Multiplicity and clustering in Taurus star forming region. II. From
  ultra-wide pairs to dense NESTs
  Multiplicity and clustering of young pre-main sequence stars appear as
critical clues to constrain the star formation process. Taurus is the
archetypical example of the most quiescent star forming regions that may still
retain primeval signatures of star formation. This work identifies local
overdense stellar structures at the 99.8\% confidence level above random
expectation using the DBSCAN algorithm, and setting its free parameters based
on the one-point correlation function and the k-nearest neighbor statistics.
Nearly half of the entire stellar population in Taurus is found to be
concentrated in 20 dense, tiny and prolate regions called NESTs (for Nested
Elementary STructures). They are regularly spaced ($\approx 2$ pc) and mainly
oriented along the gas filaments axes. Each NEST contains between 4 and 23
stars. Inside NESTs, the surface density of stars may be as high as 2500
pc$^{-2}$. Nearly half (11) of these NESTs contain about 75\% of the class 0/I
objects. The balance between Class I, II, and, III fraction within the NESTs
suggests that they may be ordered as an evolutionary temporal scheme. We have
inferred that only 20\% of stars in Taurus do not belong to any kind of stellar
groups. The mass of NESTs covers the same range as that of dense molecular
cores. The distribution in size is bimodal peaking at 12.5 and 50 kAU and the
distribution of the number of YSOs in NESTs as a function of size exhibits two
regimes. We propose that the NESTs in their two size regimes represent the
spatial imprints of stellar distribution at birth as they may have emerged
within few millions years from their natal cloud either from a single core or
from a chain of cores. We have identified them as the preferred sites of star
formation in Taurus. These NESTs are the regions of highest stellar density and
intermediate spatial scale structures between ultra-wide pairs and loose
groups.
