ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Person I-Person O O O O O B-Telescope B-Dataset O B-Telescope B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: of position and velocity or momentum, and that are conserved throughout the orbit. There are three action coordinates: radial action ( J R ), vertical action ( J Z ), and angular momentum ( L z ). By providing all three action coordinates, one can perfectly describe an entire orbit at any point in time or space. Traditionally, actions were incredibly difficult to calculate. In fact, they can only be analytically solved for a small subset of convenient galactic potentials. As computers became more advanced, astronomers developed ways to numerically approximate action coordinates. Sanders Das ( 2018 ) used the Stäckel Fudge method for approximating actions (Binney 2012 ), which interpolates on a distribution of phase-space coordinates generated from an axisymmetric potential. Resulting errors on the actions are propagated through from errors on parallax, proper motion, and radial velocity. We use the vertical actions calculated by Sanders Das ( 2018 ) to determine whether stars in our sample are members of the thick or thin disc (see Section 3.2 ). 2.4 Cross-matching and quality cuts In order to compare the motions of our planet host and stellar samples, we used Megan Bedell’s catalogue of data cross-matched between Gaia DR2 and Kepler DR25 with a 1 arcsecond search radius, downloaded on 2019 January 9. The two catalogues were matched using the RA and Dec coordinates of every star. The final cross-matched catalogue contains 197 090 stars, 1647 of which are confirmed planet hosts. We make the following quality cuts on both our planet host and field star samples: We removed stars with negative parallax values. This left our planet host sample with 1637 members and our field star sample with 195 545. We removed giants as well as massive and very-low mass dwarfs from our data by discarding stars with logg 4 and effective temperatures 4000 or >8000. We did this because Kepler was optimized for finding planets around FGK stars and therefore has a lower completeness for giants (Sliski Kipping 2014 ). This left our planet host sample with 1477 stars and our field star sample with 148 860 stars. We removed stars with relative errors in the total velocity (see Section 3 ) >10 per cent to minimize the error propagated through our analysis. Much of the error in the velocity calculation comes from uncertainties in the parallax, so making this 10 per cent cut ensures that we are only using stars with small parallax uncertainties and therefore reliable distances consistent with those in Bailer–Jones et al. ( 2018 ). This left us with two final samples of Kepler FGK dwarfs with reliable galactocentric velocities: a planet host sample with 1437 members and a field star sample with 140 918 members. Fig. 1 shows the galactocentric X-Y positions of the stars in the cross matched catalog, color-coded by how far they got in the sample selection process. Our field star sample is shown in black points and our planet host sample is shown in blue. Figure 1. Face-on view