call the basic sample (BS).

  --- -------- --------- ------- --------
    0    0.761   41587.5   41586    1.000
    1    0.208   11361.2    9952    1.142
    2    0.028    1551.8    1571    0.988
    3    0.003     141.3     252    0.561
    4   1.8E-4       9.6      85    0.114
    5   9.6E-6       0.5      36    0.015
    6   4.4E-7    2.4E-2      42   5.7E-4
    7   1.7E-8    9.4E-4      20   4.7E-5
  --- -------- --------- ------- --------

  : Distribution of the $k$-neighbourhoods of stars in the BS. For more information see text.[]{data-label="table:1"}

When a star $i$ is surrounded by $k$ neighbours, we call this case a “$k$-neighbourhood”. In the BS we found a total of 41586 zero-neighbourhoods and 9952 one-neighbourhoods, i.e. the vast majority of stars (94.3%) has less than 2 neighbours in the BS. With high probability, these are Galactic field stars (background noise). To determine an upper limit for the average density of the neighbours in the background we tentatively allowed all cases with up to 5 neighbours to be considered as background. These contain 97.9 per cent of the stars in the basic sample, which, on the other hand means that only the remaining about 2.1 per cent are signal. The average number of neighbours in the BS is 0.273 stars. So, the distribution of neighbours in the background 