# Dimensionless units

Anita Richards amsr at jb.man.ac.uk
Fri Feb 18 08:06:29 PST 2005

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> I suspect that for Jy/sr in the above example we should be using length^2
> instead of stradians, depending on what we're trying to do. Otherwise
> stradians and arcmins *are* just scaling factors, ie ratios.  In going from
> Jy/sr to Jy  you are implying that you want the value for a fixed proportion
> of a sphere (depending on the scaling factor used for stradians) but you
> haven't yet defined the projection from the sphere. If my geometry is right!
> ie we are back to defining a description for the value, not its units.

How would length^2 solve anything, since in most cases you will have
catalogues of objects at different distances, so that Jy/arcsec^2 or Jy/Sr
cannot be quantified meaningfully in length units without additional
information about distance to the object, and in some cases e.g. CMB it is
meaningless?

This problem is caused by the hidden assumptions made by astronomers which
would be OK i.e. quantifiable if they are always the same..  In a lot of
astronomy 'Jy' really means either Jy/beam (or Jy/aperture or etc.), or
Jy/source.  In that case _if_ the beam or source size is known, then Jy/Sr
can be scaled.  A very clever VO tool might be able to deduce the beam or
source size from other metdata (e.g. we might record the effective
apertures of major satellite instruments).  However this will not work if
you are trying to compare observations which are dominated by an all-sky
background (e.g. CMB) with point sources.  I cannot think of any sensible
way other than making the user enter a value to produce dimensional
compatibility.  So we do need to have something like 'angle' as a
dimension in order to recognise that Jy/Sr != Jy .

cheers
a

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Dr. Anita M. S. Richards, AstroGrid Astronomer
MERLIN/VLBI National Facility, University of Manchester,
Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, U.K.
tel +44 (0)1477 572683 (direct); 571321 (switchboard); 571618 (fax).

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