[fitsbits] [mhvk at astro.utoronto.ca: Question about FITS format for logarithmic units]

[Arnold Rots]

Well, whether you like it or not, the log(unit) syntax is
actually covered in the standard, in Section 4.3.1.

  - Arnold

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Arnold H. Rots                                          Chandra X-ray
Science Center
Smithsonian Astrophysical Observatory                   tel:  +1 617 496
7701
60 Garden Street, MS 67                                      fax:  +1 617
495 7356
Cambridge, MA 02138
arots at cfa.harvard.edu
USA
http://hea-www.harvard.edu/~arots/
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On Tue, Dec 10, 2013 at 4:47 PM, Tim Pearson <tjp at astro.caltech.edu> wrote:

> I think it is stretching things too far to use the units field to indicate
> that the quantity is logarithmic. This information belongs in the name of
> the quantity (TTYPE), not the name of the unit (TUNIT). Note that what
> matters is the quotient TTYPE/TUNIT. You can move things between TTYPE and
> TUNIT so long as the quotient is unchanged. Conventionally, the units go in
> TUNIT, but this doesn't work for logarithmic quantities.
>
> The following guidelines are from the Royal Society's report on
> "Quantities, Units, and Symbols" (1975):
> "The value of a physical quantity is equal to the product of a numerical
> value and a unit: physical quantity = numerical value x unit. Neither any
> physical quantity nor the symbol used to denote it should imply a
> particular choice of unit. Operations on equations involving physical
> quantities, units, and numerical values should follow the ordinary rules of
> algebra. ... When numerical values of a physical quantity are tabulated,
> the expression to be placed at the head of a column should be a pure
> number, such as the quotient of the symbol expressing the physical quantity
> and the symbol for the units used."
>
> In this light, a unit like "log(cm/s2)" is incorrect and meaningless: you
> cannot take the logarithm of a dimensional quantity (at least, it doesn't
> help you much to do so).
>
> If you are presenting a quantity like surface gravity ("g", say) in a FITS
> file (or indeed any sort of table) the values in the table are pure
> numbers: numerical value = quantity/unit, i.e., they are values of
> TTYPEn/TUNITn in the FITS convention. You have two options:
>
>    Quantity                     Unit
>    TTYPEn                       TUNITn
> 1. g                            m s^{-2}
> 2. log[g/(m s^{-2}]             ...
>
> The second case is a dimensionless quantity, and has no units, although
> sometime you might want to name the units as "dex".
>
> Of course, FITS keywords are inconvenient for representing units with
> exponents, but that is another issue. [Note also that FITS discourages use
> of non-SI units like cm.]
>
> The different types of magnitudes are not different units. They are
> different measures of flux (weighted by different bandpasses), albeit all
> expressed in the dimensionless logarithmic magnitude scale. So don't use
> TUNIT to indicate that the magnitudes are on the AB scale; use TTYPE or
> some other mechanism.
>
> Similar issues arise, e.g., in labeling graphs. The axis label should be
> e.g., "ln(p/MPa)", not "ln(p) [MPa]".
>
> - Tim
>
> On Dec 9, 2013, at 6:35 AM, Marten van Kerkwijk wrote:
>
> > (1) How would I indicate a dimensionless but logarithmic quantity such
> >    as dex? If I understood the standard correctly, log(surface gravity)
> >    might have the unit "log(cm/s2)", but how about a dimensionless one
> >    (like metallicity).  Would it be "log()", or, by analogy with
> >    magnitude, just "log"?
> >
> > (2) If I wanted to represent decibels, would "10*log(unit)" be
> >    recommended? Or "10^-1 log(unit)" to be more like the "deci" prefix
> >    (but which I think would be more confusing).
> >
> > (3) If I wanted to represent magnitudes *with* a unit, such as AB
> >    magnitudes, what would be the recommended format?  I only noticed
> >    "mag" without units, but is "mag(unit)" allowed?  Or would one use
> >    "-2.5*log(unit)"? (Though this would seem to break the rule that
> >    scales can only be powers of 10).
> >
> > (4) As a particularly gruelling example of the above, how would one
> >    represent AB magnitudes?  In principle, an inelegant but correct way
> >    might be "-2.5*log(10^(-0.4*48.6) mW/(m2*Hz))".  Would you have a
> >    recommendation?
>
>
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