3.1.2 Conventions, notations, nomenclature, and definitions

Author(s): Uli Bastian

The Gaia data processing, like any other complex multi-partner project, needs a set of agreed conventions and notations to be followed by all partners. Such conventions are needed to ease communication, to avoid misunderstandings and to streamline the distributed development of software for shared usage.

The DPAC consortium maintains a set of internal documents intending to collect all the necessary conventions. However, it is neither needed nor useful to expose the users of the Gaia Catalogue(s) to the full set of conventions. Instead, it is better to restrict the documentation to those which are actually of interest to the external users. Also, it is not useful to concentrate their description in one place. Rather they should be introduced where needed.

So, for instance, the definitions and notations for angular coordinates, time scales and epochs, as well as relativistic reference frames are given in the following subsections where they first appear. The agreed fundamental physical and mathematical constants are briefly described in Section 3.1.8.

The present subsection mentions only a few overarching aspects.

Physical units: The SI system

This section is mainly based on the ‘Units home page’ of the National Institute of Standards and Technology (see the NIST website), which generally agrees with IAU recommendations For interested users we recommend to read Thompson and Taylor (2008). In summary, The Gaia collaboration uses ‘acceptable SI units’ (as defined below) as default, plus a few extensions also described below. Following Thompson and Taylor (2008), we interpret the term ‘SI units’ as the seven SI base units (kg, m, s, mol, A, K, cd; see Section 4.1 in Thompson and Taylor (2008)), plus the 20 SI derived units (N, V, Hz, Gy, W, etc.; see Section 4.2 in Thompson and Taylor (2008)), plus the two SI supplementary units (rad and sr; Section 4.2.2 in Thompson and Taylor (2008)), including multiples and sub-multiples of these units formed by using SI prefixes (${\rm M}=10^{6}$, ${\rm k}=10^{3}$, $\mu=10^{-6}$, etc.; Table 5 in Thompson and Taylor (2008)). The term ‘acceptable SI units’ is taken to denote the ‘SI units’ (as defined above), plus those units accepted by the CIPM (Comité International des Poids et Mesures) for use with the SI (notably angular degree, arcminute, arcsecond, minute, hour, and day; Tables 6 and 7 in Thompson and Taylor (2008)), plus those units temporarily accepted for use with the SI (Table 9 and Section 5.2 in Thompson and Taylor (2008)), including multiples and sub-multiples of these units. We also follow Thompson and Taylor (2008) and the IAU by recognizing that the use of time intervals expressed in units of Julian years (year), distances in units of parsecs (pc) or astronomical units (au), and source brightness/luminosity in units of magnitudes (mag) is allowed. The use of the non-SI unit Å is ‘temporarily accepted’ by Thompson and Taylor (2008) and ‘deprecated’ by the IAU; we propose that this unit is not used.

Notation of units

The interested reader is strongly advised to consult Thompson and Taylor (2008); we simply list a few specific remarks which are relevant in the light of Gaia:

• The angular units degree, arcminute, arcsecond may be abbreviated as ‘deg’, ‘arcmin’, ‘arcsec’ or denoted by the conventional symbols  ${}^{\circ}$  ${}^{\prime}$  ${}^{\prime\prime}$.

• Sub-multiples of the arcsecond are denoted by ‘mas’ ($10^{-3}$ arcseconds, 1 milli-arcsecond) and ‘$\mu$as’ ($10^{-6}$ arcseconds, 1 micro-arcsecond). In an ASCII-environment ‘$\mu$as’ is allowed to degenerate into ‘muas’.

• The unit of a Julian year is denoted as ‘year’, in line with Thompson and Taylor (2008), §5.1.1. In theory, some confusion could arise when using ‘y’ instead of ‘year’. For instance the SI unit ‘Gy’ (Gray, for absorbed radiation dose) could be mis-interpreted as $10^{9}$ years. To add to this confusion, we note that the (‘temporarily accepted’) radiation unit ‘rad’ (not to be confused with radian) is defined as ‘cGy’, i.e., centi-Gray. Although in the light of Gaia, this sort of confusion is generally not expected, the unit ‘year’ should either be spelt out explicitly, or be abbreviated solely by ‘a’ (from Latin ‘annum’, following ISO and Section 8.1 of Thompson and Taylor (2008).

• The use of the phrase/unit ‘micron’ to denote $\mu$m is not allowed; this unit should be denoted as ‘$\mu$m’ (or as ‘micrometer’ in full or ‘mum’ in abbreviation in an ASCII-environment).

• Note the distinction between a bit (b) and a byte (B, meaning eight bits). Thus: 1 kb denotes one kilobit ($10^{3}$ bit) and 1 kB denotes one kilobyte ($10^{3}$ byte).

• Note the distinction between binary and decimal prefixes. For example, one kilobit (kb) denotes $10^{3}=1000$ bit but one kibibit (Kib) denotes $2^{10}=1024$ bit. The prefix kilobinary, or kibi or Ki, means $2^{10}$. More examples of binary prefixes, e.g. Mi=$2^{20}\sim 10^{6}$, Gi=$2^{30}\sim 10^{9}$ and a complete list can be found here.

Acronyms

A list of acronyms and abbreviations used in the Gaia collaboration is maintained in the internal “Glossary of acronyms” text file and is available here: Glossary of acronyms file.