Astrometric star-cluster membership probability: application to the case of M 37 with Gaia EDR3

Abstract

In this work, starting from the well-accepted relations in literature, we introduce a new formalism to compute the astrometric membership probabilities for sources in star clusters, and we provide an application to the case of the open cluster M 37. The novelty of our approach is a refined –and magnitude-dependent– modelling of the parallax distribution of the field stars. We employ the here-derived list of members to estimate the cluster’s mean systemic astrometric parameters, which are based on the most recent Gaia’s catalog (EDR3).

Astro-photometric study of M37 with Gaia and wide-field ugi–imaging

“…This sample has then been constrained on the parallax versus magnitude plane (top right panel). We divided the data into magnitude bins of 1 mag, and for each bin we calculated 𝜎 𝜛,𝑖 = 68.27 th percentile of the residuals around cluster's parallax 𝜛 (given by Griggio & Bedin 2022). We derived the red curves interpolating the points 𝜛 ± 2𝜎 𝜛,𝑖 with a spline.…”

“…We restricted our search to sources with 𝐺 BP > 18 and −0.5 < 𝐺 BP − 𝐺 RP < 0.5 where we expect to find WDs that have just recently formed and have both the same distance and reddening of M37 (𝑑 = 1.5 ± 0.1 kpc, Griggio & Bedin 2022; 𝐸 (𝐵 − 𝑉) = 0.26, Cordoni et al 2018). We selected from this region the stars with proper motions and parallaxes that are compatible within 3𝜎 with those of the cluster.…”

“…M37, also known as NGC 2099, is a rich (with an estimated total mass of ∼ 1500 M by Piskunov et al 2008), intermediate-age OC, with an angular size of about 1 deg (Griggio & Bedin 2022). As revealed by Cordoni et al (2018), this cluster exhibits an extended Main-Sequence (MS) Turn-Off, thus its precise age is still under debate; Mermilliod et al (1996) gives an age of about 400-500 Myr, compatible with the more recent estimate by Cordoni et al (2018) that gives an age of 550 Myr.…”

“…By using the method of astrometric cluster membership presented in Griggio & Bedin (2022), we have identified seven new WD member candidates that are currently at the hot end of the WD cooling sequence, which has so far been overlooked by previous searches. These new candidates include the likely central star of a planetary nebula, for which we have also obtained two sets of follow-up spectra.…”

“…As revealed by Cordoni et al (2018), this cluster exhibits an extended Main-Sequence (MS) Turn-Off, thus its precise age is still under debate; Mermilliod et al (1996) gives an age of about 400-500 Myr, compatible with the more recent estimate by Cordoni et al (2018) that gives an age of 550 Myr. M37 is located in the Auriga constellation, at a distance of about 1.4 kpc (Kharchenko et al 2005;Griggio & Bedin 2022). It has been the object of several photometric studies (e.g., Kalirai et al 2001) as well as spectroscopic investigations (e.g., ★ E-mail: massimo.griggio@inaf.it Pancino et al 2010).…”