We measure the clustering of Extremely Red Objects (EROs) in ~8 deg^2 of the
NOAO Deep Wide Field Survey Bo\"otes field in order to establish robust links
between ERO z~1.2 and local galaxy z<0.1 populations. Three different color
selection criteria from the literature are analyzed to assess the consequences
of using different criteria for selecting EROs. Specifically, our samples are
(R-K_s)>5.0 (28,724 galaxies), (I-K_s)>4.0 (22,451 galaxies) and (I-[3.6])>5.0
(64,370 galaxies). Magnitude-limited samples show the correlation length (r_0)
to increase for more luminous EROs, implying a correlation with stellar mass.
We can separate star-forming and passive ERO populations using the (K_s-[24])
and ([3.6]-[24]) colors to K_s=18.4 and [3.6]=17.5, respectively. Star-forming
and passive EROs in magnitude limited samples have different clustering
properties and host dark halo masses, and cannot be simply understood as a
single population. Based on the clustering, we find that bright passive EROs
are the likely progenitors of >4L^* elliptical galaxies. Bright EROs with
ongoing star formation were found to occupy denser environments than
star-forming galaxies in the local Universe, making these the likely
progenitors of >L^* local ellipticals. This suggests that the progenitors of
massive >4L^* local ellipticals had stopped forming stars by z>1.2, but that
the progenitors of less massive ellipticals (down to L^*) can still show
significant star formation at this epoch.Comment: 19 pages, 16 figures, 4 tables, Accepted to ApJ 27th November 201