# Astrometry

Post-publication activity

Curator: Norbert Zacharias

Astrometry is the science which deals with the positions and motions of celestial objects. Astrometry is now one of many fields of research within astronomy. Historically, astrometry was all that astronomy was about until about the 19th century. Toward the end of the 19th century not only the directions, i.e. angles between celestial objects as seen on the celestial sphere were measured but also the "quality of light", specifically the light intensity (photometry) and color (spectroscopy, light intensity as function of color or wavelength). This was the birth of astrophysics. The term astrophysics, often used to distinguish most of current astronomical research from the classical astronomy (i.e. astrometry) is misleading, because astrometry also is certainly part of physics or astrophysics. Measurements of distances to celestial objects by triangulation for example is at the core of astrometry and it forms the basis of all astrophysics; without knowing the distances to planets, satellites, stars, and galaxies, no correct understanding of the cosmos in which we live can be achieved.

Figure 1: Figure 1: The astronomical pyramid. This cartoon (circulated c.1974 by Ron Probst, UVa) illustrates that most astronomers these days are working in extragalactic astronomy, theory, and cosmology. They all depend on observations provided by fewer astronomers. The basis is formed by the very few astrometrists.

# Angles

Astrometry is about measuring angles, dealing with errors in angular measures and changes of angles with time (angular velocity), and derivation of astrophysical quantities from those measurements. A full circle can be divided into 360 degrees. A degree is subdivided into 60 arcminutes (arcmin) and 1 arcmin equals 60 arcseconds (arcsec). The full moon in the sky substends an angle of about 1/2 degree or 30 arcmin as seen from earth. The smallest angular separations or resolutions seen through an ordinary telescope on the ground is about 1 arcsec, limited by the turbulence of earth's atmosphere. Progress in astrometry in the recent decade called for smaller angular units. A milliarcsecond (mas) is 1/1000 arcsec and a microarcsecond is 1/1000 mas. The diameter of a large coin as seen from a distance of about 6000 km (New York to London) corresponds to an angle of 1 mas.

# Celestial coordinates

Astronomers use celestial coordinates on the sky to define a position (direction unit vector) of a celestial object as seen from a specific location (which can be on earth or in space) in a way similar to geographic latitude and longitude. The most commonly used system is the equatorial celestial coordinate system which has the plane of earth's equator projected onto the celestial sphere as fundamental plane. Right ascension (RA) is the angle counted in this plane from 0 to 24 hour, similar to the geographic longitude. Declination (Dec) is the angle orthogonal to RA, i.e. the angular distance from the equatorial plane with +90 degree for the celestial north pole and -90 degree for the celestial south pole. An object on the celestial equator has Dec = 0. A more detailed narrative with figures about [1] celestial coordinate systems is given by G.Kaplan.

The celestial coordinate system is established by large-angle, fundamental observations. These types of observations allow us to define a coordinate system (directions of 3 orthogonal axes) from first principles, without prior knowledge of the coordinates of stars. In the past these fundamental observations were provided by transit circle (meridian circle) telescopes at optical wavelengths for about 1500 bright stars. (H.G.Walter, O.J.Sovers, Astrometry of Fundamental Catalogues, Springer 2000). These observations were tied into the complex motion and rotation of the earth as well as other solar system bodies (sun, major and minor planets) to be able to establish a dynamical reference frame, which is made inertial (i.e. rotation free) based on celestial mechanics and law of gravitation.

In 1997 the International Astronomical Union (IAU) adopted the International Celestial Reference System (ICRS) based on more precise Very Long Baseline Interferometry (VLBI) observations with radio telescopes to define the axes of the celestial coordinate system. The catalog of about 600 compact, extragalactic sources (mainly quasars) form the International Celestial Reference Frame (ICRF), the practical realization of the ICRS. The definition of the ICRS thus is independent of the earth's motion, rotation, and its equator and is no longer a dynamical system, rather a quasi-inertial reference system with the assumption that those quasars do not move noticeably along the sky due to their enormous distances and thus are used as fixed, fiducial points to define the ICRS. The positions of most sources in the ICRF are known to about 0.1 to 1 mas, and there are no angular motions by definition.

Between 1989 and 1993 the European space mission Hipparcos observed (at visible light wavelengths) about 118,000 stars at a mean epoch of 1991.25 to an accuracy of about 1 mas per position coordinate. Because stars move (see below), the Hipparcos Catalog also had to solve for the effects of proper motion and parallax as well as just position. The Hipparcos Celestial Reference System (HCRS) was adopted by the IAU as the optical realization of the ICRS. The coordinate system of Hipparcos was aligned to the fundamental ICRS with a variety of methods (Kovalevsky et al. 1997) with 12 radio stars (visible at optical and radio wavelengths) providing the strongest link.

# Stars do move

Contrary to planets the stars seem to be at fixed positions on the sky and the familiar constellations don't change over years and centuries. However, if one looks more closely, all stars, including our Sun, do move in more or less regular orbits around the center of our Milky Way Galaxy. The projection of the real space motion of a celestial object (with respect to our solar system) onto the celestial sphere is called proper motion. This is an angular velocity (angle per time). The corresponding velocity (speed) is the tangential velocity. When the distance to an object is known, the tangential velocity can be calculated from its angular velocity. The third component of the 3-dimensional space motion of a celestial object is the motion along the line of sight (toward or way from us), which is called the radial velocity. It is mainly measured by spectroscopic methods and recently also became a topic of astrometry. High accuracy angular measures can detect changes in proper motions due to radial velocity and in 2000 the IAU adopted the resolution C2 defining "astrometric radial velocity".

There is another important motion of the stars: the apparent, annual parallactic motion. A nearby star seems to move along a small elliptical pattern with respect to distant stars over the course of a year due to the motion of the earth around the sun. You can visualize this effect by holding up a finger in front of you and looking at it alternatively with one and then the other eye. The finger seems to move with respect to the distant background. Half the diameter of this parallactic motion is called the parallax, p of a star. It is related to the distance, d of the star by:

d = 1 / p

where p is measured in arcsec and d in parsec, the standard distance unit in galactic and extragalactic astronomy. A parsec is about 3.26 light years (ly), and 1 ly = 9.467 * $$10^{15}$$ meter. A parsec is thus the distance at which the mean distance between earth and sun extends an angle of 1 arcsec. The closest star beyond our sun belongs to the alpha centauri system with d = 1.3 pc and p = 0.77 arcsec. All other stars have smaller parallaxes.

Proper motions and parallaxes were typically measured over long periods of time with large (high magnification or large plate scale) telescopes on photographic plates. This is the domain of narrow-field, small-angle, differential astrometry. However, the Hipparcos satellite and other future projects are capable of measuring small, local position changes like parallax and proper motions from large angle, global, absolute, observations. On the other hand, proper motions for most of the millions of faint stars are still known today from differential comparisons of pairs of photographic plates taken of the same area of the sky decades apart. An excellent account on star catalogs up to about 1970 is given in Eichhorn (1974). Differential observations measure the positions of celestial objects in a small area of the sky relative to other objects. This is technically easier than absolute, large-angle measures and often yields higher precision than the wide-angle measures. For more recent developments see for example IAU and USNO web links.

Another important area of astrometry is the research of double and multiple stars. Astrometric observations and determination of orbits is the only way to directly measure the masses of stars. The mass of a star is the fundamental quantity which determines the evolution and appearance of a star throughout its life. Orbital motion of course complicates the determination of parallax and proper motions, and double stars are sometimes called the "vermon" of the sky by astrometrists not working in the field of double stars. Fortunately (from the point of view of deriving masses) and unfortunately (from the point of view of using "clean" fiducial points of light for astrometric reference frame work) most stars belong to a double or multiple star system.

Finally, the era of detecting exoplanets, i.e. planets outside our solar system which orbit around other stars by astrometric means has just begun. Astrometric "wobbles" will be observed by space missions which are already being constructed. This is similar to detecting orbital motions of invisible components of certain double stars, which for example lead to the discovery of white dwarf stars in the 19th century. The astrometric method is the only way to determine the masses of those components which could either be stars or planets except when a pair of objects is seen transiting each other (orbital plane is along our line of sight).

# Astrometry today and tomorrow

This section gives an overview about all fields of astrometry and some of the exciting astrometric projects going on right now or planned for the near future.

## Topics

The area of research in astrometry can be divided by technique or objects of study. Looking at the electromagnetic spectrum there are 2 distinct "windows" for ground-based observations. Radio astrometry uses large radio telescopes and interferometric techniques, while various optical and near-infrared astrometry techniques use more or less traditional telescopes. Another way to categorize astrometry is the differentiation between wide-angle, absolute and narrow-angle, differential observations. Both categories can be found in either radio or optical astrometry. Wide-angle observations often contribute to defining a reference frame or obtaining absolute proper motions and parallaxes. Narrow-field observations are typically even more precise than wide-angle measurements, however they obtain only relative positions and motions in narrow fields of view.

Some of the important techniques used in astrometry today are a) interferometry at radio and optical wavelengths, including VLBI (see above), and the fine guidance sensors aboard the Hubble Space Telescope, b) speckle interferometry for double star observations, c) direct imaging onto 2-dimensional detectors like the charge-coupled device (CCD) and measuring photographic plates for early epoch data, and d) drift scanning by ground-based and space-based instruments.

Objects of research in astrometry range from monitoring the rotation of the earth and continental drifts, motions of solar system objects (planets, natural and artificial satellites, space navigation, asteroids), and the prediction of their future positions (ephemerides), to the kinematical and dynamical studies of our Milky Way galaxy and beyond. For practical applications by the general astronomical community the Hipparcos stars are too bright and too few and far apart. The densification of the optical reference frame toward more and fainter stars is a subject of star cataloging astrometry. Trigonometric distance measures (parallaxes) are the basis for the entire cosmic distance scale and our knowledge about types of stars (giants and dwarfs) and their absolute luminosities. Observations of the motions of star clusters and satellite galaxies around our Galaxy give insight into the distribution of matter, in particular, dark matter is a hot topic today.

Finally, astrometry overlaps with theoretical astrophysics and cosmology beyond local investigations of the distribution of dark matter. Historically astrometry provided the critical empirical evidence in support of Einstein's general theory of relativity by directly measuring the bending of light near a massive body (total solar eclipse observations) and the observation of perihelion motion of the planet Mercury. Astrometry will soon engage in further testing of the theory of gravitation by experiments of ever higher accuracy, e.g. with the Gaia and SIM space missions (see below).

Internationally, astrometric research is represented by Commission 8 (Astrometry) of the IAU. Astrometry ties also into celestial mechanics (IAU Commission 7), the system of astronomical constants and time (Com. 31), ephemerides (Com. 4), galactic structure (Com. 33), double stars (Com. 26), and others. Most of these commissions are grouped together under the IAU Division I (Fundamental Astronomy).

## Ground-based projects

The most accurate observations within our solar system to support ephemerides and space navigation are laser and radar ranging techniques to directly measure the distances to spacecraft, the moon and nearby asteroids, superseding traditional astrometric observations performed with transit circles and photography. However, for most minor planets (asteroids), the outer and trans-Neptunian planets astrometric observations are essential. Pioneering in the automated observation of solar system objects was the Naval Observatory Flagstaff Station (NOFS) 8-inch scanning transit circle, still in operation. One of the most productive projects in this area is the LINEAR program which discovered hundreds of thousands of asteroids. Ephemerides of natural satellites are being improved by new reductions and scanning of photographic plates taken over decades with state-of-the-art plate measure machines like the DAMIN (Royal Observatory Belgium).

Looking at nearby stars the 4th edition of the Yale Trigonometric Parallaxes Catalog summarizes the standard over the last century of observations, superseded in number of stars only recently by the Hipparcos Catalog and the NOFS 61in program. However, the best ground-based parallaxes are of comparable or even better accuracy (0.5 mas) than the Hipparcos parallaxes. The most active parallax observing program today is the RECONS project utilizing the 0.9m Cerro Tololo Interamerican (CTIO) telescope in Chile, targeting in particular nearby (<= 25 pc) but faint dwarf stars.

The Tycho-2 catalog of the 2.5 million brightest stars is the first step of the densification of the net of reference stars beyond the Hipparcos Catalogue. Tycho-2 is based on the star mapper data obtained on board the Hipparcos satellite, combined with over 140 ground-based star catalogs to obtain proper motions on the 2 mas/yr level. Several scanning transit circle programs (Bordeaux, Carlsberg, San Fernando) produced zone catalogs of different areas of the sky with millions of stars. The United States Naval Observatory (USNO) CCD Astrograph Catalog (UCAC) project covered the whole sky to about 16th magnitude with positional errors of 20 to 70 mas for about 80 million stars providing accurate reference stars beyond the Tycho-2 limit. Based on all applicable Schmidt telescopes sky survey plates, the USNO-B catalog contains over 1 billion objects. The Yale University and the University of San Juan, Argentina covered the sky south of Dec = -20 degrees with the Southern Proper Motion survey (SPM4) catalog of just over 100 million objects with absolute proper motions and positions to magnitude 18 and accuracies of 2 to 5 mas/yr and 20 to 100 mas, respectively. The Naval Observatory Merged Astrometric Dataset (NOMAD) combines most of the above star catalogs.

USNO is about to embark on another, deeper and more accurate all-sky survey. The "U-mouse" project utilizes the same "red lens" as the UCAC but 28 square-degree images will be taken with a new camera beginning in 2009. The limiting magnitude will be about R=18 and positions, proper motions and parallaxes will be derived on the 10 mas level for several hundred millions of stars.

## Space-based projects

The Fine Guidance Sensors (FGS) aboard the Hubble Space Telescope (HST) have been used for a limited number of very accurate astrometric observations (sub-mas) of the open cluster M35 (as an astrometric calibration area) and precise distance and mass determinations of selected, bright stars and binaries. Direct imaging with various HST CCD instruments provided high accuracy proper motions of faint stars in selected areas of the sky.

The European Space Agency (ESA) Hipparcos mission boosted the field of astrometry by orders of magnitude, providing an all-sky catalog of over 118,000 stars with positions, proper motions and parallaxes on the 1 mas (1 mas/yr) level. The biggest impact on science was achieved by the enormous number of highly accurate parallaxes, while the positions of the stars already have degraded to about 20 mas due to accumulation of errors in the proper motions.

The Joint Milliarcsecond Pathfinder Survey (JMAPS) mission aims at Hipparcos-like accuracies but for millions of stars to about 14th magnitude. In combination with Hipparcos data, proper motions near 0.1 mas/yr accuracy are expected for the bright stars. This mini-satellite, funded by DoD is expected to launch in 2012.

The next big step in space astrometry will be the ESA Gaia mission. The goal is to observe about 1 billion stars to 20th magnitude with accuracies of 0.01 to 0.2 mas, again for position, proper motions and parallaxes. Launch of Gaia is expected in 2012 and the final catalog should become available in 2020.

The SIM Lite mission will be able to observe astrometric "wobbles" on the 1 microarcsecond level and thus be capable of discovering earth-like planets around nearby stars. SIM Lite is a pointed, astrometric, mission which will observe about 20,000 selected targets down to 20th magnitude in the post-Gaia era. A large variety of science questions will be addressed by SIM Lite in addition to planet hunting, ranging from outer solar system objects to binary black holes at cosmological distances.

## References

• Eichhorn, Heinrich (1974). Astronomy of Star Positions. Frederick Ungar Publ. New York.
• Hoeg, Erik (2008). Astrometry and optics during the past 2000 years. www.astro.ku.dk/~erik/History.pdf
• Kaplan, George (2006). Coordinate Systems on the sky and IAU resolutions. aa.usno.navy.mil/faq/docs/ICRS_doc.php
• Kovalevsky, Jean et al.(1997). Astronomy and Astrophysics, 323, 620.
• Walter, H.G., Sovers, O.J.(2000). Astrometry of Fundamental Catalogues, Springer.
• Zacharias, Norbert et al.(2004). Astronomical Journal, 127, 3043.

Internal references

• Kovalevsky, Jean (2002). Modern Astrometry. Springer. A good textbook about astrometry with details on the Hipparcos mission.
• Kovalevsky,J. and Seidelmann,P.K.(2004). Fundamentals of Astrometry. Cambridge Univ.Press. Another good textbook about astrometry.
• Perryman, Michael (2009). Astronomical Applications of Astrometry, Cambridge Univ.Press. 10 years of exploitation of the Hipparcos satellite data.
• van Altena, William (2010). Introduction to Astrometry (working title), Cambridge Univ.Press (in press). A modern, basic textbook about astrometry with contributions by many expert authors.