Star clusters are the most important objects of the Galaxy, allowing to study many questions of its structure and evolution. The combination of gigantic growth of information and breakthrough growth in the accuracy of astrometric measurements allow us to talk about new aspects related to the concept of data intensive domains (DID). It is shown how the accuracy of the data and the increase in the volume of measurements accompany each other and lead to the need for intensification of processing. The latter in its turn will lead to the appearance of new important results for both star clusters and the Galaxy as a whole.
The accuracy of measuring astrometric data (proper
motions and parallaxes) is a significant aspect for the
study of open clusters. The stellar clusters belonging to
the disk of the Galaxy are traditionally named as open
clusters (OC). The stars of the OC, as a rule, are
identified by their proper motions diagrams. A cluster is
a system of genetically connected stars that have a
common motion in space. The accuracy of measurements
plays a decisive role in constructing spatial models and
studying the physics of stellar systems. The microsecond
accuracy of the angular measurements achieved at the
present time in Gaia (Global Astrometric Interferometer
for Astrophysics) project [
The discovery of the proper motions of the stars
belongs to the famous English astronomer Edmond
Halley, who in 1718 finds out that some bright stars from
the catalog of Hipparchus-Ptolemy markedly changed
their positions relative to other stars. For example, Sirius
is shifted to the south by almost half the diameter of the
Moon, [
We put an emphasis on the study of star clusters because they are space laboratories and they are located on a region of the sky with a size that accessible for fullscale observation in a telescope. Clusters are areas of high concentration of stars of different masses and types in a small area of the sky. This is effective for making observations, since they fall into one or a small number of observation frames. Group image allow to observe simultaneously so many different stars, as well as to open effectively new objects. Clusters are also convenient for the searching of exoplanets. Over 5000 exoplanet candidates have been discovered orbiting around isolated stars. Many of these stars are once formed or existed in open star clusters.
What are the characteristics of modern data for their
belonging to the category of Big Data and the possibility
of their intensive using? Modern astronomers were lucky
to work in the period when specialized satellites (space
observatories) are launched, aimed at measuring the
parameters of distant objects. The Gaia space project [
Gaia is the space telescope of ESA (European Space
Agency). It was launched in December 2013. The main
goal of the Gaia project is to compile a detailed map of
the distribution of Galactic stars. The program of
observations with this instrument is designed for five
years and will end in 2019. Then, it takes time for the
final processing of all data. The data of the first 22
months of observations are presented to this time.
Potentially Gaia catalog will allow many times to
increase the number of known OC (approximately from
4,500 to 100,000, see [
Also Gaia DR2 provide astrophysical information,
such as interstellar reddening, atmospheric parameters,
and rotational velocities, for stars brighter than G ≈ 12
mag (~5 million stars) [
With what astrometric measurements began the astronomers? Ancient Greek astronomers began work on the definition of stellar coordinates in the first half of the III century BC. The first in Europe star catalog was created by Hipparchus. This catalog included precise coordinates for 850 stars. Then the data were supplemented by Ptolemy himself and other Alexandrian astronomers, increasing the number of stars in the catalog to 1022. The size of Ptolemy's measuring instruments did not exceed 10 minutes. Classic work of Claudius Ptolemy "Almagest" appeared in 140 AD and included a full complex of astronomical knowledge of that time. Ptolemy's catalog, included in the Almagest, is the only ancient astronomical catalog that has come down to us. For each object Ptolemy gives a description of the position in the constellation, indicates the celestial coordinates and magnitudes. The value of this catalog, like the entire "Almagest", can not be overemphasized. "Almagest" for 13 centuries remained the basis of astronomical research. Only in the 15th century did another star catalog appear (Ulugbek), based on original observations, although the accuracy of the measurements did not exceed one in the Ptolemy's catalog. The first European high-precision catalog was published by Tycho Brahe at the end of the 16th century.
English astronomer Edmund Halley in 1718 found
that some bright stars from the catalog of
HipparchusPtolemy markedly changed their positions among other
stars. Among others were Sirius, shifted to the south by
almost half the diameter of the Moon (the apparent
angular diameter of the Moon at an average distance
from the Earth is 31'05"), Arcturus moved on two
diameters to the south and Aldebaran, displaced 1/4 of
the diameter of the Moon to the east. The changes could
not be attributed to the errors of the Ptolemy catalog,
which, as a rule, did not exceed 6' (1/5 of the diameter of
the Moon), [
The first international project - the "Carte du Ciel" catalog was adopted on the initiative of the astronomers of the Paris Observatory in 1887. This project involved photographing with a double overlap of the entire sky with the help of the Henry brothers astrographs (D = 230 mm, F = 3460 mm, field 2° x 2°). It was carried out only in 1938. Photographic plates (about 20,000) were measured and stored at 23 observatories in different countries. The measured coordinates of about three million stars to the 12-th mag are published. The "Sky Map" catalog has now acquired a special value as a document showing the relative positions of stars up to the 12-th magnitude throughout the sky in an epoch close to 1900. This catalog is widely used to determine the photographic proper motions of stars with a high accuracy - up to ± (0.003-0.006) "/yr with the difference of epochs of the order of 100 years.
As a result of the Hipparcos (HIgh Precision
PARarallax COllecting Satellite) [
In 2013, the European satellite Gaia was launched. The goal of this project is to measure coordinates, proper motions and parallaxes for 50 million stars with accuracy better than 10 microseconds of arcsec (1 millisecond = 1/1000 seconds, denoted by mas, 1 microsecond = 1×106 seconds denoted by μas).
The effect of increasing accuracy and an increase in the number of measurements of stellar motions with time and that gave the above accuracy of Gaia DR2 astrometry is shown in Figure 1. The main data are collected in Table 2. The measurement accuracy of this section will be discussed in the next section. The accuracy is extremely useful and needed to be able to talk about the physics of different phenomena in the OC. In Figure 1, three periods of development of the considered measurements are presented. From 1700 to 1938 - a huge increase in accuracy, almost 500 times associated with the improvement of mainly measurement techniques. The next period - the plateau from 1930 to the early 2000-th is associated with the commissioning of large mirrors, and the third period of sharp growth in accuracy, the straight line is almost vertical down! It is the development of cosmic astrometry, related to measurements from space instruments.
For a long time the answer to the question of what real velocities the stars have inside the clusters remains a mystery. Various calculations show that in such stellar systems as the OC, these velocities are extremely small, see Table 3. Mass, MSUN
dispersion, km/s 100 400 1000
The dynamics of an isolated OC is equivalent to the
classical problem of n bodies. The magnitude of the
average residual motions is presented in Table 3 for
several values of mass and cluster radius. The values
obtained from the formulas are in excellent agreement
with the observed dispersion. Although such
observations are extremely small, they are not reliable
and are made, of course, only for the nearest clusters. So
for the Pleiades, the total mass of stars can be assumed
equal to 300 solar masses and a radius of 3.5 pc. In this
case, we find the dispersion of 0.43 km/s, which agrees
perfectly with the observations of 0.42 km/s, [
Data intensive methods should be effective for working with large volumes of clusters data, as well as their processing and extraction from Gaia DR2.
Let us consider the dependence of the proper motion on parallax, expressing the angular measurements of the proper motions in the scale of spatial (tangential) velocities in km/s units. Considering the contents of the entire catalog, it is necessary to distinguish the proportion of stars having the values typical for the peculiar velocity of a star in the cluster, Table 3. Having passed this chain in the opposite direction from the value of the tangential velocity to the parallax value, it becomes clear for what volume of the catalog data this boundary is valid. Comparison of the obtained boundary with respect to the parallax with the distribution of the number of Gaia DR2 stars along the parallaxes makes it possible to reveal the expected number of stars for which π, mas up to V=20m up to V=15m 600 130 26 9 studying the motions or kinematics of stars inside the OC. Now it is possible to understand what and how many OC can be expected up to a given distance from the Sun (parallax).
Let us take the velocities characteristic of real clusters, see Figure 2. We use the formula = 4.74 , km/s. By this formula, we obtain approximately the relationship between proper motion and parallax: π=10µ, where they are expressed in the same units of measurement. A convenient ratio roughly corresponds to measurements with an accuracy of about 0.474 km/s (this value is chosen specifically from real values on Figure 2 to simplify the relationship between π and µ above), which is necessary to understand the kinematics of stars correctly estimate the processes inside the clusters. We tried to answer these and similar questions in this publication.
We see that the increase in the accuracy of astrometric measurements has slowly increased over the course of about two hundred years (from the 10 minutes at the beginning of the 18th century to the 30s at the 19th century). Over the past 20 years, there has been a real breakthrough in accuracy.
The discovery with Gaia's data of new, previously
unknown clusters, has already begun, for example [
known clusters from the different
sources. Then by Gaia DR2 data to the stars selected
within the fields of those clusters a membership rule was
apply. As a result, there were discovery of 60 new open
clusters, which are not included in the combined list.
Thanks to the quality of Gaia DR2 astrometry, the
homogeneous high precision parameters derived, [
It is very important to mention the problem of determining distances by parallaxes. The distances to the clusters are estimated through a maximum likelihood procedure, maximising the posterior probability density function with taking into account many parameters, such as the
measured average parallax for each of the membership stars and the distribution of stars inside the cluster.
smaller than ∼ 0.2 mas would be better constrained by a Bayesian approach using the star density distribution of the Milky Way or the cluster model.
The Gaia DR2 parallaxes are affected by a zero-point offset. To accounted for this bias, add +0.029 mas to all parallaxes before distance estimation.
He led to the fact that for almost all OC in the Gaia project (and in their future will be open about 100 thousand) it will be possible to study previously inaccessible processes inside the clusters. This, in turn, represents the prospect of revolutionary changes in the science of clusters. Undoubtedly, there can be methods of intensive data use.
Acknowledgments. This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. N. V. Chupina, S.