Transcript Parallax - Georgia State University

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
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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
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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