## BANYAN II: Bayesian Analysis for Nearby Young AssociatioNs II

# Membership probability without photometric information

# (Version 1.4)

**BANYAN II is a Bayesian analysis tool to determine the membership probability of candidate stars to nearby young kinematic groups. This pipeline is based on a comparison of Galactic position (XYZ) and space velocity (UVW), using a naive Bayesian classifier. We only consider well-defined moving groups closer than 100 pc and younger than 200 Myr. When radial velocity and/or distance measurements are not available, Bayesian inference has the advantage of being able to marginalize them and compute membership probabilities without them. When this is the case, BANYAN II produces statistical predictions for these quantities, according to each membership hypothesis. When a given hypothesis is respected, the agreement between trigonometric distances and BANYAN II statistical distances generally agree within 8%, whereas predicted and measured radial velocities agree within 1.6 km/s.**

All modifications included in this BANYAN II web tool with respect to the BANYAN I web tool are listed here :

The spatial and kinematic models of moving groups are modeled with 3D gaussian ellipsoids in both
BANYAN I and II, but in BANYAN II those ellipsoids are free to have axes oriented in any direction,
rather than being constrained in the local Galactic coordinates (XYZ) directions.

The list of bona fide members used in the construction of the spatial and kinematic models
was updated as of December 2013.

The field hypothesis is modeled using a Besançon Galactic model (Robin et al. 2012).

Prior probabilities are not set to unity anymore, but rather to the expected populations in
each hypothesis considered, to bring the Bayesian probabilities closer to absolute values.
This treatment of relative populations takes into account that objects with A) smaller galactic
latitude, b) smaller proper motion, c) smaller RVs and d) larger distances, are more likely to
be field contaminants.

The likelihood functions that are input in Baye's theorem are functions of X,Y,Z,U,V,W instead of
the direct observable quantities (ra, dec, pmra, pmdec, RV, distance). The reason for this preference
is that former quantities are better represented by gaussian likelihood probability density functions.

Prior likelihoods associated to marginalized parameters (distance and/or RV) are computed directly
from a Montecarlo drawing of synthetic objects from each association's spatial and kinematic model,
which means that they can have any functional form (generally not gaussians).

The details of this method are described in Gagné et al. (2014ApJ...783..121G). Please reference this work when you make use of this tool, as well as Malo et al. (2013).

All modifications included in this BANYAN II web tool with respect to the BANYAN I web tool are listed here :

The details of this method are described in Gagné et al. (2014ApJ...783..121G). Please reference this work when you make use of this tool, as well as Malo et al. (2013).

We also encourage trying David Rodriguez' convergent point analysis online tool.

We would like to thank Michael Liu for useful comments on this web page.

**Version history**.

**v1.0**

*22/12/2013*

**v1.1**

*24/12/2013*Probabilities taking into account only a RV or PLX measurement (but not both) were mistaken, due to a misdistribution of prior probabilities (every hypothesis always inherited the Beta Pictoris prior probability - depending on some cases, this could have a very small or very big effect on the probabilities). This has been fixed from this version, as well as in the v2+ of the arxiv version of Gagné et al. (2014). The ApJ version was unaffected.

**v1.2**

*3/1/2014*Probabilities taking into account either a RV or PLX measurement (or both) were slightly offset, because the ξ

_{ν}(related to RV) and ξ

_{ϖ}(related to distance) were always = 1 (See Section 3.1 of Gagné et al. 2014 for more info). This has been fixed from this version. This error was not present in the paper, and thus did not affect either the arxiv or ApJ version.

**v1.3**

*23/4/2014*RV and PLX entries without decimals were previously (mistakenly) treated as integers, hence yielding problematic results.

**v1.4**

*11/8/2015*Separated the output probabilities of "Young" and "Old" field, added the statistical RVs for the field hypotheses, and fixed glitches in the output format of statistical RVs and distances.

**The results of this tool should be interpreted with**.

__caution__**1)**We stress that a high probability in one of the associations considered here does not necessarily imply that the candidate star is young. Before an object is considered as a new bona fide member to a moving group, it must show signs of youth as well as spatial and kinematic agreement with the moving group in question (using both a RV and parallax measurements). Conversely, a high probability in the « field » hypothesis does not necessarily imply that the star is old; it simply means that it is less likely to be a member of the young associations considered here compared to the « field »

**2)**Users must keep in mind that Bayesian probabilities might be wrong when studying members of moving groups or associations not considered in our hypotheses. For example, a member of Upper Scorpius could come up as a good candidate of AB Doradus, because the models used by our tool do not consider the former.

**3)**Bayesian probabilities reported by BANYAN II will often be lower than those reported by BANYAN I, because the priors were not set to unity here, which strongly favors the field that generally has a significantly higher expected population. This means in turn that any object with Bayesian probabilities not negligible for a given moving group is worthy of further study (e.g. a 20% probability in BANYAN II could amount to a 90% probability in BANYAN I).

**4)**Bayesian probabilities calculated using a naive Bayesian classifier (which is the case in BANYAN I and II) are subject to being biased because of the independent treatment of observables that are not independent in reality. For a given object, this will not affect the relative classification rank of hypotheses (e.g. from least probable to most probable), but it will affect the absolute values of probabilities (see Hand and Yu 2001).

**5)**Results obtained here may differ from those published in Gagné et al. (2014ApJ...783..121G) as the latter includes 2MASS and WISE photometry in computing membership probabilities.

**6)**The information entered on this web page is not stored on our server.

**Instructions :**

Observational properties (UVWXYZ) of the young associations considered in the analysis :

Name | Age (Myr) | 1-σ distance range (pc) | 1-σ RV range (km/s) | U (km/s) | V (km/s) | W (km/s) | σ U' (km/s) | σ V' (km/s) | σ W' (km/s) | X (pc) | Y (pc) | Z (pc) | σ X' (pc) | σ Y' (pc) | σ Z' (pc) | # stars |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

TW Hydrae | 8 - 12 | 40 - 62 | (7) - (12) | -11.1 | -18.9 | -5.6 | 0.9 | 1.6 | 2.8 | 19.1 | -54.2 | 21.5 | 5.0 | 7.2 | 22.6 | 18 |

β Pictoris | 12 - 22 | 18 - 40 | (-9) - (16) | -11.0 | -15.6 | -9.2 | 1.4 | 1.7 | 2.5 | 7.6 | -3.5 | -14.5 | 8.2 | 13.5 | 30.7 | 33 |

Tucana-Horologium | 20 - 40 | 38 - 51 | (3) - (14) | -9.7 | -20.5 | -0.8 | 1.1 | 1.7 | 2.4 | 6.7 | -21.8 | -36.0 | 3.9 | 10.6 | 20.1 | 52 |

Columba | 20 - 40 | 26 - 63 | (19) - (26) | -12.1 | -21.3 | -5.6 | 0.5 | 1.3 | 1.7 | -28.1 | -25.8 | -28.6 | 10.5 | 17.6 | 28.3 | 21 |

Carina | 20 - 40 | 11 - 42 | (16) - (23) | -10.7 | -22.2 | -5.7 | 0.3 | 0.7 | 1.1 | 10.1 | -51.6 | -14.9 | 5.8 | 11.3 | 29.8 | 21 |

Argus | 30 - 50 | 15 - 48 | (-10) - (9) | -21.5 | -12.2 | -4.6 | 0.9 | 1.7 | 2.7 | 15.0 | -21.7 | -8.1 | 12.1 | 15.5 | 27.4 | 11 |

AB Doradus | 70 - 120 | 19 - 50 | (-11) - (29) | -7.0 | -27.2 | -13.9 | 1.2 | 1.7 | 1.9 | -2.5 | 1.3 | -16.3 | 16.3 | 20.0 | 23.5 | 54 |

Young Field | < 1000 | 66 - 169 | (-19) - (19) | -11.2 | -18.6 | -6.9 | 7.7 | 12.5 | 19.6 | 2.8 | 0.1 | -13.1 | 79.6 | 80.4 | 80.8 | - |

Old Field | > 1000 | 70 - 177 | (-34) - (32) | -11.2 | -18.6 | -6.9 | 7.7 | 12.5 | 19.6 | 2.8 | 0.1 | -13.1 | 79.6 | 80.4 | 80.8 | - |