10.4 Multidimensional analysis

Author(s): Jovan Veljanoski, Amina Helmi, Davide Massari, Maarten Breddels

We compare the statistical properties of four small regions on the sky by quantifying the degree of clustering and correlations between different observables, using the Kullback-Leibler divergence (KLD hereafter). This test allow us to establish whether any observables or a combination of thereof exhibit unexpected properties.

The selected regions on the sky are circular, have a radius of 5 , and for symmetry purposes are centred on (l,b) = (-90, -45), (-90, 45), (90, -45) and (90, 45). They are labelled ‘patch-a’, ‘patch-b’, ‘patch-c’, and ‘patch-d’, respectively. The regions contain 350 000 stars on average: ‘patch-a’ and ‘patch-d’ cover regions of high number of transits, while ‘patch-b’ and ‘patch-c’ have fewer transits. This choice reflects our expectation that different groups of observables will have differing distributions depending on the location on the sky, but also on the number of photometric or astrometric observations. For example Figure 10.32 shows how phot_g_n_obs varies across the field of each of the four patches.

We perform our tests also on a few subsets, as listed in Table 10.5. Furthermore, we have performed the KLD tests with and without the rescaling of the astrometric uncertainties by the factor F used to reweight the uncertainties (Lindegren et al. 2018, Appendix A), but we found no differences.

Table 10.5: Subsets of pre-DR2 release (1 734 629 872 sources) which have been created for further analysis and comparisons. DUPMATB is the final DR2 Catalogue.
Name Criteria Rationale # sources
BT11 G<11.5 problem stars 2 126 709
BT17 G<17 156 992 707
FT20 G>20 completeness 694 659 074
BADCOLOUR phot_bp_rp_excess_factor >2 extended obj/phot. pb. 219 241 026
DUPLICATED astrometric_duplicate_source_id != 0 duplicate or duplicated 66 223 490
GC10 all stars within 10 from Gal. Centre completeness, problems 190 567 824
EXCESSNOISENOT0 astrometric_excess_noise != 0 bad astrom. solution 1 016 632 212
PLXOVERERR5 parallax_over_error > 5 good astrometric prec. 143 960 531
visibility_periods_used > 2 AND
DUPVISA (astrometric_duplicate_source_id == 0 OR first filter attempt 1 710 610 787
astrometric_duplicate_source_id == source_id)
astrometric_matched_observations > 4 AND
DUPMATA (astrometric_duplicate_source_id == 0 OR filter towards final data 1 692 919 221
astrometric_duplicate_source_id == source_id)
DUPMATB DUPMATA plus uncertainties reweighted 1 692 919 221