This document provides a complete design description of the Space-Time Coordinate (STC) metadata for the Virtual Observatory. It explains the various components, highlights some implementation considerations, presents a complete set of UML diagrams, and discusses the relation between STC and certain other parts of the Data Model. Two implementations are discussed: XML Schema (STC-X) and String (STC-S, also known as LinearSTC).

Status of This Document

This is a Proposed Recommendation. The first release of this document (Version 1.21) was 2005 March 23. The first release of the predecessor Working Draft (Version 1.00) was 2004 July 23.

This is an IVOA Proposed Recommendation made available for public review. It is appropriate to reference this document only as a recommended standard that is under review and which may be changed before it is accepted as a full recommendation.

A list of current IVOA Recommendations and other technical documents can be found at http://www.ivoa.net/Documents/.

Acknowledgements

I gratefully acknowledge many helpful discussions with Wil O’Mullane, Alex Szalay, Jonathan McDowell, Ray Plante, Ed Shaya, Pat Dowler, David Berry, Anita Richards, Steve Allen, and many others. I am indebted to SAO, ULP, CDS, and the NSF NVO grant for support.

Contents

1 Introduction 3

2 Justification and Scope 4

3 Requirements and Use-Context 6

4 Design 7

4.1 The Metadata Components 7

4.2 Coordinate System (CoordSys) 7

4.2.1 Coordinate Frame (CoordFrame) 7

4.3 Coordinates (Coords) 7

4.3.1 Coordinate 8

4.4 Coordinate Area (CoordArea) 9

4.4.1 ScalarInterval 9

4.5 AstroCoordSys 9

4.5.1 TimeFrame 9

Table 1. Standard Reference Positions 10

Table 2. Timescales 12

4.5.2 SpaceFrame 13

Table 3. Standard Reference Frames 14

4.5.3 SpectralFrame 17

4.5.4 RedshiftFrame 17

4.6 AstroCoords 18

4.6.1 TimeCoord 18

4.6.2 SpatialCoord 19

4.6.3 SpectralCoord 20

4.7 AstroCoordArea 20

4.7.1 TimeInterval 21

4.7.2 SpatialInterval 21

4.7.3 VelocityInterval 21

4.7.4 SpectralInterval 21

4.7.5 RedshiftInterval 22

6 Conclusion and Usage Notes 25

6.1 Methods 25

6.2 Usage 26

6.2.1 Resource Profile 26

6.2.2 Query Constraint 27

6.2.3 Catalog Entry 27

6.2.4 Observational Data 27

7 Implementation 28

7.1 STC-X: XML Schema Implementation 28

7.1.1 Simplifications 28

7.2 STC-S 29

Appendix A: UML Representation 29

Appendix B: Examples 39

B.1 STCResourceProfile 39

B.2 Galaxy Catalog 41

B.3 ROSAT Image 44

B.4 Blue M81 Image from KPNO 47

B.5 Query Specification 50

Appendix C: XInclude Library of Coordinate Systems 52

Appendix D: Changes from Previous Versions 52

References 53

1 Introduction

This document attempts to explain and document the design and implementation of the Space-Time (and related coordinate axes) metadata for the Virtual Observatory. In order to make this specification optimally useful for the VO, we have generalized the Coordinate System concept and we have added a generic Coordinate Frame. Derived from these are the AstroCoordSys and the time, space, redshift, spectral frames that together make up the Space-Time Coordinate (STC) system. Coordinate and Coordinate Area also have generic as well as Astro versions. We shall use “STC” as a proper name in this document which will lead to terms like “STC coordinates”. Although we agree that such usage is linguistically deplorable, we will use it nevertheless because of the clarity it provides.

We present two implementations of STC. The fundamental implementation is provided in the XML schemata and is known as STC-X. A string implementation, based on STC-X, is known as STC-S or LinearSTC.

There are six companion files to this document:

http://www.ivoa.net/xml/STC/v1.20
http://hea-www.harvard.edu/~arots/nvometa/v1.2/stc-v1.20.xsd
is the top-level schema of the XML implementation STC-X, containing the coordinate system and coordinate area definitions.
http://www.ivoa.net/xml/STC/STCcoords/v1.20
http://hea-www.harvard.edu/~arots/nvometa/v1.2/coords-v1.20.xsd
is the STC-X schema with the coordinate value definitions.
http://www.ivoa.net/xml/STC/STCregion/v1.20
http://hea-www.harvard.edu/~arots/nvometa/v1.2/region-v1.20.xsd
is the STC-X schema for the region specification.
http://www.ivoa.net/Documents/latest/STC-X.html
documents the STC-X (XML) implementation.
http://hea-www.harvard.edu/~arots/nvometa/STCPoster.pdf
is a poster on the STC schema.
http://www.ivoa.net/Documents/latest/STC-S.html
documents the STC-S (string, or LinearSTC) implementation.

The schemas are fully up-to-date.

In the following sections we shall discuss the justification and scope for this metadata specification, the requirements and use context, a detailed design description, and some implementation considerations. Some concepts are only provided in their simplest form and we expect that more sophisticated classes will be derived (and will fit in seamlessly) as work progresses. The emphasis of this document is on the framework of the STC metadata.

2 Justification and Scope

Before we plunge into the requirements and design of these metadata structures, it may be helpful to discuss what is driving this exercise and to provide some context to the design. Our intent in this is to explain why the design needs to be fully general and extensible, leading to a certain level of complexity.

The basic justification for considering the following coordinate axes in a single metadata specification is that they are closely intertwined:

Space (including its time-derivatives, i.e., velocities)
Time
Spectral (frequency, wavelength, energy)
Redshift (Doppler velocity)

It should be emphasized that the STC design distinguishes between the spectral coordinate and the redshift coordinate (one might, after all, have to deal with a dataset containing Doppler velocities measured in different parts of the spectrum) and between redshifts and velocities (the latter are physical quantities – derivatives of spatial positions; the former represent a spectral property that is transformed via one of several formalisms to what is commonly referred to as a Doppler velocity – when we get to relativistic situations the connection with physical velocities becomes tenuous). In the presence of a redshift coordinate, the values of a spectral coordinate, if present, will contain rest frequencies.

We shall refer to these as the STC coordinates. The issue is that time is bound to a position and positions are time-variable. Similarly, spectral and redshift data are tied to reference frames that may or may not be time-variable.

In the past, most data archives have not been extremely concerned with dotting every i and crossing every t, in a meticulous specification of all the details of all coordinate axes. They assumed sets of coordinate system-related defaults. Such context-dependent defaults are quite acceptable: issues are generally well-defined, obvious, and clear for single-observatory observations, even when not all is explicitly specified. However, there are no global defaults in the VO. All implicit assumptions need to be made explicit since they will not be “obvious” anymore. One must be able to transform the coordinates of two observations to a common coordinate system; this means that every little tidbit of information needs to be documented in the metadata.

Here are some simple examples of situations and questions that need an answer, when such context-dependent defaults do not work anymore:

Are Doppler velocities optical or radio?
What is the spatial reference position for the time stamps; if corrected for pathlength, what direction was assumed?
Does “J2000” mean “FK5/J2000” or “ICRS”?
At which spatial position was this observation made?
How can we get information on Galactic background objects from solar system observations, and vice versa?

Reality dictates, though, that we allow for cases where these values are simply unknown. In the XML implementation nillable elements that are nil should be interpreted as unknown values; the burden is then on the client to determine and adopt a sensible default value. This holds true for elements named “UNKNOWN” as well. We sincerely hope that the existence of such nillable and UNKNOWN elements will not be an excuse to provide incomplete metadata in cases where the values are known.

3 Requirements and Use-Context

The top-level requirement for the design of the Space-Time Coordinate metadata can be formulated in a very simple way. It is that they:

provide sufficient and necessary information
are self-consistent

That is really all. However, to fit it into the larger VO Data Model context, we should leverage two more requirements:

the system should be extensible to include other coordinates and accommodate coordinate metadata descriptions that include axes other than the STC ones
it must be possible to define relocatable frames to accommodate, for instance, simulation data

From this one can derive secondary requirements: the metadata must include complete descriptions of the following three concepts:

the coordinate frames that anchor the STC coordinate axes, collectively referred to as the Coordinate System
a specific position in these frames, i.e., a coordinate object, that includes not only coordinate values, but also essential attributes such as errors and resolutions
the volume in coordinate space that is taken up by the data object that these metadata are attached to

In all, there are four different contexts for the use of the STC metadata:

STC Resource profile – to specify the spatial, temporal, redshift, spectral coverage of a data collection which is ultimately used by clients to determine whether or not the resource is of interest for their purposes
Query – to specify the STC constraints of a particular request
Catalog information – clearly, the response to a catalog query may contain coordinate information (e.g., positions), but it should also contain coverage information, specifically, the intersection of the catalog’s coverage and the query’s STC constraints
Observational data – here we need the volume in coordinate space that is occupied by the observational data, as well as the coordinates of the observatory; note that these may not necessarily be given in the same Coordinate System; a Pixel Coordinate System is needed for pixilated data

We will return to the use of STC in these contexts in Section 6. As commented before, the emphasis of this document is on the structure of the STC metadata. Hence, though the classes and attributes are laid out in detail, little is said about methods.

4 Design

It may be helpful to refer to the UML diagrams in Appendix A: UML Representation, while reading this section.

4.1 The Metadata Components

There are three metadata components in the design, as already noted in the derived requirements:

Coordinate system
This object contains the coordinate frames that together define a complete coordinate system. There may be one or more per document.
Coordinate values
This is an object that specifies a specific position in the space defined by the coordinate system it refers to. The object contains values, units, errors, resolution, size, and pixel size, though not all of these need be present.
Coordinate areas or ranges
This is an object that defines a volume in the coordinate space specified by the coordinate system it refers to. Regions are a special case, specifically designed for 2-D (and 3-D unit-sphere) spatial coordinates.

4.2 Coordinate System (CoordSys)

The CoordSys class is nothing more than a collection of one or more Coordinate Frames, where each frame describes a set of one or more coordinate axes that belong together.

4.2.1 Coordinate Frame (CoordFrame)

A CoordFrame object provides the metadata about one or more coordinate axes. Usually, we will be dealing with one axis. The exception is the spatial frame which may control up to three position coordinate axes, as well as their time-derivatives (velocity). CoordFrame is really the base class for coordinate frames. To ensure its full generality, this base class should only contain a name. Real-life coordinate frames should be derived from this class.

4.3 Coordinates (Coords)

The Coords object specifies a particular position in coordinate space. It requires a reference (IDREF in the XML implementation) to a CoordSys object and it is made up of one or more Coordinate objects, corresponding to the Coordinate Frames defined in the Coordinate System. All objects are optional. However, in order to constitute a meaningful Coords object, one would expect at least one of the Coordinate objects to be present.

4.3.1 Coordinate

A Coordinate is an aggregate of up to 6 objects: CoordName, CoordValue, CoordError, CoordResolution, CoordSize, and CoordPixSize. Of these, only CoordName is required to be present. The others, which in their simplest forms consist of a scalar numerical Value, are all optional, though one may doubt whether a Coordinate object that contains none of these has any meaning. Although at first sight it would seem that at least CoordValue is indispensable, we shall show that there are legitimate cases where the value may be absent. Coordinate has a single Unit attribute that applies to all components. Classes that are derived from Coordinate may differ in the data types of the objects, their structure and meaning, as well as restrict allowable values for Unit. There are currently two derived classes that have only a Name and a Value: StringCoordinate and PixelCoordinate.

The numeric elements, other than the Coordinate Value, may appear singly or in pairs. In the former case it will be obvious that a single specific value is indicated. In the latter case the pair indicates a range of values.

4.3.1.1 CoordName

This required member of Coordinate is a simple string that acts as a label, presumably taken from a limited enumerated list

4.3.1.2 CoordValue

The value of the Coordinate consists of a scalar numerical or string value and a Unit string.

4.3.1.3 CoordError

Again, this consists of a scalar Value, representing an rms[1] error. However, we expect a variety of derived classes to appear with more sophisticated error descriptions. And clearly, the multi-dimensional coordinates require more information.

4.3.1.4 CoordResolution

The resolution along the Coordinate is expressed as a FWHM [2] Value. In cases where this is a poor description, one should derive a more sophisticated class.

4.3.1.5 CoordSize

The size along the Coordinate is also expressed as a FWHM2 Value, though one might expect derived classes with more precise definitions (e.g., Holmberg[3] diameter). This object is used in three contexts: in a resource profile it indicates the typical size (e.g., FOV[4]) of datasets in the resource; in queries it serves the same purpose; and in catalog datasets it allows the server to provide Coordinate positions of objects as well as their sizes.

4.3.1.6 CoordPixSize

The pixel size (scalar Value) is often a useful figure to characterize resources, queries, and datasets, even if it only provides a typical value.

4.4 Coordinate Area (CoordArea)

The Coordinate Area class defines the volume in coordinate space that is occupied by the object it is attached to. It is an aggregate of one or more ranges in individual coordinates and is required to have a reference (IDREF in the XML implementation) to a CoordSys. Multiple ranges along each coordinate axis are OR-ed together; the ranges of different axes are logically AND-ed together.

4.4.1 ScalarInterval

A ScalarInterval consists of a LoLimit and/or a HiLimit, both of which contain a double value and a unit. Note that they do not both have to be present, but at least one of them needs to be. If only one is present, an upper or lower limit is indicated. ScalarInterval has Boolean attributes LoLimInclude and HiLimInclude and a FillFactor attribute with a value between 0 and 1 that indicates what fraction of the interval is actually covered by the data.

4.5 AstroCoordSys

The AstroCoordSys is derived from CoordSys. It still is a collection of coordinate frames, but it is required to contain specific frame classes derived from the CoordFrame base class, in addition to zero or more additional (generic) frames. The required frames are TimeFrame, SpaceFrame, and SpectralFrame; RedshiftFrame is optional.

4.5.1 TimeFrame

The Time Frame contains two or three objects: a reference position, a time scale, and, optionally, a time reference direction.

4.5.1.1 ReferencePosition

The reference position, or spatial coordinate origin, may be chosen from a standard list of such origins (StdRefPosition) or specified as a particular coordinate position (CoordOrigin). In the latter case, one may nest the origins, but eventually they should be referenced to a known standard origin. The list of standard origins includes (see Table 1): GEOCENTER, BARYCENTER, HELIOCENTER, TOPOCENTER, LSR, GALACTIC_CENTER, LOCAL_GROUP_CENTER, EMBARYCENTER, MOON, MERCURY, VENUS, MARS, JUPITER, SATURN, URANUS, NEPTUNE, PLUTO, RELOCATABLE; additional values (e.g., planetary satellites, non-planet solar system objects) are allowed, provided they are identified in a referenced ephemeris or other authoritative source (see: Section 4.5.1.4). Ultimately, one must be able to tie the coordinate origin down to the geocenter, be it through a geographic position, an IAU resolution, an orbit ephemeris, or a solar system ephemeris – unless one deals with simulation data that have a RELOCATABLE origin. Planetary Ephemeris is required for any position related to a solar system entity other than the geocenter. ReferencePosition is a standard class that is being used for all four STC frames, though there are different restrictions for the four usages. For the Time Frame LSRK, LSRD, GALACTIC_CENTER, LOCAL_GROUP_CENTER, and RELOCATABLE are not allowed values; for simulations one may want to use a custom position at the origin of the relocatable spatial frame.

Table 1. Standard Reference Positions

Reference Position	Description	Comments
GEOCENTER	Center of the earth
BARYCENTER	Center of the solar system barycenter
HELIOCENTER	Center of the sun
TOPOCENTER	“Local”; in most cases this will mean: the location of the telescope
LSR or LSRK	Kinematic Local Standard of Rest: 20 km s^-1 in the direction of GALACTIC_II(56,+23)	Only to be used for redshifts and Doppler velocities, and spectral coordinate
LSRD	Dynamic Local Standard of Rest: 16.6 km s^-1 in the direction of GALACTIC_II(53,+25)	Only to be used for redshifts and Doppler velocities, and spectral coordinate
GALACTIC_CENTER	Center of the Galaxy: 220 km s^-1 in the direction of GALACTIC_II(90,0) wrt LSRD
LOCAL_GROUP_CENTER	Center of the Local Group: 300 km s^-1 in the direction of GALACTIC_II(90,0) wrt BARYCENTER	Only to be used for redshifts and Doppler velocities, and spectral coordinate
EMBARYCENTER	Earth-moon barycenter
MOON	Center of the moon
MERCURY	Center of Mercury
VENUS	Center of Venus
MARS	Center of Mars
JUPITER	Center of Jupiter
SATURN	Center of Saturn
URANUS	Center of Uranus
NEPTUNE	Center of Neptune
PLUTO	Center of Pluto
RELOCATABLE	Relocatable center; for simulations	Only to be used for spatial coordinates
UNKNOWN	Unknown reference position	Only to be used as a last resort The client is responsible for assigning a suitable default

4.5.1.2 TimeScale

The time scale must be chosen from among the list recognized by the IAU (see Table 2): TT, TDT, ET, TAI, IAT, UTC, TDB, TEB, TCG, TCB, LST. TT is the default; TDT and ET are obsolete synonyms for TT; IAT is an unofficial synonym for TAI; and use of LST is to be discouraged. At some point other time scales may need to be added as they become recognized, such as planet- or moon-based time scales. In most cases where TDB is specified, the likely intent was TEB, so TDB may be considered a synonym of TEB; its use requires the presence of a Planetary Ephemeris. For further details, see Seidelmann & Fukushima (1992)[i] and Standish (1998)[ii].

We will allow the value LOCAL, only to be used with RELOCATABLE space frames (see: Section 4.5.1.1).

For a handy explanation of time scales, see: http://tycho.usno.navy.mil/systime.html

For a glossary of fundamental astronomy terms, see: http://syrte.obspm.fr/iauWGnfa/NFA5_B3.html

In the XML implementations the Timescale element is nillable.

Table 2. Timescales

Timescale	Description	Comments
TT	Terrestrial Time
TDT	Terrestrial Dynamic Time; synonym for TT
ET	Ephemeris Time: predecessor of, and continuous with, TT
TAI	International Atomic Time; 32.184 s behind TT
IAT	Synonym for TAI
UTC	Coordinated Universal Time; 32 s behind TAI in 2000-2005	Includes leap seconds Pre-1972 times will be assumed to be UT/GMT
TDB	Barycentric Dynamical Time; synchronous with TT, except for variations in earth’s orbital motion	In most cases where TDB is specified, TEB is really the one used
TEB	Barycentric Ephemeris Time; independent variable in solar system ephemeris, linear function of TT	Requires specification of the solar system and planetary ephemeris used
TCG	Geocentric Coordinate Time; properly relativistic time, running a factor 7∙10^-10 faster than TT
TCB	Barycentric Coordinate Time; properly relativistic time, running a factor 1.5∙10^-8 faster than TDB
LST	Local Siderial Time	Ground-based observations only
LOCAL	“Local” time	Only to be used for simulations, in conjunction with RELOCATABLE spatial coordinates

4.5.1.3 TimeRefDirection

If the Time Frame’s Reference Position is not TOPOCENTER, times have clearly been transformed from observed time at the location where the observation was made to some other spatial location. In order to effect such a transformation, a direction of origin must have been assumed for the observed phenomenon; that direction is given in TimeRefDirection.

4.5.1.4 Planetary ephemeris (if needed)

The planetary ephemeris object PlanetaryEphem indicates which solar system ephemeris was used in the AstroCoordSys. In general, this will be JPL’s DE200 or DE405 (default). It should only be present if a solar system ephemeris was used, for instance because of a planet-based ReferencePosition or the application of barycenter corrections. In addition, the information in Sections 7.2-7.5 of the Explanatory Supplement to the Astronomical Almanacⁱⁱⁱ may be considered a known authoritative source for the purpose of spatial reference frames. If the SpaceRefFrame (see: Section 4.5.2.3) is defined on a body, ephemeris information on its coordinate system (pole, primary meridian) must be included in the PlanetaryEphem.

In the XML implementations this element is nillable.

4.5.2 SpaceFrame

The Space Frame contains a reference position, a reference frame, and a coordinate flavor object.

4.5.2.1 ReferencePosition

This object is of the same class as described in Section 4.5.1.1, with the following restrictions. The value RELOCATABLE is allowed, but LSRD, LSRK, GALACTIC_CENTER, and LOCAL_GROUP_CENTER are not. Obviously, if an explicit coordinate origin is provided, those coordinates should be referenced to a different CoordSys; one may still nest them, but eventually they should be referenced to a known standard origin.

4.5.2.2 CoordFlavor

This class is peculiar to spatial coordinates. It indicates the intrinsic dimensionality of the coordinate system (1, 2, or 3), and the type of coordinates: Cartesian, spherical, unitsphere, or POLAR. For 3-dimensional SPHERICAL (because of geographical applications) we allow the special Units value “deg deg m”. The UnitSphere has default units “”. This list will likely be expanded with, for instance, cylindrical coordinates.

4.5.2.3 SpaceRefFrame

While the Reference Position pins down the origin of the spatial coordinate system, the Space Reference Frame specifies its orientation. In most cases this will be a StdFrame, consisting of a RefSystem (FK4, FK5, ECLIPTIC, ICRS, GALACTIC_I, GALACTIC_II, SUPER_GALACTIC, AZ_EL, BODY; the first three require a CoordEquinox, which is nillable in the XML implementation). The Standard Frame may be BODY if the Reference Position is specified as a solar system object. In addition, we allow solar, lunar, planetary, and planetary satellite coordinate frames (planetocentric and planetographic) as defined by Sections 7.2-7.5 of the Explanatory Supplement to the Astronomical Almanac (Seidelmann, 1992)[iii]; see also Fränz & Harper (2002)[iv]. For the most current update of cartographic coordinates and rotation rates, see Seidelmann et al. (2002)[v].

A full list of Standard Reference Frames is provided in Table 3.

Alternatively, a CustomFrame may be specified by way of the pole (Z) axis and the longitude zero-point (X-axis) directions.

We want to provide some caveats on subtle differences between various coordinate systems that may look similar.

First, one should note that the 2-dimensional spherical versions of all celestial coordinate systems are left-handed, but that their 3-dimensional Cartesian versions are right-handed.

Second, because of the definition of longitude (IAU 1970), following astronomical tradition, longitude increases westward in the planetographic coordinate frames for Mercury, Mars, Jupiter, Saturn, and Neptune (MERCURY_G, MARS_G, JUPITER_G, SATURN_G, and NEPTUNE_G – ignoring planetary satellites), since their rotation is direct (prograde); hence, these coordinate systems are also left-handed. Note that earth, sun, and moon are exempted from this rule because of even older conventions. In addition, many coordinate systems that are based on video devices are left-handed. All other coordinate systems (including all planetocentric systems) are right-handed.

Finally, beware that planetographic and planetocentric coordinates may differ in three respects:

For some, the longitudinal directions are opposite
Planetocentric latitude is based in the vector from the planet’s center, while planetographic latitude is measured with respect to the local vertical (and hence a reference spheroid needs to be adopted)
Planetocentric coordinates are longitude, latitude, and radius; planetographic coordinates are longitude, latitude, and elevation (with respect to the reference spheroid)
The origin of planetographic longitude is tied to a particular feature on the surface; planetocentric longitude’s origin is defined purely in terms of the rotational ephemeris of that feature, which may result in slight differences.

For further details, see Seidelmann (1992, Sections 4.2 and 7)ⁱⁱⁱ, Seidelmann et al. (2002)^v, and Duxbury et al. (2002)[vi].

Table 3. Standard Reference Frames

Reference Frame	Description	Comments
FK4	Fundamental Katalog, system 4; Besselian	Requires Equinox; default B1950.0 Left-handed in spherical coordinates
FK5	Fundamental Katalog, system 5; Julian	Requires Equinox; default J2000.0 Left-handed in spherical coordinates
ECLIPTIC	Ecliptic coordinates	Left-handed in spherical coordinates
ICRS	International Celestial Reference System	Left-handed in spherical coordinates
GALACTIC_I	Old Galactic coordinates	Left-handed in spherical coordinates
GALACTIC[_II]	“New” Galactic coordinates	Left-handed in spherical coordinates
SUPER_GALACTIC	Super-galactic coordinates: pole at GALACTIC_II (47.37,+6.32) origin at GALACTIC_II (137.37,0)	Left-handed in spherical coordinates
AZ_EL	Local azimuth and elevation	Ground-based observatories Azimuth: from north through east
BODY	Generic “BODY” coordinates
GEO_C	Geographic (geocentric) coordinates: longitude, latitude, geocentric distance	3-D spherical or 3-D Cartesian
GEO_D	Geodetic coordinates: longitude, latitude, elevation	Semi-major axis and inverse flattening of the reference spheroid may need to be provided; default is IAU 1976 (6378140 m, 298.2577)
MAG	Geomagnetic coordinates
GSE	Geocentric Solar Ecliptic coordinates
GSM	Geocentric Solar Magnetic coordinates
SM	Solar Magnetic coordinates
HGC	Heliographic coordinates	See Explanatory Supplement, Section 7.2
HEE	Heliocentric Earth Ecliptic coordinates
HEEQ	Heliocentric Earth Equatorial coordinates
HCI	Heliocentric Inertial coordinates
HCD	Heliocentric coordinates of Date
MERCURY_C	Planetocentric coordinates on Mercury	See Explanatory Supplement, Section 7.4
VENUS_C	Planetocentric coordinates on Venus	See Explanatory Supplement, Section 7.4
LUNA_C	Selenocentric coordinates	See Explanatory Supplement, Section 7.3
MARS_C	Planetocentric coordinates on Mars	See Explanatory Supplement, Section 7.4
JUPITER_C _III	Planetocentric coordinates on Jupiter, system III	See Explanatory Supplement, Section 7.4
SATURN_C _III	Planetocentric coordinates on Saturn, system III	See Explanatory Supplement, Section 7.4
URANUS_C _III	Planetocentric coordinates on Uranus, system III	See Explanatory Supplement, Section 7.4
NEPTUNE_C _III	Planetocentric coordinates on Neptune, system III	See Explanatory Supplement, Section 7.4
PLUTO_C	Planetocentric coordinates on Pluto	See Explanatory Supplement, Section 7.4
MERCURY_G	Planetographic coordinates on Mercury	See Explanatory Supplement, Section 7.4 Left-handed
VENUS_G	Planetographic coordinates on Venus	See Explanatory Supplement, Section 7.4
LUNA_G	Selenographic coordinates	See Explanatory Supplement, Section 7.3
MARS_G	Planetographic coordinates on Mars	See Explanatory Supplement, Section 7.4 Left-handed
JUPITER_G _III	Planetographic coordinates on Jupiter, system III	See Explanatory Supplement, Section 7.4 Left-handed
SATURN_G _III	Planetographic coordinates on Saturn, system III	See Explanatory Supplement, Section 7.4 Left-handed
URANUS_G _III	Planetographic coordinates on Uranus, system III	See Explanatory Supplement, Section 7.4
NEPTUNE_G _III	Planetographic coordinates on Neptune, system III	See Explanatory Supplement, Section 7.4 Left-handed
PLUTO_G	Planetographic coordinates on Pluto	See Explanatory Supplement, Section 7.4
UNKNOWN	Unknown reference frame	Only to be used as a last resort The client is responsible for assigning a suitable default

4.5.2.4 OffsetCenter

In order to accommodate positions that are given as offsets in Right Ascension and Declination from some specific position, the optional OffsetCenter object is provided. Note that this is purely for numeric offsets. True angle offsets should be handled through a CustomFrame.

4.5.2.5 Position Angles

Position angle definitions can be a great source of confusion. To reduce ambiguity, we will attach a Reference attribute to position angles that may have the values “North”, “X” (default), or “Y”. If the reference is “North”, position angles will be counted from north through east; this should only be used with coordinate systems where “North” has meaning. If the reference is “X” (the default), the position angle will be counted from the positive first coordinate axis through the positive second coordinate axis. If the reference is “Y”, the position angle will be counted from the positive second coordinate axis through the positive first coordinate axis. These definitions are independent of the handedness of the coordinate system. For spherical systems, the longitude is considered the first axis in this context, and latitude the second. Note that in most (though not all) cases “North” is equivalent to “Y”.

4.5.3 SpectralFrame

The Spectral Frame only contains a reference position.

4.5.3.1 ReferencePosition

This object is of the same class as described in Section 4.5.1.1, without any restrictions.

4.5.4 RedshiftFrame

The Redshift Frame contains two objects: a reference position and a Doppler definition object.

4.5.4.1 ReferencePosition

This object is of the same class as described in Section 4.5.1.1, without any restrictions.

4.5.4.2 DopplerDefinition

This object specifies what the definition of redshift is and how it should be translated to Doppler velocity. Allowed values are OPTICAL, RADIO, and RELATIVISTIC.

OPTICAL:

RADIO:

RELATIVISTIC:

It should be emphasized that Doppler velocities are formal velocities; i.e., defined by a formalism and not necessarily physical in nature. One should also note here that RELATIVISTIC is not strictly correct and we should, at some point, probably move toward compliance with the third FITS WCS paper.

An attribute indicates what the type of the values is, VELOCITY or REDSHIFT. We strongly advise against using REDSHIFT with anything but OPTICAL.

In the XML implementations this element is nillable.

4.6 AstroCoords

The AstroCoords object specifies a particular position in STC coordinate space. It requires a reference to an AstroCoordSys object and it is made up of 1 to 5 Coordinate objects, at most one each of the following:

Time of class TimeCoord
Position of class SpatialCoord
Velocity of class SpatialCoord
Redshift of class SpectralCoord
Spectrum of class SpectralCoord

Note that all objects are optional. However, in order to constitute a meaningful AstroCoords object, one would expect at least one of them to be present.

The three specialized STC Coordinate classes, TimeCoord, SpatialCoord, and SpectralCoord, are all derived from a generic base-class Coordinate (see: Section 4.3.1). Instead of providing the actual coordinate elements, the object may refer to a FITS file that provides some or all of them.

Also note that if both a Redshift coordinate and a Spectral coordinate are present, the latter will contain rest frequency values.

4.6.1 TimeCoord

The error, resolution, size, and pixel size components of this class (derived from Coordinate) are fully generic, i.e., consisting of a scalar value (double) and unit string. The allowed time units are ‘s’ (second), ‘d’ (day = 86400 s), ‘yr’ or ‘a’ (Julian year = 365.25 d), ‘cy’ (Julian century = 36525 d).

The CoordValue object in TimeCoord is of class AstronTime.

4.6.1.1 AstronTime

A time (i.e., a particular instant in history) is an aggregate of two or three objects: a TimeScale (Section 4.5.1.2), an AbsoluteTime, and, optionally, a RelativeTime (or ElapsedTime). Note that, in principle, all times are really elapsed times. The difference is that for absolute times there is an implicit agreement as to what the reference instant in time is.

4.6.1.1.1 AbsoluteTime

AbsoluteTime contains is instantiated as one of its four subclasses:

ISOTime: a time instant expressed in a subset of the ISO-8601 format; i.e., a string of format yyyy-mm-ddThh:mm:ss.sss…; the integer part of the seconds is in the range 0 to 60 for time scales that include leap seconds, 0 to 59 for all other time scales. We shall assume that ISOTime always relates to an (extrapolated) Gregorian date, independent of date and place, though caution should be exercised when using it for dates before, say, 1800 CE (some might argue 1918 CE). The earliest date that can be expressed in this format is 0001-01-01; prior to this date one should use JDTime.

2. JDTime: a decimal number (note: in principle unlimited precision!) representing the Julian Day of a particular instant.

3. MJDTime: a decimal number (note: in principle unlimited precision!) representing the Modified Julian Day of a particular instant (MJDTime = JDTime – 2,400,000.5).

4. TimeOrigin: a string with the value RELOCATABLE, primarily for simulation work, to be used in conjunction with TimeScale LOCAL and a RELOCATABLE SpaceFrame.

4.6.1.1.2 RelativeTime

Relative time is a decimal number representing the amount of time elapsed since AbsoluteTime. It includes a unit.

4.6.2 SpatialCoord

Spatial coordinates are special in that they can be explicitly multi-dimensional and that they serve positions as well as their first time derivatives (physical velocities – not to be confused with redshifts or Doppler velocities). Not only does this mean that scalar values are to be replaced by vectors, but components like errors, resolutions, and sizes become more complicated. SpatialCoord is an aggregate of CoordName, Dimensionality, CoordValue (class SCValue), CoordError, CoordResolution, CoordSize, CoordPixSize (all class MultiCoord). We stress that Dimensionality should force all components of SpatialCoord to be consistent in type and content.

It may well be that there is merit in sub-classing a VelocityCoord class, since sexagesimal formats are not needed and a time unit needs to be added. Either way, we suggest that the units for velocity be the same as for position, but that a (standard) time unit be added for the denominator.

4.6.2.1 Dimensionality

A single object of this class controls all components of the SpatialCoord class by specifying how many coordinate axes need to be represented. Note that this is distinct from the CoordFlavor object described in Section 4.5.2.2: CoordFlavor specifies the number of spatial axes defined in the AstroCoordSys; Dimensionality specifies how many of those are actually provided in the AstroCoords object – one could envision a catalog with only Right Ascensions, where the CoordFlavor would be spherical, 2-dimensional, but the dimensionality just be 1.

4.6.2.2 CoordName

This object now contains a list of <Dimensionality> strings with the names of all axes present.

4.6.2.3 SCValue

The spatial coordinate value is a vector (length determined by Dimensionality) of numbers (SValue).

4.6.2.4 MultiCoord

Expressing errors and sizes for vectors is slightly more complicated. If the errors are independent for each vector component, then a simply SValue object (vector of decimal values with a Unit) will do. If they are not independent (or if the resolution is tilted), one can either add a PosAngle (see also Section 4.5.2.5) to the SValue object, or specify the MultiCoord object through a Matrix of decimal values with a Unit. Position angles are measured following the definition in Section 4.5.2.5. In the case of spherical coordinates, all sizes, resolutions, and errors will be expressed in terms of arc lengths, for longitudes as well as for latitudes; i.e., the error in right ascension is expressed as a real arc angle, independent of declination.

4.6.3 SpectralCoord

The SpectralCoord is used for the spectral as well as the redshift components of the AstroCoords object. It is a completely generic Coordinate class (see: Section 4.3.1) where Name is a string and all other components consist of a double Value and a string Unit.

4.7 AstroCoordArea

The Coordinate Area class defines the volume in coordinate space that is occupied by (or: the coverage of):

Resource
Query
Catalog data set
Observation

It is an aggregate of one or more ranges in individual coordinates and is required to have a reference to an AstroCoordSys. Multiple ranges along each coordinate axis are OR-ed together; the ranges of different axes are logically AND-ed together.

4.7.1 TimeInterval

A TimeInterval consists of a StartTime and/or a StopTime, both of which are instantiations of AstronTime. Note that they do not both have to be present, but at least one of them needs to be. TimeInterval has Boolean attributes LoLimInclude and HiLimInclude, and attribute FillFactor (see Section 4.4.1).

4.7.2 SpatialInterval

The spatial position area has more options:

Simple intervals on a per-axis basis
Circle or sphere
Regions

Shapes: polygon, sector, circle, ellipse, convex, convex hull, sky index
Operations: intersection, union, negation

4.7.2.1 CInterval

CInterval is the vector equivalent of ScalarInterval (see: Section 4.4.1). LoLimit and HiLimit are of type SCValue (see Section 4.6.2.3).

4.7.2.2 Sphere

Since spherical regions are quite common (cone search!) these are made available as special cases. The class is an aggregate of a Center position (of type SCValue; see: Section 4.6.2.3) and a Radius (consisting of a double and a unit). The spatial coordinates of the center should be in the AstroCoordSys associated with AstroCoordArea, of course. Note that the 2-D equivalent (circle) is available in the Region class (see: Section 4.8).

4.7.2.3 SpatialRegion

This is an object of class Region (see: Section 4.8).

4.7.3 VelocityInterval

The velocity interval is an instantiation of CInterval (see: Section 4.7.2.1).

4.7.4 SpectralInterval

The SpectralInterval is derived from the generic ScalarInterval class (see: Section 4.4.1), restricting Unit to appropriate values.

4.7.5 RedshiftInterval

The RedshiftInterval is derived from the generic ScalarInterval class (see: Section 4.4.1), restricting Unit to appropriate values.

4.8 Region

The Region specification is a rather elaborate construct that allows a very flexible definition of arbitrary 2-dimensional spatial shapes. It has 9 derived classes: 5 shapes and 3 operations. Note that the result of these operations performed on one or more regions is a region. All spatial coordinates should be in the AstroCoordSys associated with AstroCoordArea (or Region), of course. The Region object has an important attribute, fill_factor (between 0.0 and 1.0; default 1.0) that indicates what fraction of the region is really filled or covered. This is particularly useful when describing a resource’s coverage.

4.8.1 Shapes

The first four shapes are 2-dimensional, while the remaining two are 3-dimensional, associated with the unit sphere. All boundaries are considered part of the inside of a shape. Different shapes in the same Region object may refer to different Coordinate Systems, although this should not be encouraged.

4.8.1.1 AllSky

This is just a short-hand object to conveniently indicate “All”.

4.8.1.2 Circle

A Circle (2-dimensional) shape (region) is an aggregate of a Center position (type SCValue; see: Section 4.6.2.3) and a Radius (consisting of a double and a unit).

4.8.1.3 Ellipse

The Ellipse (2-dimensional) is derived from the Circle by adding a minor radius and a position angle. The inheritance could, of course, have gone the other way (Circle being a special case of an Ellipse), but we felt that it is important to retain the simplest definition of a circle. Position angles are measured following the definition in Section 4.5.2.5 and refer to the first axis.

4.8.1.4 Polygon

A Polygon (2-dimensional) is an ordered list of one or more vertices. Its area is defined as that contained within the lines connecting neighboring (that is, in the ordered list) vertices. If the CoordFlavor is CARTESIAN, these lines are truly lines.

If the CoordFlavor is SPHERICAL, the lines are, by default, great-circles, unless the Vertex object contains a SmallCircle object; in that case the line connecting that vertex with its predecessor is a small-circle (parallel). The curvature of the parallel is determined by the pole of the SpatialFrame in the current AstroCoordSys, unless a PolePosition is explicitly specified in the Vertex object. It is the responsibility of the server to ensure that the positions of the two sequential vertices actually lie on a parallel that is consistent with the implied or specified pole. In order to avoid ambiguities in direction, vertices need to be less than 180° apart in both coordinates. Great circles or small circles spanning 180° require specification of an extra intermediate vertex.

The area A of a polygon with n vertices x in Cartesian space may be calculated as:

The summation is over determinants of matrices formed by the position vectors x_i of successive vertices; x_n+1 = x₁. In spherical space (left-handed coordinates) the area is:

are the polygon’s angles at the vertices. Reverse the sign for right-handed coordinates. If the coordinate system is defined on the surface of a body (rather than the celestial or unit sphere), one should multiply by the square of the radius.

The boundaries are considered part of the region. The inside of the region is defined as that part of coordinate space that is encircled by the polygon in a counter-clockwise sense. What this means is that, in a plane, if A > 0, the “inside” of the polygon is included; if A < 0, the “outside” is selected. On a sphere with a left-handed (celestial) coordinate system, if A > 0, one has identified the inside of the polygon; if A < 0, one used the “outside” angles of the polygon and the area is really. Note that the negation operation is a simple matter of reversing the order of the vertex list.

4.8.1.5 Box

A Box is a special case of a Polygon, defined purely for convenience. It is specified by a center position and size (in both coordinates) defining a cross centered on the center position and with arms extending, parallel to the coordinate axes at the center position, for half the respective sizes on either side. The box’s sides are line segments or great circles intersecting the arms of the cross in its end points at right angles with the arms.

4.8.1.6 Sector

A Sector (2-dimensional) is defined by a position of type SCValue (see: Section 4.6.2.3) and two position angles. The inside of the sector is that part of the plane or sphere that is swept by a half-line or great-circle rotating counter-clockwise from the first to the second position angle, centered on the specified position. Position angles are measured following the definition in Section 4.5.2.5.

4.8.1.7 Convex

A Convex is the convex region that is defined by an aggregate of one or more Constraints. It is defined on the surface of the unit sphere and is hence in 2-dimensional spherical space. Each Constraint selects a circular region (or point) on the unit sphere. The Convex is therefore the intersection of a collection of circles and its sides are great-circles and/or small-circles. A Constraint is specified by a 3-dimensional vector (a point on the unit sphere) and an Offset along that vector. The Constraint’s circular area is defined by the intersection of the unit sphere and the plane normal to the specified vector, intersecting it at the Offset distance from the origin. The valid range for Offset is -1 to +1, with the boundaries included. Note that a Constraint is fully equivalent to a Circle shape; hence, a Convex is equivalent to the intersection of one or more Circles. Similarly, a Convex can be described by a Polygon.

4.8.1.8 ConvexHull

A ConvexHull is defined by an unordered list of one or more points. It is the smallest convex polygon that contains all points in the list. It may be constructed as the union of the triangles that can be formed from all possible triplets of points in the list.

4.8.1.9 SkyIndex

This is currently a place holder to allow integration of the specification of regions through sky indexing schemes.

4.8.2 Operations

There are three operations defined on or between Regions. The result of each of those operations is also a Region.

4.8.2.1 Intersection

The Intersection of two Regions is the Region that is common to both (logical AND). We might consider allowing Intersections of more than two Regions.

4.8.2.2 Union

The Union of two Regions is the Region that is contained in either or both of them (logical OR). We might consider allowing Unions of more than two Regions.

4.8.2.3 Negation

The negation of a Region is the Region that is not contained in the original (logical NOT). Note that this logically leads to a Region that does not include its boundaries.

5 Projection

The metadata described in this document specify a position or the volume occupied by a dataset. In order to be able to transform the coordinates for individual Data Model components (such as pixels) one needs a Projection object as well. Such a Projection or Mapping metadata object is very much like the meat in the FITS WCS. It will be specified in a separate document. David Berry is working on this.

The way this will be realized is that a pixilated data object has three coordinate metadata objects associated with it. In addition to the Observatory Location and the Observation Location STC objects (see Section 6.2.4), there will be a pixel space metadata object. The mapping object will define the transformation between the pixel coordinate system and the Observation Location’s coordinate system.

6 Conclusion and Usage Notes

VO needs a stringent specification in order to not get into trouble later on when we want to, for instance:

use far field data for near field objects
mix data in equatorial coordinates with data in Jovian coordinates
combine pulsar observations from ground-based, spacecraft, and lunar observatories

6.1 Methods

The metadata objects described in Section 4 provide sufficient and necessary information, and ensure self-consistency. As commented before, this document focuses on the structure of the design, not on the methods. However, we can make some general observations. First, most of the client-level methods will probably appear as methods on the projection class. Second, robust design and implementation favors access to the various elements through the top-level objects. In other words, public methods should appear on the AstroCoordSys, AstroCoords, and AstroCoordArea classes, while most methods on the component classes ought to be restricted to the friend classes in the whole of the STC design structure.

Examples of methods that are obviously required:

AstroCoords: get {spatial, temporal, spectral, redshift} coordinates of object
AstroCoords: return new AstroCoords object which references a specified (presumably different) AstroCoordSys object (i.e., coordinate transformation)
AstroCoordArea: same methods as for AstroCoords, above
AstroCoordArea: return (measured) area and fill_factor of object
AstroCoordArea: is a given AstroCoords point inside or outside the region?
AstroCoordArea: constructor methods that implement the three operations on Region (negation, union, intersection)
AstroCoordArea: constructor methods that create the largest inscribing and smallest circumscribing circles and rectangles, with correct fill_factor

6.2 Usage

Here are some notes on how the various components are intended to be used in the different use contexts. The reader is reminded that the numeric components of the Coordinate elements may indicate a definite value or a range of values, depending on whether there is a single instance or a pair of instances of these components.

6.2.1 Resource Profile

The STC Resource Profile, or Coverage, describes what part of STC space is potentially covered by the datasets available from the resource. This is a potential coverage since there is no guarantee that the entire volume is covered (in particular, if the resource contains a collection of pointed observations); note that this is where the Region fill-factor is a useful attribute. Examples of resources are depositories of pointed observations, survey atlases, and catalogs. The profile consists of an AstroCoordSys object that represents the resource’s native coordinate system; an AstroCoordArea object that represents the actual coverage in the four standard STC frames; and an AstroCoords object that gives some specifics on the products in the resource. The purpose of the first two will be obvious, but the third may need some explanation. The AstroCoords object does not intend to convey a particular position, but the typical properties of datasets in the resource. The Coordinate objects will not contain a CoordValue, but CoordError, CoordResolution, CoordSize, and CoordPixSize represent typical values for the datasets, where CoordSize refers to the field-of-view. Additional AstroCoordSys objects may be required if Custom Reference Frames or Reference Positions are used.

6.2.2 Query Constraint

A query constraint is, in a way, a mirror image of a resource profile, and its structure and the meaning of its components is very much the same: the AstroCoordArea defines the coordinate volume that the query requests to be filled, while the AstroCoords components (again, with missing CoordValue), as far as present, represent desirable values for errors, resolution, pixelsize, and field-of-view (if the whole area cannot be filled at once). Additional AstroCoordSys objects may be required if Custom Reference Frames or Reference Positions are used.

6.2.3 Catalog Entry

The STC object that accompanies the return of catalog information (typically a table of selected catalog entries) is set up slightly differently. The AstroCoordSys provides the usual coordinate system information, of course. The AstroCoordArea describes the coverage of the returned information; that will usually be the intersection of the query coverage with the resource (catalog) coverage. The AstroCoords object will generally refer to the catalog data that are being returned; i.e., its components are likely to refer to columns in the table that the STC object is associated with (such as galaxy positions, sizes, and redshifts) or have specific values if they happen to be constant for all entries (for instance, errors or resolution). Since Catalog objects may contain columns for multiple coordinate systems, or entries using different systems, we need to allow multiples of all three STC objects.

6.2.4 Observational Data

In this context two STC objects are required. One describes the location of the observatory (AstroCoordSys and AstroCoords; note that this may refer to an orbit ephemeris file for spacecraft). The other STC object describes the volume in coordinate space that is occupied by the observational data: AstroCoordSys, AstroCoordArea (the field-of-view), and AstroCoords (to convey errors, resolution, and pixel size). The information about the observatory’s location is essential, in particular for near-field/far-field spatial transformations and time transformations. Note that its velocity is also needed, either explicitly or implicitly. This is a typical case where metadata that are “obvious” (and often implied) in the context of a particular observatory’s archive needs to be made explicit. Additional AstroCoordSys objects may be required for either STC object if Custom Reference Frames or Reference Positions are used.

As noted in Section 5, there is a third Coordinate metadata element in the case of pixilated data. A Mapping element will define the transformation between the Observation Location and the Pixel Space.

One should be aware that in those cases the AstroCoordArea object associated with the Observation Locations defines the volume occupied by the data, and that this will be contained in, but may be smaller than, the CoordArea object associated with the Pixel Space.

7 Implementation

7.1 STC-X: XML Schema Implementation

The design of Section 4 has been implemented in three XML schemata, as stated in Section 1. http://www.ivoa.net/Documents/latest/STC-X.html provides documentation for this implementation.

The present document will gradually be expanded with more examples in Appendix B: Examples.

One important thing to note is that the schema implementation will allow all elements to contain actual values or to refer to another element; this will allow integration into VOTable where such references would be to table columns. Another notable implementation detail is that coordinate components are allowed to be provided in FITS file. The schemas include a mechanism to associate particular elements with specific binary table columns. This is particularly of interest in conjunction with spacecraft orbit ephemerides.

7.1.1 Simplifications

Simplifications are allowed as long as the requirements are not compromised. They come in two categories.

7.1.1.1 Descriptions

Since it was decided to allow the use of XInclude in the schemas, we will create a library of common element instances with distinctive ID values. Consequently, it will not be necessary to create, for instance, commonly used coordinate systems in each XML document; instead, a simple XInclude to a library entry will perform the equivalent task.

7.1.1.2 Parsers

One option is to design schemas that contain subsets, in such a way that instantiations are upward compatible with the full schema. However, the simpler solution is to provide the canned elements in the XInclude library with unique and distinctive ID values, so that parsers do not need to process the entire coordinate system description but can simply rely on the ID.

7.2 STC-S

STC-S, also known as LinearSTC, is a string, or command line, implementation, based on the XML schemata. It allows one to specify an STC object in a simple phrase with sensible defaults and without redundancy. There are certain restrictions, though. The design of this specification is such that a one-to-one conversion to and from XML documents is possible. It is especially intended for applications like ADQL/S and Dublin Core descriptions. For details, see the document referenced in Section 1: http://www.ivoa.net/Documents/latest/STC-S.html.

Appendix A: UML Representation

The following pages contain the STC design in UML diagrams.

Appendix B: Examples

B.1 STCResourceProfile

Resource profile for the Chandra X-ray Observatory Data Archive

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<Name>Space</Name>

<ICRS/>

</SpaceFrame>

<Name>Energy</Name>

</SpectralFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="ICRS-TT-CXO">

<crd:Time unit="s">

<crd:Name>Time</crd:Name>

<crd:Error>0.0001</crd:Error>

<crd:Resolution>0.000016</crd:Resolution>

<crd:Resolution>3.0</crd:Resolution>

<crd:Size>1000</crd:Size>

<crd:Size>170000</crd:Size>

</crd:Time>

<crd:Position2D unit="arcsec">

<crd:Name>Position</crd:Name>

<crd:Error2>1.0 1.0</crd:Error2>

<crd:Resolution2>0.5 0.5</crd:Resolution2>

<crd:Size2>1000 1000</crd:Size2>

<crd:Size2>4000 4000</crd:Size2>

</crd:Position2D>

<crd:Spectral unit="keV">

<crd:Name>Energy</crd:Name>

<crd:Error>0.1</crd:Error>

<crd:Resolution>0.02</crd:Resolution>

<crd:Resolution>2.0</crd:Resolution>

<crd:Size>2</crd:Size>

<crd:Size>10</crd:Size>

</crd:Spectral>

</crd:AstroCoords>

<crd:Timescale>TT</crd:Timescale>

<crd:ISOTime>1999-07-23T16:00:00</crd:ISOTime>

</StartTime>

</TimeInterval>

<reg:AllSky fill_factor="0.02"/>

</Region>

</SpectralInterval>

</AstroCoordArea>

</STCResourceProfile>

B.2 Galaxy Catalog

This example shows the STC specification for a fictitious catalog of galaxies that covers RA from 9 to 18 hours and Dec from 20 to 70 degrees, observed between JD 2440000 and 2441000, in a band between 5000 and 6500 Å, providing (RA,Dec; FK4:B1950.0) with errors and sizes, proper motions, barycentric radial velocities, as well as Supergalactic coordinates and Galactocentric radial velocities, with errors; these quantities are supposed to be provided in columns 3-14 of an associated table.

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<Name>PosEq</Name>

<FK4>

</FK4>

</SpaceFrame>

<Name>Optical</Name>

</SpectralFrame>

<Name>DopplerVelocity</Name>

<DopplerDefinition>OPTICAL</DopplerDefinition>

</RedshiftFrame>

</AstroCoordSystem>

</TimeFrame>

<SUPER_GALACTIC/>

</SpaceFrame>

<Name>Optical</Name>

</SpectralFrame>

<Name>DopplerVelocity</Name>

<DopplerDefinition>OPTICAL</DopplerDefinition>

<GALACTIC_CENTER/>

</RedshiftFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="B1950-OPTICAL-ET">

<crd:Position2D unit="deg">

<crd:Name>RA,Dec</crd:Name>

<crd:Value2Ref>Column3</crd:Value2Ref>

<crd:Error2Ref>Column4</crd:Error2Ref>

<crd:Size2Ref>Column5</crd:Size2Ref>

</crd:Position2D>

<crd:Velocity2D unit="arcsec" vel_time_unit="a">

<crd:Name>ProperMotion</crd:Name>

<crd:Value2Ref>Column6</crd:Value2Ref>

<crd:Error2Ref>Column7</crd:Error2Ref>

</crd:Velocity2D>

<crd:Redshift unit="km" vel_time_unit="s">

<crd:Name>Vrad(barycenter)</crd:Name>

<crd:ValueRef>Column8</crd:ValueRef>

<crd:ErrorRef>Column9</crd:ErrorRef>

</crd:Redshift>

</crd:AstroCoords>

<crd:AstroCoords coord_system_id="SGC-OPTICAL-ET">

<crd:Position2D unit="deg">

<crd:Name>SGLong,SGLat</crd:Name>

<crd:Value2Ref>Column10</crd:Value2Ref>

<crd:Error2Ref>Column11</crd:Error2Ref>

<crd:Size2Ref>Column12</crd:Size2Ref>

</crd:Position2D>

<crd:Redshift unit="km" vel_time_unit="s">

<crd:Name>Vrad(Galcenter)</crd:Name>

<crd:ValueRef>Column13</crd:ValueRef>

<crd:ErrorRef>Column14</crd:ErrorRef>

</crd:Redshift>

</crd:AstroCoords>

<crd:Timescale>ET</crd:Timescale>

<crd:JDTime>2440000</crd:JDTime>

</StartTime>

<crd:Timescale>ET</crd:Timescale>

<crd:JDTime>2441000</crd:JDTime>

</StopTime>

</TimeInterval>

<reg:Polygon unit="deg">

<reg:Vertex>

<reg:Position>270 20</reg:Position>

</reg:Vertex>

<reg:Vertex>

<reg:Position>90 20</reg:Position>

<reg:SmallCircle/>

</reg:Vertex>

<reg:Vertex>

<reg:Position>90 70</reg:Position>

</reg:Vertex>

<reg:Vertex>

<reg:Position>270 70</reg:Position>

<reg:SmallCircle/>

</reg:Vertex>

</reg:Polygon>

</Region>

</SpectralInterval>

</RedshiftInterval>

</AstroCoordArea>

</CatalogEntryLocation>

B.3 ROSAT Image

The following document describes the STC metadata for a ROSAT image. Note that the observatory position is contained in an orbit ephemeris file.

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<FK5>

</FK5>

</SpaceFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="FK5-UTC-VEL">

<crd:CoordFile>

<crd:FITSFile hdu_num="1"> http://MySpace.edu/OrbitEphemeris.fits </crd:FITSFile>

<crd:FITSTime>

<crd:Name>Time</crd:Name>

<crd:Value>TIME</crd:Value>

</crd:FITSTime>

<crd:FITSPosition>

<crd:Name>Position</crd:Name>

<crd:Value>X,Y,Z</crd:Value>

</crd:FITSPosition>

<crd:FITSVelocity>

<crd:Name>Velocity</crd:Name>

<crd:Value>VX,VY,VZ</crd:Value>

</crd:FITSVelocity>

</crd:CoordFile>

</crd:AstroCoords>

</ObservatoryLocation>

<Name>TimeUTC</Name>

</TimeFrame>

<Name>FK5Spher</Name>

<FK5>

</FK5>

</SpaceFrame>

<Name>Energy</Name>

</SpectralFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="FK5-UTC-Energy">

<crd:Time unit="s">

<crd:Name>Time</crd:Name>

<crd:TimeInstant>

<crd:Timescale>UTC</crd:Timescale>

<crd:MJDTime>49192.57</crd:MJDTime>

</crd:TimeInstant>

<crd:Error>0.1</crd:Error>

<crd:Resolution>22955</crd:Resolution>

<crd:PixSize>22955</crd:PixSize>

</crd:Time>

<crd:Position2D unit="deg">

<crd:Name>RA,Dec</crd:Name>

<crd:Value2>233.73 23.49</crd:Value2>

<crd:Error2>0.005 0.005</crd:Error2>

<crd:Resolution2>0.01 0.01</crd:Resolution2>

<crd:PixSize2>0.0041667 0.0041667 </crd:PixSize2>

</crd:Position2D>

<crd:Spectral unit="keV">

<crd:Name>Energy</crd:Name>

<crd:Value>1.0</crd:Value>

<crd:Error>0.1</crd:Error>

<crd:Resolution>2.3</crd:Resolution>

<crd:PixSize>2.3</crd:PixSize>

</crd:Spectral>

</crd:AstroCoords>

<crd:Timescale>UTC</crd:Timescale>

<crd:ISOTime>1993-07-24T13:47:39 </crd:ISOTime>

</StartTime>

<crd:Timescale>UTC</crd:Timescale>

<crd:ISOTime>1993-08-03T21:17:42 </crd:ISOTime>

</StopTime>

</TimeInterval>

<reg:Circle unit="deg">

<reg:Center>233.73 23.49</reg:Center>

<reg:Radius>1.0</reg:Radius>

</reg:Circle>

</Region>

</SpectralInterval>

</AstroCoordArea>

</ObservationLocation>

</PixelCoordFrame>

</PixelCoordFrame>

</PixelCoordSystem>

</CoordScalarInterval>

</CoordScalarInterval>

</PixelCoordArea>

</PixelSpace>

</ObsDataLocation>

B.4 Blue M81 Image from KPNO

The following example describes a blue 1000 s exposure of M81 taken at Kitt Peak. IT is half a degree in size, has 0.3” pixels, a resolution of 0.8”, and an absolute astrometric uncertainty of 1”. The metadata values specific to KPNO and to this image are printed in bold.

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<Name>GeoLongLatElev</Name>

<GEO_D/>

</SpaceFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="KPNO">

<crd:Position3D unit="deg deg m">

<crd:Name>LongLatElev</crd:Name>

<crd:Value3>248.4056 31.9586 2158</crd:Value3>

</crd:Position3D>

</crd:AstroCoords>

</ObservatoryLocation>

</TimeFrame>

<Name>Equatorial</Name>

<ICRS/>

</SpaceFrame>

<Name>Wavelength</Name>

</SpectralFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="ICRS-TT-WAVELENGTH-TOPO">

<crd:Time unit="s">

<crd:Name>Time</crd:Name>

<crd:TimeInstant>

<crd:Timescale>TT</crd:Timescale>

<crd:ISOTime>2004-07-15T08:23:56 </crd:ISOTime>

</crd:TimeInstant>

<crd:PixSize>1000</crd:PixSize>

</crd:Time>

<crd:Position2D unit="deg">

<crd:Name>RA,Dec</crd:Name>

<crd:Value2>148.88821 69.06529</crd:Value2>

<crd:Error2>0.0003 0.0003</crd:Error2>

<crd:Resolution2>0.00025 0.00025 </crd:Resolution2>

<crd:PixSize2>0.0001 0.0001</crd:PixSize2>

</crd:Position2D>

<crd:Spectral unit="Angstrom">

<crd:Name>Lambda</crd:Name>

<crd:Value>4600</crd:Value>

<crd:Resolution>400</crd:Resolution>

<crd:PixSize>400</crd:PixSize>

</crd:Spectral>

</crd:AstroCoords>

<crd:Timescale>TT</crd:Timescale>

<crd:ISOTime>2004-07-15T08:17:36 </crd:ISOTime>

</StartTime>

<crd:Timescale>TT</crd:Timescale>

<crd:ISOTime>2004-07-15T08:30:16 </crd:ISOTime>

</StopTime>

</TimeInterval>

</Coord2VecInterval>

</PositionInterval>

</SpectralInterval>

</AstroCoordArea>

</ObservationLocation>

</PixelCoordFrame>

</PixelCoordFrame>

</PixelCoordSystem>

</CoordScalarInterval>

</CoordScalarInterval>

</PixelCoordArea>

</PixelSpace>

</ObsDataLocation>

B.5 Query Specification

This example provides the STC specifications for a query that is looking for 40 arcmin images of the field 2 degrees around M81, taken since 1900, with a resolution of 1” and a pixel size of 0.5”, broadband between 4000 and 7000 Å.

<?xml version="1.0" encoding="UTF-8"?>

</TimeFrame>

<Name>Equatorial</Name>

<ICRS/>

</SpaceFrame>

<Name>Wavelength</Name>

</SpectralFrame>

</AstroCoordSystem>

<crd:AstroCoords coord_system_id="ICRS-TT-BARY">

<crd:Position2D unit="deg">

<crd:Name>RA,Dec</crd:Name>

<crd:Resolution2>0.0001 0.0001</crd:Resolution2>

<crd:Resolution2>0.0003 0.0003</crd:Resolution2>

<crd:Size2>0.5 0.5</crd:Size2>

<crd:Size2>0.67 0.67</crd:Size2>

<crd:PixSize2>0.00005 0.00005</crd:PixSize2>

<crd:PixSize2>0.00015 0.00015</crd:PixSize2>

</crd:Position2D>

<crd:Spectral unit="Angstrom">

<crd:Name>Lambda</crd:Name>

<crd:Resolution>300</crd:Resolution>

<crd:Resolution>600</crd:Resolution>

</crd:Spectral>

</crd:AstroCoords>

<crd:Timescale>TT</crd:Timescale>

<crd:ISOTime>1900-01-01T00:00:00</crd:ISOTime>

</StartTime>

</TimeInterval>

<reg:Circle unit="deg">

<reg:Center>148.9 69.1</reg:Center>

<reg:Radius>2</reg:Radius>

</reg:Circle>

</Region>

</SpectralInterval>

</AstroCoordArea>

</SearchLocation>

Appendix C: XInclude Library of Coordinate Systems

[TBD]

Appendix D: Changes from Previous Versions

From V0.5 to V0.51:

Added STCResourceProfile example in Appendix B.

From V0.51 to V0.6:

Finished schemas resulting in some tweaks to the design.

From V0.6 to V1.0:

Added solar and planetary reference frames.
Enumerated spatial reference positions, reference frames, and time scales in tables.
Added mechanism to reference coordinate values in FITS files.
Added examples
Release as Working Draft

From V1.0 to V1.10:

Added Pixel Space
Allow nillable (specifically unknown) elements; for some an UNKNOWN element has been added
Allow definite values as well as ranges (note that this means there may be 0, 1, or 2 Error, Resolution, Size, PixSize elements: 0 means N/A, 1 is a definite value, 2 define a range)
Specify rest frequencies (through the Spectral axis, in the presence of a Redshift axis)
General clarifications
AllSky was added to Region as a convenient mnemonic for “all”
Added rest frequency specification

From V1.10 to V1.20:

Distinguished LSRK and LSRD; replaced SUPER_GALACTIC_CENTER by LOCAL_GROUP_CENTER
Added Box shape to Region
Require polygon sides to be less than 180°; added explanation on defining inside and outside
Added LinearSTC implementation
Subtle changes to the schemata to force validation under Xerces-J2; this did not change anything but made the schemata a little uglier
Changed units “micron” and “A” to “um” and “Angstrom”, respectively, consistent with the FITS standard
Added timescale TEB, with references
Added warning on use of ISOTime and restricted its use explicitly
Added an explicit definition of Position Angle; in the XML implementation it is now an element, rather than an attribute (see, e.g., Ellipse)
Added a reference spheroid to GEO_D, changed GEO to GEO_C
Added an explicit discussion of planetographic and planetocentric coordinate systems, with references, as well as a discussion of right-handed and left-handed systems
Removed GEOGRAPHIC CoordFlavor, replacing it by 3-dimensional SPHERICAL, and added POLAR

From V1.20 to V1.21:

Corrected the catalog entry example in B.2, adding proper motion columns
General clarifications
Changed name of LinearSTC to STC-S; XML implementation is STC-X
Reformatted to new template
Promoted to Proposed Recommendation

References

[3] A photometric measure of the diameter of galaxies