Parallax

1
(No Transcript)
2

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

3

• 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
4
El Yunque National Forest, Puerto Rico
El Yunque National Forest, Puerto Rico
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
Secular Parallax (sort of)
5
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
Statistical Parallax
6
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.

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
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
Spectroscopic Parallax
8
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
Photometric Parallax
9
10

• 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
p (arcsec)
2 AU
p (arcsec)
The Ideal Case
10
11

• 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
p (arcsec)
2 AU
p (arcsec)
The Ideal Case
11
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
How Stars Move
12
13
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
Proper Motion
Improper Motion
How Stars Move
13
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 (Barnards
  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
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
Ways the Earth moves
15
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
Atmospheric Effects
16
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
Atmospheric Effects
17
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

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
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 MJ companion to Barnards 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
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

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
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
The CTIO 0.9m
21
22
(No Transcript)
23
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
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, dont 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
25

• These stars were chosen for being solitary and
  bright, but not saturated
• Note that Ive 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
2
a
3
4
5
6
The Reference Field
25
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
Reduction to an absolute frame
26
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.

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
28

• Corrections for a flat surface (The Mapmakers
  problem)
• Full conversion from x,y to RA (a) Dec (d)
• 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
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
Removing other motion
29
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)

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
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
The Reference Field is also moving
31
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
Reduction to Absolute
32
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
Photometric Parallax
33
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
A partial list of sources of error
34
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. ltDictionary.com
  http//dictionary.reference.com/browse/Parallaxgt.
  
• 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
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
Project ISPI
36
37
(No Transcript)