4. SPECIFICATION OF UNITS

Unless agreed otherwise, units should conform with the recommendations of the IAU Style Manual (McNally [1988]). Unfortunately, this manual defines units as they would appear in a published document rather than as they must appear in plain character form. George & Angelini ([1995]) and Ochsenbein et al. ([1996]) have prepared detailed documents on this subject upon which the following remarks are based. In particular, the following tables are taken from George & Angelini's manuscript (with some changes and additions). Readers should consult these references for examples and expanded discussion. We allow the possibility that the interpretation of CUNITia may depend on conventions established for the CTYPEia associated with them. For example, units specified by "s" might mean SI seconds or seconds of sidereal time.

The basic units string, called str1 and str2 in Table 3, is composed of a unit string taken from Col. 2 of the IAU-recognized units in Table 5 or the extended astronomical units in Table 6. All units from the former and selected units from the latter may be preceded, with no intervening blanks by a single character (two for deca) taken from Table 4 and representing scale factors mostly in steps of 10³. Compound prefixes (e.g., ZYeV for 10⁴⁵ eV) are prohibited. A compound string may then be created from these simple strings by one of the notations in Table 3. A unit raised to a power is indicated by the unit string followed, with no intervening blanks, by the optional symbols ** or ^- followed by the power given as a numeric expression, called expr in Table 3. The power may be a simple integer, with or without sign, optionally surrounded by parentheses. It may also be a decimal number (e.g., 1.5, .5) or a ratio of two integers (e.g. 7/9), with or without sign, which are always surrounded by parentheses. Thus meters squared is indicated by m**(2), m**+2, m+2, m2, m-2, m-(+2), etc. and per meter cubed is indicated by m**-3, m-3, m-(-3), /m3, and so forth. Meters to the three halves may be indicated by m(1.5), m-(1.5), m**(1.5), m(3/2), m**(3/2), and m-(3/2), but not by m-3/2 or m1.5.

Note that functions such as log actually require dimensionless arguments, so, by log(Hz), for example, we actually mean log(x/1Hz). The final string to be given as the value of CUNITia is the compound string, or a compound of compounds, preceded by an optional numeric multiplier of the form 10**k, 10^k, or 10±k where k is an integer, optionally surrounded by parentheses with the sign character required in the third form in the absence of parentheses. FITS writers are encouraged to use the numeric multiplier only when the available standard scale factors of Table 4 will not suffice. Parentheses are used for symbol grouping and are strongly recommended whenever the order of operations might be subject to misinterpretation. A blank character implies multiplication which can also be conveyed explicitly with an asterisk or a period. Therefore, although blanks are allowed as symbol separators, their use is discouraged. Two examples are '10^**(46)erg/s' and 'sqrt(erg/pixel/s/GHz)'. Note that case is significant throughout. The IAU style manual forbids the use of more than one solidus (/) character in a units string. In the present conventions, normal mathematical precedence rules are assumed to apply, and we, therefore, allow more than one solidus. However, authors might wish to consider, for example, 'sqrt(erg/(pixel.s.GHz))' instead of the form given previously.

Table 6. Additional allowed units.

Quantity		Unit	Meaning	Notes
		String
plane angle		deg	degree of arc	/180 rad
		arcmin	minute of arc	1/60 deg
		arcsec	second of arc	1/3600 deg
		mas	milli-second of arc	1/3600000 deg
time		min	minute
		h	hour
		d	day	86400 s
	†	a	year (Julian)	31557600 s (365.25 d), peta a (Pa) forbidden
	†	yr	year (Julian)	a is IAU-style
energy*	†	eV	electron volt	1.6021765×10-19 J
	‡	erg	erg	10-7 J
		Ry	rydberg	1/2 (2e2 / hc)2 mec2 = 13.605692 eV
mass*		solMass	solar mass	1.9891×1030 kg
		u	unified atomic mass unit	1.6605387×10-27 kg
luminosity		solLum	Solar luminosity	3.8268×1026 W
length	‡	Angstrom	angstrom	10-10 m
		solRad	Solar radius	6.9599×108 m
		AU	astronomical unit	1.49598×1011 m
		lyr	light year	9.460730×1015 m
	†	pc	parsec	3.0857×1016 m
events		count	count
		ct	count
		photon	photon
		ph	photon
flux density	†	Jy	jansky	10-26 W m-2 Hz-1
	†	mag	(stellar) magnitude
	†	R	rayleigh	1010 / (4) photons m-2 s-1 sr-1
magnetic field	†‡	G	gauss	10-4 T
area		pixel	(image/detector) pixel
		pix	(image/detector) pixel
	†‡	barn	barn	10-28 m2
Miscellaneous "units"
		D	debye	1/3 ×10-29 C.m
		Sun	relative to Sun	e.g. abundances
		chan	(detector) channel
		bin	numerous applications	(including the 1-d analogue of pixel)
		voxel	3-d analogue of pixel
	†	bit	binary information unit
	†	byte	(computer) byte	8 bit
		adu	Analog-to-digital converter
		beam	beam area of observation	as in Jy/beam
† - addition of prefixes for decimal multiples and submultiples are allowed.
‡ - deprecated in IAU Style Manual (McNally [1988]) but still in use.
* - conversion factors from CODATA Internationally recommended values of the fundamental physical constants 1998 (http://physics.nist.gov/cuu/Constants/)