The Local Group in the cosmic web
  We explore the characteristics of the cosmic web around Local Group(LG) like
pairs using a cosmological simulation in the $\Lambda$CDM cosmology. We use the
Hessian of the gravitational potential to classify regions on scales of $\sim
2$ Mpc as a peak, sheet, filament or void. The sample of LG counterparts is
represented by two samples of halo pairs. The first is a general sample
composed by pairs with similar masses and isolation criteria as observed for
the LG. The second is a subset with additional observed kinematic constraints
such as relative pair velocity and separation. We find that the pairs in the LG
sample with all constraints are: (i) Preferentially located in filaments and
sheets, (ii) Located in in a narrow range of local overdensity $0<\delta<2$,
web ellipticity $0.1<e<1.0$ and prolateness $-0.4<p<0.4$. (iii) Strongly
aligned with the cosmic web. The alignments are such that the pair orbital
angular momentum tends to be perpendicular to the smallest tidal eigenvector,
$\hat{e}_3$, which lies along the filament direction or the sheet plane. A
stronger alignment is present for the vector linking the two halos with the
vector $\hat{e}_3$. Additionally, we fail to find a strong correlation of the
spin of each halo in the pair with the cosmic web. All these trends are
expected to a great extent from the selection on the LG total mass on the
general sample. Applied to the observed LG, there is a potential conflict
between the alignments of the different planes of satellites and the numerical
evidence for satellite accretion along filaments; the direction defined by
$\hat{e}_3$. This highlights the relevance of achieving a precise
characterization of the place of the LG in the cosmic web in the cosmological
context provided by $\Lambda$CDM.
