#### 3.8 The data units window

This window allows you to inspect, set or convert the units of the data values of your spectra.

The most trivial use of these is simply to document what type of units your spectra are measured in. However, a more powerful use of data units can be made when displaying more than one spectrum in a plot. In that case you can request that the data values of all the spectra are transformed into the same system, so you can compare values in Janskys with those in other flux per unit frequency and per unit wavelength systems (note to activate this option you must have the Options->Match coordinates and/or fluxes menu item selected in the plot window). For instance all the following systems are understood as fluxes and can be intercompared:

 Jy ($Jansky$) W/m^2/Hz ($W\ast {m}^{-2}\ast H{z}^{-1}$) W/m^2/Angstrom ($W\ast {m}^{-2}\ast Angstro{m}^{-1}$) W/cm^2/um ($W\ast c{m}^{-2}\ast u{m}^{-1}$) erg/cm^2/s/Hz ($erg\ast c{m}^{-2}\ast {s}^{-1}\ast H{z}^{-1}$) erg/cm^2/s/Angstrom ($erg\ast c{m}^{-2}\ast {s}^{-1}\ast Angstro{m}^{-1}$)

Plus variations like $Joules$ instead of $ergs$ or maybe $Nm$, etc. When reading unit strings like W/m^2/Hz you should say Watts per metre squared per Hertz, which is actually mathematically the same as the expressions shown in to the right in parentheses ($W\ast {m}^{-2}\ast H{z}^{-1}$ in this case). Note that dimensionally equivalent unit strings to those above maybe be recognised and re-formatted.

In addition to flux systems dimensionally similar ones can also be used and transformed between in a plot, things like temperature. SPLAT-VO understands that $K$ and $mK$ are temperatures in Kelvins and milliKelvins, same for units like $eV$ and $keV$.

The units are described using strings that follow the conventions in FITS-WCS paper I Representation of World Coordinate in FITS by Greisen & Calabretta, and processed by the Starlink AST library (SUN/211). The following section is copied from SUN/211 for convenience. Not all units are relevant to data values (AST also provides the underlying coordinate transformations used in SPLAT-VO) and as noted above not all possible unit strings can be understood as fluxes (although support for more types is expected, for instance temperatures and magnitudes).

The adopted syntax is that described in FITS-WCS paper I Representation of World Coordinate in FITS by Greisen & Calabretta. We distinguish here between “basic” units and “derived” units: derived units are defined in terms of other units (either derived or basic), whereas basic units have no such definitions. Derived units may be represented by their own symbol (e.g. “Jy”—the Jansky) or by a mathematical expression which combines other symbols and constants to form a definition of the unit (e.g. “km/s”—kilometres per second). Unit symbols may be prefixed by a string representing a standard multiple or sub-multiple.

In addition to the unit symbols listed in FITS-WCS Paper I, any other arbitrary unit symbol may be used, with the proviso that it will not be possible to convert between spectra using such units. The exception to this is if both spectra refer to the same unknown unit string. For instance, an axis with unknown unit symbol "flop" could be converted to an axis with unit "Mflop" (Mega-flop).

Unit symbols (optionally prefixed with a multiple or sub-multiple) can be combined together using a limited range of mathematical operators and functions, to produce new units. Such expressions may also contain parentheses and numerical constants (these may optionally use “scientific” notation including an “E” character to represent the power of 10).

The following tables list the symbols for the basic and derived units which may be included in a units string, the standard prefixes for multiples and sub-multiples, and the strings which may be used to represent mathematical operators and functions.

 Basic units Quantity Symbol Full Name length m metre mass g gram time s second plane angle rad radian solid angle sr steradian temperature K Kelvin electric current A Ampere amount of substance mol mole luminous intensity cd candela
 Prefixes for multiples & sub-multiples Sub-multiple Name Prefix Sub-multiple Name Prefix $1{0}^{-1}$ deci d $10$ deca da $1{0}^{-2}$ centi c $1{0}^{2}$ hecto h $1{0}^{-3}$ milli m $1{0}^{3}$ kilo k $1{0}^{-6}$ micro u $1{0}^{6}$ mega M $1{0}^{-9}$ nano n $1{0}^{9}$ giga G $1{0}^{-12}$ pico p $1{0}^{12}$ tera T $1{0}^{-15}$ femto f $1{0}^{15}$ peta P $1{0}^{-18}$ atto a $1{0}^{18}$ exa E $1{0}^{-21}$ zepto z $1{0}^{21}$ zetta Z $1{0}^{-24}$ yocto y $1{0}^{24}$ yotta Y
 Mathematical operators & functions String Meaning sym1 sym2 multiplication (a space) sym1*sym2 multiplication (an asterisk) sym1.sym2 multiplication (a dot) sym1/sym2 division sym1**y exponentiation ($y$ must be a numerical constant) sym1^y exponentiation ($y$ must be a numerical constant) log(sym1) common logarithm ln(sym1) natural logarithm exp(sym1) exponential sqrt(sym1) square root
 Derived units Quantity Symbol Full Name Definition area barn barn 1.0E-28 m**2 area pix pixel area pixel pixel electric capacitance F Farad C/V electric charge C Coulomb A s electric conductance S Siemens A/V electric potential V Volt J/C electric resistance Ohm Ohm V/A energy J Joule N m energy Ry Rydberg 13.605692 eV energy eV electron-Volt 1.60217733E-19 J energy erg erg 1.0E-7 J events count count events ct count events ph photon events photon photon flux density Jy Jansky 1.0E-26 W /m**2 /Hz flux density R Rayleigh 1.0E10/(4*PI) photon.m**-2 /s/sr flux density mag magnitude force N Newton kg m/s**2 frequency Hz Hertz 1/s illuminance lx lux lm/m**2 inductance H Henry Wb/A length AU astronomical unit 1.49598E11 m length Angstrom Angstrom 1.0E-10 m length lyr light year 9.460730E15 m length pc parsec 3.0867E16 m length solRad solar radius 6.9599E8 m luminosity solLum solar luminosity 3.8268E26 W luminous flux lm lumen cd sr magnetic field G Gauss 1.0E-4 T magnetic flux Wb Weber V s mass solMass solar mass 1.9891E30 kg mass u unified atomic mass unit 1.6605387E-27 kg magnetic flux density T Tesla Wb/m**2 plane angle arcmin arc-minute 1/60 deg plane angle arcsec arc-second 1/3600 deg plane angle mas milli-arcsecond 1/3600000 deg plane angle deg degree pi/180 rad power W Watt J/s pressure, stress Pa Pascal N/m**2 time a year 31557600 s time d day 86400 s time h hour 3600 s time yr year 31557600 s time min minute 60 s D Debye 1.0E-29/3 C.m

Accelerator keys

• Control-n Convert from current data units to UI values.
• Control-s Set data units to UI values.
• Control-w Close the window.
• F1 Display help on SPLAT-VO.
• Shift-F1 Display help on window.