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We utilize the second data release of GAIA proper motions and parallaxes to calculate velocity projections in the direction of Galactic latitude, b, and longitude, l, for all 1,113 SBK2 fast rotators identified in our analysis, see Figure 4.1. Blue and green boxes have been drawn over obvious clumps of stars which may be indicative of kinematics groups, i.e. groups of stars that share a common spatial motion.

These clumps were identified by eye in Figure 4.1 and the boxes drawn “by hand” to select the candidate members. This initial by eye identification selected clumps in: C00, two in C04, two in C05, C11, C12, C13, two in C14, and two in C15. The number of stars that fall within these boxes are listed in the third column of Table 4.1.

Some of these clumps in fact represent nearby star clusters that were specifically targeted by theK2 campaign: C04 targeted the Hyades and Pleiades star clusters, C05 targeted the Beehive star cluster, and C13 targeted the Hyades star cluster again. In addition, C15 targeted the Upper Scorpius star forming region, a site of very recent star formation that may contain two or more kinematic groups that one could classify as very young NYMGs. Clearly, several of the fast rotators identified in our analysis happen to be members of these clusters/associations.

Table 4.1: Number of Candidates for Star Clusters and NYMGs

Field Kinematic Candidates Kinematic + Dist. Cluster/Group Distance Candidates (pc) C00 Green 7 - - C01 Green 13 - - C04 Green 21 18 Hyades C04 Blue 179 155 Pleiades C05 Blue 21 21 C05 Group C05 Green 22 18 Beehive C11 Green 25 17 C11 Group C12 Green 12 12 C12 Group C13 Green 45 40 Hyades C14 Green 12 - - C14 Blue 24 14 C14 Group

C15 Blue 12 11 Lower Sco

C15 Green 13 6 Upper Sco

We do not have radial velocities for most of these stars, and we therefore cannot place them within a 3-dimensional velocity space diagram; all we have is the 2-dimensional pro- jection of the stars motions in the plane of the sky. In order to confirm membership in these clusters/associations, we use the distance measurements provided by GAIA. We proceed in

the following manner: (1) we first select the stars that fall within the boxes in Figure 4.1 for further consideration; (2) we then plot the distance distribution of these stars to determine if the clumping in velocity also corresponds to a clumping in physical space. The spatial distributions are shown in Figure 4.2.

Figure 4.2 Frequency histograms of GAIA distances for eachK2 field. The red histograms are all SBK2 stars, the green and blue bins represent the stars falling in the green and blue boxes drawn in Figure 4.1.

The stars within the boxes in C00, C01, and the green box in C14 do not show significant clustering in space; stars in NYMGs are expected to be spread over a volume of about a few

tens of parsecs, and stars from these particular clumps are spread over significantly larger distances. The Hyades/Pleiades/Beehive candidates in C04, C05, and C13, on the other hand, show obvious clustering in space as one would expect from compact open clusters. Likewise the stars in the Upper Scorpius star forming region in C15 show significant spatial clustering. Interestingly, the kinematic groups in field C05, C11, C12, and the blue box in C14 all appear to have clustering in distance as well, making them all possible members of NYMGs. We slice the groups of stars in distance space using the distance ranges listed in Table 4.2 and identify the stars within these distance ranges as likely candidate members of these groups. The number of stars that remain after this selection process are listed in the fourth column of Table 4.1. Lists of these candidates members are presented in Appendix B. We then plot the velocity space projections again of the fast rotators that also fall within these distance ranges, see Figure 4.3.

Table 4.2: Distance Ranges for Star Clusters and Candi- date NYMGs

Field Range Cluster

(pc) 04/13 25-75 Hyades 04 105-155 Pleiades 05 25-125 C05 Group 05 155-205 Beehive 11 90-150 C11 Group 12 25-125 C12 Group 13 25-75 C13 Group 14 60-120 C14 Group 15 40-100 Lower Scorpius 15 100-150 Upper Scorpius

Figure 4.3 Kinematics of all the fast rotators that fall within the within the distance limits set in Table 4.2; the stars this time are all shown in the plane-of-sky velocity plot. The red circles are the Hyades cluster candidates, yellow circles are the Pleiades cluster candidates, green circles are the Beehive cluster candidates. The blue and pink circles are the candidates for the Upper Scorpius and Lower scorpius star forming associations, respectively. The pink, green, cyan, and red squares are the candidates for the possible young moving groups in C05, C11 C12, and C14, respectively.

The known clusters and groups are plotted as color circles in Figure 4.3. In the case of the Hyades (red), Pleiades (yellow) and Beehive (green) clusters, we see that they are fairly compact in 2D velocity space, which is what one would expect from a compact cluster of gravitationally bound stars. Conversely, Upper (pink) and Lower (blue) Sco are more spread out, which is consistent with the idea that these stars are only loose associations, are not

gravitationally bound, and will likely disperse over time. The candidate groups of stars in C05, C11 C12, and C14 (squares) likewise show a relatively large scatter, more similar to the Upper and Lower Sco associations. The larger dispersion in velocity would be consistent with a larger spatial scatter, which means the group would likely be a moving group and not a cluster.

We have searched the literature for know moving groups in the direction of these Kepler

fields, but have found no known NYMG that would match the motion of those stars. We therefore suggest that the groups identified in C05, C11, C12, and C14 may be members of four new NYMGs, identified here for the first time.

For the nearby cluster candidates, a significant fraction of our fast rotators were previ- ously known members. Indeed we have cross-matched the Pleiades, Hyades, and Beehive candidates with known lists of these groups (Douglas et al. 2014; Covey et al. 2016; Sarro et al. 2014; Wang et al. 1996) and find that we have recovered 100, 13, and 15 bona fide members, respectively. On the other hand, many of the stars we identify as cluster members do not appear to be previously known, this includes 56 stars in the Pleiades, 6 stars in the Hyades, and 2 stars in the Beehive. All these stars are listed and noted in Appendix B.