.
The Green Bank Observatory is a facility of the National Science Foundation 
operated under cooperative agreement by Associated Universities, Inc. 
The Arecibo Observatory is a facility of the National Science Foundation 
operated under cooperative agreement by the University of Central Florida 
in alliance with Yang Enterprises, Inc. and Universidad Metropolitana.

\textit{Software:} \texttt{enterprise} \citep{enterprise}, \texttt{PAL2} \citep{evh17a}, \texttt{PTMCMCSampler} \citep{evh17b}





\subsection{Signal and noise models}
\label{sec:signal}

Consider a GW source whose location in equatorial coordinates 
is given by declination $\delta$ and right ascension $\alpha$. 
It is convenient to write the sky position in terms of the polar angle $\theta$ 
and azimuthal angle $\phi$, 
which are related to $\delta$ and $\alpha$ by 
$\theta = \pi/2-\delta$ and $\phi = \alpha$.
The emitted GWs can be written in terms of two polarizations:
\begin{equation}
	h_{ab}(t,\hat{\Omega}) = e_{ab}^{+}(\hat{\Omega}) \; h_+(t,\hat{\Omega}) + e_{ab}^{\times}(\hat{\Omega}) \; h_\times(t,\hat{\Omega}) \,,
\end{equation}
where $\hat{\Omega}$ is a unit vector from the GW source to the Solar System barycenter (SSB), 
$h_{+,\times}$ are the polarization amplitudes, 
and $e_{ab}^{+,\times}$ are the polarization tensors. 
The polarization tensors can be written in the SSB frame as \citep{wahlquist1987}
\begin{eqnarray}
	e_{ab}^{+}(\hat{\Omega}) &=& \hat{m}_a \; \hat{m}_b - \hat{n}_a \; \hat{n}_b \,, \\
	e_{ab}^{\times}(\hat{\Omega}) &=& \hat{m}_a \; \hat{n}_b + \hat{n}_a \; \hat{m}_b \,,
\end{eqnarray}
where
\begin{eqnarray}
	\hat{\Omega} &=& -\sin\theta \cos\phi \; \hat{x} - \sin\theta \sin\phi \; \hat{y} - \cos\theta \; \hat{z} \,, \\
	\hat{m} &=& -\sin\phi \; \hat{x} + \cos\phi \; \hat{y} \,, \\
	\hat{n} &=& -\cos\theta \cos\phi \; \hat{x} - \cos\theta \sin\phi \; \hat{y} + \sin\theta \; \hat{z} \,.
\end{eqnarray}
The response of a pulsar to the source is described by the antenna pattern functions $F^+$ and $F^\times$ \citep{sv2010,esc2012,thg+2016},
\begin{eqnarray}
	F^+(\hat{\Omega}) &=& \frac{1}{2} \frac{(\hat{m} \cdot \hat{p})^2 - (\hat{n} \cdot \hat{p})^2}{1+\hat{\Omega} \cdot \hat{p}} \,, \\
	F^\times(\hat{\Omega}) &=& \frac{(\hat{m} \cdot \hat{p}) (\hat{n} \cdot \hat{p})}{1+\hat{\Omega} \cdot \hat{p}} \,,
\end{eqnarray}
where $\hat{p}$ is a unit vector pointing from the Earth to the pulsar.

The effect of a GW on a pulsar's residuals can be written as
\begin{equation}
	s(t, \hat{\Omega}) = F^+(\hat{\Omega}) \; \Delta s_+(t) + F^\times(\hat{\Omega}) \; \Delta s_\times(t) \,,
\end{equation}
where $\Delta s_{+,\times}$ is the difference between the signal induced at the Earth and at the pulsar 
(the so-called ``Earth term'' and ``pulsar term''), 
\begin{equation}
	\Delta s_{+,\times}(t) = s_{+,\times}(t_p) - s_{+,\times}(t) \,,
\end{equation}
where $t$ is the time at which the GW passes the SSB and $t_p$ is the time at which it passes the pulsar. 
From geometry, we can relate $t$ and $t_p$ by
\begin{equation}
	t_p = t - L (1 + \hat{\Omega} \cdot \hat{p}) \,,
	\label{eq:pulsar_time}
\end{equation}
where $L$ is the distance to the pulsar.

For a circular binary, at zeroth post-Newtonian (0-PN) order, $s_{+,\times}$ is given by \citep{wahlquist1987,lwk+2011,cc2010}
\begin{eqnarray}
	s_+(t) &=& \frac{\mathcal{M}^{5/3}}{d_L \, \omega(t)^{1/3}} \left[ -\sin 2\Phi(t) \, \left(1+\cos^2i\right) \, \cos2\psi \right. \nonumber \\
			&& \left. - 2 \cos 2\Phi(t) \, \cos i \, \sin 2\psi \right] \,, \label{eq:signal1} \\
	s_\times(t) &=& \frac{\mathcal{M}^{5/3}}{d_L \, \omega(t)^{1/3}} \left[ -\sin 2\Phi(t) \, \left(1+\cos^2i\right) \, \sin2\psi \right. \nonumber \\
			&& \left. + 2 \cos 2\Phi(t) \, \cos i \, \cos 2\psi \right] \,, \label{eq:signal2}
\end{eqnarray}
where $i$ is the inclination angle of the SMBHB, $\psi$ is the GW polarization angle, 
$d_L$ is the luminosity distance to the source, 
and $\mathcal{M} \equiv (m_1 m_2)^{3/5}/(m_1+m_2)^{1/5}$ 
is a combination of the black hole masses $m_1$ and $m_2$ 
called the ``chirp mass.'' 
Note that the variables $\mathcal{M}$ and $\omega$ are the observed redshifted values, 
which are related to the rest-frame values $\mathcal{M}_r$ and $\omega_r$ according to
\begin{eqnarray}
	\mathcal{M}_r &=& \frac{\mathcal{M}}{1+z} \,, \\
	\omega_r &=& \omega (1+z) \,.
\end{eqnarray}
Currently PTAs are only sensitive to sources in the local Universe for which $(1+z) \approx 1$.

For a circular binary, 
the orbital angular frequency is related to the GW frequency by $\omega_0 = \pi f_\mathrm{gw}$, 
where $\omega_0 = \omega(t_0)$. 
For our search, we defined the reference time $t_0$ as 31 December 2015 (MJD 57387), 
which corresponded to the last day data were taken for the 11-year data set. 
The orbital phase and frequency of the SMBHB are given by \citepalias{abb+14}
\begin{eqnarray}
	\Phi(t) &=& \Phi_0 + \frac{1}{32} \mathcal{M}^{-5/3} \left[ \omega_0^{-5/3} - \omega(t)^{-5/3} \right] \,, \\
	\omega(t) &=& \omega_0 \left( 1 - \frac{256}{5} \mathcal{M}^{5/3} \omega_0^{8/3} t \right)^{-3/8} \,,
\end{eqnarray}
where $\Phi_0$ and $\omega_0$ are the initial orbital phase and frequency, respectively. 
Unlike in \citetalias{abb+14}, we used the full expression for $\omega(t)$ in our signal model 
rather than treating the GW frequency at the Earth as a constant, 
as high-chirp-mass binaries will evolve significantly over the timescale of our observations. 

Our noise model for individual pulsars included both white noise and red noise. 
We used the same white noise model as \citetalias{abb+14}, 
which has three parameters: EFAC, EQUAD, and ECORR. 
The EFAC parameter scales the TOA uncertainties, 
and the EQUAD parameter adds white noise in quadrature. 
The ECORR parameter describes additional white noise 
added in quadrature that is 
