Catch a Star 2002

The Hyades

The Hyades is one of the most spectacle view from the winter sky. It is our nearest open cluster neighbour. The name of the cluster comes from the Greek mythology. Hyades are daughters of Aethra and Atlas (the giant who carried the heavens on his shoulders), so they are half-sisters of the Pleiades. The legends say that they were very attached to their brother Hays. One day, while Hays was hunting, he was killed by a lion. The Hyades were so overcome with grief they committed suicide. Zeus turned them into a cluster of stars and placed them in the constellation Taurus, the Bull. The god was grateful to them because they nursed his son, Dionysus. 

"The Moon wades through Hyades bright, Foretelling heavier rain." The Greek Gadez, ("Hyades" in Latin) means "to rain". It's so because the wet period attends their morning and evening setting in the later parts of May and November. Pliny wrote of them as being "a violent and troublesome stars causing storms and tempests raging both on land and sea". Thus they have always been considered most notable by all who were dependent upon the weather. In fact, they are related with the rain in almost every country. Among the Romans the Hyades were known as the Little pigs. Maybe because the continual rains of the season of their setting made the roads so muddy that the stars seemed to delight in dirt, like swine! Or because the cluster looks like a pig's jaw. The Hyades were compared with the human life, with a torch, a Temple, or Wagon between the Hindus… 

Occasional Arabic titles were Al Mijdah, a Triangular Spoon, and Al Kilas, the Little She Camels. Another author made the word Al Kallas, which means the Boiling Sea. Generally, however, in that country, the Hyades were known as Al Dabaran, referring to Aldebaran, the brightest star, but outside of the cluster, as we understood with the new technologies. 

In our country - Bulgaria Aldebaran and Hyades are known as the Piper and "horo" (traditional bulgarian dance in which dancers form a ring around the piper such as the stars in Hyades surrounded Aldebaran).
 
 

LOCATION

Except for the Ursa Major Moving Cluster, which is not apparent visually as a distinct cluster, the Hyades are the nearest open cluster to the Solar system, located at a distance of 151 light years and estimated to be 660 million years old.
 

The Hyades is unmistakable sight on the winter's night sky. The most bright stars of the Hyades form the Bull's head, except the burning left eye Aldebaran. They are seen both by a naked eye and with binoculars, covering a 30°-wide site. It contains several hundred stars, but we can see about 40. Its real diameter is about 16 ly. 

THE STARS

Open clusters are very interesting to astronomers, since the stars in them form a mixed group of types, which have these properties:
1. the stars in the cluster are almost in the same distance;
2. the stars have approximately the same age;
3. the stars have about the same chemical composition, and
4. the stars have different masses, ranging from about 80-100 solar masses for the most massive stars in very young clusters to less than about 0.08 solar masses.

The most convenient way to describe the stars in the Hyades is to use the HERTZSPRUNG-RUSSEL (H-R) DIAGRAM

Armed with spectral type and apparent magnitude of a group of stars you can construct a Hertzsprung-Russel diagram (HRD) also known as a color-magnitude diagram. The spectral type of a star is just a letter and a number that designates what kind of a star it is. O stars are the hottest, and M stars are the coolest stars. Because the stars in open clusters are formed in nearly the same time and they have similar chemical composition, the H-R diagram gives us important information about stellar evolution. In the Hyades there is a big variety of stars - some red and blue supergiants, but most of the stars are main sequence stars. Mass of the brightest stars on the main sequence is a good indication of the age of the cluster. Using this the astronomers age them a bit more than half a billion years or a middle-aged open cluster. Most of the stars in the Hyades are of spectral class G and K and are average in size, with temperatures that are comparable to that of the Sun. It is so because the forming of the open clusters has started when the matter in the Galaxy's disc had been already enriched with heavier chemical elements. They are results of the biggest "first generation" stars and consequently faster evolving. The nebular variable star T Tauri is part of this cluster. The Hyades is important as a fundamental calibration point in the distance scale of the universe. Because it is one of the closest of the open clusters, measurements of parallaxes of its stars as well as the relationship between the apparent and absolute magnitudes of some of its member stars yield similar distance results. 

More detail information about some prominent / interesting stars in the Hyades 

71 Tauri (HD 28052; F0 IV-V) is an enigmatic object for two reasons: first it is the second brightest X-ray source in the Hyades, yet early F stars as a rule are not strong coronal emitters; and second it lies a magnitude above the cluster main sequence, but radial velocity studies and speckle imaging suggest that it is single.

The star q¹ Tauri is roughly in the middle of the Hyades star cluster. q¹ Tauri is a red giant, a star that was at one time like the Sun, but has now reached stellar "old age". Red giants form when a star begins to run out of  hydrogen - a normal star's main energy source - which leads to an expansion, cooling, and an increase in total luminosity.

V471 Tauri is pre-cataclysmic, eclipsing-spectroscopic binary. One of the components is magnetic white dwarf with T_eff=35000K, which is 13000K hotter than single white dwarfs in the Hyades.

PAST AND FUTURE

Stars born in the clusters rather then as individuals, condensing out of separate cosmic gas and dust clouds within the diffuse nebula many light years across. By these reason they form physically related groups of stars, held together by mutual gravitational attraction. These groups are known as star clusters. According their main characteristics they are separated in two different types - open clusters and globular clusters. About 300 open clusters have been discover in the Galaxy. They all occur throw out her spiral arms. One of these clusters is Hyades.

Open cluster are being born all the time. In many clouds visible as bright diffuse nebulae, star formation still take place at this moment. The process of formation takes only a considerably short time compared to the life time of the cluster, so that all member stars are of similar age. Also, as all the stars in a cluster formed from the same diffuse nebula, they are all of similar initial chemical composition. Their likely age can be determinate by examine its population. If it contains many very hot stars, it must be young - since such stars burns out quickly, or evolve to a red giants. If it contains red giants and white dwarfs, it must be old. 

Most open clusters have only a short life as stellar swarms. As they drift along their orbits, some of their members escape the cluster, due to velocity changes in mutual closer encounters, tidal forces in the galactic gravitational field, and encounters with field stars and interstellar clouds crossing their way. An average open cluster has spread most of its member stars along its path after several 100 million years; only few of them have an age counted by billions of years. The escaped individual stars continue to orbit the Galaxy on their own as field stars: All field stars in our and the external galaxies are thought to have their origin in clusters quite probably.

THE HYADES AND THE PLEIADES

There are two prominent open star clusters, visible to the unaided eye, the Pleiades and the Hyades. Both of them are located in the constellation Taurus and have been known since prehistoric times. The Hyades and the Pleiades (M45) were mentioned by Hesiod between 1000 and 700 B.C., and by a number of other ancient authors, including Homer, Pliny, Vergil, Horace and Ovid. Taurus is above Orion and nearly overhead. The three brightest stars of Taurus form a narrow V-shape, lying on its side above right shoulder of Orion. The brightest star in Taurus is Aldebaran. The cluster of stars surrounding Aldebaran are the Hyades. The Pleiades, known as the seven sisters, are higher in the sky about 10 degrees from Aldebaran. Both the Hyades and the Pliades are naked eye and binocular objects. The difference is that the Hyades are very scattered open cluster opposite to the Pleiades which are much more compact. The reasons are different distances and ages of two clusters. 

Distance: 
The Pleiades (375 ly) are almost two and half times more farther the Hyades (151 ly). These results have been derived from satellite called Hipparcos (an acronym for High Precision Parallax Collecting Satellite), which have been launched in 1989 from European Space Agency (ESA). This device was designed to use trigonometry to directly measure distances to the closest stars and its positions. The accurate distances (to within ten percent of the true value) have been achieved for more than 22,000 stars. The data have proved very interesting and there have been plenty of surprises. In addition, many well known stars turned out to be much farther away than previously believed. Particularly surprising are the values obtained for the Pleiades cluster. At 375 light years, this group of stars seems to be located 15% closer than previous estimates. The Hyades, on the other hand, were located considerably further away than expected - 151 ly.

Age:
The Pleiades are younger then the Hyades which is clearly seen when we compare their HR diagrams. The Pleiades belongs to the group of the younger open cluster. Their age is around 100 million years. Almost all of the stars are on the main sequence. No O stars and few B stars, but lots of A and fainter. The stars are surrounded with nebulosity associated with the Pleiades. The Hyades is middle age cluster. They have some red giants, brightest main sequence stars around F. Age a bit less than 1 billion years. 

To compare other characteristics of the Hyades and the Pleiades we will use the sophisticated scheme which was introduced by R.J. Trumpler. This scheme consists of three parts, characterizing the cluster's degree of concentration, the range of brightness of its stars, and the richness, as follows:

Concentration:
     I - Detached; strong concentration toward center 
     II - Detached; weak concentration toward center 
     III - Detached; no concentration toward center 
     IV - Not well detached from surrounding star field 
In our opinion both the Pleiades and the Hyades are from the second class since they are quite scattered. 

Range in Brightness:
     1 - Small range in brightness
     2 - Moderate range in brightness
     3 - Large range in brightness
We consider that both the Pleiades and the Hyades belongs to the third class.

Richness:
     p - Poor: Less than 50 stars
     m -  Moderately rich: 50 to 100 stars
     r - Rich: More than 100 stars
According to this classification Pleiades and Hyades belongs to the group of rich open clusters, but undoubtedly Pleiades with their almost four hundred star are more rich then the Hyades.
 
 

DISTANCE EXERCISE

Moving Clusters method

Yet William J. Kaufmann II wrote in the 1994 edition of his text: "Because the distance to the Hyades cluster is the most accurately determined of all stellar distances, it provides the basis upon which all other astronomical distances are determined".

Background and Theory

The zero point for the entire cosmic distance scale, out to the farthest reaches of the observable universe, has been based upon the distance to Hyades star cluster. It is a bit unsettling to think that even over the past decade, distance determinations to this cluster have varied by as much as 15%. What's the problem? From ground-based telescopes, reliable parallaxes for individual stars can be measured out to about 40 parsecs. At 40-50 parsecs, the Hyades cluster is just beyond this distance. As a result, other (often ingenious) methods have been required to find the distance to this star cluster. Most distance determinations used for the Hyades have either been based upon the convergent point method or have been judged according to their agreement or disagreement with it. The geometry used is relatively simple, but before we discuss how to use the method, we must define and explain some important concepts. 

The positions of stars are not really fixed. They only seem that way because of our crude measuring instruments or our limited observational time period (a few hundred years, at most). We can determine their motion in space by measuring two quantities: the proper motion and the radial velocity.

1. Proper Motion: Proper motion (usually denoted by the Greek letter m) is the angular change in position of a star across our line of sight, measured in arc seconds per year.

2. Radial Velocity: The absorption lines in a stellar spectrum will be shifted in wavelength if the star is moving towards or away from us. 

If a group of stars is moving together (as happens in a cluster), we can sketch the motion of each star in space. Just as two parallel railroad tracks appear to converge in the distance, so also will parallel star paths. This point of convergence is determined on a chart of the sky by simply extending the lines of proper motion of each star, and finding their point of intersection. The angle of sight between a star and the convergent point is measured on the chart, or in the sky. This angle is denoted by the greek letter q.

Terms:
Using the table of sky co-ordinates of the Hyades' stars, try to determine roughly:
1. The right ascension and the declination of the cluster's centre.
2. Compare your results with the real ones. 

Given:
1. Table of sky co-ordinates of six of the stars: 

2. Co-ordinates of the centre of the cluster (from sky catalogues): RA = 4^h 26^m, Dec = +15° 52'

Working out:

1a. Converting of RA from hh:mm:ss format to decimal format
Example:
If 1 hour RA = 15°, 1 min RA = 15' (0.25°), 1sec RA = 15"(0.00417°) then:
3^h50^m15^s = 3 * 15° + 50 *.025° + 15 * 0.00417° = 45 + 12.5 + 0.06 = 57.56°
57.56° / 15 = 3^h.8375

1b. Converting of Dec from dd:mm:ss format to decimal format
Example:
If 1' = 0.0166°, 1" = 0.0003° then:
17°10'47" = 17° + 10 * 0.0166 + 47 * 0.0003 = 17°.1797
 

1c. Calculating of average RA and Dec of the centre of the cluster:
Average RA = (RA₁ + RA₂ +... + RA₆) / 6 = (3^h.8375 + 4^h.1414 +... + 5^h.1103) / 6 = 4^h.54 = 4^h 31^m
Average Dec = (Dec₁ + Dec₂ +... +Dec₆) / 6 = (17°.1797 + 05°.3944 +... + 27°.9686) / 6 = 16°.44 = 16° 26' 

Because of the spherical "shape" of the sky and the formula we used (arithmetic mean) the calculated results are approximate. 

2. Comparing the results
Difference in RA = RA_calc - RA_real = 4^h 31^m - 4^h 26^m = 00^h 05^m
Difference in Dec = Dec_calc - Dec_real = 16° 26' - 15° 52' = 00° 34'
 
 

Task II.

Terms:
Using the given information about the co-ordinates, proper motion and radial velocity of Hyades' stars and online sources of the co-ordinates of the convergent point.
1. For the stars of Hyades determine the angle q to the convergent point and calculate the real velocity, using the formula

2. Using the data from table below, determinate the distance to each star and the average distance to the Hyades. 
3. Explain the difference between all the results?

Given:
1. Table with information about the co-ordinates, proper angular motion and radial velocity of stars:

Working out:

1a. Looking for q :
From online sources the real sky co-ordinates of the convergent point are: RA=6^h08^m, Dec=+9°6' 

RA_conv.point - RA_star = q_RA
Dec_conv.point - Dec_star = q_Dec
q = sqrt (q_RA²  +q_Dec² )
 
 
 

Example:
q_RA1 = RA_conv.point - RA_star1 = 6^h08^m - 3^h50^m15^s = 91.9995° - 57.5625° = 34.4370°
q_Dec1 = Dec_conv.point - Dec_star1 =  9°06' - 17°10'47" = -8.0797° 
q = sqrt [34.4370² + (-8.0797)²]= 35.37° = 35° 22' 

Results for q see in table below.

1b. Calculating of the real velocity of the stars
Example:
V_star1 = V_{r star1} / cosq_star1= 31.6 / cos35.4° = 38.8km/h 

Results for V see in table below.
Average V for the cluster is:
V_med = (V_star1 + V_star2 +... + V_star6) / 6 = (38.8 + 41. 4 +... + 45.3) / 6 = 43.4 km/h 

Real results, found in internet:
Stefanik and Latham (1985), From 84 stars, Vo = 47.5 km/s, RA = 6.66 h, Dec = 10.85°
Detweiler (1984), 39 stars, 39.1+/- 0.2 km/s, RA = 6.23 hours, Dec = 6.7° 

2. Determination of the distance to each star and the average distance to the Hyades
 

From the right-angle triangle of speeds: V_t / V_r = tgq
We also know that: V_t = m * d
Therefore: d = (V_r * tgq) / m
If: V_r [km/sec], m[rad/sec], then: d [km] 

But we're looking: d [ly] and m ["/yr] and convert:
m ["/yr] = m [rad/sec] * (1 / 206265) * (1 / 362.25 * 24 * 3600)
d [ly] = d [km] * 300000 * 365.25 * 24 * 3600 

So the formula  d = (V_r * tgq) / m  turns to: d = 0.688 * (V_r * tgq) / m, where: d [ly] and m ["/yr]
If 1pc = 3.2615ly then: d = (V_r * tgq) / 4.74 * m, where: d[pc] 

Table of results:

Calculation of average distance to the star cluster Hyades:
d_med = (d_star1 + d_star2 +... + d_star6) / 6 = (31.3 + 28.4 +... 41.9) / 6 = 38.6pc

Real results:
Schwan (1991), based on 62 stars, distance 47.9 pc
Hanson (1975), based on 59 stars, distance 45.4 pc.
Gunn et al. (1988), based on HST results, distance 48.3 pc.
Brown et al. (1997), based on 134 stars, distance 46.34 pc 

3. Explanation of the differences between all the results

In all tasks the differences between the calculated values and the real ones are based on non-sufficient number of stars, also on the inaccuracy of the calculation method and accumulated calculation errors as while. It must be stated that the real results used for comparison are based on different methods with differences between them and it can not be defined which of them is the most accurate.
 
 

REFERENCES AND USEFUL LINKS

Allen R. Hinckey., Star names Their Lore and Meaning, Dover Publication Inc., New York
Bonov A., Mitove i Legendi za Suzvezdiyata, Nauka i izkustvo, Sofia, 1976, p.63-70 (in Bulgarian)
Kaufmann William J., II; Universe, Fourth Edition, p. 341
Minnart M., Prakticheskaya Astronomia, Moscow, 1971, p.183-185 (in Russian)
Webb S. , Measuring the Universe, Praxis Publishing Ltd, Chichester, UK 1999, p. 122-124
Zigel F.Y., Sokrovista Zvezdnogo Neba, Nauka, Moscow, 1986, p.120-126 (in Russian)
Sky Catalogue 2000.0, Vol.2, Cambridge Univ. Press and Sky Publishing Corp., Cambridge, Mass, 1985, p. xlvii

Distance to the Hyades via Moving-Cluster Parallax
The Hyades and the Moving Cluster Method
The Distance to the Hyades Cluster
The Hyades - So Close, and Now, So Familiar
Color-Magnitude Diagrams
The Hyades, Melotte 25
Hyades in 3D