8 0.9; do ./bin/cosmiccal/astcosmiccal
--luminositydist --oradiation=0.0 --omatter=0.9 --olambda=${OmLam0} --H0=70
--redshift=9 --quiet; done
60195.685626
61050.531477
68513.496031
69868.259418


[1] https://savannah.gnu.org/bugs/?65195

[2] https://codeberg.org/boud/cosmdist/src/branch/main/lib/get_pm_dist.c









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