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Determination of membership probability is a key process in an open cluster study. When done properly, intrinsic properties of stellar populations may be retrieved accurately using standard astronomical procedures (such as isochrone fitting). Using an appropriate mathematical apparatus, retrieval of desired kinematic separation may be done in a straightforward manner. Non-parametric methodology introduced by Cabrera-Cano & Alfaro (1990) served as a conceptual framework that gave rise to creation of a new system called Clusterix.

Overall design

Left panel of every Clusterix page contains main menu that consists of five links:

  • Open cluster search link leads to the main page that offers a possibility to search for specific open cluster using its name (see Main page for more details).
  • Lists of open clusters is a link that allows user to list open clusters stored in a specific database.
  • About link contains basic information about Clusterix software and its creators.
  • Help is self-explanatory.
  • Log page describes latest changes that have been made in the Clusterix system.

Information presented by the page footer are then related to the technologies that were used during the website development. Also, a link to the web page of the Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University together with contact to the creator of Clusterix software are present.

Main page

The easiest way to start with Clusterix application is to use the form on the main page, that allows you to select open cluster by simply choosing the database and filling in sufficiently descriptive name of desired stellar object.

Form presented on the main page.

Database definition [1] allows you to select the database of your interest. It is probable, that offered databases consists of different data retrieved from different sources (e.g. from PPMXL, 2MASS, etc.), the selection of the database is therefore a very important part of the membership determination and should not be underestimated. The selection of open cluster [2] is then possible by submitting [3] a string describing queried cluster in one of the following formats:

  • New General Catalogue (NGC) format
  • The Messier Catalogue (M) format
  • Cluster name

Success of the search is dependent on the quality of database interface and other factors that may not be covered by the Clusterix functionality. Proposed formats, however, should be always appropriate when looking for certain open cluster.

Lists of open clusters

Every connected database may be inspected for available open clusters by following corresponding link in the main menu. Brief description of database is followed by an intuitive list of open clusters:

  • Cluster name corresponds to the most commonly used designation of presented open cluster.
  • Right ascension and Declination values describe central coordinates of open cluster.
  • Radius refers to the cluster radius proposed by the inspected database.
  • Evaluate header indicates, that by following the corresponding link, user will be redirected to the cluster detail, that offers an opportunity to evaluate membership probabilities.

In order to ease the browsing of available clusters, pagination is enabled by links (major letters) that are present on the very top of the page.

Cluster detail

Clusterix page describing selected open cluster is the most important element of the system. First of all, basic information about the cluster are summarized in the table that allows user to create an overall picture of available data.

Details of investigated open cluster.

Diameter [1] of open cluster is expressed in arcmins as a value proposed by selected database. Many databases offer only rough estimate which is why discretion is advised when interpreting this value. Central coordinates [2] of investigated cluster are given in standard equatorial coordinate system.

According to the non-parametric methodology, used to estimate membership probabilities, first step of the procedure is to separate two kinematic groups. First one ("cluster + field" selection) is group formed by stars that belongs to the cluster and surrounding stellar background. Second group ("field" selection) than consists only of "background" stars. The blue bar [3] quantifies number of stars belonging to those groups, according to the restrictions defined via the form which is described in following paragraphs.

Total number of available stars is then described by the orange bar [4]. Hence, sum of numbers corresponding to "cluster + field" and "field" selections could never be greater than this value.

Requested parameters

Bottom of the "Cluster detail" page contains form, that collects input parameters needed for successful membership determination. Vast majority of fields is self-explanatory, some of them, however, require further description.

Details of investigated open cluster.

Central coordinates [1] of investigated open cluster are given in standard equatorial coordinate system. Two radiuses [2] should be set in accordance with requirements of non-parametric methodology as described in previous paragraphs. While inner radius should embrace all cluster stars, the ring between the inner and outter radius should contain only stars belonging to stellar background (for more information, see paper by Cabrera-Cano & Alfaro).

Furthermore, many other restrictions may be placed upon the input data. Investigated dataset may be for example restricted to contain only stars with proper motion [3] and/or proper motion errors [4] within certain limits that are defined via equations:

μ > sqrt(μ_α^2 + μ_δ^2) (proper motion cutoff)
μ_err > sqrt(μ_α_err^2 + μ_δ_err^2) proper motion error cutoff

where μ and μ_err are the restrictions given by the user. Also, stars exceeding certain magnitude [5] may be ommited in the membership determination process.

Correct determination of smoothing [6] and γ threshold [7] parameters requires deeper understanding of applied non-parametric methodology (which may be attained from Galadí-Enríquez et al.), for practical purposes, however, values proposed by the Clusterix system may be considered to be optimal.

Once all parameters are set, membership determination may be evoked by submitting [9] the data. Changes made by the restrictions may be inspected visually by replotting [8] the stellar field visualisation which is located above the described form.

Results

Results are presented through a table that consists of individual stars with assigned membership probabilities. Description presented by the header of the table is self-explanatory:

  • Star no. represents the number of the star retrieved from the input dataset.
  • Right ascension and Declination describes position of the star.
  • Magnitude property is self-evident.
  • Cluster star property represents simplified conclusion of whether star belongs to cluster population.
  • Probability describes the probability that star belongs to the investigated cluster.

Stars are sorted in ascending order according to assigned membership probability.