A How do I define Open cluster membership?

[tomwilliam]

I'm doing a study using Gaia DR2 data, and in particular trying to analyse the photometric data for groups of stars which some authors believe to be loosely gravitationally bound in open clusters.
I am trying to find out a reasonable way of establishing cluster membership, before analysing the data in more detail, but I'm very new to this and it's not easy to grasp.

I'm looking at 3 techniques to determine cluster membership: Kth nearest neighbour (KNN), radial density profile and a Principal Component Analysis, but all of these techniques give me some problems.
- For KNN, I get a number of clusters in a given plot, but I'm not sure how to work out which stars belong in which cluster. I'm using TopCat software.
- For the radial density profile - which seems a very logical way of distinguishing cluster members from field stars, I'm unsure about how to do this in practice. How do I find the centre from which to plot the density as a function of radius? Can this be automated, or is it a manual procedure?
- For PCA, I can plot some interesting graphs, but all I do is manage to reduce a wide set of photometric and spectrographic data to a single plot of 5 components along a principal component of variance. I'm not sure what I can or should do to proceed from here.
I realize this is a rather vague set of questions, but any pointers would be welcome. I'm in learning mode.

 

[stefan r]

I believe the definition is a group of stars that formed from the same cloud. Chaos happens so it is not likely that the clusters will behave in a simple or consistent way. The cloud was gravitationaly bound. Now they are swinging past each other and interacting with the rest of the galaxy.

 

[tomwilliam]

Sorry - I think I wasn't clear in my original post. I'm not looking for the definition of an open cluster, which you've summarised well, but I'm trying to define* membership of that cluster. I am studying some of the properties of a few open clusters, as identified by other authors using Gaia DR2 data, to draw some conclusions about their (common) origin, metallicity, kinematics, etc. The first step, however, is distinguishing members of the cluster from stars which just happen to be swinging by or which have drifted into the group but which aren't gravitationally bound to the rest.
One way of doing this is to increase the sophistication from simply looking at visible clusters from positions in the sky, and instead to look at clusters in phase space, using proper motions. That way you combine their positions with information about their velocities. Once you plot the stars in this way, you can clearly see clustering effects.
However, you still need a scientific way of distinguishing what is in the cluster and what is simply part of the background field. There are different ways introduced in the literature for determining this, such as those I mentioned in my original post.
Radial density profile for example: you plot the density of stars as a function of radius from the centre of the cluster. Then, you establish a cutoff, below which we're no longer in the cluster but we're in the background field density. That seems logical, but I'm not sure how to do it practically. How do you establish the centre of the cluster, and are there any tools to do this?
The other two techniques I mentioned are similarly problematic, and I was wondering if anyone had any experience using these techniques who could help me proceed.
Thanks

* In retrospect, I should have used the word "determine" instead of "define"

 

[Ratman]

Phase space is the right place to look for clusters, as some interlopers may be crossing the same region of space. Stars born out of one molecular cloud should have low velocity dispersion (except for some runaway stars, which were gravitationally scattered or have watched supernova from the front seat). The conservation of momentum suggest to look for the centre of mass, but I guess the centre of light might be good enough approximation. The interlopers have in general too high velocity wrt the centre, and background stars will have different parallax. You should be able to place the cutoff(s) after analysing distributions of these parameters.

 

[Tom.G]

Way out of my field, but Google helped.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4038101/

Although some were useless, Google found millions of hits with:
https://www.google.com/search?&q=finding+clusters+in+scatter+plots

 

[ohwilleke]

There are discussions in several of the recent papers on the topic regarding the methodology they used to assign cluster membership, such as this paper and several of the other papers cited to by it. The linked paper and its abstract are as follows:

A second galaxy missing dark matter in the NGC1052 group
Pieter van Dokkum, Shany Danieli, Roberto Abraham, Charlie Conroy, Aaron J. Romanowsky
(Submitted on 17 Jan 2019)
The ultra-diffuse galaxy NGC1052-DF2 has a very low velocity dispersion, indicating that it has little or no dark matter. Here we report the discovery of a second galaxy in this class, residing in the same group. NGC1052-DF4 closely resembles NGC1052-DF2 in terms of its size, surface brightness, and morphology; has a similar distance of D=19.9±2.8 Mpc; and has a similar population of luminous globular clusters extending out to 7 kpc from the center of the galaxy. Accurate radial velocities of seven clusters were obtained with the Low Resolution Imaging Spectrograph on the Keck I telescope. Their median velocity is ⟨v⟩=1445 km/s, close to the central velocity of 22 galaxies in the NGC1052 group. The rms spread of the observed velocities is very small at σobs=5.8 km/s. Taking observational uncertainties into account we determine an intrinsic velocity dispersion of σintr=4.2+4.4−2.2 km/s, consistent with the expected value from the stars alone (σstars≈7 km/s) and lower than expected from a standard NFW halo (σhalo∼30 km/s). We conclude that NGC1052-DF2 is not an isolated case but that a class of such objects exists. The origin of these large, faint galaxies with an excess of luminous globular clusters and an apparent lack of dark matter is, at present, not understood.
Comments: Submitted to ApJ Letters
Subjects: Astrophysics of Galaxies (astro-ph.GA)
Cite as: arXiv:1901.05973 [astro-ph.GA]
(or arXiv:1901.05973v1 [astro-ph.GA] for this version)

See also

Open clusters in APOGEE and GALAH: Combining Gaia and ground-based spectroscopic surveys
R. Carrera (1), A. Bragaglia (2), T. Cantat-Gaudin (3), A. Vallenari (1), L. Balaguer-Núñez (3), D. Bossini (1), L. Casamiquela (4), C. Jordi (3), R. Sordo(1), C. Soubiran (4) ((1) INAF-Osservatorio Astronomico di Padova, vicolo dell'Osservatorio 5, 35122 Padova, Italy, (2) INAF-Osservatorio di Astrofisica e Scienza dello Spazio, via P. Gobetti 93/3, 40129 Bologna, Italy, (3) Institut de Ci\`encies del Cosmos, Universitat de Barcelona (IEEC-UB), Mart\'i i Franqu\`es 1, E-08028 Barcelona, Spain, (4) Laboratoire d'Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, all\'ee Geoffroy Saint-Hilaire, F-33615 Pessac, France)
(Submitted on 27 Jan 2019)
Context: Open clusters are ideal laboratories to investigate a variety of astrophysical topics, from the properties of the Galactic disk to stellar evolutionary models. Knowing their metallicity and possibly detailed chemical abundances is therefore important. However, the number of systems with chemical abundances determined from high resolution spectroscopy is still small.\\ Aims: To increase the number of open clusters with radial velocities and chemical abundances determined from high resolution spectroscopy we used publicly available catalogues of surveys in combination with Gaia data.\\ Methods: Open cluster stars have been identified in the APOGEE and GALAH spectroscopic surveys by cross-matching their latest data releases with stars for which high-probability astrometric membership has been derived in many clusters on the basis of the Gaia second data release.\\ Results: Radial velocities have been determined for 131 and 14 clusters from APOGEE and GALAH data, respectively. This is the first radial velocity determination from high resolution spectra for 16 systems. Iron abundances have been obtained for 90 and 14 systems from APOGEE and GALAH samples, respectively. To our knowledge 66 of these clusters (57 in APOGEE and 9 in GALAH) do not have previous determinations in the literature. For 90 and 7 clusters in the APOGEE and GALAH samples, respectively, we have also determined average abundances for Na, Mg, Al, Si, Ca, Cr, Mn, and Ni.
Comments: 20 pages, accepte for publication in Astronomy & Astrophysics
Subjects: Astrophysics of Galaxies (astro-ph.GA)
Cite as: arXiv:1901.09302 [astro-ph.GA]
(or arXiv:1901.09302v1 [astro-ph.GA] for this version)