VOSTAT main page

The Hyades & surrounding stars

1. Acquire a VOTable from the Hipparcos Main Catalogue with stars in and around the Hyades. It has been made available as a local copy.
   In general you can get this or any other catalog from Vizier by following the steps below. http://vizier.u-strasbg.fr/cgi-bin/VizieR?-source=I/239/hip_main
   Choose Query setup: 9999 maxiumum, XML-VOTable(DTD) layout
   Output preferences: Compute nothing, Sort by Position
   Query: Show 4 columns -- Vmag, pmRA, pmDE, and B-V
   Constraints -- RA(ICRS) = 0 .. 120, Plx = 18 .. 34
   This generates a table (locally called hyades_hip.vot) of 2212 bright stars with 0<RA<8 hours and distance 29<d<56 parsecs. The columns give the magnitude, color, and proper motion vector for each star. Note that the B-V value is missing for ~1% of the stars. Note also that Vizier adds two identifying columns after the 4 requested columns, recno & HIP, which are identical. They can be considered to be the rank in RA.

2. V magnitude descriptive statistics
   
   Process: Mean, median & Shapiro-Wilk's test
   Select 2 columns with similar units, Vmag &; B-V, and process boxplot These quickly show some basic characteristics of a univariate dataset. We find the mean +/- s.d. = 8.22 +/- 1.89 and the quartiles are 6.99 (25%), 8.22 (50%, median), and 9.56 (75%). But even though the mean and medians are the same, the distribution is not at all consistent with a Gaussian (P=10^-7). The boxplot shows a few bright-star outliers with V<3 magnitudes.
   

3. V magnitude density estimation
   
   Process: Histogram
   The "density" is the statistician's term for the differential distribution function. Looking at the histogram, one can now clearly see the non-Gaussian asymmetry in the V distribution. Compare the histogram with Sturges' and Scott's rules for bin width .
   
   Process: Kernel smoothing
   Try Gaussian and rectangular (i.e. boxcar) convolution functions; note the latter is noisier. The help file provides details on the convolution method. The user can also choose bandwidths.
   

4. Bivariate correlations
   
   Select: 5 columns (Vmag, pmRA, pmDE, B-V, recno)
   Process: Correlation matrix
   This gives the strength of correlation between pairs of variables using Pearson's linear correlation coefficient and Spearman's rho. For each statistic, the output gives the statistic values, the number of points (not the missing B-V entries), and the probability that no correlation is present. Note the dataset is dominated by correlations. Note also that Pearson's statistic is insensitive to the subtle link between the proper motion components.
   
   Select: 2 columns (Vmag and B-V)
   Process: X-Y plot
   Here we display the most famous structure in the dataset: the color-magnitude of bright stars showing the main sequence, giant branch (with red clump stars), and a few Hyades white dwarfs.
   
   Select: B-V and pmDE
   Process: X-Y plot
   Here we explore a less familiar scatter plot for subtler effects. This plot of color vs. proper motion shows non-Gaussian distributions with strong heteroscedasticity (i.e. the scatter, but not the mean, of the proper motion depends on color). This is because the hotter stars are kinematically younger. A plot of B-V vs. recno (i.e. right ascension) shows a small clump of hot Hyades members.
   

5. Multivariate clustering
   Select: 4 columns (Vmag, B-V, pmRA, pmDE)
   Process: Agglomerative nesting (agnes)
   This is one of many classification techniques, several of which should be implemented into VOStat in the future. Here the stars "closest" to each other in the 4-dimensional space are sequentially merged into progressively larger groups. The output is a dendrogram showing the "leaves" merging into "branches" and finally a "trunk". The scientist must decide whether "closeness" is measured in a Euclidean (distance squared) or Manhatten (distance) metric, and how group are defined. Single linkage, which astronomers call the "friends-of-friends" algorithm, produces stringy clusters, while complete linkage produces hyperspherical clusters and average linkage (a common choice) is in between. Ward's criterion (another common choice) produces the maximum-likelihood cluster discrimination under the hypothesis of multinormal structures.

Training set: One can explore the relationship between the Hipparcos dataset of 2212 stars, which have non-Hyades stars, and a more carefully selected sample of Hyades members. The votable contains ~450 Hyades members discussed by I.N. Reid (1992) with Vmag, B-V, pmRA and pmDE. Beware that the columns are in different order, and the proper motion units differ by a factor of 10, from the Hipparcos VOTable dataset. It is userful to note that these confirmed Hyades members have kinematics in the range pmRA = 110 +/- 40 mas/yr and rmDE = -30 +/- 40 mas/yr.