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

[Marten van Kerkwijk]

Dear Colleagues,

At the suggestion of Lucio, I'm forwarding my query regarding the use of
logarithmic units in FITS here.  Any answers most appreciated!

With all best wishes,

Marten van Kerkwijk

-- 
Prof. M. H. van Kerkwijk
Dept. of Astronomy & Astroph., 50 St George St., Toronto, ON, M5S 3H4, Canada
McLennan Labs, room 1203B, tel: +1(416)9467288, fax: +1(416)9467287
mhvk at astro.utoronto.ca, http://www.astro.utoronto.ca/~mhvk


From: Marten van Kerkwijk <mhvk at astro.utoronto.ca>
To: lucio at lambrate.inaf.it 
Subject: Question about FITS format for logarithmic units
CC: perry at stsci.edu, mdboom at gmail.com
Date: Sun, 08 Dec 2013 21:15:16 -0500
Message-ID: <87a9ga22iz.fsf at dolphin.astro.utoronto.ca>

Dear Dr Chiappetti,

I am helping to ensure that units can be read from and written to fits
format correctly in the astropy package [1] (CC Michael Droettboom,
STScI, primary maintainer, and Perry Greenfield, STScI representative on
the IAUFWG), and I have a few questions about the use of logarithmic
units such as magnitudes, to which I could not find a clear answer in
the (otherwise very nice) A&A article on the FITS standard.  If hope
you can answer these, or could point me to someone who can.

My specific questions are:

(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?

With all best regards,

Marten van Kerkwijk

p.s.  I earlier wrote Dr Pence with this question, but did not receive a
      reply.  Please let me know if I should be contacting someone else
      with these questions.