3 Celestial coordinate systems

As mentioned in Sect. 2.1, Paper I defined "4-3'' form for the CTYPE ia keyword value; i.e., the first four characters specify the coordinate type, the fifth character is a "-'', and the remaining three characters specify an algorithm code for computing the world coordinate value. Thus while the right half specifies the transformation to be applied in computing the spherical coordinate pair, $(\alpha ,\delta )$, the left half simply identifies the celestial system with which $(\alpha ,\delta )$ are to be associated. In this sense CTYPE ia contains an active part which drives the transformation and a passive part which describes the results.

Consistent with past practice, an equatorial coordinate pair is denoted by RA- and DEC-, and other celestial systems are of the formxLON and xLAT for longitude and latitude pairs, where x = G for galactic, E for ecliptic, H for helioecliptic, and S for supergalactic coordinates. Since representation of planetary, lunar and solar coordinate systems could exceed the 26 possibilities afforded by the single character x, we also here allow yzLN and yzLT pairs. Additional values of x and yz will undoubtedly be defined. A basic requirement, however, is that the coordinate system be right-handed and that the pole be at latitude $+90\hbox{$^\circ$ }$. A coordinate pair such as azimuth and zenith distance would have to be represented as a negative azimuth and elevation with implied conversion. In some situations negation of the longitude coordinate may be implemented via a sign reversal of the appropriate CDELT ia. It remains the responsibility of the authors of new coordinate system types to define them properly and to gain general recognition for them from the FITS community. However, FITS interpreters should be able to associate coordinate pairs even if the particular coordinate system is not recognized.

Paper I clarified that, while the subscript of CRPIX ja and the jsubscript of PC i_ja and CD i_ja refer to pixel coordinate elements, the i subscript of PC i_ja and CD i_ja and the subscripts of CDELT ia, CTYPE ia and CRVAL ia refer to world coordinate elements. However we now have three different sets of world coordinates, (x,y), $(\phi,\theta)$, and $(\alpha ,\delta )$. This leads us to associate x, $\phi$, and $\alpha$ on the one hand, and y, $\theta$, and $\delta$ on the other. This simply means, for example, that if CTYPE3 = 'GLON-AIT', then the third element of the intermediate world coordinate calculated via Eq. (1) corresponds to what we have been calling the x-coordinate in the plane of projection, the association being between $\alpha$ and x. In this way pairs of CTYPE ia with complementary left halves and matching right halves define which elements of the intermediate world coordinate vector form the plane of projection.

   
3.1 Equatorial and ecliptic coordinates

Several systems of equatorial coordinates (right ascension and declination) are in common use. Apart from the International Celestial Reference System (ICRS, IAU 1998), the axes of which are by definition fixed with respect to the celestial sphere, each system is parameterized by time. In particular, mean equatorial coordinates (Hohenkerk et al. 1992) are defined in terms of the epoch (i.e. instant of time) of the mean equator and equinox (i.e. pole and origin of right ascension). The same applies for ecliptic coordinate systems. Several additional keywords are therefore required to specify these systems fully. We introduce the new keyword

RADESYS a (character-valued)

to specify the particular system. Recognized values are given in Table 2. Apart from FK4-NO-E these keywords are applicable to ecliptic as well as equatorial coordinates.

 

 

Table 2: Allowed values of RADESYS a.

RADESYS a	Definition
ICRS	International Celestial Reference System
FK5	mean place,
	new (IAU 1984) system
FK4	mean place,
	old (Bessell-Newcomb) system
FK4-NO-E	mean place,
	old system but without e-terms
GAPPT	geocentric apparent place,
	IAU 1984 system

Wells et al. (1981) introduced the keyword EPOCH to mean the epoch of the mean equator and equinox. However we here replace it with

EQUINOX a (floating-valued),

since the word "epoch'' is often used in astrometry to refer to the time of observation. The new keyword takes preference over EPOCH if both are given. Note that EQUINOX a applies to ecliptic as well as to equatorial coordinates.

For RADESYS a values of FK4 and FK4-NO-E, any stated equinox is Besselian and, if neither EQUINOX a nor EPOCH are given, a default of 1950.0 is to be taken. For FK5, any stated equinox is Julian and, if neither keyword is given, it defaults to 2000.0.

If the EQUINOX a keyword is given it should always be accompanied by RADESYS a. However, if it should happen to appear by itself then RADESYS a defaults to FK4 if EQUINOX a < 1984.0, or to FK5 if EQUINOX a $\ge\ 1984.0$. Note that these defaults, while probably true of older files using the EPOCH keyword, are not required of them.

RADESYSa defaults to ICRS if both it and EQUINOX a are absent.

Geocentric apparent equatorial and ecliptic coordinates (GAPPT) require the epoch of the equator and equinox of date. This will be taken as the time of observation rather than EQUINOX a. The time of observation may also be required for other astrometric purposes in addition to the usual astrophysical uses, for example, to specify when the mean place was correct in accounting for proper motion, including "fictitious'' proper motions in the conversion between the FK4 and FK5 systems. The old DATE-OBS keyword may be used for this purpose. However, to provide a more convenient specification we here introduce the new keyword

MJD-OBS (floating-valued),

that provides DATE-OBS as a Modified Julian Date ( ${\rm JD} - 2~400~000.5$) but is identical to it in all other respects. MJD-OBS does not have a version code since there can only be one time of observation. Following the year-2000 conventions for DATE keywords (Bunclark & Rots 1996), this time refers by default to the start of the observation unless another interpretation is clearly explained in the comment field. In the present case the distinction is not important. We leave it to future agreements to clarify systems of time measurement and other matters related to time.

The combination of CTYPE ia, RADESYS a, and EQUINOX a define the coordinate system of the CRVAL ia and of the celestial coordinates that result from the sequence of transformations summarized by Fig. 1. However, FK4 coordinates are not strictly spherical since they include a contribution from the elliptic terms of aberration, the so-called "e-terms'' which amount to $\leq$343 milliarcsec. Strictly speaking, therefore, a map obtained from, say, a radio synthesis telescope, should be regarded as FK4-NO-E unless it has been appropriately resampled or a distortion correction provided (Paper IV). In common usage, however, CRVAL ia for such maps is usually given in FK4 coordinates. In doing so, the e-terms are effectively corrected to first order only.