Gaia data allows for search for extended stellar structures in phase (coordinates plus velocities) space. We describe a method of using DBSCAN clustering algorithm, which is used to group closelypacked-together data points, to a list of preliminary selected pairs of stars, with parameters expected to be found within stellar streams and comoving groups: loose structures in which stars are not gravitationally bound, but do share motion and evolutionary properties. To test our approach, we construct a model population of background stars, and use pair-constructing and clustering algorithms on it. Results show that transitioning to a list of pairs sharply reveals structures not presented in background model, which then become more apparent targets in coordinates-velocities phase space for DBSCAN algorithm thanks to now increased relative density of the extended stellar structure.
Astrometric space mission Gaia of European Space Agency provides data on
positions, proper motions, and parallaxes of stars with previously unseen precision
and scale (> 1.5 billion sources) [
We aim to combine the binary star search and clustering approaches: we use
our algorithm designed for search of ultrawide binaries described in [
This paper describes this work still in progress by presenting the results of using such approach to a region of 30x30 deg in the sky, for stars between 100 and 1000 pc from the Sun. Paper is divided in two sections: first describes the principles behind creating the preliminary list of pairs, and the second one describes creating a model distribution of stars and applying the clustering algorithm to real and model data. 2
Assembling a preliminary pairs catalogue involves picking several parameters of stellar pairs and putting a constraints of them. Search for pairs then is done by ifltering lists of all possible pairs in the catalogue to fit the constraints. These constraints are based on what values of these parameters are expected to be met in pairs of stars constituting extended stellar structures.
Most obvious first criteria is stars being spatially close to one another. We limit projected separation between stars to 1 parsec. This limit also allow us to significantly optimise pairs catalogue assembly process by subdividing search region into smaller regions on the celestial sphere, sizes of which is determined by maximum possible coordinate separation of a pair and then searching for pairs just within these sub-regions and in neighbouring ones. This allows to decrease computation complexity from C ∗ N 2 to C ∗ N 2/M , where N is the number of stars and M is the number of regions (M = 1537 in reviewed case, which 0.004 0.002 0.000 75000 50000 25000 0 400 600 800 1000 1200 1400 Dis ance mean:-1.30 Distance median:14.66
Probability:1.47 to be within 5.0 pc
meant a transition from impractically long to quite fast computation time).
This optimisation is reviewed in more detail in article [
Parallaxes = 2.00, 1.94 mas, errors: 0.50mas, 0.40mas.
−1000 −500 0
500 parsec
In regards to data on stellar positions there is a significant diference between treating errors of position on stellar sphere (right ascension and declination) and radial distance (parallax). Errors of parallax are larger, also, the way distance to the star is determined as inverse of parallax, coupled with the fact that absolute error of parallax is not directly related to value of parallax, means that: 1. relative errors of parallax become larger for distant stars 2. symmetric errors of parallax values lead to asymmetric errors in distance determination.
For Gaia sample we use in this article (distances of 100 - 1000 parsec from the Sun) mean error of parallax is 0.58 mas (milliarcseconds), which corresponds to uncertainty of -370/+1380 parsec for star with actual distance of 1000 pc. Uncertainty of position on celestial sphere is negligible compared to distance uncertainties.
Accounting for radial distance between stars thus cannot be done by simply placing a constraint on apparent measured distances diference. We use two approaches simultaneously. First approach is imposing limits on parameter labelled (1) Here π 1, π 2 are parallaxes of components, and σ π 1 , σ π 2 are their errors. Negative values indicate that parallaxes are too diferent for stars to be close even if we allow overlap within 3 standard deviations for both components. Highly positive values indicate that errors are too large to tell with certainty that stars are close together. Values that are positive, but close to zero indicate either that we can say that stars are close together with relative certainty, or that the sum of errors happened to be close to parallax diference (even if it is large).
To diferentiate between these two scenarios, we use a second approach: a model to simulate probability density distribution of radial distance between stars by modelling probability density of distance to Sun for both stars, based on their given parallaxes and their errors. We then integrate over limit (-5pc, +5pc) for each pair to determine probability of them being within 5 pc of one another along line-of-sight (P5) (See Fig. 1). We do not model this directly for each actual pair, instead values for P5 in pairs are interpolated from grid of 26000 pre-computed points in 4-parameter (π 1, △π , σ π 1 , σ π 2 ) space covering all the possible values in our sample densely enough.
These two metrics do somewhat correlate (See Fig. 2): most of the pairs
with negative parallax consistencies have P5 < 0.2%, and high P5 is mostly
associated with positive but not very high π cons. We also noted an increased
density of pairs with 0 < π cons < 1 in region with proper motion diference of
stars < 2mas/yr and projected relative motion of < 3km/s. Resulting constrains
on pairs parameters used are:
– projected separation < 1 pc
– projected relative motion < 3 km/s
– proper motion diference < 6 mas/yr
– parallax consistency within −0.1 < π cons < 1 and P5 > 0.5%.
When deciding on constraints on pairs properties, we guide ourselves with
theoretical and model considerations from [
Aim of the stellar background model is to produce ”mock” catalogue of stars which would be known to not contain any clusters, streams, or other stellar structures. This catalogue then undergoes the same process of constructing preliminary pairs and their clustering as a real catalogue, to check our algorithm for not treating random overdensities in field stars distribution as an actual extended stellar system.
Model we use is the following: stars are first generated uniformly within same
region of sky as the real sample, but in a broader range of distances: 50 - 2000
pc instead of 100 - 1000. To simulate the efect of parallax errors on measuring
actual parallaxes, each star is assigned a “real” parallax in mas (1000./distance)
and a parallax measurement error. Distribution of parallax errors was made to
mimic that of the real sample (a combination of two Gaussian distributions and
an exponential distribution was found to be representing the real distribution the
best). “Measured” star parallaxes are obtained by modifying their “real”
parallaxes by a random number drawn from normal distribution with the standard
deviation equal to parallax error. After that the dataset is cropped to 100 - 1000
pc of “measured” distance. Stars get a random galactocentric velocity
components (U, V, W) with dispersions of 35, 30, and 20 km/s respectively to simulate
actual movement of stars in solar neighbourhood [
We apply a DBSCAN clustering algorithm to both real and model data. Clustering is done in 4-coordinate space (2 for positions on the sky and 2 proper motions). Radial distance is not considered due to parallax errors stretching any stellar structure in line-of-sight direction too much, restrictions on π cons and P5 on pair composition phase are considered to be suficient to take distances into account. Varying the DBSCAN clustering parameters shows that for majority of parameter values where real data is subdivided into reasonable amount of clusters, model data is all marked as background. Fig. 5 shows clustering result for possible pair of parameters, subdividing the data into 21 clusters and ”background” pairs. 4
We used Gaia EDR3 data for constructing a stellar pairs catalogue with properties for pairs expected to be found within clusters and extended stellar structures. With selected parameters, pairs distribution display structures of high density which are easily seen against the ’background” pairs. Comparison with using the same approach to stellar background model of similar density shows that this dense structures cannot be attributed to random overdensities of uniform, featureless distribution of stars. High contrast of such areas compared to background eases the clustering task for algorithms of unsupervised learning, like DBSCAN which we use in this article.
Further work will include comparison of these structures with known extended stellar structures and clusters, tuning parameters of pairing and clustering to better recognize stellar structures, using other means for determining the existence of evolutinary relationship between found structures and comparison with models of stellar systems evolution to explain the observed stellar system qualities.
Acknowledgements. This work is supervised by Dr. Dana Kovaleva, Department of Physics of stellar systems, Institute of Astronomy of Russian Academy of Sciences. The work has made use of data from the European Space Agency (ESA) mission Gaia processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The study was partially supported by Russian Foundation for Basic Research (Project no. 20-52-12009).