Photometric redshift galaxies as tracers of the filamentary network
  Galaxy filaments are the dominant feature in the overall structure of the
cosmic web. The study of the filamentary web is an important aspect in
understanding galaxy evolution and the evolution of matter in the Universe. A
map of the filamentary structure is an adequate probe of the web. We propose
that photometric redshift galaxies are significantly positively associated with
the filamentary structure detected from the spatial distribution of
spectroscopic redshift galaxies. The catalogues of spectroscopic and
photometric galaxies are seen as point-process realisations in a sphere, and
the catalogue of filamentary spines is proposed to be a realisation of a random
set in a sphere. The positive association between these sets was studied using
a bivariate $J-$function, which is a summary statistics studying clustering. A
quotient $D$ was built to estimate the distance distribution of the filamentary
spine to galaxies in comparison to the distance distribution of the filamentary
spine to random points in $3-$dimensional Euclidean space. This measure gives a
physical distance scale to the distances between filamentary spines and the
studied sets of galaxies. The bivariate $J-$function shows a statistically
significant clustering effect in between filamentary spines and photometric
redshift galaxies. The quotient $D$ confirms the previous result that smaller
distances exist with higher probability between the photometric galaxies and
filaments. The trend of smaller distances between the objects grows stronger at
higher redshift. Additionally, the quotient $D$ for photometric galaxies gives
a rough estimate for the filamentary spine width of about $1$~Mpc. Photometric
redshift galaxies are positively associated with filamentary spines detected
from the spatial distribution of spectroscopic galaxies.
