Amateurs and Hipparcos

Yet there is another aspect of this technological revolution which I think has not been stressed enough. It is related to the fact that today we have almost immediate access to a big part of the data gathered by professional observers, while at the same time we also have the communications, hardware and software facilities to download, store and analyze selected portions of those data. As an example of this, we can look at some HST images only weeks after they are acquired, and at least in principle it is possible that some of us could recognize in them something of value that had not been perceived by the few professionals dedicated to them. After all, it is not unusual that a second examination of old photographs brings out discoveries which had been ignored by the original observers.

The beneficiaries of this new situation are, of course, armchair amateurs. Not since the nineteenth century we have been in a better position to participate in the development of our science. Of course not all fields are equally suitable for us. We cannot even think of competing with professionals in areas like cosmology, stellar models, spectroscopy or celestial mechanics. Our knowledge of mathematics or physics is usually not deep enough. Instead, we should focus in data transformation, analysis, display and interpretation, by means of basic mathematics and the same statistics which many of us are already using in our daily business. For instance, to display and recognize the spongy distribution of galaxies in nearby space, including clusters, voids and perhaps even bubbles, all that is needed is a sizable catalogue of galaxies with some tens of thousands of positions and radial velocities, a little knowledge of spherical trigonometry, a state of the art PC and some practice with commercial spreadsheets.

Even in these areas we have disadvantages relative to professionals. In the first place, it is almost impossible for us to have access to the entire bibliography about the subject we have chosen for our research. It is a little frustrating to think that you have found something new, only to be told later that it was already discovered by some Russian or Japanese scientist. Secondly, it is not easy to investigate any subject without receiving feedback from your colleagues. Finally there is the difficulty of finding a suitable place to publish the conclusions. Be it a local astronomy magazine or perhaps a web site, what are the chances that professional science will ever take notice of our efforts?

Our advantages, if any, are in our numbers, of course, but also in the different approach to problem solving that we bring with us from our professional activities. Everybody knows that customers are much more complex than stars. Galactic research should not be more difficult than market research!

This is only the beginning. Soon I may be able to apply coordinate transformations, adjust for solar motion, select special spectral types, compute absolute magnitudes and plot Hertzsprung Russell diagrams, just the same kind of things you see in the professional Journals, if you ever had one in your hands.

What types of research can you perform on these data?

• Compute the distance of the Hyades or any other nearby cluster, with better accuracy than any previous work.
• Discover new clusters by finding clumps in the five dimensional space formed by the two positions and two proper motions in Right Ascension and Declination, and by the parallax of each star.
• See what field stars anywhere in the sky probably belong to the Hyades moving group.
• Compare cluster H-R diagrams with those of selected field stars.

In what follows I will present several examples of my own investigations.

The usual way to determine the distance of a distant cluster is to plot the HR diagram, adjust it for interstellar extinction and reddening, and then compare its Main Sequence with the standard Main Sequence known from studies of nearby field stars or the Hyades cluster. The magnitude difference for stars of the same color gives the so called Distance Modulus, which in turn provides the distance. Unfortunately these distances are not very accurate because the Main Sequence is not a line but a broad stripe, as we will see later. With Hipparcos the situation has changed completely, because it was able to measure the parallaxes of its individual stars with an accuracy better than 10%, purely by geometric means. Let us then derive a new and more accurate distance for this cluster as a whole.

Our first problem was to identify which stars belong to the cluster and which are field stars in the same line of sight. The cluster's diameter is stated as 50' of arc, but to be sure of not loosing anything I extracted from the Catalogue all stars in a 3° × 3° field centered on the cluster. I loaded the file, 49 stars in all, into my spreadsheet and started the analysis.  To see which stars were candidates for the cluster, I plotted an X-Y diagram with the proper motions in R.A. and declination. In this chart it can be seen at first glance a concentration of stars with proper motions between -15 and -20 in R.A. and between 8 and 13 in declination. To verify that all these stars are at about the same distance from us, I plotted both proper motions against the parallax. This second chart shows that the cluster stars have measured parallaxes between .0065" and .008". Based on this analysis, a total of 17 Hipparcos stars belong to IC 2602. Applying standard statistical formulae to these stars, we obtain a cluster parallax of 0.00706" ± 0.00007", corresponding to a distance of 141.6 parsecs with a probable error of 1%. This is much better than the accuracy for which the Hyades' distance was known a decade ago.

In Hipparcos there is no information on star ages or metal content, but we can differentiate the Populations in our neighborhood by measuring their velocities relative to our local standard of rest. Population I should move slowly to stay confined to the galactic plane, while Population II should move much faster in order to get high into the halo or even to reach the galactic center. Though radial velocities are generally unknown for Hipparcos stars, we do have distances and transverse angular motions, the product of which gives the velocity component at right angles to our line of sight. These velocities must be corrected for the Sun's motion in space and for galactic differential rotation; lots of trigonometric formulae but nothing that is outside the reach of an amateur.

First I selected those stars with high quality parallaxes (arbitrarily set at prob. error < 7%), 9869 stars in all, a size manageable with a spreadsheet. Then I computed absolute magnitudes (Mv) and transverse velocities, with the previously mentioned corrections. By selecting different velocity ranges and plotting Mv versus color (B-V) we have the Herzprung-Russell diagram for those subsets of stars. Of course total velocities are higher than transverse velocities, because of the unknown radial velocity. As a consequence, the only thing we can say for sure of these diagrams is that there are no stars in it with total velocities smaller than the labeled transverse velocity.

Some of these diagrams (with about 150 stars each) are shown on this page. A clear evolution can be seen, especially when you look at the left (bluest) and upper (brightest) ending of the diagonal stripe across the diagram.

The series of charts show that the brightest of the slow moving stars reach to Mv = -2 and B-V = -0.2, those that move at about our Sun's velocity (20 km/s) get to Mv = +0.5 and B-V = 0.0, even faster moving stars (36 km/s) get to Mv = 2.5 and B-V = 0.3, and the fastest (>100 km/s) only reach to Mv = 4 and B-V = 0.5. The fact that the Turning Point of each subset of stars is so clearly defined, means that each group has a well determined minimum age for its components, because all stars to the left of this Point have already evolved to the end of their lives. The fact that the Turning Point position is a continuos function of the transverse velocities implies that we are not seeing separate discrete populations but just one single population, with evolving parameters as a function of velocity.

It seems that the key point to establish is the reason for this velocity distribution. Were the high speed stars born far from the galactic plane, at a very early stage of galactic formation (like globular clusters), or were they born with small velocities in the vicinity of the galactic plane, to be later accelerated by some cumulative process, so that the older stars move faster today? To answer this question it would help to know the minimum age for the stars in each diagram.  This is a theoretical subject that of course is outside the scope of an amateur study, but there is an indirect way in which we can estimate the minimum ages as a function of transverse velocities.

This method is based on the comparison of these diagrams with those for nearby open clusters. There is a close match between the Turning Point of the Hyades, for example, and that of the stars with transverse velocities around 28 km/s. As the age of the Hyades is estimated at 660 million years, the 28 km/s group of stars should have this same age as its lower limit. Repeating the process with different clusters we can estimate minimum ages as a function of transverse velocities. Because of the qualitative nature of the comparison, the fit is only approximate. The following table shows the results for some clusters:

The table does not contain older clusters because those do not have stars bright enough to be included in Hipparcos data. It would be very interesting to compare their HR diagrams, obtained from other sources, with the fastest moving Hipparcos stars.

The search proceeds by filtering narrow parallax ranges, until some grouping is seen in one of the plots. Once that happens, the other plot must be filtered to include only the stars of that grouping. If the second plot also shows a grouping, we have discovered a clump in five-dimensional space. This is what I did while investigating a 25° × 20° area in the constellation of Lupus. After trying several parallax ranges, I found that with 6 < Plx < 9, there was a clump in Proper Motions at -25 < pmRA < -15 and -31 < pmDEC < 20. When filtering the Positions plot with these ranges, a distinct group could be seen near RA = 236° and DEC = -35°, with a diameter of about 3°. Nine Hipparcos stars are probable members of this cluster (HIPP. 76395, 76945, 77038, 77135, 77150, 77286, 77315, 77317, 77713), the brightest of which is the naked eye star Psi² Lupi. The cluster parallax turns out to be 0.00797" ± 0.00020", placing it at a distance of 128 parsecs.

Assuming that the stars' positions are distributed randomly in the area under investigation, and considering the observed distribution of parallaxes and proper motions, an average of 0.7 stars should have been found in the five-dimensional volume where the cluster is. The fact that we have found 9 stars in the same area speaks in favor of it being a real cluster and not a chance aggregation.

The accompanying HR diagram shows the stars of this group together with those of the Vt=7 Km/s population. It seems to be a young cluster, resembling IC 2391, which is about 40 million years old. Most of the stars in the new cluster fit quite well in the Main Sequence, with the exception of the faintest and reddest (HIPP. 77135), which may be an interloper.