The velocity definition<\/b><\/h2>\n
This is how the velocity is defined from the resultant wavelength or frequency shifts (most astronomical velocity data is just the doppler shift represented as a velocity — and that can be done in several ways). In what follows the velocity of the source (in the reference frame of your choice) is given by v, and the remainder of the symbols are pretty self-explanatory. There are three different definitions that the JCMTOT can handle:<\/p>\n
- \n
- RADIO — This is the default for JCMT observations. In this, the frequency, nu, for a velocity (with respect to the given frame of reference) is given by \u03bd = \u03bdrest<\/sub>(1 – v\/c)as is traditional in radio astronomy. Here, \u03bdrest<\/sub> is the rest frequency, and c the velocity of light.
\nThis corresponds tov\/c = (\u03bdrest<\/sub> – \u03bd)\/\u03bdrest<\/sub>.<\/li>\n- OPTICAL — The `optical’ definition is more easily related to
\nredshift z and wavelength \u03bb. Thus the resultant \u03bb = \u03bbrest<\/sub>(1 + z).
\nThis then corresponds tov\/c = z = (\u03bb – \u03bbrest<\/sub>)\/\u03bbrest<\/sub>.<\/li>\n- RELATIVISTIC — Relativistic definition. Defined by \u03bd = sqrt((1 – v\/c)\/(1 + v\/c)).Alternatively, this can be rewritten asv = c[(1-(\u03bd\/\u03bdrest<\/sub>)2<\/sup>)\/(1+(\u03bd\/\u03bdrest<\/sub>)2<\/sup>)].This is the relativistic doppler shift if you assume that the shift is due only to a velocity along the line of sight in the special relativistic sense. It is not true for partly transversal velocities, cosmological redshifts or other reasons for redshifts such as gravitation. It has been argued that this definition of velocity scale (as computed from redshift data) was invented to further confuse the issue — one more possible definition. There is no guarantee that it will give a more correct velocity than the other scales.<\/li>\n<\/ul>\n
Note that for large velocities is it important to make sure that you are using the right velocity definition. The difference can easily cause your line to fall partly or wholly outside the spectrometer window. For instance the
\ndifference between the radio and optical definition for a velocity of 10000km\/s is 250MHz. This is half the typical spectrometer bandwidth.<\/p>\nIf one is observing highly redshifted objects it is important to know the redshift accurately. Using the redshift definition given above a small uncertainty Delta-z in the redshift translates into a uncertainty \u03b4\u03bd in the redshifted frequency via the relation<\/p>\n
\u03b4z = -(z+1)2<\/sup>\u03b4\u03bd\/\u03bdrest<\/sub>.<\/p>\n
So, for example, if you are using a 1000-MHz spectrometer window, you need to know the frequency to better than, say, 250MHz, which for a redshifted frequency of 350GHz and a redshift of 2.0, means that the maximum tolerable redshift error is +<\/span>0.0021. In general the redshift needs to be known accurately to at least three decimal places.<\/p>\n
How to convert data between velocity frames<\/h2>\n
to convert processed data from the JCMT Science Archive<\/a>, which is in Barycentric frequency, into radio line-of-sight velocity (
) in LSRK. You can use the following Starlink<\/a> commands to do this, assuming you have started with a file named \u2018archive_file.fits\u2019. These would be copied into a terminal, after setting up the Starlink software within that terminal. The lines starting with a # symbol are comments.<\/p>\n
# Load the convert package to enable conversion from FITS to NDF\r\nconvert\r\n\r\n# Convert your archive file into Starlink Data Format (NDF)\r\nfits2ndf archive_file.fits archive_file.sdf\r\n\r\n# Load the KAPPA package (contains many useful routines)\r\nkappa\r\n\r\n# Set the 3rd axis of the coordinate system to be in units of radio velocity\r\nwcsattrib ndf=archive_file.sdf mode=set name=system\\(3\\) newval=vrad\r\n\r\n# Set the standard of rest to be the LSRK\r\nwcsattrib ndf=archive_file.sdf mode=set name=StdofRest newval=LSRK\r\n\r\n# OPTIONAL: if fits output is required, convert the file back to fits\r\nndf2fits archive_file.sdf archive_file_radiovelocity.fits\r\n<\/pre>\n
Sometimes it is also needed to add together spectral data from moving targets (eg comets) onto a \u2018source\u2019 (\u2018cometocentric\u2019) velocity scale: this can be done by doing:<\/p>\n
makecube <rawdatafile00099> system=GAPPT alignsys=TRUE out=out99.sdf\r\nwcsattrib out99.sdf set alignoffset 1\r\nwcsattrib out99.sdf set skyrefis origin\r\nwcsattrib out99.sdf set sourceVRF topocentric\r\nwcsattrib out99.sdf set stdofrest source\r\nwcsattrib out99.sdf set alignstdofrest source\r\nwcsattrib out99.sdf set SourceVel <velocity>\r\n\r\nwcmosaic out*.dat . . .<\/pre>\n","protected":false},"excerpt":{"rendered":"For a typical galactic object, the velocity is assumed to be given with respect to the kinematical local standard of rest (`LSR’), and to be defined according to the radio astronomy standard. In such cases, these are the system defaults, so if you really want something else, it is worth\u2026 Continue reading<\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":162,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/1643"}],"collection":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/comments?post=1643"}],"version-history":[{"count":19,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/1643\/revisions"}],"predecessor-version":[{"id":12628,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/1643\/revisions\/12628"}],"up":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/162"}],"wp:attachment":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/media?parent=1643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- OPTICAL — The `optical’ definition is more easily related to