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

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Presentation on theme: "The Art and Science of PARALLAX Adric R. Riedel 2008 04 14."— Presentation transcript:

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

3 Parallax 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 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

4 El Yunque National Forest, Puerto Rico

5 Secular Parallax (sort of) 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

6 Statistical Parallax 6 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 Orbital Parallax 7 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. 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 i

8 Spectroscopic Parallax 8 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

9 Photometric Parallax 9 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

10 The Ideal Case 10 Use the baseline of the Earth; measure the angle through which a star moves. 2 AU π (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

11 The Ideal Case 11 But how do we know how the star moved from time to time? Background stars! 2 AU π (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

12 How Stars Move 12 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 How Stars Move 13 CENSORED Proper MotionImproper Motion 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

14 14 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

15 Ways the Earth moves 15 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

16 Atmospheric Effects 16 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

17 Atmospheric Effects 17 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

18 Telescope Effects 18 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 Plate Tilt 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

19 The Sad Tale of Peter van de Kamp 19 Director of the Sproul Observatory at Swarthmore University Conducted a long-running search for planets around nearby stars using astrometric perturbations Reported a 12 M J companion to Barnard’s Star in 1963, revised to two planets in 1969. Peter van de Kamp, 1901-1995 The Guru of Astrometry 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 The Sad Tale of Peter van de Kamp 20 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 Peter van de Kamp, 1901-1995 The Guru of Astrometry 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 The CTIO 0.9m 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 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

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23 Observations 23 The best times to take parallax frames: Sunrise Sunset At these times you get the maximum parallatic angles Observable during the night Behind the sun 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 The Reference Field 24 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

25 The Reference Field 25 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 1 2 3 45 6 7 8 a 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 Reduction to an absolute frame 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 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

27 Centroiding 27 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. A good star for centroidingA bad star for centroiding (binary) Note that second lobe 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 Observational Corrections 28 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

29 Removing other motion 29 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

30 Parallax! 30 P alpha is the fraction of the parallax in RA, P delta 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

31 The Reference Field is also moving 31 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 Reduction to Absolute 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) 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 33 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

34 A partial list of sources of error 34 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

35 35 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.. 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

36 Project ISPI 36 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

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