Specdre Extension v.0.7

The items of the Extension as introduced with Specdre version 0.7 are described below. All top-level items are optional, but each is either complete or absent.

• .SPECAXIS is an _INTEGER scalar which defaults to 1. Its value is the number of the spectroscopic axis. This is the axis along which the one-dimensional `spectroscopic subsets' extend. It must be greater than or equal to 1 and less than or equal to the number of axes in <myndf>. A change of specaxis may render other components invalid as regards their values or shapes.

• .RESTFRAME is a _CHAR*32 scalar which defaults to `unknown'. Its value describes the rest frame used to express the observed frequency, wavelength, radial velocity, or redshift.

• .INDEXREFR is a _REAL or _DOUBLE scalar which defaults to 1. Its value is the index of refraction needed to convert frequency into wavelength and vice versa.

• .FREQREF is a _REAL or _DOUBLE scalar which defaults to the bad value. Its value is the reference frequency needed to convert between radial velocity and redshift on the one hand and frequency on the other hand. The value is evaluated together with .FREQUNIT:

  
  

  $$\nu_0={\it freqref}*10^{\it frequnit}*{\rm Hz}$$
  
  

• .FREQUNIT is an _INTEGER scalar which defaults to 0. Its value is the common logarithm of the unit used for .FREQREF divided by Hertz. Note that this item is not of type _CHAR, _REAL or _DOUBLE.

• .SPECVALS is an NDF structure with data, label and units components. .SPECVALS.DATA_ARRAY is a _REAL or _DOUBLE array which has the same shape as <myndf>. It defaults to a multiple copy of the centre array of the spectroscopic axis <myndf>.AXIS(specaxis).DATA_ARRAY. This structure contains spectroscopic axis values (either wavelength, or frequency, or velocity, or redshift) for each pixel of the data cube. Labels and units must be stored with this data structure. Their default values are copies from the spectroscopic axis <myndf>.AXIS( specaxis).LABEL, .UNITS in the main NDF or `unknown' if the axis has no label or unit. A modification of spectroscopic values may render parts of .RESULTS invalid, but no rules are formulated in this respect. This structure must not contain bad values.

• .SPECWIDS is an NDF structure with only a data component. .SPECWIDS.DATA_ARRAY is a _REAL or _DOUBLE array which has the same shape as <myndf>. It defaults to (i) a derivative from .SPECVALS in the way prescribed by SUN/33, or (ii) to a multiple copy of the width array of the spectroscopic axis. Just as .SPECVALS contains the multidimensional array of spectroscopic values for the pixel centres, this array contains the spectroscopic widths for the pixels. Labels and units are not to be stored with this data structure. This structure is always considered together with .SPECVALS. It must not contain bad values.

• .COVRS is an NDF-type structure with only a data component. .COVRS.DATA_ARRAY is a _REAL or _DOUBLE array which has the same shape as <myndf>. .COVRS defaults to non-existence. The meaning is as follows: for some reason pixels belonging to the same spectroscopic subset may be interrelated. While no complete covariance matrix is stored, this structure holds the sum over the rows of the covariance matrix (cf. Meyerdierks, 1992¹). For multi-dimensional data note that this holds information only about the interrelation within any one spectroscopic subset, not between different such subsets. That means we know only about interrelation along the spectroscopic axis (within a spectrum) but not perpendicular to that axis (between spectra).

• .RESULTS is an NDF-type structure with data and variance components and a number of extensions in the .MORE component. All these extensions are HDS vectors. They have either one element per component or one element per parameter. The shape of the .RESULTS structure is defined by (i) the shape of <myndf>, (ii) the total number of parameters tnpar > 0, (iii) the number of components ncomp > 0. Each component has allocated a certain number of parameters npara(comp) >= 0. The total number of parameters must be

  
  

  $$tnpar\geq\sum_{comp=1}^{ncomp}npara(comp)$$
  
  

  while the parameter index for any component runs from

  
  

  $$para1(comp)=\sum_{i=1}^{comp-1}npara(i)+1 \mbox{\phantom{mmm}to\phantom{mmm}} para2(comp)=\sum_{i=1}^{comp}npara(i)$$
  
  

  Components are additive, i.e. the combined result is the sum of all those components that can be evaluated.

  Note that the concept of a component is different from that of a transition or a kinematic component: a component is a line feature you can discern in the spectrum. Any component can in general be assigned a transition and a radial velocity. So you may have several components belonging to the same transition and several components of similar velocity belonging to different transitions. You may at any time decide that a discernible component has been misidentified and just change its identification. The concept of a component is even more general, in that it can be the continuum, in which case there is in general no laboratory frequency for identification.

  There is, however, a restriction for data sets with more than one spectrum. Any component may differ from spectrum to spectrum only by the fitted values. The mathematical type and identification of components is common to all spectra.