Frequency parameters

CHANGE-SIDEBAND	Using user-nominated I.F. change labelling to other s.b.
REGRID-SPECTRUM	Sample onto new (regular) grid (Scrunching)
SET-LINE-REST-FREQ	For cases where this is not defined in spectrum header
SET-SITE-PARAMETERS	Set up obseratory longitude etc for LSR corrections.
SET-VELOCITY-FRAME	Change velocity frame/law for display of spectra.
SET-X-SCALE	Choose units for X-axis of scan (plots and elsewhere)
SHIFT-SPECTRUM	Shift data laterally in spectrum
SHOW-X-SCALE	Show limits and units of X-axis scale

In all cases where it is relevant the choice of units for the X-axis is governed by responses to SET-X-SCALE. This allows the use of numbered points, frequency or velocity, or of arbitrary units.

Both frequency and velocity can be plotted in any one of four frames of reference, using either the so-called ``radio'' or ``optical'' velocity laws or a full relativistic velocity law (which, however, does not take into account the possible effect of the transverse velocity of the source). The default frame for display of frequencies or velocities is the one in which the data were observed. Note, however, that the frequency offset applied when the observation is made allows for both the motion of the reference frame with respect to the telescope, and for the additional velocity of the source with respect to the selected frame. For display purposes the only correction made is to the reference frame, so that frequency scales would be as measured with a frequency counter by an observer at rest in the frame, while velocities are those that she would deduce by applying the appropriate form of doppler correction.

The reference frames and velocity scaling laws supported within SPECX are as listed below:

Reference Frames

Telluric:	In this frame the plotted velocities and frequencies are the telluric values, i.e.as measured in the frame of reference in which the telescope is at rest.
LSR:	Here velocities and frequencies are plotted relative to the local standard of rest (LSR). That is, the doppler shift due to the orbital and rotational motion of the earth about the sun, and the drift velocity of the sun relative to the local stars, has been subtracted before frequency or velocity scaling.
Heliocentric:	Velocities and frequencies are plotted relative to a frame in which the sun is at rest, or, if the velocity parameter in SET-VEL-FRAME is non-zero, in a frame with a radial velocity offset from that of the sun by the nominated amount.
Geocentric:	Velocities and frequencies are plotted relative to a frame in which the centre of the earth is at rest, or, if the velocity parameter in SET-VEL-FRAME is non-zero, in a frame with a radial velocity offset from that of the centre of the earth by the nominated amount.

Velocity laws

Radio	$v \equiv - c\Delta f/f_0$
Optical	$v \equiv c\Delta\lambda/\lambda_0 = -c\Delta f/f$
Relativistic	$v \equiv c(\frac{1-(f/f_0^2)}{1+(f/f_0)^2})$

where $c$ is the speed of light, and $\Delta f = f-f_0$ throughout.

Spectra plotted on absolute frequency scales will have the image sideband frequency plotted at the top of the spectrum. This will not be accurate, however, unless the velocity frame for plotting is the one in which the source is at rest. It is possible to display data in a different frame from that in which it was observed by using the command SET-VELOCITY-FRAME. As well as selecting the reference frame and velocity law, this also allows you to set an offset velocity with respect to that frame. Thus data observed using the radio definition of velocity, with a known $v_{lsr}$, frequency in the source rest frame, can be displayed by selecting the LSR frame but with velocity offset $v_{off}=v_{lsr}$. Similarly, in this new frame velocities will those as deduced by an observer at rest with respect to the source.

As the exact frequency or velocity in various reference frames is dependent on the lsr velocity at the time of observation it is necessary for the program to know the line rest frequency for some of the options. SPECX assumes that the line rest frequency is the same as given in the scan header, but the default can be changed by using SET-LINE-REST-FREQ(uencies). The current x-axis scaling and range may be shown by SHOW-X-SCALE.

For display in most frames (other than the observed one) SPECX must be able to work out the velocity of the telescope with respect to the astronomical reference frame in the direction of the source. It must therefore know where the telescope was -- use SET-SITE-PARAMETERS to give it this information. Although this is strictly speaking not true when the display frame and observing frame are identical, it is far easier to code this problem by always converting to the telluric frame and then converting back to the desired astronomical frame, and so the site parameters must always be set if the highest accuracy is required for the frequency calculation.

Since most binary operations (ADD-SPECTRA, AVERAGE etc.) are performed on a channel-by-channel basis, it is sometimes necessary to resample one spectrum onto the frequency or velocity sampling of another. Use REGRID-SPECTRUM.

The spectrum can be shifted in x using SHIFT-SPECTRUM (useful for bringing a line into the centre channel for example). SHIFT-SPECTRUM changes the vlsr of the spectrum so that the line is still plotted at the same velocity, although it will move within the total ``passband" or spectrum. In order to correct mistakes in the data file etc it is necessary to change the observing frequency or the vlsr (using VLSR = nn.mm for example). Sometimes it may be necessary to do both to average together data taken at different times.

An experimental facility is provided to let you change the header parameters to give appropriate scaling for a line appearing in the image sideband. Until mid-1993 the I.F. and sideband were not stored in the GSD header, so for data taken before this time these must be known and quoted in response to the appropriate prompts. You can also plot the image sideband frequency by using absolute frequency scales, and setting the velocity frame to be that in which the source is at rest -- the image sideband frequency will be indicated at the top of the box.

From V6.1 onwards, the frequency algorithm includes a polynomial correction to the frequency scale. This is provided in case the supplied data is not on a regular grid -- as may be the case for an AOS for example. You turn the polynomial correction on and off in SET-X-SCALES; the actual coefficients -- up to 6 for a 5th order polynomial -- are entered directly into the array FRQCOEFF and can also be turned on and off by setting the logical variable FCORRECT. If FCORRECT is set true, then the operation of REGRID is to transfer the data onto a regular grid in frequency space, and to set FCORRECT false so that the spectrum will continue to be plotted correctly.