FGS Instrument Handbook for Cycle 24

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7.4	Epoch-Level Processing

7.4.1 Parallax, Proper Motion, and Reflex Motion

7.4.2 Binary Stars and Orbital Elements

Astrometry takes time. This is true whether the goal is to determine the parallax, proper motion, or reflex motion of an object measured in Position mode, or the orbital elements of a binary system observed in Transfer mode. By its very nature, astrometry looks for changes to the arrangement of objects on the sky, and as a result, observations taken over several different visits must be compared to one another. Relating the observations from different epochs is discussed. A more detailed discussion is provided in then FGS Data Handbook.

7.4.1 Parallax, Proper Motion, and Reflex Motion

In order to measure the proper motion and parallax of an object observed in Position mode with the FGS, the data from the individual visits must be combined to form a virtual plate. This virtual plate is derived from an optimal mapping of all of the visit level plates onto a common plate using the method of least-squares to minimize the residuals of all reference stars (the plate solution). This mapping function is used to map the science target at each visit onto the virtual plate. In this way, the parallax, proper motion, and perhaps reflex motion (perturbations caused by a gravitationally bound companion) can be determined.

If enough reference stars are available (> 5), six parameter plate solutions - allowing for independent scale adjustments along each of the astrometer’s X and Y axes - can be applied. Otherwise the four parameter model must be applied.

The residuals of the reference stars in the plate solution determine the overall astrometric performance of the telescope as a function of the number of visits expended. FGS3 achieved ~1.2 mas (rms) precision per HST orbit, while FGS1r has demonstrated ~0.8 mas rms precision per HST orbit. Given that the overall astrometric accuracy scales as while random (Poisson) errors dominate, it can be anticipated that, for example, FGS1r will yield parallax measurements accurate to 0.3 mas in as little as 12 HST orbits if an optimal observing strategy is employed. (Below ~0.2 mas irreducible systematic errors dominate, such as the conversion of relative to absolute parallax.)

STScI can provide the analysis tools (developed by the STAT at the University of Texas) needed to perform a plate solution from multiple Position mode visits. These tools are available as stand-alone software packages and scripts that can be delivered via ftp from STScI. Supporting documentation is being developed. Please see the FGS Web page for further updates.

7.4.2 Binary Stars and Orbital Elements

Transfer mode observations of binary stars provide the angular separation and position angle of the components at each epoch (as well as their difference in brightness). Once the binary has been observed at a sufficient number of phases in its orbit, the system’s orbital parameters can be solved. The result will be knowledge of the orbit’s inclination, eccentricity, period, and angular extent of its semi-major axis. If the parallax of the object is known, then the physical size of the orbit can be computed to yield the total mass of the system.

For a binary that was observed along with Position mode observations of reference stars, it is possible to determine the binary’s parallax and proper motion, and the motion of the components about the system’s barycenter, which then yields the component masses. This, along with the differential and system photometry (also measured by the FGS), provides the mass-luminosity relation.

STScI can provide observers, via ftp, with the appropriate analysis tools needed to analyze Transfer mode observations of binary star systems. These tools are standalone software packages written by STScI based upon algorithms developed by the STAT at the Lowell Observatory. These packages allow one to deconvolve the binary star Transfer mode data in order to determine the angular separation and relative brightness of the components at each epoch of observation. Documentation of these packages will be made available during Cycle 24. Check the FGS Web page for updates.

Figure 7.1: CALFGSA Common Processing Tasks

Figure 7.2: CALFGSA Transfer Mode Processing Tasks

Figure 7.3: CALFGSB Position Mode Processing