# Gaia DR2 distances to Collinder 419 and NGC 2264 and new astrometric orbits for HD 193 322 Aa,Ab and 15 Mon Aa,Ab

## TL;DR

This study uses Gaia DR2 data and new astrometric orbit calculations to determine distances to stellar groups Collinder 419 and NGC 2264, and derives new orbits for key binary systems HD 193 322 Aa,Ab and 15 Mon Aa,Ab, enhancing understanding of their properties.

## Contribution

It introduces a novel method combining Gaia data with a new orbit calculation code to measure stellar group distances and derive binary orbits, improving accuracy and understanding of these systems.

## Key findings

- Distances: 1006+37-34 pc for Collinder 419, 719+-16 pc for NGC 2264
- NGC 2264 subclusters are at similar distances and show proper motion
- Eccentric orbits for HD 193 322 Aa,Ab and 15 Mon Aa,Ab with periods of 44 and 108 years respectively.

## Abstract

[ABRIDGED] CONTEXT: Gaia DR2 has opened a trove of astrometric and photometric data for Galactic clusters close to the Sun. Lucky imaging has been an operational technique to measure the positions of visual binary systems for a decade and a half, enough to apply its results to the calculation of orbits of some massive multiple systems within ~1 kpc of the Sun. AIMS: We are measuring distances to Galactic stellar groups containing O stars and I start with two of them: Collinder 419 in Cygnus and NGC 2264 in Monoceros. I also aim to derive new astrometric orbits for the Aa,Ab components for the main ionizing sources for both clusters: HD 193 322 and 15 Mon, respectively. METHODS: First, I present a method that uses Gaia DR2 photometry, positions, proper motions, and parallaxes to obtain the membership and distance of a stellar group and apply it to Collinder 419 and NGC 2264. Second, I present a new code that calculates astrometric orbits by searching the whole 7-parameter orbit space and apply it to HD 193 322 Aa,Ab and 15 Mon Aa,Ab using as input literature data from the Washington Double Star Catalog (WDS) and the AstraLux measurements recently presented by Ma\'iz Apell\'aniz et al. (2019). RESULTS: I obtain Gaia DR2 distances of 1006+37-34 pc for Collinder 419 and 719+-16 pc for NGC 2264, with the main contribution to the uncertainties coming from the spatial covariance of the parallaxes. The two NGC 2264 subclusters are at the same distance (within the uncertainties) and they show a significant relative proper motion. The distances are shown to be robust. HD 193 322 Aa,Ab follows an eccentric (e = 0.58+0.03-0.04) orbit with a period of 44+-1 a and the three stars it contains have a total mass of 76.1+9.9-7.4 M_Sol. The orbit of 15 Mon Aa,Ab is even more eccentric (e = 0.770+0.023-0.030), with a period of 108+-12 a and a total mass of 45.1+3.6-3.3 M_Sol for its two stars.