# Dimensionless units

David Berry dsb at ast.man.ac.uk
Thu Feb 17 08:07:17 PST 2005

```Pedro,

> the example case mentioned before about comparing Jy with Jy/sr, has to do with
> point versus extended source information. Whether a
> source is extended will have to be stated in the metadata, and if a
> source is extended and the flux is given in Jy/sr, the solid angle
> subtended by the observation under which the flux is being given
> (basically the extension of the source, I guess) should appear there.

I agreed that to create a conversion from Jy to Jy/sr, a solid angle is
required from somewhere.

> Then, clients would get this piece of information (from the SED data
> model, for example) and handle it. There is no other way to compare Jy
> with Jy/sr, as the second is a relative measurement (relative to a
> certain area). This problem is inherent to the type of data, and not to
> whether you use dimensional analysis or unit string parsing to make the
> comparison.

My question was really more to do with whether a dimensional analysis
approach can tell that no simple conversion is possible between Jy and
Jy/sr. Presumably if I have two flux density data sets, one in units of Jy
and one in units of mJy, each with a dimensional analysis, it would be
simple to determine the conversion between the data sets on the basis of
the dimensional analysis (the dimensions themselves would be equal but the
scale factor would differ). But if my second data set was not flux density,
but surface brightness in units of Jy/sr, how would the conversion
software recognize that the conversion is *not* possible? Since "sr" is
dimensionless, the dimensional analysis of Jy and Jy/sr are identical.
So in this case how does the conversion code realise that it is dealing
with "Jy/sr" and not "Jy"? Adding more meta data to indicate source
extension is not enough since, even if you have flag indicating that the
source is extended, you still have to determine if the data represents the
integrated flux of the extended source in Jy or the surface brightness of
the extended source in Jy/sr.

Also, thinking of magnitudes, the dimensional analysis for "mag" would
presumably be blank. So how does the code identify what it can and
cannot do with the units?

David

```