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The Art and Science of PARALLAX Adric R. Riedel 2008 04 14

The Art and Science of PARALLAX Adric R. Riedel 2008 04 14. Parallax is the apparent angular displacement of an object due to a change in the observing position (in space and/or time) There are seven common ways to get distance from parallax: Trigonometric Photometric (sort of)

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The Art and Science of PARALLAX Adric R. Riedel 2008 04 14

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  1. The Art and Science of PARALLAX Adric R. Riedel 2008 04 14

  2. Parallax is the apparent angular displacement of an object due to a change in the observing position (in space and/or time) • There are seven common ways to get distance from parallax: • Trigonometric • Photometric (sort of) • Spectroscopic (sort of) • Orbital • Secular • Statistical • Stereoscopic General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Parallax 3

  3. El Yunque National Forest, Puerto Rico El Yunque National Forest, Puerto Rico

  4. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Secular Parallax (sort of) 5

  5. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Statistical Parallax 6

  6. With a resolved binary, find the: • angular diameter of the orbit • period of the orbit • inclination of the orbit • v sin i of the orbit. • With period and velocity you can find the linear size of the orbit • Compare to angular size and get a distance estimate. i General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Orbital Parallax 7

  7. Get a spectral type • Find out what the Mv of the star should be for that spectral type • Compute a distance modulus • Limited accuracy; spectral types are wide bins General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Spectroscopic Parallax 8

  8. Use magnitudes and colors to estimate absolute magnitudes • No longer reliant on specific types but assumes all are main-sequence General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Photometric Parallax 9

  9. Use the baseline of the Earth; measure the angle through which a star moves. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited π(arcsec) 2 AU π (arcsec) The Ideal Case 10

  10. But how do we know how the star moved from time to time? • Background stars! General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited π (arcsec) 2 AU π (arcsec) The Ideal Case 11

  11. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited How Stars Move 12

  12. CENSORED Proxima Centauri (CTIO 2002-2007) General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Improper Motion Proper Motion How Stars Move 13

  13. Around a barycenter (astrometric perturbation) • Definitely real and observable • Secular acceleration • Second-order effect • A side effect of projecting straight-line motion onto a line of sight • Has been observed for a few stars (Barnard’s Star, Alpha Cen) • Can be ignored for smaller motions • Around the center of the galaxy • In principle this effect is there, but negligible over the 100+ years astrometric parallax has been done General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Other ways stars can move 14

  14. Orbits the solar system barycenter • Perturbations by the other planets (and the moon) directly • RECONS uses the DE405 ephemerides produced by JPL • Precession (360 degrees in 26,000 years is 49.8 arcsec per year) • All coordinates are transformed to J2000. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Ways the Earth moves 15

  15. Atmospheric extinction • Only observe stars close to the meridian (does nothing for stars at high declinations) • Know the airmass; keep measuring (nearby) standards throughout the night • Avoid clouds Extra Airmass = Bad General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Atmospheric Effects 16

  16. Atmospheric color distortion • aka Differential Color Refraction (DCR) • Only observe stars close to the meridian (not helpful for stars at high declinations) • Observe standards throughout the night • Choose reference stars of similar color (Where available) General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Atmospheric Effects 17

  17. Tilted field of view • Easily corrected by knowing the actual positions and separations of stars; find plate constants • Warped/nonlinear field of view • Inconsistent Plate Scale • Requires careful correction for warping General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Plate Tilt Field of View Telescope Effects 18

  18. Director of the Sproul Observatory at Swarthmore University • Conducted a long-running search for planets around nearby stars using astrometric perturbations • Reported a 12 MJ companion to Barnard’s Star in 1963, revised to two planets in 1969. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Peter van de Kamp, 1901-1995 The Guru of Astrometry The Sad Tale of Peter van de Kamp 19

  19. With collaborators, found many more planets around other stars. • All perturbations were exactly the same. • Gatewood & Eichhorn (1973) determined it was instrumental wobble in the Sproul reflector, coincident with telescope upgrades. • Planets have since been found to exist around other stars General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Peter van de Kamp, 1901-1995 The Guru of Astrometry The Sad Tale of Peter van de Kamp 20

  20. Underwent a Telescope Control System upgrade in April 2005 • Pixel scale is still 0.401”, on average and across each segment measured. • Rotation has changed, but is consistent afterward General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited The CTIO 0.9m 21

  21. The best times to take parallax frames: Sunrise Sunset At these times you get the maximum parallatic angles Observable during the night General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Behind the sun Observations 23

  22. Stars (five to fifteen) are identified around the target object. • Their positions are used to denote a reference frame • All other images are rotated and scaled to match the reference frame • Scaling can be avoided by using the same telescope setup for all operations • Be wary of changes to rotation and plate scale due to telescope servicing (we recalculate anyway) • Also, don’t let the telescope age General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited The Reference Field 24

  23. These stars were chosen for being solitary and bright, but not saturated • Note that I’ve already broken my own rule • Not so sure about star #4 either • One frame per night is identified by hand, the rest are done automatically General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited 1 7 8 a 2 3 5 4 6 The Reference Field 25

  24. This is done by “Dependencies” (D), which contain all the rotation, translation and scaling necessary to place each reference star in each frame where it's supposed to be. • These look nasty. • The position of the target star is calculated based on the average of these dependencies. • All of this is done with IRAF routines General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Reduction to an absolute frame 26

  25. A bad star for centroiding (binary) Note that second lobe A good star for centroiding • We centroid to ~1/50 of a pixel (0.00802 arcsec) • With more images come smaller net position errors • Centroiding requires high accuracy, and good PSFs • Not good for barely-resolved binaries or tracking errors • New centroiding algorithm introduced last year. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Centroiding 27

  26. Corrections for a flat surface (The Mapmaker’s problem) • Full conversion from x,y to RA (α) & Dec (δ): • For very small fields: General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Observational Corrections 28

  27. Using the reference frame, the proper motion (and secular acceleration) are removed. • Parallax accuracy is limited by these factors • The two years of data now provide just the parallax motion General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Removing other motion 29

  28. Palpha is the fraction of the parallax in RA, Pdelta in DEC. • They give the direction of the parallax wobble at a given time (usually, J2000 since we already have the star's position then) General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Parallax! 30

  29. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited The Reference Field is also moving 31

  30. The true parallax is obtained against a truly fixed background. Motions of the reference stars must be taken out. • Each term must be corrected (the position and secular acceleration are ignorable though) • RECONS calculates photometric distances to the background stars, and adds the parallax they produce (decreasing the distance) General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Reduction to Absolute 32

  31. Use magnitudes and colors to estimate absolute magnitudes • No longer reliant on specific types but assumes all are main-sequence General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Photometric Parallax 33

  32. Centroiding • DCR • Bad seeing • Limits of proper motion accuracy • Time coverage too short/sparse • Too few reference stars • Variable reference stars • Poor photometric parallax to reference stars (giants, binaries) • Poor positioning of reference stars • Bad aperture correction • Plate tilt • Defocus • Cosmic Rays • Plate scaling and rotation • Deterioration of the telescope • Modifications to the telescope • Tracking errors • Weather • The Seasons • Marvin General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited A partial list of sources of error 34

  33. Finch, C. “A Step by Step Guide to Parallax Reduction” (internal) 2007. • Henry, T. et al. 2004, AJ, 128, 2460H • Jao, W.C. “CTIOPI Photometry Reduction User Guide” • Van de Kamp, P. “Stellar Paths”, D. Reidel Publishing, The Netherlands, 1981 • "Parallax." Dictionary.com Unabridged (v 1.1). Random House, Inc. 14 Apr. 2008. <Dictionary.com http://dictionary.reference.com/browse/Parallax>. • Special thanks to: • Todd Henry • Wei-Chun Jao • John Subasavage • Jennifer Winters General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Works Cited 35

  34. General Definition Types of Parallax The ideal case How stars move How the Earth moves Atmospheric effects Telescope effects Van de Kamp Observations The Reference Field Absolute Frame Reduction to Parallax Reduction to Absolute Errors Works Cited Future Work Project ISPI 36

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