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PH512
Professor Michael Smith
MULTIMEDIA ASTRONOMY
School of Physical Sciences
Convenor Prof. Michael Smith
Taught in Spring Term
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PH512
ECTS Credits 7.5
Kent Credits 15 at Level H
Assignment 3: Astrometry
1. Introduction
Astrometry is the branch of astronomy that relates to precise
measurements and explanations of the positions and movements of
stars and other celestial bodies.
Although once thought of as an esoteric field with little useful
application for the future, the information obtained by astrometric
measurements is now very important in contemporary research into
the kinematics and physical origin of our Solar System and our
Galaxy, the Milky Way.
Astrometry: the branch of astronomy concerned with the
measurement of the positions of celestial bodies on the celestial
sphere, conditions such as precession, nutation, and proper
motion that cause the positions to change with time, and
corrections to the positions due to distortions in the optics,
atmosphere refraction, and aberration caused by the Earth’s
motion.
Astronomers use astrometric techniques for the tracking of nearEarth objects.
It has been also been used to detect extrasolar planets by
measuring the displacement they cause in their parent star's
apparent position on the sky, due to their mutual orbit around the
center of mass of the system.
NASA's planned Space Interferometry Mission (SIM PlanetQuest
will utilize astrometric techniques to detect terrestrial planets orbiting
200 or so of the nearest solar-type stars.
Gaia is a European Space Agency (ESA) astrometry space mission,
and a successor to the ESA Hipparcos mission. It was included
within the context of the ESA Horizon 2000 Plus long-term scientific
programme in 2000. It is expected to be launched by the ESA in the
second half of 2011, and will be operated in a Lissajous orbit around
the Sun-Earth L2 Lagrangian point.
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Gaia will compile a catalogue of approximately one billion stars to
magnitude 20. Its objectives comprise:
 astrometric (or positional) measurements, determining the
positions, distances, and annual proper motions of stars with
an accuracy of about 20 µas (microarcsecond) at 15 mag, and
200 µas at 20 mag
2. Coordinates
Accurate astrometric measurements of the position of an object, have as a goal
the determination of the sky coordinates of that object.
Common Coordinate Systems Used in Astronomy
– Horizon (altitude, azimuth system)
– Equatorial
– Ecliptic
– Galactic
Typical sky coordinates are the equatorial coordinates "Right
Ascension" (RA) and "Declination" (Dec), analogous to longitude and
latitude on the Earth.
One must also specify the specific "epoch," or year, of the equatorial
coordinate system being used, since the coordinate grid is defined by the
Earth's orientation, and the Earth slowly "precesses".
Most commonly 1950.0 or by now 2000.0 (noting that there is a slight
difference between Besselian B1950 and Julian J2000 epochs, so these two
systems are not related solely by precession).
Related concepts are sidereal time (right ascension currently crossing the
observer's meridian) and hour angle (RA difference between an object and the
sidereal time).
Declination is defined purely by the Earth's equator and poles;
right ascension requires an arbitrary zero point.
In general the FITS world coordinate system (WCS) of an image is defined by keywords in
the FITS header. The basic idea is that each axis of the image has a coordinate type, a
reference point given by a pixel value, a coordinate value, and an increment. A rotation
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parameter may also exist for each axis.
A common of set of keywords used to define the WCS of an image are:
CRVAL n coordinate value at reference point
CRPIX n array location of the reference point in pixels
CDELT n coordinate increment at reference point
CTYPE n axis type (8 characters)
CROTA n rotation from stated coordinate type.
Aberration Observations from a moving platform (all observations) suffer
aberration in the arrival direction of starlight, due to the finite speed of light
(a.k.a. the umbrella effect). To high accuracy, if we look at an angle θ to the
instantaneous motion with respect to some constant reference frame (say the
Sun's motion), the displacement is δ θ = v sin θ /c. The amplitude of this
annual aberration is 30 km/s × 206264.8 arcsec / c or 20 arcseconds in each
direction.
A given star then sweeps out an apparent ellipse of this semi-major axis each
year. There also exists diurnal aberration, caused by the Earth's rotation; its
amplitude is much smaller at 0.32 arcsecond. Differential aberration across the
field of view is actually an issue for HST observations; one doesn't want to pick
the wrong instrument as the primary for certain observations as that will induce
PSF blurring in one far from the optical axis.
There are several effects that cause the coordinates of a star to
deviate from those given in star catalogues.
– Precession
– Nutation
– Proper Motion
– Parallax
– Atmospheric Refraction
3. Narrow-field astrometry
Most high-precision astrometry uses differential measures across a
small field, using some set of local standard stars (an exception
is the Hipparcos global solution).
Here, we define some mapping from celestial to image coordinates,
and determine the constants of the mapping by using coordinates
of well-known stars in the same image. This determination as
known historically as a plate solution.
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The reference stars must finally tie back into sets of fundamental
stars, measured using transit or zenith instruments fixed to the
Earth. Such sets include the FK3 and FK4, Perth-70, and at lower
accuracy but larger numbers, the SAO and HST-GSC Guide Star
Catalogues. The USNO catalogue is a significant improvement over
the GSC.
CCD stellar astrometry has demonstrated 1 millarcsecond
absolute stellar proper motions with respect to background field
galaxiIn an ideal world, one would like to have a selection of
background point sources like quasars as reference points.
However, given the small size of first generation CCD's the
probability of having even one quasar in the field of view is
extremely smaespositional accuracy. This level of precision
means that proper motions of distant objects can be determined on
time scales of 10 years or less.
4 Astrometric solutions: the SDSS
Need a set of equations to connect the position of guide stars with
the object star.
Need a model for the Point Spread Function (PSF). The PSF is in
general a complicated function of position on each detector
1. Take the brightest stars
SDSS: Postage Stamps: cut out postage stamps and measure
centroids for bright stars on the photometric CCD frame.
Cut out a 29 × 29 pixel (11.5 arcsec × 11.5 arcsec) subraster
("postage stamp")
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2. Determine their Centroids.
An object's centroid is defined as the first moment of its light
distribution.
Since this is a noisy estimate for most objects in the survey, the
following technique is used to better estimate the centroid. First, an
object's image is smoothed using a two-dimensional Gaussian with
an adaptive smoothing length scaled to the PSF in that frame.
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Quartic interpolation is used to find the maximum in a 3 × 3 pixel
subraster centered on the peak pixel in the smoothed image.
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This gives a biased estimate of the centroid in the presence of an
asymmetric PSF. PSP uses bright stars to determine the shape of
the PSF as a smoothly varying function of CCD column and row for
each frame. Thus, the PSF at the position of each object is
determined to high accuracy. The centroid of the PSF at the position
of the object is measured using both the first moment and quartic
interpolation after smoothing by the PSF. The difference in centroids
measured for the PSF using the two algorithms is a measure of the
bias introduced by the use of the quartic interpolation algorithm. This
bias is typically a few tens of milliarcseconds but can be as large as
100 mas. The difference is added to the quartic interpolation centroid
measured for the object, yielding a high signal-to-noise ratio
estimate of the first-moment centroid of the object.
http://iopscience.iop.org/1538-3881/125/3/1559/fulltext
http://adsabs.harvard.edu/cgi-bin/bib_query?2003AJ....125.1559P
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The absolute accuracy of the r astrometry is difficult to gauge, as
there are no astrometric catalogs as deep and accurate as the SDSS
itself.