text:
\section{Introduction}
\label{sec:intro}

Neutron stars in binaries are spinning objects~\cite{Lorimer:2008se}.
The most famous example is the double pulsar PSR J0737-3039 for which
the orbital period, both spin periods, as well as
both spin down rates are known~\cite{Lyne:2004cj}.
The faster spinning pulsar in this system has a spin
period of $P=22.70$~ms (PSR J0737-3039A)~\cite{Burgay:2003jj}, which
corresponds to a dimensionless spin of
$\chi\sim0.02$~\cite{Tichy:2011gw,Damour:2012yf,Brown:2012qf,Hannam:2013uu}.
This is the fastest spinning pulsar in a binary system observed so far.
From the orbital period we can estimate that
this system will merge in about $85$~My due to emission of
gravitational waves (GWs).
Over this time period the faster spin will decrease by only about
$20\%$ if we assume spin down is due to magnetic dipole
radiation~\cite{Tichy:2011gw}. Thus we do expect spin effects
near merger, even though the other spin is much smaller and plays no big
role for this system.

A value of $\chi\sim0.02$ may appear rather small.  For black
hole systems $\chi\leq1$ is expected to approach $1$ in some
cases.
A theoretical limit for isolated neutron stars described by a
large class of nuclear equations of state and uniform
rotation is $\chi\sim0.7$~\cite{Lo:2010bj}. Configurations with
$\chi>1$ are however possible if, for example,
differential rotation is allowed, e.g.~\cite{Duez:2004nf}.
It is not clear whether or how many of these
large spin, single neutron stars can be found in binaries.
Theoretical limits for neutron star in binaries depend on the
mechanism of binary formation and binary history
and are difficult to predict precisely~\cite{Lorimer:2008se}.
Given that the observed neutron star spin in binaries is
comparatively small, star rotation is often ignored when modeling
likely astrophysical neutron star mergers.

Binary neutron stars (BNS)
are a primary source of GWs. Advanced
interferometric configurations in LIGO and Virgo experiments are
expected to detect from $0.4$ to $400$ events per year, starting from
2018-2019 (or even from
2016)~\cite{Abadie:2010cf,Aasi:2013wya}. At the expected
sensitivities, neglecting spin effects in template-based searches of
BNS can lead to substantial losses in the matched filter signal-to-noise
ratio for the inspiral~\cite{Ajith:2011ec,Brown:2012qf}.
Template waveforms of the inspiral phase that cover most of the
relevant frequency band are typically constructed with postNewtonian
approximants.
However, of particular interest is also the detection of the
late-inspiral-merger waveforms, because such signals can be used to
constrain the high-density equation of state (EOS) of neutron
stars~\cite{Read:2009yp,Damour:2012yf,DelPozzo:2013ala}.
Differently from the inspiral case, precise merger waveforms can be
constructed only by means of numerical relativity
simulations, e.g.~\cite{Baiotti:2011am,Bernuzzi:2011aq,Bernuzzi:2012ci,Hotokezaka:2013mm}.

Although spin is one of the elementary parameters of a binary system,
most studies of BNS to date have not
considered neutron stars with realistic rotation.
Almost all BNS simulations have started
from initial data which have been constructed as (quasiequilibrium)
stationary solutions in circular orbits, within either the
corotational~\cite{Baumgarte:1997xi,Mathews:1997pf,Marronetti:1998xv}
or the irrotational~\cite{Bonazzola:1998yq,Marronetti:1999ya,
  Uryu:1999uu,Taniguchi:2002ns,Uryu:2005vv,Uryu:2009ye} approach.
There is spin in the corotational case, but it is determined by the
orbital period and describes an unrealistic configuration
because of the low viscosity of neutron star
matter~\cite{Bildsten:1992ApJ...400..175B}.

Numerical simulations of BNS mergers in full
general relativity have reached a high degree of precision and
detail. Recent developments include radiation
transport~\cite{Sekiguchi:2011zd}, microphysical equations of
state~\cite{Sekiguchi:2011mc}, nonideal
magnetohydrodynamics~\cite{Palenzuela:2013hu}, as well as highly
eccentric
mergers~\cite{Gold:2011df,East:2012ww}. See~\cite{Faber:2012rw} for a
review and more references. In all these simulations the
Einstein equations are solved without any approximation as a 3+1
evolution system for a given initial configuration.
Most BNS
simulations have focused on irrotational configurations.
In this case the stars' spin is neglected, and not modeled in the
simulations. A way to construct quasiequilibrium BNS initial data
in circular orbits with spins has been recently proposed
in~\cite{Tichy:2011gw,Tichy:2012rp}. The
\emph{constant rotational velocity} (CRV) formalism developed there
is, to date, the only consistent method to produce realistic initial
data for BNS mergers with spins
(see~\cite{Marronetti:2003gk,Baumgarte:2009fw}
for earlier approximate approaches).

In this work we report dynamical evolutions of BNS
initial data constructed with the CRV approach.
We study the dynamics of the last three orbits, merger and postmerger
phase, of equal-masses BNS configurations with spins aligned or
antialigned to the orbital angular momentum. The rotational period of
each star is moderate and compatible with astrophysical observations.
We propose two simple ways to estimate the dimensionless spins
of the binary and show that both agree within $\sim10\%$.
The dynamics and gravitational radiation emitted are systematically
compared with an irrotational configuration with the same rest mass.
The orbital evolution is studied by means of gauge-invariant binding
energy vs.\ orbital angular momentum curves~\cite{Damour:2011fu}. We
compare these curves with a binary black hole simulation and with analytical
models, show consistency of the results, and extract the different
contributions to the binding energy from spin and tidal interactions.
The merger remnant is also investigated, focusing in particular on the
effect of rotation on the hypermassive neutron star.

Our results are the fundamental first step towards the use of
CRV initial data for modeling rotating stars in BNS mergers.
In particular, we show that even moderate spins have a significant
impact on the merger dynamics and on the gravitational radiation
emitted.
Numerical relativity simulations aiming at an accurate description of
the gravitational waves emitted by these sources should take into
account the rotation of the star.

General relativistic evolutions of spinning neutron stars
have been considered for a long time in the corotational approach,
both in full general relativity and in the conformally flat approximation,
see e.g.~\cite{Shibata:1999wm,Oechslin:2007gn}
and~\cite{Faber:2012rw} for other references.
More recently, alternative approaches have been
proposed in~\cite{Kastaun:2013mv,Tsatsin:2013jca}. Both works employ
constraint-violating initial data produced by superposing either
two boosted single-star configurations or an arbitrary velocity
pattern. Such data violate both Einstein constraints and some
hydrodynamical stationarity conditions.
It is unclear how these initial data relate with the ones used in this
work. Thus, in the following, we do not attempt a direct comparison of
the results, but just point out certain similarities.

The paper is organized as follows. In Sec.~\ref{sec:ID} we review main
aspects of the initial data and describe how to estimate the spin of
our configurations. The numerical method is summarized in
Sec.~\ref{sec:nummeth}. The dynamics of the numerical evolutions is
analyzed in Sec.~\ref{sec:dyn}, by considering: (i)~the analysis of
the orbital motion with binding energy vs.\ orbital angular
momentum curves; and (ii)~the postmerger phase
and a mode analysis of the hyper-massive neutron star in the merger
remnant. Gravitational radiation is discussed in Sec.~\ref{sec:gws}. We
conclude in Sec.~\ref{sec:conc}.

Dimensionless units $G=c=M_\odot=1$ are employed hereafter, physical
units are sometimes explicitly given in the text for clarity.

\section{Equilibrium configurations}
\label{sec:ID}

\begin{table*}[t]
  \centering
  \caption{ \label{tab:models}
    BNS configurations considered in this work.
    All initial data are for equal mass configurations,
    where each star has a baryonic mass $M_b=1.625$.
    The polytropic exponent and constant are $\Gamma=2$ and
    $K=123.6489$.
    Spins are aligned or antialigned to the orbital angular
    momentum.
    The columns contain the following information:
    the name of the configuration,
    the rotational part of the fluid velocity given in terms of the
    angular velocity $\omega^z$,
    ADM mass and ADM angular momentum of the binary,
    the gravitational mass $M_s$ of a single star in isolation,
    the spin $S_s$ of an isolated star with same $\omega^z$ and $M_b$,
    and the corresponding dimensionless spin $\chi_s$,
    the spin estimate $S$ using the irrotational configuration as reference point,
    and the corresponding dimensionless spin $\chi$.
    $\Gamma$ configurations are evolved with $\Gamma$-law EOS, $P$
    configurations with the polytrope (barotropic evolutions).}
   \begin{tabular}{c|ccccccccc}
     \hline
    Name & $\omega^z$& $M_{\rm ADM}$ & $J_{\rm ADM}$ & $M_s$ & $S_s$ &$\chi_s$& $S$& $\chi$ \\
    \hline
    $\Gamma_{050}^{--}$ & -0.00230 & 2.99932 & 8.69761  & 1.51496 &-0.11449 &-0.0499 &-0.10224 &-0.0419 \\
    $\Gamma_{025}^{--}$ & -0.00115 & 2.99911 & 8.79949 & 1.51487 &-0.05710 &-0.0249 &-0.05130 &-0.0198 \\
    $\Gamma_{000}$  &  0.00000 & 2.99903 & 8.90209  & 1.51484 & 0.00000 & 0.0000 & 0.00000 & 0.0000 \\
    $\Gamma_{025}^{++}$ &  0.00115 & 2.99907 & 9.00585 & 1.51487 & 0.05710 & 0.0249 & 0.05188 & 0.0252 \\
    $\Gamma_{050}^{++}$ &  0.00230 & 2.99926 & 9.11092  & 1.51496 & 0.11449 & 0.0499 & 0.10442 & 0.0480 \\
    \hline
    $P_{100}^{--}$ & -0.00460 & 3.00012 & 8.49472  & 1.51533 &-0.23128 &-0.1007 &-0.20368 &-0.0861 \\
    $P_{000}$  &  0.00000 & 2.99903 & 8.90209  & 1.51484 & 0.00000 & 0.0000 & 0.00000 & 0.0000 \\
    $P_{100}^{++}$ &  0.00460 & 2.99993 & 9.32688 & 1.51533 & 0.23128 & 0.1007 & 0.21240 & 0.0950 \\
    \hline
   \end{tabular}
 \end{table*}

\subsection{A review of the CRV approach}
\label{sec:ID:crv}

The initial data used here are constructed using the CRV
method~\cite{Tichy:2011gw,Tichy:2012rp}. For this method
we use the Wilson-Mathews approach~\cite{Wilson:1995uh,Wilson:1996ty},
which is also known as conformal thin sandwich formalism~\cite{York:1998hy},
for the metric variables together with certain assumptions.
The first assumption is the existence of an approximate helical
Killing vector $\xi^{\mu}$, such that
\begin{equation}
\pounds_{\xi} g_{\mu\nu} \approx 0 .
\end{equation}
We also assume similar equations for scalar matter quantities such as
the specific enthalpy $h$. However, the
4-velocity $u^{\mu}$ is treated differently and it is not assumed that
$\pounds_{\xi} u^{\mu}$  vanishes. Instead
we write
\begin{equation}
{u}^{\mu} = \frac{1}{h}(\nabla^{\mu}\phi + w^{\mu}) ,
\label{4-vecolicy}
\end{equation}
where $\nabla^{\mu}\phi$ and $w^{\mu}$
are the irrotational and rotational parts of the fluid velocity.
We then assume that
\begin{equation}
\label{assumption1}
\gamma_i^{\nu} \pounds_{\xi} \left(\nabla_{\nu}\phi\right) \approx 0 ,
\end{equation}
so the time derivative of the irrotational piece of the
fluid velocity vanishes in corotating coordinates.
We also assume
\begin{equation}
\label{assumption2}
\gamma_i^{\nu} \pounds_{\frac{\nabla \phi}{h u^0}} w_{\nu}
\approx 0 ,
\end{equation}
and
\begin{equation}
\label{assumption3}
^{(3)}\!\pounds_{\frac{w}{h u^0}} w_i \approx 0,
\end{equation}
which describe the fact that the rotational piece of the fluid velocity
is constant along the world line of the star center. These latter two
assumptions lead to the name constant rotational velocity method.

For the data considered here we set
\begin{equation}
\label{w_choice}
{w}^i = \epsilon^{ijk} \omega^j (x^k - x_{C*}^k) .
\end{equation}
where $x_{C*}^i$ is the center of the star (defined as the point with the
highest rest mass density) and where $\omega^i$ is an arbitrarily chosen
angular velocity vector. In~\cite{Tichy:2012rp} we have verified that this
specific choice leads to only a negligible shear,
so that we can avoid any substantial differential rotation.

This method is implemented in the
SGRID code~\cite{Tichy:2006qn,Tichy:2009yr,Tichy:2009zr}
which is used to construct the initial data. We then import these data into
the BAM code (see below)
by spectral interpolation onto BAM's grid points.

\subsection{Selected configurations}
\label{sec:ID:conf}

The initial configurations considered in this work are $\Gamma=2$
polytropes, $p=K\rho^\Gamma$, with $K=123.6489$,
individual rest mass (or baryonic mass)
$M_b=1.625$ and different rotational states. Table~\ref{tab:models}
summarizes the main properties of the models.
The rotation state of each star is characterized by its
angular velocity $\omega^i$.
For the simulations described here we have chosen $\omega^i$ to point
along the $z$-direction, with the values given in Tab.~\ref{tab:models}.
If we use $P = 2\pi / \omega^z$ to define a spin period for each star, the
different spinning configurations in Tab.~\ref{tab:models} correspond to
periods of $6.7$, $13.4$ and $26.9$~ms. Notice, however, that these periods
are not exactly the spin periods an observer at infinity would
measure. As we show in Appendix~\ref{app:singlestar}
the spin periods observed at infinity are about 10\% larger.
The initial data employed in this work are selected from
equilibrium sequences similar to those computed
in~\cite{Tichy:2012rp}; some details are given in
Appendix~\ref{app:IDseq}.

The individual isolation masses of the irrotational model are
$M_{\rm  TOV}=1.51484$, which is equivalent to the ADM
mass of a TOV star with the same rest mass as the binary's individual
$M_b=1.625$.
All the binary models have about the same proper separation of
$D\approx40.4$ ($59$~km).
The ADM masses differ by a maximum of $0.04\%$.
The CRV formalism~\cite{Tichy:2011gw,Tichy:2012rp}
allows us to construct
single rotating star configurations by assuming that the approximate
Killing vector $\xi^{\mu}$ is the timelike Killing
vector $\xi^{\mu}=(1,0,0,0)$. We have thus computed
single star models with half the rest mass of the binary and the
same $\omega^z$. Each model is characterized by an ADM mass
$M_s$ and an ADM angular momentum $S_s$. For the nonrotating model of
course $M_s=M_{\rm TOV}$ and $S_s=0$; other values are reported in
Tab.~\ref{tab:models}. We will make use of these values in the
following sections. We define $M=2M_{\rm TOV}$, and scale the time in
the plots with this mass.

Additionally to these BNS configurations, we consider a
nonspinning equal-masses binary black hole (BBH) run.
The initial configuration is identical to the one in Tab.~III
of~\cite{Walther:2009ng} with an initial separation of $\approx11$ and
an eccentricity of $\approx 0.0002$.

\subsection{Spin estimates}
\label{sec:ID:spin}

In the CRV approach the natural quantity
describing the spinning motion is $\omega^i$, however in the context
of GWs it is convenient to consider ``a spin''. Since the spin
of a single star in a binary is not unambiguously defined
in general relativity, we propose here two simple different ways of
estimating the spin magnitude $S$.

A simple method (which to our knowledge is new in this context)
is to consider single stars in isolation with the same
rest mass and the same $\omega^z$, computed as described in
Sec~\ref{sec:ID:conf}. These stars have a well defined angular
momentum $S_s$.
We then take the spin to be
\begin{equation}
\label{eq:spinestimate1}
S \approx S_s \ ,
\end{equation}
and the dimensionless spin to be $\chi_s=S_s/M_s^2$. These values are
reported in Tab.~\ref{tab:models}.

A second estimate is given by comparing each spinning configuration with
the irrotational one. From Tab.~\ref{tab:models} we observe that the
spin does not contribute significantly to the ADM masses. Assuming
that the differences in the total angular momentum are due to the
spins of the stars, we write
\begin{equation}
\label{eq:spinestimate2}
S \approx (J_{\rm ADM} - J_{\rm ADM}^{\rm irr})/2 \ .
\end{equation}
Dimensionless spin values are given then by $\chi=S/M_s^2$.
The results are stated in Tab.~\ref{tab:models} and differ from
the previous estimate by $\sim 10\%$.

A precise value of the dimensionless spin is necessary to construct
binding energy vs.\ orbital angular momentum curves. We will show that
a nontrivial agreement with analytical results can be obtained using
Eq.~\eqref{eq:spinestimate1}.

\section{Numerical method}
\label{sec:nummeth}

\begin{table}[t]
  \centering
  \caption{ \label{tab:grid}
    Summary of the grid configurations used for the evolutions,
    see Sec.~\ref{sec:nummeth} for a detailed description.}
  \begin{tabular}{ccccccccccc}
    \hline
    Name & $L$ & $l^{\rm mv}$ & $n^{\rm mv}$ &
    $h_{L-1}$ & $n$ & $h_0$ \\
   \hline
   L1 & 6 & 2 & 128 & 0.225  & 128 & 7.20    \\
   L2 & 6 & 2 & 144 & 0.200  & 144 & 6.40    \\
   M & 6 & 2 & 168  & 0.171  & 168 & 5.49    \\
   H & 6 & 2 & 192 & 0.150  & 192 & 4.80    \\
    \hline
  \end{tabular}
\end{table}

Simulations are performed with the BAM
code~\cite{Thierfelder:2011yi,Brugmann:2008zz,Bruegmann:2003aw,Bruegmann:1997uc}.
The Einstein equations are written in 3+1 BSSNOK
form~\cite{Nakamura:1987zz,Shibata:1995we,Baumgarte:1998te}.
1+log and gamma-driver conditions are
employed for the evolutions of lapse and shift,
respectively~\cite{Bona:1994a,Alcubierre:2002kk,vanMeter:2006vi};
see~\cite{Thierfelder:2010dv} for a study of gauge condition performance in
handling gravitational collapse.
General-relativistic hydrodynamics (GRHD) equations are solved in
conservative form by defining Eulerian conservative variables from the
rest-mass density $\rho$, pressure $p$, internal energy $\epsilon$, and
3-velocity, $v^i$.
An equation of state closes the system.
We consider evolutions with a $\Gamma$-law EOS
\begin{equation}
p =(\Gamma-1) \rho \epsilon ,
\end{equation}
with $\Gamma=2$ for most of the configurations. Some control runs with a
polytropic EOS, thus forcing a barotropic evolution, have also been
performed (see Tab.~\ref{tab:models}.)

The evolution algorithm is based on the method-of-lines with explicit
4th order Runge-Kutta time integrators. Finite differences (4th order
stencils) are employed for the spatial derivatives of the metric.
GRHD is solved by means of a high-resolution-shock-capturing
method~\cite{Thierfelder:2011yi} based on primitive reconstruction
and the Local-Lax-Friedrichs (LLF) central scheme for the numerical
fluxes. Primitive reconstruction is performed with the 5th order WENO
scheme of~\cite{Borges20083191}, which has been found to be important
for long term accuracy~\cite{Bernuzzi:2012ci,Bernuzzi:2011aq}.
The numerical domain is made of a hierarchy of cell-centered nested
Cartesian grids. The hierarchy consists of $L$ levels of refinement labeled
by~$l = 0,...,L-1$. A refinement level $l$ has one or more
Cartesian grids with constant grid spacing $h_l$ and $n$ points per
direction. The  refinement factor is two such that $h_l = h_0/2^l$. The grids
are properly nested in that the coordinate extent of any grid at
level~$l$, $l > 0$, is completely covered by the grids at level~$l-1$.
Some of the mesh refinement levels $l>l^{\rm mv}$ can be dynamically moved and adapted
during the time evolution according to the technique of~``moving boxes''.
The Berger-Oliger algorithm is employed for the time stepping~\cite{Berger:1984zza},
though only on the inner levels. Interpolation in
Berger-Oliger time stepping is performed at second order. A
Courant-Friedrich-Lewy factor of~$0.25$ is employed in all runs.
We refer the reader to~\cite{Thierfelder:2011yi,Brugmann:2008zz} for more details.

The grid configurations considered in this work are reported in
Tab.~\ref{tab:grid}. Because we evolve equal-mass binaries, we use
bitant symmetry (evolving only the half space $z>0$) without loss of
generality. We experimentally found that the nonconservative mesh
refinement in BAM can lead to rest mass violations during the postmerger
phase (when mass crosses AMR boundaries), and in turn degrade the
quality of the simulation in the long-term. In order to minimize this
systematic source of error, the number of points in the moving levels
is set equal to the nonmoving ones; see
Appendix~\ref{app:tests} for more details.
This is different from what was done in previous BAM
simulations, that instead mostly focused on the orbital phase,
e.g.~\cite{Thierfelder:2011yi}.

Gravitational radiation is computed by means of the Weyl
scalar~\cite{Brugmann:2008zz} on a coordinate sphere of radius $r=400$. The
scalar is projected onto spin weighted spherical harmonics to compute
the multipoles $\psi^4_{lm}$. The metric multipoles $h_{lm}$ are calculated
by integrating the relation $\psi^4_{lm}=\ddot{h}_{lm}$. We use a
frequency-domain procedure with a low-frequency cutoff~\cite{Reisswig:2011CQGra..28s5015R}. The signal is integrated from the
very beginning of the simulation, in  order to include also the
initial burst of radiation related to the conformal flatness of the initial
data.
The radiated energy and angular momentum perpendicular to the orbital
plane are calculated as
\begin{align}
\mathcal{E}_{\rm rad} &=\dfrac{1}{16\pi}\sum_{l,m}^{l_{\rm max}} \int_{0}^t dt'\left|r\,\dot{h}_{lm}(t')\right|^2\\
\mathcal{J}_{z\ \rm rad} &=\dfrac{1}{16\pi}\sum_{l,m}^{l_{\rm max}}\int_{0}^{t}d t' m\left[r^2\,h_{lm}(t')\dot{h}_{lm}^*(t')\right] \ ,
\end{align}
with $l_{\rm max}=8$. In the calculation of the total angular momentum
$\mathcal{J}_{\rm rad}$ we also include the $\mathcal{J}_{x,y\ \rm
  rad}$ components, although their contribution is nonzero only in the
postmerger phase and in practice negligible.

\section{Dynamics}
\label{sec:dyn}

In this section we discuss the effect of the star's rotation on the
binary dynamics. We formally define the merger as the peak of the
amplitude $|r\,h_{22}|$ (Sec.~\ref{sec:gws}), but recall that the two
stars come in contact well before (see e.g.~discussion
in~\cite{Bernuzzi:2011aq} and below).
First we describe the orbital phase, i.e.~evolution up
to merger, then we consider the postmerger phase.

\begin{figure*}[t]
  \centering
    \includegraphics[width=0.32\textwidth]{fig01a.png}
    \includegraphics[width=0.32\textwidth]{fig01b.png}
    \includegraphics[width=0.32\textwidth]{fig01c.png}\\
    %
    \includegraphics[width=0.32\textwidth]{fig01d.png}
    \includegraphics[width=0.32\textwidth]{fig01e.png}
    \includegraphics[width=0.32\textwidth]{fig01f.png}\\

    \includegraphics[width=0.32\textwidth]{fig01g.png}
    \includegraphics[width=0.32\textwidth]{fig01h.png}
    \includegraphics[width=0.32\textwidth]{fig01i.png}
    \caption{ \label{fig:snap2d}
      Snapshots of $\log_{10}\rho$ and $(v^x,v^y)$ on the orbital
      plane. Rows from top to bottom refer to initial, contact and
      merger times.
      Columns from left to right refer to models $\Gamma_{050}^{--}$, $\Gamma_{000}$ and $\Gamma_{050}^{++}$,
      respectively. Note the different spatial scales.}
\end{figure*}

\subsection{Orbital motion}
\label{sec:dyn1}

\begin{figure}[t]
  \centering
    \includegraphics[width=0.5\textwidth]{fig02.pdf}
    \caption{ \label{fig:Ejearly} Binding energy vs.\ orbital angular
      momentum curves for models $\Gamma_{050}^{--}$,
      $\Gamma_{050}^{++}$ and $\Gamma_{000}$.
      Top: $E(\ell)$ curves for numerical data (solid lines),
      3PN (dotted lines), and EOB (dashed lines).
      Bottom: Differences $\Delta E = E-E^{X}$ between numerical
      data and 3PN (dotted) and EOB curves (dashed).
      The uncertainty on the numerical data is shown in light
      gray.}
\end{figure}

\begin{figure*}[]
  \centering
  \includegraphics[width=1.\textwidth]{fig03.pdf}
    \caption{ \label{fig:Ej}
      Binding energy vs.\ orbital angular
      momentum curves for $\Gamma$-models and a nonspinning BBH run.
      Left: $E(\ell)$ curves for BNS and BBH data. Diamonds and
      bullets indicate the approximate moment of
      contact (corresponding to the snapshots of
      Fig.~\ref{fig:snap2d}) and the moment of merger, respectively.
      Right: Different contributions to the binding energy in
      Eq.~\eqref{eq:Epieces}, extracted
      from differences of data sets as described in the text. The
      uncertainty of the numerical data
      is shown as the gray shaded region. The vertical dashed
      lines refer to the approximate moment of contact and to the merger
      for $\Gamma_{000}$.
      $e^{025}_T$ and $e^{050}_T$ coincide in this plot.
      Doubling the spin
      approximately doubles the spin-orbit effect in the binding energy.
      For $0.05$ the spin-orbit term is larger than the
      tidal term until $\ell\sim3.65$.}
\end{figure*}

Figure~\ref{fig:snap2d} shows snapshots of the rest-mass density and
fluid's velocity $(v^x,v^y)$ on the orbital plane for the representative
models $\Gamma_{050}^{--}$, $\Gamma_{000}$, and $\Gamma_{050}^{++}$ (columns). We
focus on these since they are the $\Gamma$-law EOS
evolutions with the highest spin magnitudes. In the plot,
the stars orbit each other counterclockwise. The top
row refers to the initial time; comparing the central panel
($\Gamma_{000}$) with the left ($\Gamma_{050}^{--}$) and the right
($\Gamma_{050}^{++}$), one can see only a very small difference in the velocity
pattern due to the rotational state of the CRV data with respect to the
irrotational flow.
The central row refers to a simulation time at which the cores of the
two stars come in contact, i.e.~rest-mass density layers
$\rho\sim10^{-4}$ ($10^{14}\ \text{g/cm}^3$) of the two stars touch
each other in the characteristic shearing contact,
e.g.~\cite{Sekiguchi:2011zd}.
The proper distance between the stars, as calculated from the local
minima of the lapse function or local maxima of $\rho$, is about
$D\sim30$ at this moment.
Note also the very different orbital phases of the three models at
this moment, revealing that the moderate initial spins had a significant
effect after only about $1.5$ orbits.
The last row refers to the merger time, after approximately three
orbits (six-seven GW cycles, see below), at which hyper massive
neutron stars (HMNSs) are formed for the three configurations.  The
HMNSs appear similar in the snapshots, but their angular momentum is
actually different and different dynamics follows (see Sec.~\ref{sec:dyn2}.)

The orbital dynamics of the irrotational model is consistent with what was
previously observed in
e.g.~\cite{Thierfelder:2011yi} for the same initial configuration
computed with the Lorene code (see also Appendix~\ref{app:tests}).
The star rotation changes this picture: for spins aligned with
the orbital angular momentum the inspiral is longer for larger spin
magnitudes, while for antialigned spins the inspiral is shorter
for larger spin magnitudes. This effect can be understood in term of
spin-orbit interaction~\cite{Damour:2001tu}.
Analogously to what happens to corotating/counter-rotating circular
orbits in Kerr spacetimes, the last-stable-spherical orbit moves
outwards (inwards) for antialigned (aligned) spin configurations with
respect to the nonspinning case~\cite{Damour:2001tu}.
The analogous result in binary black hole
simulations is sometimes called ``hang-up''~\cite{Campanelli:2006uy}.
In BNS mergers it has been discussed recently in~\cite{Kastaun:2013mv,Tsatsin:2013jca}.
Spin-orbit interactions thus change quantitatively the binary
dynamics, and we quantify this aspect in the following.

A gauge invariant way to analyze the binary dynamics from numerical
relativity data is to consider binding energy  vs.\ orbital angular
momentum curves, as proposed in~\cite{Damour:2011fu}.
In the present context these curves allow us to characterize the
dynamics generated by CRV initial data.
We compute the dimensionless binding energy and angular momentum per
reduced mass as~\footnote{
  The notation for the angular momentum is slightly different
  from~\cite{Damour:2011fu}.}
\begin{align}
\label{Ebdef}
{E} &= \left[(M_{\rm ADM}(t=0)- \mathcal{E}_{\rm rad})/M-1\right] \nu^{-1} \\
\label{jdef}
\ell  &= (L - \mathcal{J}_{\rm rad})(M^2\nu)^{-1} \ ,
\end{align}
respectively, where $\nu=1/4$ is the symmetric mass ratio, and the
isolation mass $M$ is taken as $M=2 M_s$, see Table~\ref{tab:models}.
The initial angular momentum $L$ is computed from the
spin estimates of Sec.~\ref{sec:ID:spin} as
\begin{equation}
L = J_{\rm ADM}(t=0) - 2 S_s \ ,
\end{equation}
and coincides with $ J_{\rm ADM}(t=0)$ for the irrotational
configuration. Eq.~\eqref{jdef} assumes that $\mathcal{J}_{\rm rad}$
only affects $\ell$, i.e. the spin magnitude remains constant.
This can be justified on a PN basis, and, in general, it holds
for small, aligned spins.

\begin{table}[t]
  \centering
  \caption{ \label{tab:dynamics}
    Dynamical quantities during orbital motion.
    Simulation time, gravitational wave
    frequency, angular momentum, and energy are reported at the
    moments of contact and merger. Note the contact time is not a well
    defined quantity, and just reported to give a rough
    estimate. Frequencies uncertainties of about $10$\%.}
  \begin{tabular}{c|cccc|cccc}
    \hline
    Name & $t_c/M$ & $M\omega_c$ & $\ell_c$ & $E_c\times10^{2}$ & $t_m/M$ & $M \omega_m$ & $\ell_m$ & $E_m\times10^{2}$ \\
    \hline
    $\Gamma_{050}^{--}$ & 499 & 0.067 & 3.64 & -4.89 & 551 & 0.124 & 3.58 & -5.19 \\
    $\Gamma_{025}^{--}$ & 514 & 0.065 & 3.63 & -4.90 & 575 & 0.128 & 3.55 & -5.36\\
    $\Gamma_{000}$      & 531 & 0.069 & 3.62 & -4.92 & 595 & 0.127 & 3.53 & -5.44 \\
    $\Gamma_{025}^{++}$ & 549 & 0.070 & 3.61 & -4.95 & 618 & 0.125 & 3.51 & -5.47\\
    $\Gamma_{050}^{++}$ & 570 & 0.071 & 3.60 & -4.99 & 636 & 0.123 & 3.50 & -5.48 \\
    \hline
    \end{tabular}
\end{table}

The numerical data $E(\ell)$ are compared to \emph{point-mass}
analytical results: a postNewtonian~(PN) and an
effective-one-body~(EOB)~\cite{Buonanno:1998gg,Buonanno:2000ef}
curve.
In this work we employ the 3PN binding energy expression including
next-to-next-to-leading order spin-orbit coupling as given by Eq.~(43)
of~\cite{Nagar:2011fx}, and indicate it as ${E}^{\rm 3PN}(\ell)$.
The result rely on earlier achievements in PN theory, among others
see~\cite{Kidder:1992fr,Kidder:1995zr,Tagoshi:2000zg,Blanchet:2004ek,Faye:2006gx,Damour:2007nc,Steinhoff:2007mb}.
Additionally, we also consider the curve $E^{\rm EOB}(\ell)$
constructed within the EOB approach in the
adiabatic limit. For simplicity, we use the EOB model for
spinning binaries introduced in~\cite{Damour:2001tu}. Similarly, the
nonspinning part of the model is taken at 3PN
accuracy~\cite{Damour:2000we} only and it is resummed with a $(1,3)$
Pad\'e approximant
(see~\cite{Barausse:2011dq,Damour:2012ky,Bini:2013PhRvD..87l1501B,Pan:2013rra} for
recent theoretical developments of the EOB model.)
The next-to-leading-order~\cite{Damour:2008qf} and
next-next-to-leading-order~\cite{Nagar:2011fx} spin-orbit
couplings are included in the Hamiltonian.
We restrict ourselves to the leading order spin-spin term for
simplicity, although the spin-spin interaction is known at
next-to-leading order~\cite{Balmelli:2013PhRvD..87l4036B}.

There is evidence that irrotational conformally flat initial data
sequences are quite close to the 3PN result for a sufficiently large
binary separation,
e.g.~\cite{Uryu:2009ye} (and also Appendix~\ref{app:IDseq}). However, we
recall that the conformally flat approximation introduces errors
already at 2PN level~\cite{Damour:2000we}. On the other hand, the
3PN-EOB adiabatic curve has been found to correctly reproduce nonspinning
numerical relativity data of different mass ratios up to
$\ell\sim3.55$~\cite{Damour:2011fu}. The same reference has shown
that the 3PN-EOB curve is instead remarkably close to numerical data
up to the last stable orbit of the EOB potential ($\ell\sim3.28$), and it is an
accurate diagnostic of the \emph{conservative dynamics} of the system.
(See~\cite{Bernuzzi:2012ci} for the case of neutron star mergers with
irrotational data.)

The curves ${E}(\ell)$ at early simulation times are shown in
Fig.~\ref{fig:Ejearly} for models $\Gamma_{050}^{--}$, $\Gamma_{000}$, and
$\Gamma_{050}^{++}$, together with the PN and EOB curves computed with the
spin values as estimated in Sec.~\ref{sec:ID:spin}.
These curves are quite sensitive to small variations in the values of
the initial masses, angular momentum and spins. For example, they require $M_{\rm
  ADM}$ and $M_s$ accurate up to four digits. The uncertainty on the
numerical data is also shown. It is estimated considering $\Gamma_{000}$
data at different resolutions (grid configurations H and L2) and
including the uncertainty of the initial ADM values as measured from
different SGRID resolutions. Both errors are added in quadrature.
The bottom panel shows the differences $\Delta{E}={E}-{E}^{X}$ of
numerical data with respect to the $X=$~3PN and the $X=$~EOB curves with the
relative spin values.

We experimentally observe that, for all the configurations considered in
this work, the spin estimate in Eq.~\eqref{eq:spinestimate1} leads
to ${E}(\ell)$ curves closer to the PN and EOB ones at early times
than Eq.~\eqref{eq:spinestimate2}.
Thus, we use in the figure and in the following that estimate.
Note that this choice assumes that the spin is almost constant along
the sequences.

As shown in Fig.~\ref{fig:Ejearly}, the dynamics starts between the PN
and EOB curves, and rapidly depart from the initial state,
$\ell\sim3.87$ (see inset). This variation is due to the emission of the
artificial gravitational radiation related to the conformally flat assumption of
the CRV data. In complete analogy with the nonspinning binary black
hole case and irrotational case, the numerical evolution settles very
quickly close to the EOB curve (with the proper
spin)~\cite{Damour:2011fu,Bernuzzi:2012ci}.
The difference between the EOB curves and the numerical data at early
times is within the error-bars: the tidal contribution cannot be
distinguished with present data (the same happens comparing BNS and BBH,
see below).

A clear hierarchy among the PN and EOB curves with different spins can
be observed. This effect is due to spin-orbit interactions:
antialigned configuration are more bound and aligned configurations
are less bound than irrotational (cf.~``hang-up''). The numerical
curves consistently respect such hierarchy from early times to merger
(see below).
During the early-times evolution, the binaries binding energies depart
systematically from the EOB, and
close to contact ($\ell_c\sim3.63$), the
deviation becomes significant. Note in the bottom panel how the
differences between EOB and numerical data for different spins are
essentially indistinguishable. This fact clearly suggests that the
deviation is due to finite size effects.

The curves ${E}(\ell)$ up to merger are shown in
Fig.~\ref{fig:Ej} (left panel) for
models $\Gamma_{050}^{--}$, $\Gamma_{000}$, and $\Gamma_{050}^{++}$
together with the one for the nonspinning BBH
run. At early times (see inset) the BBH system is less bound than the
irrotational configuration, but within the data uncertainty.
As observed for the EOB curve, for $\ell\to\ell_c$ tidal contributions
become progressively more important and the systems become more bound
deviating systematically from the BBH curve. Merger occurs at
$\ell_m\sim3.58$, $3.53$, $3.50$ for $\Gamma_{050}^{--}$,
$\Gamma_{000}$ and $\Gamma_{050}^{++}$,  respectively. At merger, the aligned spin
configurations are more bound than the antialigned one.
See also Tab.~\ref{tab:dynamics} for a
collection of relevant numbers for all the configurations.

In order to gain insight into the role
of spin and tidal interactions during the
merger phase, we make the assumption that
\begin{equation}
\label{eq:Epieces}
{E} \approx e_0 + e_{SO} + e_{SS} + e_T \ ,
\end{equation}
i.e.~that the binding energy of a spinning BNS configuration can be
approximated by the \emph{sum} of four separate contributions: a
nonspinning point-mass (black-hole) term $e_0$, a spin-orbit (SO) term
$e_{SO}$, spin-spin (SS) term $e_{SS}$, and a tidal (T) term
$e_T$. The different terms have PN contributions starting from
1.5PN~(SO), 2PN~(SS) and 5PN~(T).
All the four terms in~\eqref{eq:Epieces} can be calculated using the
simulation data, e.g.~the four runs $\Gamma_{000}$, $\Gamma^{++}_{050}$,
$\Gamma^{--}_{050}$, and BBH. Below we distinguish between
the terms in the ansatz ($e_x$) and the numerical curves
(${E}^Y_X$, as the relative model name).
The SO term has structure of the form
$\propto\mathbf{L}\cdot\mathbf{S}$, so for aligned/antialigned spins
$e_{SO}\propto2\,{\rm sign}(S)|\mathbf{L}||\mathbf{S}|$.
Similarly, the SS term has structure
$\propto\mathbf{S}_1\cdot\mathbf{S}_2$, so it does not change sign if
both spins flip.
A $++$ binary configuration has a repulsive SO contribution
($e_{SO}>0$), whereas a $--$ one with the same spin magnitude has an
attractive SO contribution ($e_{SO}<0$) to the binding energy.
However, as mentioned above, the aligned spin configurations give a
more negative binding energy at merger than the antialigned
configurations (compare with~\cite{Damour:2001tu}.)

The SO term is calculated by the combination of the
aligned/antialigned spins runs with the same magnitude,
i.e.~$e_{SO}\approx({E}^{++}_{050}-{E}^{--}_{050})/2$.
Obviously we pose $e_0\approx {E}_{\rm BBH}$ and $e_0 + e_T
\approx{E}_{000}$, and calculate $e_T$ from the difference
${E}_{000}-{E}_{\rm BBH}$.
The SS term is estimated as $e_{SS}\approx
({E}^{++}_{050}+{E}^{--}_{050})/2 - {E}_{000}$.
The different terms $e_x$ are reported in the right panel of
Fig.~\ref{fig:Ej}. The SS contribution is the smallest negative, at
the level of the uncertainty of the data. At the moderate spins used here,
SS interactions are essentially not resolved in the simulation.
On the other hand, the curves $e_{SO}$ and $e_T$ are well
resolved. We observe that, for $\chi=0.05$, the $e_{SO}$ is the
dominant contribution to the binding energy up to
$\ell\sim3.65$. After this point, $e_T$ becomes dominant.
This corresponds to intuition since the
dynamics reaches the hydrodynamical regime (see
Fig.~\ref{fig:snap2d}). Towards merger (not visible in the plot) the
differences between the $e_{SO}$ and $e_{T}$ become progressively
larger.

An independent estimate of $e_{SO}$, $e_T$, and $e_{SS}$ is also given
by using the data of the other two simulations $\Gamma_{025}$,  see
right panel of Fig.~\ref{fig:Ej}. We
obtain similar results, and in particular the $e_T$ terms exactly
coincide as they should.
There is one important difference though. In the case
$\chi=0.025$, the $e_{T}$ term is the largest negative term already at
early simulation times.  Thus during the last three orbits the binding
energy is ``tidally dominated'' as in the irrotational case.

We mention that, while the SS term is poorly resolved, its presence is
clearly suggested by looking at the difference ${E}_{000}-{E}^{++}_{050}$ and
${E}^{--}_{050}-{E}_{000}$. The two combinations approximate $e_{SO}\pm
e_{SS}$, with the SS term entering with a different sign. We find
that, as expected, the former is less bound, the latter is more by a
small amount. Similarly, inspection of the quantity
$({E}_{050}^{++}-{E}_{050}^{--})/2-{E}_{BBH} \approx e_T +e_{SS}$, leads
to a curve very close to $e_T$, only slightly more bound.
This suggests that there is no significant coupling between SO and
tidal contributions (as assumed in Eq.~\eqref{eq:Epieces}), even after contact.

Finally, note that for $\ell\lesssim\ell_c$ the spin term $e_{SO}+e_{SS}$ is
probably influenced by hydrodynamical effects, so its correct
interpretation may be nontrivial.
We also mention that similar results and conclusions
are obtained by using the EOB curves instead of the BBH data.

\subsection{Merger remnant}
\label{sec:dyn2}

\begin{figure}[t]
  \centering
    \includegraphics[width=0.49\textwidth]{fig04.pdf}
    \caption{ \label{fig:rhomax} Evolution of the
      maximum mass-density $\rho(t)$ (normalized by its initial value)
      for the configurations
      $\Gamma_{050}^{++}$, $\Gamma_{025}^{++}$, $\Gamma_{000}$,
      $\Gamma_{025}^{--}$ and $\Gamma_{050}^{--}$ (upper panel) and
      for the configurations $P_{100}^{++}$, $P_{000}$ and $P_{100}^{--}$
      (lower panel). Note the different $x$-axes.}
\end{figure}

 \begin{figure}[t]
  \centering
     \includegraphics[width=0.49\textwidth]{fig05.pdf}
    \caption{ \label{fig:rhomode} Evolution of projections $\rho_m(t)$
      for $m=1,2,3,4$ and different models. From top to bottom:
      $\Gamma_{050}^{--}$, $\Gamma_{000}$, $\Gamma_{050}^{++}$.}
\end{figure}

 \begin{figure*}[t]
  \centering
    \includegraphics[width=0.47\textwidth]{fig06a.pdf} \quad
    \includegraphics[width=0.47\textwidth]{fig06b.png}
    \caption{ \label{fig:fourier}
      Fourier analysis of the rest mass projections $\rho_m$.
      Left: Power spectral density (PSD) of $\rho_{max}(t)$ and
      $\rho_2(t)$ for $\Gamma_{000}$,
      $\Gamma_{025}^{++}$, $\Gamma_{050}^{++}$.
      Right: Spectrogram of the quantity
      $\rho_{12}(t)\equiv\rho_1(t)+\rho_2(t)$
      in model $\Gamma_{050}^{++}$.}
\end{figure*}

All the configurations evolved with the $\Gamma$-law EOS
form, at merger, HMNSs characterized by different rotational states.
In our simulations the HMNS is only supported by centrifugal forces
and thermal pressure (we include neither magnetic fields nor cooling
mechanisms). The angular momentum support is radiated away in GWs on
dynamical timescales, and the HMNS finally collapses. This happens
after about $1500$~M ($\sim22$~ms) from formation in the irrotational
model. The dimensionless angular momentum magnitude per reduced mass
of the HMNS is approximately $j\approx\ell_m\pm2\chi/\nu$ (assuming
$\chi\sim const$), e.g.~$j\sim3.18$, $3.53$, $3.9$ for $\Gamma_{050}^{--}$,
$\Gamma_{000}$, and $\Gamma_{050}^{++}$, respectively.
We thus expect that configurations with
antialigned spins will collapse earlier, whereas configurations with
aligned spins will collapse later.

In Fig.~\ref{fig:rhomax}
we show the evolution of the maximum rest mass density,
$\rho_{max}(t)$, for evolutions with the $\Gamma$-law EOS (upper panel)
and the polytropic EOS (lower panel). The oscillations visible in the plot
correspond to quasiradial modes (see below and Sec.~\ref{sec:gws}).
The average rest mass density increases linearly in time
to about a critical density, $\rho_c\sim 2 \rho_{max}(t=0)$
($\rho_c\sim 1.2 \cdot 10^{15}$~$\text{g/cm}^3$), at which collapse
happens. As expected, we observe that model $\Gamma_{050}^{--}$ collapses
after approximately two quasiradial oscillations, model
$\Gamma_{025}^{--}$ after five, and  model $\Gamma_{025}^{++}$ after
twelve. Model $\Gamma_{050}^{++}$ survives for several dynamical timescales
and does not collapse until the end of the simulation ($t\sim 4000$~M.)
We have not evolved $\Gamma_{050}^{++}$ further since (i)~long-term
simulations can become inaccurate (see Appendix~\ref{app:tests}), and
(ii)~on these timescales other physical effects like magnetic fields
and neutrino cooling, presently not included, play an important role,
e.g.~\cite{Sekiguchi:2011mc,Paschalidis:2012ff,Hotokezaka:2013PhRvD..88d4026H,Deaton:2013sla}.
However, considering a linear trend in $\rho_{max}(t)$, we
extrapolate that collapse should happen at about $\sim167000$~M
($\sim272$~ms) after merger.

The lower panel of Fig.~\ref{fig:rhomax} refers to configurations
evolved with a polytropic EOS.
Since in this case thermal pressure support is absent, collapse
occurs much earlier than for the $\Gamma$-law EOS.
The HMNS of the irrotational configuration collapses after about
one quasiradial oscillation; model $P_{100}^{--}$ promptly collapses without
HMNS formation, and model $P_{100}^{++}$ collapses after few
oscillations.

During its evolution the HMNS oscillates nonlinearly and becomes
progressively more compact. The oscillations modes can be identified
as the quasiradial mode, the $m=2$ $f$-mode, and nonlinear
combinations of them, e.g.~\cite{Shibata:1999wm,Stergioulas:2011gd}.
A way to characterize nonlinear modes is to project the rest-mass
density onto spherical harmonics, e.g.~\cite{Baiotti:2008nf}. For
simplicity, we consider $\rho(x,y,z=0,t)$ in the orbital plane $z=0$ and
the projections~\cite{Stergioulas:2011gd}
\begin{equation}
\label{eq:rhom}
\rho_m(t) = \int  \rho(x,y,z=0,t) e^{i m \phi(x,y)} \text{d}x \text{d}y \ .
\end{equation}
In Fig.~\ref{fig:rhomode} we report the evolution of the first
projections $m=1,2,3,4$ for some representative runs.
The figure shows that the dominant mode is the $m=2$ mode.
Actually, the projection/mode with larger amplitude is the
quasiradial one ($m=0$, also visible in $\rho_{max}$
Fig.~\ref{fig:rhomax}). As we shall discuss later, however, this mode
has a frequency too low to be visible in the GW spectrum.
The evolution of $\rho_m(t)$ is qualitatively similar in the
different configurations, with differences only related to the
collapse time. A strong $m=1$ mode appears in \emph{all} simulations
before collapse (see e.g.~the central panel) and also
dominates the evolution of $\Gamma_{050}^{++}$ after $t\sim3500$~M.
We interpret it as a physical hydrodynamical effect due to mode
couplings, but we cannot rule out that it is triggered by some
numerical effect.

\begin{table}[t]
  \centering
  \caption{ \label{tab:fpeak}
    Peak frequencies of the power spectral density (PSD) of $\rho_m$
    and $\rho_{max}$. They are estimated by fitting a Gaussian of
    standard deviation $\sigma$. The value of the latter
    is reported in parenthesis.}
  \begin{tabular}{cccc}
    \hline
    & $m=0$ & $m=1$ & $m=2$ \\
    \hline
    $\Gamma_{000}$      & 584 (34) & 1543 (38) & 2974 (114) \\
    $\Gamma_{025}^{++}$ & 594 (34) & 1482 (38) & 2871 (103) \\
    $\Gamma_{050}^{++}$ & 671 (13) & 1341 (13) & 2738 (76) \\
   \hline
  \end{tabular}
\end{table}

In order to extract the mode frequencies, we perform a Fourier
analysis of the $\rho_m$ projections and $\rho_{max}$. The
quasiradial mode is best extracted from the latter. The Fourier
transform is performed only in the part of the signal after merger,
i.e.~$t>t_m$.
Some of the relevant results are summarized in
Fig.~\ref{fig:fourier}, where we show on the left the spectra of
$\rho_{max}$ for lower frequencies and $\rho_{2}$ for higher frequencies for
different models and on the right the spectrogram of
model $\Gamma_{050}^{++}$. Focusing on the left panel, we observe that
the spectrum is composed of few frequencies;  we identify $m=0,1,2$ modes
together with nonlinear couplings
``$2\pm0$''~\cite{Stergioulas:2011gd,Dimmelmeier:2005zk,Baiotti:2008nf}. For
model $\Gamma_{050}^{++}$ the highest power is actually found at the
``2-0'' frequency in $\rho_2$.

The peak frequencies for the different modes and models are stated in
Tab.~\ref{tab:fpeak} for the relevant case of spin aligned with the
orbital angular momentum.  The frequency peak of the $m=2$ mode
becomes larger the smaller the HMNS rotation is. This is because the
HMNS with more angular momentum support is less compact, and the proper
frequencies decrease if the compactness decreases (compare with
sequences of a single rotating star with the same rest mass
in~\cite{Dimmelmeier:2005zk}).
Notably, for model $\Gamma_{050}^{++}$ the observed frequency shift
with respect to the irrotational configuration is 236~Hz. The value is
significant at the $1$-$\sigma$ level, see Tab.~\ref{tab:fpeak}.
Differently from the $m=2$ mode, the frequency of the quasiradial
mode ($m=0$) is found to increase for HMNS with larger angular
momentum. As discussed in~\cite{Stergioulas:2011gd}, the quasiradial
mode frequency depends on the compactness of the HMNS and on how close
the star model is to the collapse-instability threshold.
The larger the compactness, the larger the mode frequency is; but
configurations close to the instability threshold can have smaller
frequencies since the instability threshold is a neutral point.
We interpret our results according to the above argument: HMNSs with
larger angular momentum support are further from collapse threshold and thus
have higher frequencies.

The spectra lines appear broad due to the highly dynamical nature of
the HMNS. Investigating the dynamical excitation of the modes by a
spectrogram, we find that
(i)~the modes are ``instantaneously'' characterized by relatively narrow peaks;
(ii)~different modes dominate different parts of the signal;
(iii)~some of the peaks ``drift'' towards higher frequencies as the
HMNS becomes more compact.
The right panel of Fig.~\ref{fig:fourier} shows the spectrogram of
the quantity $\rho_{12}(t)\equiv \rho_1(t)+\rho_2(t)$
for $\Gamma_{050}^{++}$.
At early times the $m=0$ (quasiradial) mode dominates the
$\rho_{12}$ spectrum, but around $t\sim2000$~M the $m=2$ becomes
the main oscillation
mode.  A ``drift'' of the $m=2$ mode towards higher frequencies is visible,
which corresponds to the fact that the HMNS becomes more compact.
The ``2-0'' coupling remains the secondary peak during the whole
simulation. The $m=3$ and ``2+0'' modes are also visible. At the very end of
the evolution the $m=1$ mode has the largest power.

\begin{table}[t]
  \centering
  \caption{ \label{tab:remnant}
      Important quantities for the merger remnant. Stated are the black hole mass, the dimensionless spin of
      the black hole, and the absolute disk mass of the surrounding disk as well as the percentage with respect
      to the total baryonic mass. }
  \begin{tabular}{l|cccc|ccc}
    \hline
    &  $\Gamma_{050}^{--}$ & $\Gamma_{025}^{--}$ & $\Gamma_{000}$ & $\Gamma_{025}^{++}$ & P$_{100}^{--}$ & P$_{000}$ & P$_{100}^{++}$ \\
    \hline
    $M_{BH}$             & 2.92  & 2.88  & 2.85  &  2.86  & 2.95  & 2.94  & 2.89 \\
    $\chi_{BH}$          & 0.80  & 0.79  & 0.78  &  0.79  & 0.81  & 0.83  & 0.84 \\
    $M_{\rm b,\ disk}$   & 0.039 & 0.068 & 0.081 &  0.082 & 0.006 & 0.021 & 0.065 \\
    $M_{\rm b,\ disk}/M_b$ & 1.2\% & 2.1\% & 2.5\% &  2.5\% & 0.2\% & 0.6\% & 2.0\% \\
   \hline
  \end{tabular}
\end{table}

Finally, we briefly discuss the black hole and the remnant disk.
All simulations (except $\Gamma_{050}^{++}$) result in a
black hole surrounded by a nonmassive accretion disk.
Tab.~\ref{tab:remnant} summarizes the irreducible mass and the
dimensionless spin of the black
hole, and the rest mass of the disk.
The black hole mass is larger for antialigned spin configurations and spin
magnitude, and a monotonic trend is observed for smaller spin and aligned
spin configurations. The opposite holds for the disk mass.
The spin of the black hole is larger for
aligned configurations in barotropic evolutions.
This effect is not visible in the $\Gamma$-law simulations, in which
the more massive disk probably has also larger angular momentum.
The maximum spin produced is $0.84$, which is consistent
with the upper limit found in~\cite{Kastaun:2013mv}.
Notice that all reported quantities are affected by large uncertainties, and
they should be considered only as a qualitative indication.
For example the uncertainty on the black hole mass calculated from
$L_2$ and $H$ runs of  the irrotational configuration is $\sim 0.01$.

\section{Gravitational radiation}
\label{sec:gws}

\begin{figure}[t]
  \centering
    \includegraphics[width=0.49\textwidth]{fig07.pdf}
    \caption{ \label{fig:EJRad} Energy (solid lines) and angular
      momentum (dashed lines) radiated in GWs for models
      $\Gamma_{050}^{--}$,$\Gamma_{000}$, and $\Gamma_{050}^{++}$.}
\end{figure}

\begin{figure*}[t]
  \centering
    \includegraphics[width=0.48\textwidth]{fig08a.pdf} \quad
    \includegraphics[width=0.48\textwidth]{fig08b.pdf}
    \caption{ \label{fig:waves} Gravitational wave
      signal for models $\Gamma_{050}^{--}$,
      $\Gamma_{000}$, and $\Gamma_{050}^{++}$.
      Left: Inspiral waveforms $\Re{(r\, h_{22})}$ and $r|h_{22}|$,
      and frequency $M \omega_{22}$.
      Right: Full signal $\Re{(r\, h_{22})}$.}
\end{figure*}

\begin{figure}[t]
  \centering
    \includegraphics[width=0.49\textwidth]{fig09.png}
    \caption{ \label{fig:HMNSgw} Fourier analysis of the $l=2$
      postmerger waveform multipoles and matter projection $\rho_2$
      for model $\Gamma_{050}^{++}$. The waveform frequencies strongly
      correlate with the fluid's modes.}
\end{figure}

The dynamics described in Sec.~\ref{sec:dyn} is relatively simple (but
far from trivial). For sufficiently high spin magnitudes,
$\chi\sim0.05$, the SO interaction is a significant repulsive
(attractive) contribution for aligned (antialigned) spins
configurations. For aligned configuration the SO competes with finite
size effects. At merger, however, binaries with aligned spins are more
bound. HMNSs are formed with more or less angular momentum support
than in the irrotational configuration ($j\sim\ell_m \pm 2\chi/\nu$);
thus they are either closer or farther from the collapse threshold
(radial instability point). We discuss in this section how the emitted
gravitational radiation encodes all this.

The total energy and angular momentum emitted in GWs quite differ in
the different models, as can be seen from Fig.~\ref{fig:EJRad}.
The irrotational configuration emits about $1.2\%$ of the initial ADM mass
and $18\%$ of the initial angular momentum. $\Gamma_{050}^{--}$ emits about
the same amount, but in about half the time. To the end of the
simulation, $\Gamma_{050}^{++}$ has emitted $0.8\%$ of the initial mass and
about $15\%$ of the initial angular momentum.  In all the cases, the
main emission channel is the $l=m=2$ multipole that alone accounts for
$\sim97\%$ of the emitted energy. However, in the postmerger phase
other channels are clearly excited; the largest amplitudes are
observed in the $l=2$, $m=0$, the $l=3$, $m=3,2$, and the $l=m=4$ modes
(in that order).

Figure~\ref{fig:waves} (left panel) shows the $l=m=2$ inspiral waveforms,
focusing again on the models $\Gamma_{050}^{--}$, $\Gamma_{000}$ and $\Gamma_{050}^{++}$
for clarity.
Intermediate results are of course found for the other models.
The upper-left panel shows the real part and amplitude of the $l=m=2$ mode
of the GWs, the lower-left panel the GW frequency
$M\omega_{22}=-\Im(\dot{h}_{22}/h_{22})$; note the retarded time in the $x$-axis.
The merger times, computed at the peak of $|rh_{22}|$, are
$t_m\sim595,\ 551,\ 636 M $ for $\Gamma_{000}$, $\Gamma_{050}^{--}$ and
$\Gamma_{050}^{++}$, respectively (see also
Tab.~\ref{tab:dynamics}). The peaks of the wave amplitude are all very
close to $\sim0.7$.
The GW frequency corresponding to the peak of the wave amplitude is
smallest for aligned spin.
At merger $M\omega_{22}\sim0.127,0.124,0.123$
for $\Gamma_{000}$, $\Gamma_{050}^{--}$, and $\Gamma_{050}^{++}$, respectively.
At contact instead $M\omega_{22}\sim0.069,0.067,0.071$. Note that
these frequencies have uncertainties of about $10\%$.
The effect of spin-orbit  interaction is clearly visible from the plot.
Computing the accumulated phase of the GW, we find that the
irrotational configuration emits 7.0 GW cycles to merger;
$\Gamma_{050}^{--}$ emits 6.3 cycles and $\Gamma_{050}^{++}$ emits 7.3 cycles.
This phase difference results from the dynamics discussed in
Sec.~\ref{sec:dyn1}, and encodes the interplay of spins and tidal
interactions.

Let us finally discuss the emission from the
HMNS. Figure~\ref{fig:waves} (right panel) shows the $l=m=2$ complete
waveform. The earlier the HMNS collapses, the larger the amplitude
of the wave in the postmerger phase is.
As also shown in
Fig.~\ref{fig:EJRad}, model $\Gamma_{050}^{--}$ emits more energy
and angular momentum than $\Gamma_{000}$ and $\Gamma_{050}^{++}$ during the
first $\sim600$~M after merger.
In order to identify the origin of the emission, we perform a Fourier
analysis of the $l=m=2$ and $l=2$ $m=0$ multipoles, and compare this with
the mode analysis of Sec.~\ref{sec:dyn2}. As in the previous section,
we consider only the signal at $t>t_m$.
A relevant example of this analysis is summarized in
Fig.~\ref{fig:HMNSgw}. The spectra of the waves and matter
modes strongly correlate: the HMNS modes are the main emitters during
the postmerger phase~\cite{Stergioulas:2011gd}.
We stress that the complete GW spectrum includes also the inspiral part
of the GW signal. In particular, the merger happens at GW frequencies of $\sim
1.2-1.3$~kHz, and, up to these frequencies, the spectrum is dominated
by the inspiral. Thus the quasiradial mode frequency of the HMNS is
not observable, whereas the $m=2$ and ``$2\pm0$'' peaks form the main
postmerger signal.

In~\cite{Oechslin:2007gn,Bauswein:2011tp} (see
also~\cite{Hotokezaka:2013PhRvD..88d4026H}) it is shown that the frequency of the
peak of the GW (postmerger) spectrum is strongly dependent on the
EOS, and, to a lesser extent, on the
total mass, mass ratio and spin. The latter aspect has been investigated by
comparing irrotational and corotational configurations for a few
models, and no significant frequency shift was observed.
The long wave train of model
$\Gamma_{050}^{++}$ allows us to resolve a significant frequency shift,
suggesting that spin effects may be more important
than previously thought. Note that a shift towards \emph{lower}
frequencies can favor GW detection by advanced interferometers.

\section{Conclusion}
\label{sec:conc}

We have studied BNS mergers in numerical relativity with a
realistic prescription for the spin. Consistent initial data have been
produced with the CRV approach and evolved for the first time.

We have considered moderate star rotations corresponding to
dimensionless spin magnitudes of $\chi=0.025, 0.05$,
and direction aligned or antialigned with the orbital angular
momentum. The dimensionless spins $\chi$ are estimated by considering
the angular momentum and masses of stars in isolation with the same
rotational state as in the binary. We have investigated the orbital
dynamics of the system by means of gauge invariant ${E}(\ell)$
curves~\cite{Damour:2011fu}.

Our simple proposal for the estimation of $\chi$ proved to be robust,
and allows us to show consistency with PN and EOB energy curves at
early-times. Using energy curves we have also compared, for the
first time to our knowledge, BNS and BBH dynamics
(see~\cite{Foucart:2013psa} for a waveform-based comparison of the
case BBH--mixed binary.) We extracted and isolated different
contributions to the binding energy, namely the point-mass nonspinning
leading term, the spin-orbit and spin-spin terms and the tidal term.
The analysis indicates that the spin-orbit contribution to the binding
energy dominates over tidal contributions up to contact (GW frequencies
$M\omega_{22}\sim0.07$) for $\chi\sim0.05$. The
spin-spin term, on the other hand, is so small that it is not well resolved in
the simulations. No significant couplings between tidal and spin-orbit
terms are found, even at a stage in which the simulation is in the
hydrodynamical regime (at this point, however, the interpretation of
``spin-orbit'' probably breaks down.)

The spin-orbit interactions significantly change the GW signal
emitted. During the three orbit evolution we observe an accumulated
phase differences up to $0.7$ GW cycles (over three orbits) between
the irrotation configuration and the spinning ones ($\chi=0.05$), that
is we obtain first quantitative results for orbital ``hang-up'' and
``speed-up'' effects. A precise modeling of the late-inspiral-merger
waveforms, as in~\cite{Bernuzzi:2012ci}, needs to include spin effects
even for moderate magnitudes.
Long-term (several orbits)
simulations are planned for a thorough investigation of this aspect,
together with detailed waveform phasing analysis and comparison with
analytical models. Extensive simulations with different EOSs will be
also important to check the universal relations recently proposed
in~\cite{Bernuzzi:2014kca}.

We have also investigated spin effects on the formation and collapse of the
merger remnants (HMNSs), and the hydrodynamical evolution the HMNS
modes~\cite{Stergioulas:2011gd}. The star rotation influences the
HMNS produced at merger by augmenting (aligned spin configuration) or
reducing (antialigned) the angular momentum support. Earlier or
delayed collapse of several milliseconds is thus observed depending
on the spins orientation.
We have found that characteristic frequencies of
the HMNS are shifted to \emph{lower} values by rotation. This suggest
that spin effects may be more important
than previously thought. HMNS modes are the main emitters of GWs in the
postmerger phase, and they may allow for a precise determination of the
neutron star radius in a GW detection~\cite{Bauswein:2011tp}. Extensive
evolutions of CRV configurations for various EOSs and spins are
needed in order to assess the role of spin and to obtain accurate
phenomenological relations for frequency vs.\ radius.

Future work should also be devoted to understanding the impact of our result on
GW astronomy.
We expect that some aspects of spin in BNS can be modeled similarly to the GW
analysis for nonprecessing spinning
BBHs~\cite{Ajith:2009bn,Hannam:2010ec,Santamaria:2010yb,Hannam:2007wf}.
Furthermore, it would be important to explore the
relevance of spin-orbit corrections in the construction of templates
for detecting the star's EOS~\cite{Damour:2012yf,Favata:2013rwa},
possibly applying realistic data analysis
settings~\cite{DelPozzo:2013ala}.
In the relevant case of aligned spin configurations, spin-orbit
effects actually compete with finite size effects.
One might expect that, for some realistic spin magnitudes, this could
affect the measurability of the
EOS (tidal polarizability parameters) when spin is not properly taken into
account. Similarly, if the spin is estimated from the early
inspiral, a bias in the spin magnitude could
significantly affect the measure of the tidal
parameters~\cite{Damour:2012yf}.

\begin{acknowledgments}
  It is a pleasure to thank Alessandro Nagar for valuable comments and
  interactions, and Simone Balmelli for providing us with the EOB
  curves. We are also grateful to Nathan Kieran Johnson-McDaniel and
  Andreas Weyhausen for interesting discussions.
  This work was supported in part by DFG Grant SFB/Transregio~7
  ``Gravitational Wave Astronomy'', the Graduierten-Akademie Jena,
  and NSF Grants PHY-1204334 and PHY-1305387.
  Simulations were performed on SuperMUC (LRZ) and JUROPA (JSC).
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Notes: Corner competition; Corralling Johnson
Drew Dougherty
Texans TV Host
Notes from the Texans' practice and locker room on Thursday at Reliant Stadium:
Corner playThe cornerback competition between Kareem Jackson and Jason Allen continues, as each has started multiple games this season. Jackson was the starter in Baltimore after returning from a knee injury, while Allen started against the Steelers and Raiders in Weeks 4 and 5. Both defensive coordinator Wade Phillips and Gary Kubiak weighed in on the pair after Thursday's practice.
"We're going to play guys in the game the way we need to play them," Phillips said.
Jackson played the majority of the snaps against Baltimore, but Kubiak elaborated on what Phillips said about both players seeing time against Tennessee.
"I think he'll play more," Kubiak said of Allen. "I do think Kareem played very well in the game and he continues to practice very well. They're going to both play and how it's going to pan out numbers-wise, we'll wait and see."
Improving the run game
After struggling on Sunday in Baltimore, Arian Foster said that he needed to play better. The 2010 All-Pro ball-carrier gained 49 yards on 15 carries. Foster and the Texans want to improve, but know that there's a long way to go before the season concludes.
"We had lulls last year and as a team, you're going to have lulls throughout the season," Foster said. "It's a long season, so we just got to not panic, do what we do and I think we'll be fine."
Kubiak also thinks the rushing attack will get better, and knows that Foster is only at the beginning.
"I think Arian's fine," Kubiak said. "My point is he's played in three games this year. Most of the guys that have played in three games are coming out of preseason and here we go, it's the regular season. Well we're in Week 7, so that's the difference. I don't want him to get frustrated and that's why I make that comment to ya'll and I've said the same thing to him."
Corralling Johnson2009 rushing champ Chris Johnson has struggled to regain the form of his first three seasons in the league, as he's only amassed 250 yards on 83 rushing attempts. He may have just a 3.0 yards per carry ratio, but the Texans defenders are still wary of what he can do to an opposing defense.
"You got to have everybody watching him all the time because he doesn't run the ball where the hole is all the time," Phillips said. "If it's not blocked here, go somewhere else. We don't want to get him started on a big game. That's for sure."
Nose tackle Shaun Cody also isn't discounting Johnson, despite the slow start to 2011.
"He could explode at any time," Cody said. "He's that kind of back who can make big plays happen. He's fast, makes something out of nothing and he's a very talented back. He's fast as heck so we got to definitely corral him."
"He's a home run hitter. Looks like the (Texas) Rangers need him." – Defensive coordinator Wade Phillips on the big-play ability of Titans' running back Chris Johnson.
"He's the head man, so if he says I played well, then I must have did alright." –Cornerback Kareem Jackson on hearing that Gary Kubiak said he played well in Baltimore.
Breakfast: DeAndre Hopkins' on Keke Coutee
All-Pro WR DeAndre Hopkins shared his early impressions of rookie WR Keke Coutee
Breakfast: Mathieu's expectations are changed
Tyrann Mathieu's been able to narrow his focus in his time with the Texans.
The Leftovers: Safeties, Sleepers & Rehabbers
Drew Dougherty answered fan questions about a variety of topics.

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Are you thinking of running for the LWN Committee? I do hope so! We're a great bunch of people who are working hard together to achieve equality for women in our party.
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Well let me clear up the first question right away: Yes Lady, you are good enough.
The right candidate is a trickier question. The answer is almost certainly yes. But it's probably not as simple as you think.
We're a working committee. As a very small and mostly voluntary led organisation we need people who can commit to delivering and can commit to spending time and effort on our projects. We want to continue to deliver at the high level we currently do. We'd like to do more – we'd always like to do more! How can you help us to do that?
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Сара Бальцер (;  3 квітня 1995 року) — французька фехтувальниця на шаблях, срібна призерка Олімпійських ігор 2020 року, призерка чемпіонату Європи.

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text:
Columns | Bob Bowman's East Texas
Hardin's East Texas Roots
by Bob Bowman
Most of us associate John Wesley Hardin--the man often called Texas' most famous gunfighter--with regions beyond East Texas, but the truth is that Hardin had deep roots in the pineywoods.
Born on May 26, 1853, at Bonham, Hardin was the son of John and Elizabeth Hardin. His father was a Methodist minister who named his son for the eighteenth century English religious leader, hoping that young John would become a preacher, too.
In 1861, while living with his parents at Sumpter in Trinity County, nine-year-old John Wesley first saw a man killed when John Rulf pulled a Bowie knife and slashed the jugular of Turner Evans during a property dispute.
Hardin later wrote about the incident: "If you wish to be successful in life, be temperate and control your passions."
But, six years later in a Sumpter schoolyard, Hardin's own passions erupted when he stabbed a fellow student twice in the chest and back, claiming the boy had accused him of writing a line of doggerel about a female student.
A year later, Hardin's passions flared again during a fight with a black man named Mage at a sugar cane mill near Moscow. Onlookers broke up the fight, but Hardin later shot and killed Mage on a lonely road near Moscow.
Learning that soldiers from the post-Civil War reconstruction government were looking for him, Hardin decided to hunt down his accusers. He ambushed and killed three soldiers at a creek crossing in Trinity County. Thus, by the age of fifteen, Hardin had already killed four men.
In 1871 Hardin went up the Chisholm Trail as a cowboy and reportedly killed seven people on the trail and another three when he arrived in Abilene, Kansas. After allegedly backing down Wild Bill Hickok, Hardin returned to Texas.
Clinging to his East Texas roots, he came back to the pineywoods on numerous occasions.
On a visit to Polk County relatives, he and a cousin rode to Trinity County, where they got into a gambling argument. Hardin was badly wounded and his friends shuffled him around East Texas until they reached Redland, a community near Lufkin.
There, Hardin was to recover at a friend's house, but his stay was brief. Two lawmen surprised him and wounded him again, but he killed both men with a shotgun.
Hardin knew he could run no further and sent the word to Cherokee County Sheriff Richard Reagan, an old friend, that he would surrender only to the lawman.
The sheriff and four deputies arrived the next day. As Hardin gave up his pistol, Reagan's deputies thought he was drawing on the sheriff. A shot rang out and Hardin was wounded a third time. Reagan carried Hardin to his hotel in Rusk, where two weeks of nursing by the sheriff's family saved his life.
After killing a deputy sheriff in Brown County, Hardin was captured in Florida, tried for murder and sentenced to 25 years in prison.
In prison, he studied the law, read theological books, and was superintendent of the prison's Sunday School. When he was pardoned in 1894, he was admitted to practice law.
In 1895, he moved to El Paso, but his old habits were hard to break. He look as his lover the wife of a client, Martin Morose. When Morose found out about the affair, Hardin hired several men, including Constable John Selman, to assassinate him.
On a hot August day in 1894, Selman, shot Hardin in the Acme Saloon because he was never paid for murdering Morose.
© Bob Bowman August 22, 2011 Column
More Bob Bowman's East Texas ›
A weekly column syndicated in 109 East Texas newspapers
More on John Wesley Hardin
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The Killing of John Wesley Hardin by Murray Montgomery
John Wesley Hardin Slept Here by Mike Cox
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text:
Vexillum (Latein, Plural vexilla) war ein Feldzeichen der römischen Armee. Als einziges der römischen Feldzeichen (signum) bestand das vexillum aus Stoff und ist daher Vorläufer heutiger Fahnen und Flaggen. Das viereckige Stück Stoff hing dabei von einem Querholz herab, das an einer Tragestange befestigt war. Das Fahnentuch war gewöhnlich rot gefärbt und zeigte zum Teil Inschriften und bildliche Darstellungen.

Verwendet wurde das vexillum von einer Vielzahl verschiedener Einheiten: zum einen von der Legionskavallerie (equites legionis) und Auxiliareinheiten, zum anderen auch von temporären Abordnungen (Detachementen), die dementsprechend auch als vexillatio betitelt wurden. Vermutlich war das vexillum aber auch eines der drei Hauptfeldzeichen der ganzen Legion, neben Legionsadler (aquila) und imago.

Das vexillum diente auch als Signalflagge oder wurde hochrangigen Offizieren als militärische Auszeichnung verliehen, so z. B. Marcus Agrippa.

Vexillarius
Das vexillum wurde vom vexillarius getragen (auch vexillifer genannt). Als vexillarii wurden jedoch auch Angehörige einer vexillatio bezeichnet sowie die Veteranen, die nach Ablauf ihrer eigentlichen Dienstzeit (sub aquila) ihren Reservedienst (sub vexillo) ableisteten. In vielen mittelalterlichen und frühneuzeitlichen Heeren entspricht dem vexillarius der Bannerherr.

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Römisches Feldzeichen
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text:
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Second, McGuire had just moved into a new apartment. The house across the street from the McGuires' house, in Perth Amboy, New Jersey, "was once the governor's home, and the governor was William.
"They had Tom Hanks and Jon Lovitz and Billy Crystal over to the house all the time," Zweibel said. "Lunatics" (2012), a novel co-written with Dave Barry; "Benjamin Franklin: Huge Pain in My ___".
Park Towne Place Apartments offers studio-3 bedroom rentals starting at $1389/ month. Park Towne Place Apartments is located at 2200 Benjamin Franklin.
Franklin Township is a civil township located in Portage County, Ohio, United States. It is located along the Cuyahoga River in Northeast Ohio.
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Jun 25, 2013. The Ben Franklin House has a particularly storied history. Places in 1982 before being renovated as 412 luxury rental apartments in 1990.
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May 8, 2006. I believe you're probably speaking of the Ben Franklin House apartments. It's now a fairly upscale rental property. Check out this link to confirm:.
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chilly January night in 2003, the Berley family was dining out for the last time before brother Eric returned to his philosophy studies at William & Mary the following day. Just over a year before, the Berleys had purchased a. Continue reading →
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So unless the House of Representatives votes to approve said gifts. in which the King of France gifted Benjamin Franklin a diamond-encrusted snuff box. Worries that Franklin could become corrupted.
Friends of murder victim Michael Shields didn't know what to do about the blood stain on the pavement outside his Amity Township apartment long after authorities. Shields resided in the 600 block.
"When doctors and dentists used to take cash," Feige told me, "they'd store up a hundred thousand dollars in the basement, then take it to Mexico and buy a house. image of the famously frugal.
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Grady said the project would "extend the vitality" of the area around Logan Square and the Benjamin Franklin Parkway. On a former empty lot on Callowhill Street, the 227-unit Granary apartment.
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Prior to the Gazette, local residents had to rely on Benjamin Franklin's Philadelphia newspaper. "If you look at the eastern side, you can see the outline of a two-story stone house, which is where.
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SNOW HILL — One of Greene County's favorite daughters was laid to rest Monday.
Jean Rouse Preston, a state legislator for 20 years, was buried at Fairview Cemetery in La Grange following a service at the chapel at Taylor-Tyson Funeral Service in Snow Hill. She died Jan. 10 from complications from a fall she suffered while on vacation in Waterbury, Conn.
Preston, from Emerald Isle, most recently represented Carteret, Craven and Pamlico counties in the N.C. Senate. She had decided against seeking re-election in 2012 to spend more time with her family.
Before retiring and moving to Emerald Isle — starting a career in politics — Preston was an educator. She graduated from East Carolina University in 1957 with a degree in business education, and taught business classes in Wilson and Greene counties, as well as Lenoir Community College. She later returned to ECU to receive her Master's degree in education in 1973.
Over the course of her career, she became Greene County director of reading for K-12 students and the program administrator for children with special needs.
"We knew that we could always have her ear," said Patrick Miller, Greene County superintendent of schools. "She would always listen, and she was very responsive. We would always, certainly, have something to talk about — even if we didn't agree on the issues we could talk about home. I would add that there were very few times we didn't agree on the issues. She was a very generous person. She was always quick with a smile and made you feel right at home."
Miller gave special thanks to the Rouse family foundation, of which Preston was a board member.
"The Rouse family has a foundation, and they were very generous with donating back to the Greene County community," Miller said. "They were very instrumental and made large donations for the Greene County Parks and Recreation complex, for the new gym floor and for new bleachers in the gym at Greene Central High School."
He added, "For that, we are more than grateful because there's no way we could have funded those projects without their help."
Before retiring, Preston served as the principal and director of education at the Barnes School at the Caswell Developmental Center.
But with retirement and the passing of husband Hugh Forbes Hardy, Preston moved to Carteret County, where she later married retired U.S. Army Col. John Edward Preston. She made her first run for the N.C. House of Representatives in 1992, serving seven terms before being elected to three terms in the N.C. Senate.
"She was helpful to me when I first got in the House," said N.C. Sen. Louis Pate, who first won election to the House in 1994. "She had served a term or so when I first got there, and she was very friendly towards me and most helpful, helping get my bearings as to what I was supposed to do and how you went about having your influence felt, and that sort of thing. I was lucky enough to be able to follow her over to the Senate and served this most recent term with her."
Pate said he admired her for her assistance to him and to his campaign, where Preston was "instrumental" to his efforts in Greene County in the 2010 Senate race.
In her six years in the Senate, Preston was the co-chair of the Senate Committee on Education/Higher Education and the Senate Appropriations Subcommittee on Education/Higher Education.
"Jean Preston was a pioneer in the field of special education who dedicated her life to ensuring our children have the brightest future possible," Senate President Pro Tempore Phil Berger, R-Rockingham, said in a statement. "As a legislator, Sen. Preston worked tirelessly on education reform and on achieving better results for our students. She was legendary in her district for an amazing work ethic and commitment to providing outstanding constituent service.
"Sen. Preston was a dear friend, and my colleagues and I will miss her greatly."


If two teams play at Madison Square Garden and no one is there to witness it, did the games actually occur?
That will be the quandary the Big East faces in 2014 if the league listens to the pleas of its basketball coaches and allows everyone into the conference tournament.
The Big East is convening this week in Florida and included in its crowded agenda, the conference is trying to hash out its future hoops tourneys. Next season it will actually shrink -- there will be 15 members of the Big East, but UConn, due to its APR punishment won't be able to participate, so that's a manageable 14-team membership.
And so on Monday night, the Garden would swing open its doors to … SMU versus Central Florida and DePaul versus Houston for a play-in game.
Would they sell tickets for that or just give Larry Brown and Oliver Purnell sandwich boards and bells and let them hand out tickets to unsuspecting tourists strolling down 8th Avenue?
We're all crying uncle here, so please stop.
Big East basketball already has watered down its product to an unrecognizable glob of mush. Let's not roll the tournament into the sewer, too.
We have endured the Tuesday night warm-up games for a few years now and while fans haven't left putting needles in their eyes, they haven't exactly been disappointed when the buzzer mercifully sounds.
But now we're talking about actual play-in games. Chances are, you'll see teams with abominable records whose only hope at the postseason is a national pandemic that afflicts only the top 100 basketball rosters in the country.
To paraphrase my friend, longtime Associated Press writer Jack Scheuer, it would be guaranteed VVVB hoops (very, very, very bad).
Worse, there is even a worry that the Garden might not be able to extend its commitment to Monday. The current contract does not give the league access until Tuesday and would consequently have to be renegotiated. If it couldn't be, the games would have to be played somewhere in the New York area.
What in heavens' name is the point of that?
A play-in game to make your conference tournament, played at some random outpost that looks like New York but isn't quite New York.
They can call it the Hoboken Opening Round.
Coaches long have argued that teams deserve the right for the "full tournament experience" and that keeping people out of the Big East tournament only gives itchy trigger-fingered administrators cause to fire a coach who can't get his team to New York.
Because finishing 18th out of 18 apparently merits a pay raise.
Sorry, this isn't pee-wee rec ball. Not everyone gets a trophy. Not everyone gets to play.
Besides, if you play a Big East tournament game and no one is there to see it, were you really there in the first place?