Multiplicity and clustering in Taurus star-forming region. I. Unexpected
  ultra-wide pairs of high-order multiplicity in Taurus
  We collected the multiplicity data of stars in Taurus to build an up-to-date
stellar/multiplicity catalog. After a general study of nearest-neighbor
statistics on spatial random distribution, we introduce the one-point
correlation $\Psi$ function to complement the pair correlation function and
define the spatial regimes departing from randomness in Taurus. We then perform
a set of statistical studies to characterize the binary regime that prevails in
Taurus. The $\Psi$ function in Taurus has a scale-free trend with a similar
exponent as the correlation function at small scale. It extends almost 3
decades up to $\sim 60$ kAU showing a potential extended wide binary regime.
This was hidden in the correlation function due to the clustering pattern
blending. Distinguishing two stellar populations, single stars versus multiple
systems (separation $ \leq 1$ kAU), within Class II/III stars observed at high
angular resolution, we highlight a major spatial neighborhood difference
between the two populations using nearest-neighbor statistics. The multiple
systems are three times more likely to have a distant companion within 10 kAU
when compared to single stars. We show that this is due to the presence of most
probable physical ultra-wide pairs. These UWPs are biased towards high
multiplicity and higher-stellar-mass components at shorter separations. The
multiplicity fraction per ultra-wide pair with separation less than 10 kAU may
be as high as 83.5 $\pm$ 19.6\%. We suggest that these young pre-main sequence
UWPs may be pristine imprints of their spatial configuration at birth resulting
from a cascade fragmentation scenario of the natal molecular core. They could
be the older counterparts, at least for those separated by less than 10 kAU, to
the $\le$ 0.5 Myr prestellar cores/Class 0 multiple objects observed at
radio/mm wavelengths.
