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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: 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 • Trigonometric • Photometric (sort of) • Spectroscopic (sort of) • Orbital • Secular • Statistical • Stereoscopic 3 Parallax El Yunque National Forest, Puerto Rico El Yunque National Forest, Puerto Rico 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 5 Secular Parallax (sort of) 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 6 Statistical Parallax • With a resolved binary, find the: • angular diameter of the orbit 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 7 • 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. Orbital Parallax i • Get a spectral type 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 8 • 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 Spectroscopic Parallax • Use magnitudes and colors to estimate absolute magnitudes • No longer reliant on specific types but assumes all are mainsequence 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 9 Photometric Parallax 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 10 2 AU • Use the baseline of the Earth; measure the angle through which a star moves. π (arcsec) π (arcsec) The Ideal Case But how do we know how the star moved from time to time? 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 11 2 AU Background stars! π (arcsec) π (arcsec) The Ideal Case 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 12 How Stars Move 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 13 CENSORED Improper Motion Proper Motion How Stars Move • Around a barycenter (astrometric perturbation) • Definitely real and observable 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 14 • 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 Other ways stars can move • Orbits the solar system barycenter 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 15 • 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. Ways the Earth moves • Atmospheric extinction 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 16 • 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 Atmospheric Effects Extra Airmass = Bad • Atmospheric color distortion • aka Differential Color Refraction (DCR) 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 17 • 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) Atmospheric Effects • Tilted field of view 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 • Easily corrected by knowing the actual positions and separations of stars; find plate constants • Warped/nonlinear field of view Plate Tilt • Inconsistent Plate Scale • Requires careful correction for warping Field of View 18 Telescope Effects • Director of the Sproul Observatory at Swarthmore University 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 • 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. Peter van de Kamp, 1901-1995 The Guru of Astrometry 19 The Sad Tale of Peter van de Kamp • With collaborators, found many more planets 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 20 • 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 Peter van de Kamp, 1901-1995 The Guru of Astrometry The Sad Tale of Peter van de Kamp 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 21 • 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 The CTIO 0.9m The best times to take parallax frames: 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 Observable during the night Sunrise Sunset At these times you get the maximum parallatic angles Behind the sun 23 Observations • Stars (five to fifteen) are identified around the target object. • Their positions are used to denote a reference frame 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 24 • 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 The Reference Field • These stars were chosen for being solitary and bright, but not saturated 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 25 • Note that I’ve already broken my own rule 1 7 • Not so sure about star #4 either 8 a • One frame per night is identified by hand, the rest are done automatically 5 6 The Reference Field 2 4 3 • 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 • • 26 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 Reduction to an absolute frame • We centroid to ~1/50 of a pixel (0.00802 arcsec) 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 • 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. A bad A good star for star centroiding for centroiding (binary) Note that second lobe 27 Centroiding 0 ,0 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 28 , • Corrections for a flat surface (The Mapmaker’s problem) • Full conversion from x,y to RA (α) & Dec (δ): x tan sin sin 0 y cos 0 sin sin 0 y cos 0 1 x2 y2 • For very small fields: y x sec 0 Observational Corrections Using the reference frame, the proper motion (and secular acceleration) are removed. • 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 29 • • Parallax accuracy is limited by these factors The two years of data now provide just the parallax motion Removing other 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 30 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) Parallax! 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 31 The Reference Field is also moving • 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 32 • • 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) Reduction to Absolute • Use magnitudes and colors to estimate absolute magnitudes • No longer reliant on specific types but assumes all are mainsequence 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 33 Photometric Parallax 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 34 • Centroiding • Plate tilt • DCR • Defocus • Bad seeing • Cosmic Rays • Limits of proper motion accuracy • Plate scaling and rotation • Time coverage too short/sparse • Deterioration of the telescope • Too few reference stars • Modifications to the telescope • Variable reference stars • Tracking errors • Poor photometric parallax to • Weather reference stars (giants, binaries) • The Seasons • Poor positioning of reference stars • Marvin • Bad aperture correction A partial list of sources of error 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 • 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 35 Works Cited 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 36 Project ISPI