iau_STARPV The routines iau_PVSTAR and iau_STARPV are inverses of each other, and notes on both are located here. -------------------------------------------------------------------------- Note by PTW 7 June 2000 BACKGROUND The rigorous calculation of proper motion, and indeed the conversion from one epoch to another of all the observables of a star, involves transforming the catalogue data (RA, Dec, proper motion, parallax, radial velocity) into a space motion vector (one of our "pv-vectors"). This is normally done using formulae that ignore the finite speed of light; see, for example, Section 3.23 of the Explanatory Supplement. However, the procedure is flawed, by which I mean that it gives answers which are physically wrong: A The pv-vector describes the apparent direction of the star, not its geometrical direction. This is because the proper motion during the light time has been neglected. B For a non-zero radial velocity, the changing light time affects the apparent proper motion. This (classical) effect seems to have been overlooked since it was pointed out by Schwarzschild in 1894. C The transformation is Galilean, not Lorentzian; the effects of special relativity have been neglected. I think there are good reasons for us to continue observing the `A' convention. If an object with a detectable proper motion has a distance which is unknown, or known only inaccurately, there are wild uncertainties in the resulting space motion vector. In any case, once you have the space motion vector, extrapolation to any epoch is trivial. The `B' omission is much more serious, with very little to justify it apart from tradition. Although it has only a small effect for stars, it can distort the space motion estimate for some extragalactic sources enough to produce an appearance of superluminal motion. As for the previous item, `C' can be justified only by appealing to simplicity and tradition. WHAT IAU_STARPV AND IAU_PVSTAR DO The iau_STARPV routine transforms catalogue data into a space motion vector; the iau_PVSTAR routine performs the inverse operation. A 10 Mpc "celestial sphere" is used, to deal with sources whose distances are not known. The allowable speed is also kept within physically realistic bounds, to deal with sources which have proper motion but unknown (or grossly overestimated) distances. The routines use a formulation published by P.Stumpff in 1985, to implement the catalogue-to-space-motion transformation correctly. The `A' (light-time ) convention is retained, so that the space motion vectors are very similar to ones calculated in the conventional way. However, the `B' and `C' omissions are corrected: the light-time effects on proper motion are properly handled, and the transformation complies with special relativity. PERFORMANCE The two routines are accurate inverses, such that catalogue data put through iau_STARPV and then restored using iau_PVSTAR emerge almost unchanged. Compared with the conventional formulae, the pv-vectors produced by iau_STARPV are very close but not identical. However, when an epoch difference is introduced, the differences in the resulting second-epoch catalogue data are negligible for all cases involving existing data. CONCLUSIONS Although the vectors themselves differ significantly from ones calculated in the conventional way, in normal applications such vectors are never more than intermediate results. Therefore it is harmless to use the new routines in place of the old, and the improvements are then in place ready for the much more accurate star data that will be available in a few years' time. APPENDIX: TIMESCALE CONSIDERATIONS Dainis Dravins & Lennart Lindegren (Lund Observatory), recently circulated a draft IAU resolution on the definition of a spectroscopic radial-velocity measure. As far as I can tell, this is complementary to the role of iau_STARPV/iau_PVSTAR: * We already refer observations to the barycentre when we are producing catalogues or reporting results, and this includes radial velocity. * However, although the barycentre is routinely used as a standard of rest, the correction from observed radial velocity has traditionally been done in the Newtonian way, missing two post-Newtonian steps: 1) The conversion from topocentric velocity to barycentric velocity should be a Lorentz transformation. 2) The timescale should be changed from topocentric proper time (TT or TAI for instance) to barycentric coordinate time (TCB). * The routines iau_STARPV and iau_PVSTAR assume that these steps have been taken already. They then do this: RA/Dec, PM, parallax, RV | V iau_STARPV | V x,y,z,xd,yd,zd | V RA/Dec, PM, parallax, RV The transformations differ from the usual text-book ones in two respects: (i) The (classical) interaction between light-time and radial velocity is correctly handled. (ii) Lorentz transformations are used for adding velocities. In addition, the timescale is barycentric coordinate time throughout. The transformation between the observer's proper time and TCB is left to the caller to look after. * The logic applies to receipt of any periodic signals from a distant source. If the physics at the distant source is to be right, and in particular if existing units of mass etc are to apply, then the time transformation must be correctly handled. Pulsar observers already routinely do this for correcting phase observations to the barycentre. If I have understood the IAU proposal, it is pointing out that spectral observers must do the same when interpreting Doppler shifts. * The transformation between TT and TCB involves a rate change (of about 1 + 1.5E-8) and some periodic terms. The latter (implemented in the draft SOFA routine iau_DTDB) are important for pulsar observers because they directly affect phase (by +/- 1.7 ms over the year). Spectroscopists are more interested in the derivative of the function. --------------------------------------------------------------------------