Subject: calculating cosmological distances the practical way

From: Phillip Helbig <[email-masked]>
Date: 16 Apr 1996 13:34:28 GMT

Of fundamental importance for much of extragalactic astronomy and cosmology
is the calculation of distances from redshifts.  There are various types
of distances, and the nonlinearity with redshift makes the problem of
cosmological distance calculation much more involved than in the conventional
case.  In addition, closed solutions are only valid in special cases which
correspond to cosmological models which might not be a good approximation
to reality.  Although a general solution in terms of elliptic integrals
exists, a practical implementation is lacking.  Even this complex approach,
however, must neglect the influence of inhomogeneities on the calculation
of distances from redshifts, which for realistic scenarios is comparable
to the influence of the `conventional' cosmological parameters.

The present programme by Perlmutter et al. to determine cosmological 
parameters through the magnitude-redshift relation for supernovae Ia
is a contemporary example where interesting things can be learned by
looking at the behaviour of distances at redshifts where the linear
approximation is no longer valid.  Another area is gravitational lensing,
where lensing statistics will hopefully set the tightest constraints
on the cosmological parameters (with the possible exception of a successor
to COBE) in the near future.

My colleague Rainer Kayser has derived a second-order differential equation
for calculating distances from redshifts, valid in all Friedmann-Lemaitre
cosmological models, including inhomogeneous ones, that is, where a certain
fraction of the matter is distributed clumpily.  (Classically, complete
homogeneity is assumed.)  This degree of inhomogeneity can also be a function
of redshift.  Together with Tom Schramm we've written a paper describing
this method of distance calculation, which has been submitted to Astronomy
and Astrophysics.

We have also developed a numerical implementation in strictly standard
FORTRAN77, designed for the practical cosmologist and extragalactic
astronomer who needs a `black box' for converting between redshifts and
distances.  The box can be opened, as we make the source code available.

The A&A paper (PostScript), the source code and a user's guide to the 
routines (PostScript) is available from

   ftp://ftp.uni-hamburg.de/pub/misc/astronomy/angsiz.uu

or from the preprint servers as

   astro-ph 9603028

>from which it is ALSO possible to obtain only the A&A paper (choose
`PostScript'; choosing source will give you the paper in LaTeX and a
uuencoded compressed tar archive containing the PostScript user's guide
and the FORTRAN routines).  Another possibility is to check out

   http://www.hs.uni-hamburg.de/
   english/persons/helbig/Research/Publications/Info/angsiz.html

(all one one line, of course) and follow the links to what you need.
The FORTRAN code is available as ASCII and the paper and user's 
guide are available as PostScript or as gzipped PostScript.

Feel free to send me email with comments, questions, problems, bug
reports etc.  Put ANGSIZ in the subject line.  If you desire, you can
be placed on a mailing list to be informed of any changes in the code
(bug fixes, etc.).  If anyone has any problems with access by the methods
outlined above, I can also send you everything by email (uuencoded compressed
(or gzipped) tar (or BACKUP) archives) or even paper versions of the A&A
paper and user's guide.  (I've made no provisions for a paper version of
the FORTRAN routines, i.e., punched cards, though I can send a printout
of the code, of course:)

--
Phillip Helbig         Email ....................... [email-masked]
Hamburger Sternwarte   Tel. ................................. +49 40 7252 4110
Gojenbergsweg 112      Fax .................................. +49 40 7252 4198
D-21029 Hamburg        http://www.hs.uni-hamburg.de/english/persons/helbig.html

I don't speak for the Hamburg Observatory; the Observatory doesn't speak for me