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

The Art and Science of

PARALLAXAdric R. Riedel 2008 04 14

Parallax3

General DefinitionTypes of Parallax

The ideal caseHow stars move

How the Earth movesAtmospheric effectsTelescope effects

Van de KampObservations

The Reference FieldAbsolute Frame

Reduction to ParallaxReduction to Absolute

ErrorsWorks 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

El Yunque National Forest, Puerto Rico

El Yunque National Forest, Puerto Rico

Secular Parallax (sort of)5







ErrorsWorks Cited

Statistical Parallax6







ErrorsWorks Cited

Orbital Parallax7

• 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.







ErrorsWorks Cited

i

Spectroscopic Parallax8

• 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







ErrorsWorks Cited

Photometric Parallax9

• Use magnitudes and colors to estimate absolute magnitudes

• No longer reliant on specific types but assumes all are main-sequenceGeneral Definition

Types of ParallaxThe ideal case

How stars moveHow the Earth movesAtmospheric effectsTelescope effects




ErrorsWorks Cited

The Ideal Case10

• Use the baseline of the Earth; measure the angle through which a star moves.

2 A

U π (arcsec)

π (arcsec)







ErrorsWorks Cited

The Ideal Case11

But how do we know how the star moved from time to time?

Background stars!

2 A

U π (arcsec)

π (arcsec)







ErrorsWorks Cited

How Stars Move12







ErrorsWorks Cited

How Stars Move13

CENSORED

Proper Motion

Improper Motion

Proxima Centauri (CTIO 2002-2007)







ErrorsWorks Cited

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







ErrorsWorks Cited

Other ways stars can move

Ways the Earth moves15

• 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.







ErrorsWorks Cited

Atmospheric Effects16

• 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







ErrorsWorks Cited

Atmospheric Effects17

• 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)







ErrorsWorks Cited

Telescope Effects18

• 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







ErrorsWorks Cited

The Sad Tale of Peter van de Kamp19

• 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. Peter van de Kamp, 1901-1995

The Guru of Astrometry







ErrorsWorks Cited

The Sad Tale of Peter van de Kamp20

• 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, 1901-1995The Guru of Astrometry







ErrorsWorks Cited

The CTIO 0.9m21

• 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







ErrorsWorks Cited

Observations23

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







ErrorsWorks Cited

The Reference Field24

• 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







ErrorsWorks Cited

The Reference Field25

• 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

345

6

7

8

a







ErrorsWorks Cited

Reduction to an absolute frame26

• 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







ErrorsWorks Cited

Centroiding27

• 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







ErrorsWorks Cited

Observational Corrections28

• Corrections for a flat surface (The Mapmaker’s problem)

• Full conversion from x,y to RA (α) & Dec (δ):

• For very small fields:

00 cossin

tansin

y

x

22

00

1

cossinsin

yx

y

y0sec x

00 , ,







ErrorsWorks Cited

Removing other motion29

• 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







ErrorsWorks Cited

Parallax!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)







ErrorsWorks Cited

The Reference Field is also moving31







ErrorsWorks Cited

Reduction to Absolute32

• 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)







ErrorsWorks Cited

Photometric Parallax33

• Use magnitudes and colors to estimate absolute magnitudes

• No longer reliant on specific types but assumes all are main-sequenceGeneral Definition

Types of ParallaxThe ideal case

How stars moveHow the Earth movesAtmospheric effectsTelescope effects




ErrorsWorks Cited

A partial list of sources of error34

• 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







ErrorsWorks Cited

Works Cited35

• 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







ErrorsWorks Cited

Project ISPI36







ErrorsWorks CitedFuture Work

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

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