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| The Hyades - So Close, and Now, So Familiar | |
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Mercury, May/June 1998 Table of Contents
Anthony
G. A. Brown Outlining the head of Taurus the Bull, stars in the Hyades cluster are important to us. Oh, they give us pleasure to behold, but they also enable us to measure the universe. A careful examination of the proper motions of all fixed stars in the catalogues published by Messr. Main and Stone...has led me to a somewhat interesting result. I find that in parts of the heavens the stars exhibit a well-marked tendency to drift in a definite direction. In the catalogues of proper motions, owing to the way in which stars are arranged, this tendency is masked; but when the proper motions are indicated in maps, by affixing to each star a small arrow whose length and direction indicate the magnitude and direction of the star's proper motion, the star-drift (as the phenomenon may be termed) becomes very evident. The most famous of these "star-drifts" in the heavens discussed by Richard A. Proctor in his entry in the 1869 Proceedings of the Royal Society of London is the Hyades star cluster. It is the nearest moderately rich star cluster and can easily be seen with the naked eye: All the stars around Taurus's "V"-shaped head, with the exception of red Aldebaran, are cluster members. Because of its proximity the Hyades cluster has always played a central role in astronomy. It forms the first rung on the ladder of the distance scale of the universe and provides astronomers with an excellent laboratory for testing their theories of stellar structure and evolution. Astrometry and the Measurement of Stellar Distances The subject of astrometry, the measurement of stellar positions in the sky, is the oldest discipline in astronomy. It was the Greek astronomer Hipparchus who around 150 BCE produced the first systematic catalogue of stellar positions. Edmund Halley compared Hipparchus's measurements with those of his 18th-century contemporaries and discovered in 1718 that three stars were not at their expected positions; from this he deduced they have their own proper motion. Gradual improvements in measurement precision showed that many more stars have proper motions, and the realization by William Herschel that these motions could be partly explained by the motion of the Sun itself, suggested that some stars may be close enough to the Sun to measure their distances using their trigonometric parallaxes. The parallax of a nearby star is its apparent, annual, angular movement on the sky due to Earth's motion around the Sun-the star appears to move back and forth relative to more distant, background stars. The size of this displacement, together with the known Earth-Sun distance, gives the distance to the star. This technique provides a direct measure of stars' distances independent of any assumptions about, for instance, the brightnesses of the stars. The measurement of parallaxes is, thus, of fundamental importance to astronomy. Notwithstanding the efforts made since Herschel's time, however, the measurement of stellar parallaxes is very difficult in practice and can only be done accurately for relatively few stars close to the Sun (within roughly 120 lightyears). For stars outside this small solar neighborhood, the uncertainties associated with their measured parallaxes are simply too large. This poses serious problems because not all types of stars are located near the Sun. Notably, there are no nearby Cepheid variables. For these late-life stars there exists a very well defined relation between the regular timing of their brightness variations and their average true brightnesses. Therefore, by simply measuring the time for the periodic variations in a Cepheid's apparent brightness, one immediately knows the star's distance. We do need at least one independent direct measurement of a Cepheid's distance, however, to calibrate this technique. This is where the Hyades cluster comes in. Using the fact that the Hyades stars move parallel in space, one can deduce the distance to the cluster using the ingenious convergent-point method (see Hyades SideBar). Like parallax measurement, this is also a geometrical method for measuring distances that is independent of any properties of the individual stars. And once the distance to the Hyades is known, one can use the technique of main-sequence fitting to derive distances to other clusters located much further away (see box). Some of these far-away clusters contain Cepheids, which we find in other galaxies outside our own. Thus, the Hyades star cluster is a fundamental stepping stone in our path to deriving distances to stars and galaxies, and ultimately, to determining the size and age of the universe. Doing All That Measuring From Space Although the distance to the Hyades has been derived many times, the uncertainties in this distance have always remained relatively large. This is because the convergent-point method, which is in principle very simple, is in practice fraught with many uncertainties: There may be errors in the measured proper motions of the stars; some of the stars under study may not be actual members of the Hyades cluster; and motions of the cluster members are not perfectly parallel. All these effects lead to errors in the derived cluster distance. The only way really to obtain an accurate calibration of the distance scale of our universe then, is to measure accurate parallaxes for as many types of stars as possible (including the Hyades cluster stars) in order to obtain direct distance measurements. For this reason, a proposal was made in France in the 1960s to carry out astrometrical measurements from outer space. The advantages of such a spaceborne operation are that one can perform measurements for thousands of stars in only a few years, which is impractical from the ground, and that the measurements can be made in a very precise, uniform way all over the sky, which avoids the systematic differences that exist among ground-based astrometric measurements for different parts of the sky (differences that exist because such measurements were made by different observatories). The proposal ultimately led to the 1989 launch of the European Space Agency's HIgh Precision PARallax COllecting Satellite, a spacecraft named in memory of Hipparchus that measured positions, parallaxes, and proper motions for over 100,000 stars. The precision with which these measurements were carried out was one milli-arcsecond (an arcsecond is 1/3600th of a degree, and a milli-arcsecond is one thousandth of that). To put this degree of precision in perspective, consider that the human Hipparchus was able to measure stellar position to about one degree, which corresponds to the angular height of a man seen from 100 meters. Modern ground-based astrometric measurements can discern the height of a man from 4000 kilometers. The satellite HIPPARCOS, however, can see a man standing on the Moon at a distance of 380,000 kilometers! These precision figures translate into uncertainties of only 5% in the distances to individual stars in the Hyades cluster. This means that averaging about one hundred of these individual distances will lead to a cluster distance known to better than 1%. This kind of accuracy for distance measurements is unprecedented in astronomy. A Three-Dimensional View of the Hyades The HIPPARCOS Catalogue, containing positions, parallaxes, and proper motions for about 118,000 stars, became available in August 1996 and represents 37 months of measurements by the satellite. Immediately following its release, astronomers from the European Space Agency, Leiden Observatory, Observatoire de Paris-Meudon, University of Lausanne, and Observatoire de la Côte d'Azur started work on the analysis of the HIPPARCOS data for the Hyades cluster. The first thing they set out to do was to isolate members of the Hyades cluster from all the other stars surrounding the cluster. Remember that although Aldebaran is part of the "V"-shape in Taurus, it is not a member of the Hyades-it is actually much closer to the Sun. These non-members had to be weeded out first; the weeding was accomplished by again making use of the fact that the cluster stars have the same velocity through space. And to search for Hyades stars, it was possible for the first time to use directly measured, three-dimensional velocities of the stars by combining the stars' parallaxes, proper motions, and radial velocities (measured from the ground, see Hyades SideBar). This led to a very secure list of true Hyades cluster members that could subsequently be studied in detail. Based on this list, the distance to the Hyades cluster was determined to be 46.34 parsecs, or 151 lightyears, with an uncertainty of less than 0.27 parsec (one lightyear). Figure 1 shows a number of recent distance determinations for the Hyades cluster together with the HIPPARCOS distance (rightmost point). The other distance determinations are based on a variety of different techniques, many of them invoking some form of the convergent-point method. The vertical lines through the points indicate the uncertainty of each distance determination; note the considerable spread in the Hyades distances prior to the HIPPARCOS result, indicative of that uncertainty. The HIPPARCOS measurements firmly tie down the distance to the cluster and also lead to an explanation of the discrepancies among the previous results. Figure 3 shows the structure of the cluster in more detail: three projections of the cluster on the three principal coordinate planes of the Milky Way Galaxy. In the plots, the Earth is located at the origin (0, 0) of the coordinate system, the X-axis points towards the center of our Galaxy, the Y-axis points in the direction in which the Sun orbits the Galactic center, and the Z-axis points upwards, perpendicular to the plane of the Milky Way. The distances along the axes are given in parsecs. From the images and plots we can clearly see the Hyades consists of a concentrated central part surrounded by a more diffuse halo of stars. That central part (within a diameter of roughly 65 lightyears) is bound together by the mutual gravitational attraction of the stars there. The "halo" stars originated with the rest of the Hyades stars when the cluster was born but have gradually moved away from the central regions and are no longer bound to the cluster. However, they (and their remains after their deaths) will remain in its vicinity for some time before being completely dispersed throughout the Galaxy. There are several reasons why a particular star may escape the central, gravitationally bound regions of the cluster. As it orbits the center of the cluster, the gravitational pull of all the other stars will lead to slight changes in the particular star's velocity and may ultimately lead to its gradual wandering away from cluster center. And if the star is far enough away from the center, the gravitational forces of the Galaxy will come to dominate those due to the cluster, and the star will find itself no longer bound to the cluster, but rather to the Galaxy. Another mechanism that can remove stars from a cluster's center are star-star encounters. In the dense central regions, where stars pass closer to each other than in the diffuse, outer halo, encounters between stars or, more importantly, between single stars and double stars, can lead to the rapid ejection from the cluster's center of one of the stars taking part in the encounter. Just consider the analogous gravitational slingshot effect that we use to accelerate interplanetary spacecraft: The spacecraft falls in its trajectory just close enough to a big planet to get a velocity kick. And finally, a star cluster may also lose stars during encounters with other massive objects such as giant interstellar clouds of gas and dust. All these effects will together ultimately lead to the total dissolution of the Hyades cluster at some point in the future. Apart from the velocities of the Hyades members, the stars' distances are now known well enough for us to construct for the first time a three-dimensional picture of the arrangement of stars in the cluster. The image on the left shows the constellation Taurus, easily identified by the "V"-shape of the Bull's head (except for the Aldeberan,the large sphere in the middle, which is much closer to the Sun than the Hyades), and the image on the right is Hyades as seen from Earth if we could discern the cluster's three-dimensional structure with the naked eye. Each sphere in the picture represents one star, and all spheres are the same size. Hence, stars closer to us appear as larger spheres. Note, however, that relative sphere sizes do not reflect brightness differences among the cluster stars. This image of the Hyades shows that the cluster members are strongly concentrated towards the center. A movie of the 3D Hyades cluster has been created by the author and can be viewed at http://astro.estec.esa.nl/Hipparcos.
Taurus
and the Hyades. This image shows all the stars that are part of the Hyades cluster as seen from Earth. Note the strong concentration of cluster members towards the center. The images below show the structure of the cluster in more detail: three projections of the cluster on the three principal coordinate planes of the Milky Way Galaxy. In the plots, the Earth is located at the origin (0, 0) of the coordinate system, the X-axis points towards the center of our Galaxy, the Y-axis points in the direction in which the Sun orbits the Galactic center, and the Z-axis points upwards, perpendicular to the plane of the Milky Way. The distances along the axes are given in parsecs. From the images and plots we can clearly see the Hyades consists of a concentrated central part surrounded by a more diffuse halo of stars. That central part (within a diameter of roughly 65 lightyears) is bound together by the mutual gravitational attraction of the stars there. The "halo" stars originated with the rest of the Hyades stars when the cluster was born but have gradually moved away from the central regions and are no longer bound to the cluster. However, they (and their remains after their deaths) will remain in its vicinity for some time before being completely dispersed throughout the Galaxy. There are several reasons why a particular star may escape the central, gravitationally bound regions of the cluster. As it orbits the center of the cluster, the gravitational pull of all the other stars will lead to slight changes in the particular star's velocity and may ultimately lead to its gradual wandering away from cluster center. And if the star is far enough away from the center, the gravitational forces of the Galaxy will come to dominate those due to the cluster, and the star will find itself no longer bound to the cluster, but rather to the Galaxy. Another mechanism that can remove stars from a cluster's center are star-star encounters. In the dense central regions, where stars pass closer to each other than in the diffuse, outer halo, encounters between stars or, more importantly, between single stars and double stars, can lead to the rapid ejection from the cluster's center of one of the stars taking part in the encounter. Just consider the analogous gravitational slingshot effect that we use to accelerate interplanetary spacecraft: The spacecraft falls in its trajectory just close enough to a big planet to get a velocity kick. And finally, a star cluster may also lose stars during encounters with other massive objects such as giant interstellar clouds of gas and dust. All these effects will together ultimately lead to the total dissolution of the Hyades cluster at some point in the future. How long has the Hyades cluster survived all these destructive forces? This question brings us to discuss the Hyades main-sequence in the Hertzsprung-Russell diagram, a topic of central importance in astronomy. Because the distances to the Hyades stars can be obtained from a geometrical method, the stars can be placed in the theoretical H-R diagram (with their true luminosities as opposed to their apparent luminosities). The location of the stars along the Hyades main-sequence can then be used to test and even calibrate different models of stellar evolution. And perhaps more importantly, the position of the Hyades main-sequence in the H-R diagram is important if one wants to use the main-sequence fitting technique (see Hyades SideBar) for distance determinations. With the HIPPARCOS data, specifically stellar parallaxes, it is now possible to circumvent the problems associated with the convergent-point method and directly place each individual Hyades star in the H-R diagram. The result is shown in the image below for the stars located within 10 parsecs of the cluster's center. The closed symbols represent the single stars; the open symbols, known double stars. The plot's horizontal axis corresponds to the stars' (B-V) index, or color. Low values of (B-V) correspond to blue stars, high values to red stars. The blue stars are also the more massive ones, evolving more quickly than the less-massive, red stars. The plot's vertical axis indicates the absolute magnitude, or true brightness, of the stars. Some cluster characteristics are immediately discernible from this plot. The four isolated stars near the top are four red giants in the center of the Hyades cluster. These are the most evolved stars in this diagram; the other stars define the Hyades main-sequence. Note that the double stars often lie above the main-sequence defined by the single stars: They appear brighter when both components of the double star are measured simultaneously. The red part of the main-sequence (lower right) contains low-mass stars that have not moved from their positions in the H-R diagram since they started their lives as main-sequence stars. These stars define the so-called zero-age main-sequence of the Hyades. The positions of the redder, single stars in the H-R diagram were used to model this zero-age main-sequence. Theoretical calculations show that the zero-age main-sequence of the Hyades is best modeled by assuming that the cluster's stars contain the same amount of helium as the Sun, even though it is known that Hyades stars are slightly brighter and more "metal-rich," or heavy-element abundant, than the Sun. Once the amount of metals and helium in the Hyades is known, one can calculate how the stars will evolve in the H-R diagram. And from these and intermediate calculations, we find the age of the Hyades to be 625 million years, making it a middle-aged cluster. (Compared to the oldest open clusters or globulars, the Hyades is a relatively young cluster, but compared to the Pleiades it is quite old.) There's More. . .There's Always More So can we now close the "Hyades case"? Not quite. A number of questions still remain unanswered about this cluster. Intracluster
motions. The
Hyades moving-group. Mass
segregation. As far as our hope of obtaining more accurate measurements are concerned, the future looks promising. Several national and international space agencies are already considering or planning future space-astrometry missions that will carry out measurements 10 to 100 times more accurate than those by HIPPARCOS! One of these possible missions is the Global Astrometric Interferometer for Astrophysics, currently under consideration by the European Space Agency. Early plans are for the instrument to carry out astrometric measurements to a precision of 10 millionths of an arcsecond. And these measurements would be performed not for a hundred thousand stars, but for 50 million stars, with less precise measurements (up to milli-arcseconds) for up to a billion stars to apparent magnitudes as faint as 20! This would not only greatly advance our knowledge of the Hyades star cluster, but would also enable us to construct a detailed, three-dimensional map of a large portion of our Galaxy for the first time. ANTHONY G. A. BROWN is a postdoctoral fellow at the Instituto de Astronomía of the Universidad Nacional Autónoma de México at Ensenada in Baja California. His research interests are the formation and evolution of star clusters, and he is currently involved in the concept and technology study for the ESA's GAIA mission. While not pursuing his astronomical research, he is occupied by the excellent wines and food in Ensenada. His email address is brown@bufadora.astrosen.unam.mx. The Convergent-Point Method and Main-Sequence Fitting Before the HIPPARCOS mission, it was very difficult to get reliable distances to individual stars in the Hyades cluster by measuring their parallaxes because the cluster is located just beyond the distance for which one can more or less easily get good parallaxes from the ground. Hence, other geometrical methods were devised to measure stellar distances. The most widely used method is the so-called convergent-point method. This technique makes use of the fact that stars in a cluster follow roughly parallel trajectories through space, as shown in Figure 5a: The parallel motions will result in the stars' apparent motions on the sky converging toward a single point, the convergent point. This is analogous to railroad tracks apparently meeting each other in the distance as you look along them. That the proper motions of the Hyades stars do indeed point to a particular spot on the sky is illustrated in Figure 5b.
Figure 5a
Figure 5b One can use this perspective effect to measure the distances to the stars in the cluster in the following way. Consider the motion of a cluster star as seen from Earth in Figure 5c. This space-velocity points in the direction of the convergent point and is perceived by us as the sum of two components-the velocity along our line of sight, the star's radial velocity, and the velocity perpendicular to our line of sight, the star's proper motion. Now, a star's radial velocity can be measured from its spectrum, and its proper motion is determined by measuring its angular speed through space (i.e., arcseconds per year).
Figure 5c Thus, knowing the proper motions of stars in a cluster can enable one to find the directions of the stars' space velocities. This direction is identified in the diagram as the angle q. From a star's radial velocity and the angle q, one can then calculate the space velocity and also the velocity of the star perpendicular to the line of sight. The latter is measured in kilometers per second, but we also know the proper motion in arcseconds per year. A comparison of these two numbers will yield the distance to the star. And this technique can be applied to every star in the cluster. Though conceptually very simple, the method relies heavily on a couple of assumptions. First, we assume the stars move strictly parallel through space. This assumption is not valid in reality, however. The stars move through the cluster with small velocities, and the cluster itself may be rotating. These effects lead to errors in the convergent-point determinations and in the derived distances. Second, we assume that all the stars under study are actually members of the same cluster (so we can assume they move parallel!). The unintentional inclusion of non-cluster stars in the analysis leads to errors. In spite of these error-inducing assumptions, the convergent-point method applied to data from ground-based observations has yielded a distance for the Hyades with an accuracy that could not be achieved otherwise from the ground. And once the Hyades distance is known, one can measure distances to other clusters. The way this works is illustrated in Figure 6: By observing stars in a cluster, we determine their apparent brightnesses and colors, which we in turn use to place them in an observational Hertzsprung-Russell diagram. The Hyades main-sequence is the middle line. We know how far away the Hyades are, and by comparing the brightnesses of stars in other clusters to those of the Hyades stars, we can deduce distances to stars in those other clusters. Two main sequences for other clusters are also shown in Figure 6, one from stars in a cluster closer than the Hyades (appearing brighter) and one from stars in a cluster further away (and thus fainter). This main-sequence comparison is best done using the whole main-sequence rather than individual stars. But the method has some uncertainty. We must assume that the main sequences of different clusters can actually be compared. Other clusters' stars may have different compositions from those in the Hyades, making them intrinsically brighter or fainter (that is, not due to their distance).
Figure 6 Additionally, the shapes of the main-sequences may differ, and this makes the measurement of brightness differences even more complicated. Nevertheless, this is still a very powerful method for extending distance measurements out to far-away clusters, and it is one of the fundamental building blocks for building the distance scale of the universe. |
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