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\documentclass[journal]{rmaa}


\title{A reassessment of the kinematics of PV Cephei based\\ on accurate proper motion measurements}


\author{
L. Loinard,\altaffilmark{1} 
L.~F. Rodr\'iguez,\altaffilmark{1} 
L. G\'omez,\altaffilmark{2} 
J. Cant\'o,\altaffilmark{3} 
A.~C. Raga,\altaffilmark{4} 
A.~A. Goodman,\altaffilmark{5} 
and H.~G. Arce\altaffilmark{6}}   

\altaffiltext{1}{Centro de Radioastronom\'ia y Astrof\'isica, Universidad Nacional Aut\'onoma de M\'exico, Morelia, Mexico.}
\altaffiltext{2}{Max-Planck-Institut f\"ur Radioastronomie, Bonn, Germany (Member of the International Max Planck Research 
School for Astronomy and Astrophysics at the Universities of Bonn and Cologne).}
\altaffiltext{3}{Instituto de Astronom\'ia, Universidad Nacional Aut\'o\-noma de M\'exico, Mexico.}
\altaffiltext{4}{Instituto de Ciencias Nucleares, Universidad Nacional Aut\'onoma de M\'exico, Mexico.}
\altaffiltext{5}{Harvard-Smithsonian Center for Astrophysics, Cambridge, USA.}
\altaffiltext{6}{Yale University, New Haven, USA.}


\fulladdresses{
\item Laurent Loinard and Luis F. Rodr\'iguez: Centro de Radiostronom\'ia y Astrof\'isica, Universidad Nacional Aut\'onoma de M\'exico, 
Apdo. Postal 3-72 (Xangari), 58089 Morelia, Michoac\'an, Mexico (l.loinard,~l.rodriguez@crya.unam.mx).
\item Laura G\'omez: Max-Planck-Institut f\"ur Radioastronomie, Auf dem H\"ugel 69, 53121 Bonn, Germany (lgomez@mpifr.de).
\item Jorge Cant\'o: Instituto de Astronom\'ia, Universidad Nacional Aut\'onoma de M\'exico, Apdo. Postal 70-264, 04510 M\'exico, D. F., Mexico.
\item  Alejandro C. Raga:  Instituto de Ciencias Nucleares, Universidad Nacional Aut\'onoma de M\'exico, Apdo. Postal 70-543, 04510 M\'exico, D. F., 
Mexico (raga@nucleares.unam.mx).
\item Alyssa A. Goodman: Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA (agoodman@cfa.harvard.edu).
\item Hector G. Arce: Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520, USA (hector.arce@yale.edu).} 


\shortauthor{Loinard et al.}

\shorttitle{Proper Motions of PV Cep}

\listofauthors{L.~Loinard, L.~F.~Rodr\'iguez, L.~G\'omez, J.~Cant\'o, A.~C.~Raga, A.~A.~Goodman, \&amp; H.~G. Arce}

\indexauthor{Loinard, L.}
\indexauthor{Rodr\'iguez, L.~F.}
\indexauthor{G\'omez, L.}
\indexauthor{Cant\'o, J.}
\indexauthor{Raga, A.~C.}
\indexauthor{Goodman, A.~A.}
\indexauthor{Arce, H.~G.}


\SetVolume{46} 
\SetYear{2010}
\ReceivedDate{2010 June 15} 
\AcceptedDate{2010 August 2} 


\resumen{Presentamos dos observaciones de la estrella de pre-secuencia principal PV Cephei tomadas con el Very Large Array con una 
separaci\'on de 10.5 a\~nos. Estos datos implican que los movimientos propios de esta estrella son $\mu_\alpha \cos \delta=+10.9 \pm 3.0$~mas~a\~no$^{-1}$; 
$\mu_\delta=+0.2 \pm 1.8$~mas~a\~no$^{-1}$, muy similares a los ya conocidos para HD 200775, la estrella B2Ve que domina la iluminaci\'on 
de la cercana nebulosa de reflexi\'on NGC~7023. Este resultado sugiere que PV Cephei no es una estrella desbocada con movimientos r\'apidos, 
como se hab\'ia sugerido en anteriores estudios. La alta velocidad de PV Cep se hab\'ia inferido de los desplazamientos sistem\'aticos 
hacia el este de los bisectores de pares sucesivos de objetos Herbig Haro a lo largo de su chorro. Estos desplazamientos sistem\'aticos 
podr\'ian, en realidad, deberse a una asimetr\'ia en los mecanismos de eyecci\'on, o en la distribuci\'on del material circunestelar.\smallskip}
 
\abstract{We present two Very Large Array observations of the pre-main-sequence star PV Cephei, taken with a separation of 10.5~years. 
These data show that the proper motions of this star are $\mu_\alpha \cos \delta = +10.9 \pm 3.0$~mas~yr$^{-1}$; $\mu_\delta = +0.2 \pm 1.8$~mas~yr$^{-1}$, 
very similar to those --previously known-- of HD 200775, the B2Ve star that dominates the illumination of the nearby reflection nebula 
NGC~7023. This result suggests that PV Cephei is not a rapidly moving runaway star as suggested by previous studies. The large velocity 
of PV Cephei had been inferred from the systematic eastward displacement of the bisectors of successive pairs of Herbig Haro knots along 
its flow. These systematic shifts might instead result from an intrinsic asymmetry in the ejection mechanisms, or in the distribution of 
the circumstellar material.\medskip}


\addkeyword{astrometry} 
\addkeyword{ISM: individual (PV Cep)}
\addkeyword{ISM: jets and outflows}
\addkeyword{stars: pre-main sequence}


\begin{document}

\maketitle

\section{Introduction}


%%%%% TABLA 1

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{Characteristics of PV Cep}
\begin{tabular}{lcl}
\toprule
Spectral type &amp;  &amp; A5 \\
R-band magnitude &amp;  &amp; $R=11.1$ \\
Distance &amp;  &amp; $d=430^{+155}_{-91}$~pc \\
Mean position (Equinox J2000, &amp;  &amp; $\alpha=20^h 45^m 53\rlap.^{s}9550 \pm 0\rlap.^{s}0014$  \\
\,\,\,\,\,\,Epoch 2002.26) &amp;  &amp; $\delta=67^\circ 57{'} 38\rlap.{''}681 \pm 0\rlap.{''}008$ \\
\bottomrule
\label{tab:2}
\end{tabular}
\vspace{0.1cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Compact stellar clusters as well as multiple stellar systems with three or more members can be dynamically unstable (e.g., Valtonen \&amp; Mikkola 
1991; Poveda, Ruiz, \&amp; Allen 1967). Indeed, close few body encounters occurring within them can lead to the acceleration of one or more of the 
system members, which --if the acceleration is sufficient-- can escape their birthplace and become runaway stars. It is important to search for 
direct observational evidence of these energetic events, because if they occurred with sufficient frequency during the earliest stages of 
star-formation, they could have a significant impact on the very outcome of the star-forming process (Reipurth 2000). Arguably the most promising 
case so far, is that of the BN/KL region in Orion where three stars (including BN itself) are moving away at about 30~km~s$^{-1}$ from a common 
point of origin, which happens to be near the center of the massive KL outflow (Rodr\'iguez et al. 2005; G\'omez et al. 2005, 2008; Zapata et al. 
2009). The dynamical disruption in that case, appears to have occurred a mere 500 years ago.

Goodman \&amp; Arce (2004, hereafter GA2004) have suggested that the star PV Cephei (hereafter PV Cep) might be another potential candidate. PV Cep 
(Table~1) is a Herbig Ae/Be star (Li et al. 1994) that drives a well-studied giant Herbig Haro (HH) flow (Reipurth, Bally, \&amp; Devine 1997; G\'omez, 
Whitney, \&amp; Kenyon 1997; Arce \&amp; Goodman 2002a,b; GA2004). It is located about $1\rlap.{\arcdeg}5$ west of the reflection nebula NGC~7023, and the centroid 
velocity of its CO emission is similar to that of the CO emission from NGC~7023 itself (Cohen et al. 1981). Because of this shared kinematics, it 
is very likely that PV Cep and NGC~7023 are at the same distance from the Sun. The measured trigonometric parallax of HD~200775 (MWC 361, $V=7.4$~mag) 
the B2Ve star that dominates the illumination of NGC~7023 (Herbig 1960) yields a distance for the entire region of 430$^{+155}_{-91}$ pc (Perryman 
et al. 1997). This value is consistent with the somewhat older estimate of 500~pc used by GA2004. NGC~7023 is associated with a compact cluster 
of young stars that contains a number of low luminosity pre-main-sequence objects (Lepine \&amp; Rieu 1974).

The suggestion by GA2004 that PV Cep might be a runaway star was based on a careful analysis of the kinematics and morphology of the gas surrounding 
PV Cep. The strongest argument follows from a study of the distribution of successive pairs of HH knots located at nearly equal distances from PV Cep 
along its jet. The segments joining such successive pairs of knots are expected to pass through the source driving the flow --- if the latter is stationary. 
In the case of PV Cep, however, GA2004 found that the bisectors of the segments were systematically shifted eastward of the source, and increasingly 
more so, as older HH pairs were considered. This suggests that the source used to be somewhat to the east of its current position, and thus, that it 
is moving westward relative to its surroundings. Assuming that the HH knots along the flow are fully detached clumps, GA2004 estimated the velocity of 
the central source to be 22~km~s$^{-1}$ (see discussion in \S~2). Most remarkably, the velocity vector obtained by GA2004 points almost exactly {\em away} 
from NGC~7023, as if PV Cep had been ejected from NGC~7023 about 10$^5$~yr ago (see their Figure~6). Thus, PV Cep might indeed provide us with an example 
of a runaway star dynamically ejected from its (still identifiable) parent cluster. Note, however, that the conclusions of GA2004 were based on an 
analysis of the kinematics and morphology of the gas surrounding PV Cep, and {\em not} on a direct measurement of the relative proper motion between 
PV Cep and NGC~7023. In the present paper (\S\S~3 and 4), we will provide such a direct measurement, combining published optical proper motions of the 
brightest star in NGC~7023 and new radio measurements of the proper motion of PV Cep itself. 


\section{A re-analysis of the bisector results}

Several theoretical models (both analytic and numerical) have been proposed to explain the curved morphology presented by some HH jets. Cant\'o 
\&amp; Raga (1995) have developed an analytical model that treats the problem of a {\em steady} jet interacting with a sidewind. More recently, 
Masciadri \&amp; Raga (2001) presented numerical simulations of a {\em variable} jet in a sidewind and identified two different regimes. For low-amplitude 
variability (caused by moderate changes in the jet ejection velocity), small working surfaces (i.e., HH knots) are created along the jet, and they 
travel following the path predicted by the steady jet model of Cant\'o \&amp; Raga (1995). On the other hand, large working surfaces created by larger 
changes in the jet ejection velocity eventually become detached ``clumps'' that travel on somewhat straighter trajectories. 


\subsection{Analytic solution for fully detached clumps}

\vspace{0.05cm}

In their analysis of the bisectors of successive HH pairs, GA2004 assumed that the ejecta had become detached clumps, and integrated the equations 
of motion numerically to obtain the trajectory of the clumps. Recently, however, Cant\'o et al. (2008) showed that the idealized case of fully 
detached clumps has a completely analytic solution, which produces trajectories similar to those obtained in numerical simulation. To examine that 
analytic solution in the case of PV Cep, we assume (following GA2004) that PV Cep is moving relative to the ambient gas in a direction exactly 
perpendicular to that of its jet. The velocity of the star relative to the surroundings is taken to be $v_*$, and individual clumps of mass $M$ are 
ejected at a velocity $v_e$ (see Figure~\ref{fig:models}a for a schematic description). The trajectory is parametrized by a distance $s_0$ (Cant\'o 
et al. 2008) given by:
\begin{equation}
s_0 \equiv {3 \over 4} \left( {M v_0^4 \over \xi \rho_0 c^4} \right)^{1/3}\,.
\end{equation}

\vspace{0.15cm}

\noindent Here, $\xi$ is a constant of integration whose numerical value is $\xi=14$ (Cant\'o et al. 2008), $c$ is the isothermal sound speed of the clump 
material, and $\rho_0$ is the density of the ambient gas. In the present case, where $v_*$ and $v_e$ are perpendicular, $v_0$ is simply 
\begin{equation}
v_0 = \sqrt{v_*^2+v_e^2}\,. 
\end{equation}

\vspace{0.15cm}

\noindent If one further defines the angle $\theta$ as
\begin{equation}
\tan \theta = {v_e \over v_*}\,,
\end{equation}
the equation of the trajectory is given analytically by:
\begin{equation}
x = {y \over \tan \theta}-4s_0\left( {v_* \over v_0} \right) \left[ 1- \left( 1-{y \over s_0 \sin \theta}\right)^{1/4}\right]\,.
\end{equation}


%%%%%% FIGURA 1

\begin{figure}[!t]
\vspace{0.05cm}
\centering
\includegraphics[width=0.99\columnwidth]{lloinardfig1.eps}
\caption{(a) Schematic diagram of a star which ejects a bipolar outflow along the positive $x$-axis, in a direction 
perpendicular to the motion of the star with respect to the surrounding environment. In the frame of reference of 
the star, the environment moves towards the left along the $y$-axis, producing a curvature in the bipolar outflow 
system. (b) and (c) The black filled circles show the positions of the ejecta relative to the source according to 
the results of GA2004, and the dashed lines represent the best fit for fully detached clumps [Panel~(b); see \S~2.1] 
and for a continuous jet [Panel~(c); see \S~2.2].}
\label{fig:models}
\vspace{0.3cm}
\end{figure} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\vspace{0.15cm}

\noindent Following GA2004, we adopt  $v_e=350$~km~s$^{-1}$ and $\rho_0=1.5 \times 10^3$~cm$^{-3}$. A good fit to the data points (shown in Figure~\ref{fig:models}a) 
is obtained for $v_*=22$~km~s$^{-1}$, provided that $s_0 \approx 6.4 \times 10^{18}$~cm. This, in turn, implies $M \approx 2 \times 10^{-4}~M_\odot$ if the 
value for $c$ is taken to be 3.2~km~s$^{-1}$ as suggested by GA2004. A comparison between the analytic trajectory obtained using these parameters and the 
path obtained numerically by GA2004 (see their Figure~2) shows that the analytical and numerical trajectories agree extremely well.

It should be mentioned that $c$ in equation~(1) is the isothermal sound speed {\em of the ejecta}. Such ejecta are believed to be ionized, so 
the appropriate sound speed is $c \approx 10$~km~s$^{-1}$. In their analysis, however, GA2004 used $c=3.2$~km~s$^{-1}$, the typical velocity 
dispersion of the {\em ambient} molecular gas. From equation~(1), it is clear that to obtain a similar value of $s_0$ for $c=10$~km~s$^{-1}$ 
without resorting to unreasonable assumptions for $\rho_0$ and $v_0$, one has to increase the mass of the ejecta by nearly two orders of 
magnitude, to about $1.5 \times 10^{-2}~M_\odot$. Even if one allows $v_e$ to increase to 400~km~s$^{-1}$ and $\rho_0$ to decrease to 1000~cm$^{-3}$, 
the ejecta must still have masses of order $10^{-2}~M_\odot$. Moreover, the transverse velocity of the star must then be increased to about 40~km~s$^{-1}$ 
to obtain a good fit. We conclude that if the ejecta from PV Cep are indeed fully detached clumps of ionized gas, they must be very massive\footnote{As 
a consequence, in this scenario, PV Cep must have undergone episodes of extremely high accretion/ejection.}, and the velocity of PV Cep might be 
even larger that the 22~km~s$^{-1}$ proposed by GA2004.


\subsection{The HH knots of PV Cep as part of an underlying continuous jet}

The trajectories considered in \S~2.1 appropriately describe jets in which large amplitude perturbations leading to fully detached clumps have 
developed. As mentioned earlier, lower amplitude perturbations create HH knots that travel along different paths: those predicted by the analytical 
model of Cant\'o \&amp; Raga (1995). Moreover, the analysis of Masciadri \&amp; Raga (2001) shows that a smaller sidewind velocity is necessary to create 
a given jet curvature if the HH knots are such small perturbations along an underlying continuous jet than if they are fully detached clumps. 
Well-defined HH knots suggestive of detached clumps are certainly present along the jet driven by PV Cep (GA2004, and references therein). There 
is also evidence, however, for an underlying continuous jet which is always ``on''. Indeed, the very existence of steady, compact centimeter radio 
emission associated with PV Cep (which traces free-free emission from the base of an ionized flow; see \S~3 below) demonstrates that such a continuous 
jet exists and that the ejection of matter is not fully episodic. The detection of water masers (Marvel 2005) and of high velocity entrained molecular 
gas (Arce \&amp; Goodman 2002b) in the immediate vicinity of PV Cep confirm the existence of such a steady jet. Let us, therefore, estimate the sidewind 
velocity that would be required to explain the bisector results of GA2004 in a steady wind scenario. The applicability of this model to the specific 
case of PV Cep will be discussed in \S~5.

As shown by Cant\'o \&amp; Raga (1995), in the vicinity of the source, a bipolar flow in a sidewind approximately follows a parabolical shape\footnote{Farther 
out, the jet moves on nearly straight trajectories aligned with the direction of the side wind (Cant\'o \&amp; Raga 1995). Since the knots in PV Cep are 
clearly not moving perpendicularly to the direction of the jet (GA2004), the portion of the jet considered here can be assumed to be parabolic.} (with 
both the jet and the counterjet on the same parabola) described by
\begin{equation}
y={x^2\over 2\lambda}\,,
\label{zy}
\end{equation}
\noindent where $x$ is parallel to the initial outflow direction, and $y$ is the coordinate perpendicular to $x$ and parallel to the motion of 
the source (Figure~\ref{fig:models}a). This relation is valid for the case in which the motion of the source is perpendicular to the ejection. 
The distance $\lambda$ in equation~(\ref{zy}) is given by
$$\lambda \equiv \left({{\dot M} v_e^3\over \pi c^2\rho_0 v_*^2}\right)^{1/2}=~{\rm 7.8\times 10^{18}~cm}~~~~~~~~~~~~~~~~$$
$$\times \left({{\dot M}\over 10^{-7}~M_\odot~{\rm yr}^{-1}}\right)^{1/2} \left({v_e\over 100\,{\rm ~km\, s}^{-1}}\right)^{3/2}~~~~~$$
\begin{equation}
\times \left({\rho_0\over 10^3{\rm ~cm}^{-3}}\right)^{-1/2} \left({v_*\over 1\,{\rm ~km\,s}^{-1}}\right)^{-1}\,,~~~~~~~~~
\label{lam}
\end{equation}
\noindent where $\dot M$ is the mass-loss rate, and the other parameters have the same meaning as before. The best fit to the observed positions 
reported by GA2004 using equation~(\ref{zy}) yields $\lambda=4.64\times 10^{19}$~cm.  With this value, we can now use equation~(\ref{lam}) to 
determine the required velocity for the environment:
$$\left({v_*\over 1\,{\rm km\,s}^{-1}}\right)=0.17 \left({{\dot M}\over 10^{-7}{\rm ~M}_\odot{\rm yr}^{-1}}\right)^{1/2} ~~~~~~~~~~~~~~~ $$
\begin{equation} 
~~~~~~~~~~~~ \times \left({v_e\over 100\,{\rm ~km\, s}^{-1}}\right)^{3/2} \left({\rho_0\over 10^3{\rm ~cm}^{-3}}\right)^{-1/2}.
\label{va}
\end{equation} 
Finally, using the values $v_e=350$~km~s$^{-1}$ and $\rho_0=1500$~cm$^{-3}$ determined by GA2004, we obtain $v_*=0.9$~km~s$^{-1}$, assuming a mass 
loss rate ${\dot M}=10^{-7}~M_\odot$~yr$^{-1}$. The corresponding trajectory is shown in Figure~\ref{fig:models}c.


%%%%% FIGURA 2

\begin{figure*}[!t]
\centering
\includegraphics[width=0.92\textwidth]{lloinardfig2.eps}
\caption{VLA 3.6 cm images of PV Cep for 1997.03 (left) and 2007.50 (right). The contours are $-3$, 3, 4, 5, 6, 7, 
8, 10, 12 and 14 times 19 and 12~$\mu$Jy~beam$^{-1}$, the rms noise of the first and second epochs, respectively. 
The cross marks the position and positional error at the 1997.03 epoch. The half-power synthesized beam for each 
epoch ($0\rlap.{''}48 \times 0\rlap.{''}28$ ; PA = $+86^\circ$ for 1997.03 and $0\rlap.{''}30 \times 0\rlap.{''}24$; 
PA = $+39^\circ$ for 2007.50) is shown in the bottom left corner of the images.}
\label{fig:data}
\vspace{0.3cm}
\end{figure*}   

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Thus, a very modest relative motion --of the order of the typical stellar velocity dispersion in newborn stellar clusters-- between PV Cep and 
its surroundings would be required to explain the bisector results of GA2004 in the case of a continuous jet. We will return to this point in \S~5.


\section{Observations}

In this paper, we will make use of 3.6 cm continuum observations obtained on 1997 January 10 and 2007 July 2 with the Very Large Array (VLA) of 
the NRAO\footnote{The National Radio Astronomy Observatory is operated by Associated Universities Inc. under cooperative agreement with the National 
Science Foundation.} in its most extended (A) configuration. This combination of wavelength and configuration provides an angular resolution of 
about $0\rlap.{''}3$ for images with natural weighting.  The absolute amplitude calibrator was 1331+305 (with an adopted flux density of 5.20~Jy 
at 8.4~GHz) and the phase calibrator was 2022+616, with bootstrapped flux densities of $3.36\pm0.03$~Jy and $3.07\pm0.02$~Jy, for the first and 
second epochs, respectively. For the first epoch only 14 of the 27 antennas of the VLA were used, with an on-source integration time of 4.2~hours. 
For the second epoch we used 23 of the 27 antennas of the VLA, with an on-source integration time of 3.2~hours. The data were edited and calibrated 
using the Astronomical Image Processing System (AIPS) software package (Greisen 2003).

To ensure accurate astrometry, the position of the calibrator 2022+616 for the 1997 observations was updated to the refined position given in the 
VLA catalog of calibrators for 2007. The continuum images shown in Figure~\ref{fig:data} were used to measure the positions and flux densities of 
PV Cep for the two epochs (Table~2). The source appears to be unresolved at both epochs, and the emission is most probably free-free radiation from 
ionized gas at the base of the outflow driven by PV Cep (i.e., Eisl\"offel et al. 2000). The small variation in flux density between the two epochs 
is common for this type of sources (e.g., Galv\'an-Madrid, \'Avila, \&amp; Rodr\'iguez 2004), and most likely reflects moderate variability either of 
the mass-loss rate or of the velocity of the wind.  


%%%%% TABLA 2

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{Positions and Flux Densities for PV Cep}
\small
\begin{tabular}{cccc}
\toprule
&amp; \multicolumn{2}{c}{Position} &amp; 3.6 cm Flux \\
\cmidrule{2-3} 
Epoch   &amp; $\alpha$(J2000)                                 &amp; $\delta$(J2000)                                    &amp; Density (mJy) \\
\midrule
1997.03 &amp; $20^h 45^m 53\rlap.^{s}9449 \pm 0\rlap.^{s}0051$  &amp; $67^\circ 57{'} 38\rlap.{''}680 \pm 0\rlap.{''}017$ &amp; $0.14\pm0.02$ \\
2007.50 &amp; $20^h 45^m 53\rlap.^{s}9651 \pm 0\rlap.^{s}0014$  &amp; $67^\circ 57{'} 38\rlap.{''}682 \pm 0\rlap.{''}008$ &amp; $0.18\pm0.01$ \\
\bottomrule
\label{tab:1}
\end{tabular}
\vspace{0.1cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


As can be seen in Figure~\ref{fig:data} and Table~2, the source shows a small displacement ($\sim 0\rlap.{''}11$ toward the east. The proper motions 
of the source measured over the 10.47 year time baseline of the observations are $\mu_\alpha \cos \delta = +10.9 \pm 3.0$~mas~yr$^{-1}$; 
$\mu_\delta = +0.2 \pm 1.8$~mas~yr$^{-1}$. The base of the jet driven by PV Cep (as traced by the radio emission) is expected to follow closely the 
motion of the star itself, because the emission is largely dominated by the highest density gas in the wind, which is located very close to the star 
since the gas density typically falls as $n(r) \propto r^{-2}$. The high accuracy with which VLA observations of free-free emission from young stars 
can trace the stellar motions themselves can be seen, for instance, from the multi-epoch observations of IRAS~16293-2422 (Loinard et al. 2007; Pech 
et al. 2010) or of T Tau N (Loinard, Rodr\'iguez, \&amp; Rodr\'iguez 2003). Thus, the proper motions measured here can safely be assumed to represent the 
motion of PV Cep. 


\section{Results}

To test the proposal of GA2004 that PV Cep might be moving at $\sim 22$~km~s$^{-1}$ away from NGC~7023, one must compare the proper motion of 
PV Cep derived above with the proper motion of stars within NGC~7023. The only star of NGC~7023 (and indeed, the only star within a few degrees 
of PV Cep) for which we found reliable published proper motions is HD~200775, the bright star responsible for most of the illumination of 
NGC~7023 (see \S~1). Since it is the brightest member of the cluster, HD~200775 is likely to be very near its center of mass, and its proper 
motion should provide a good estimate of the proper motion of the entire cluster. The most recent reported proper motion for HD~200775 can be 
found in Ducourant et al. (2005)\footnote{Indeed, Ducourant et al. (2005) also report proper motions for PV Cep. However, their values of 
$\mu_\alpha \cos \delta=-3 \pm 7$~mas~yr$^{-1}$; $\mu_\delta=-14 \pm 7$~mas~yr$^{-1}$ have significantly larger errors than our measurements.}; 
they give $\mu_\alpha \cos \delta = +11 \pm 2$~mas~yr$^{-1}$; $\mu_\delta = +2 \pm 2$~mas~yr$^{-1}$. HD~200775 is also contained in the Hipparcos 
catalog, where the reported proper motions are $\mu_\alpha \cos \delta = +6.74 \pm 0.64$~mas~yr$^{-1}$; $\mu_\delta = -1.48 \pm 0.54$~mas~yr$^{-1}$. 
These two values are consistent with one another at the $1.5\sigma$ level.

The relative motion between PV Cep and NGC~7023 (obtained by subtracting the proper motion of PV Cep measured above from that of NGC~7023) is 
\begin{eqnarray}
\Delta ( \mu_\alpha \cos \delta) = +0.1 \pm 3.6~\mathrm{mas~yr}^{-1}\,, \nonumber \\ 
\Delta ( \mu_\delta) = +1.8 \pm 2.7~\mathrm{mas~yr}^{-1}\,, \nonumber
\end{eqnarray}
\noindent if the values quoted by Ducourant et al. (2005) are used. Using the Hipparcos figures, we obtain:
\begin{eqnarray}
\Delta ( \mu_\alpha \cos \delta) = - 4.2 \pm 3.1~\mathrm{mas~yr}^{-1}\,, \nonumber \\ 
\Delta ( \mu_\delta) = -1.7 \pm 1.9~\mathrm{mas~yr}^{-1}\,. \nonumber
\end{eqnarray}
\noindent Recall that GA2004 predicted a relative velocity of 22~km~s$^{-1}$ toward the west, corresponding to a relative proper motion (almost 
entirely in right ascension) of $\Delta ( \mu_\alpha \cos \delta) = + 9.3~\mathrm{mas~yr}^{-1}$. The observed values are inconsistent at the $3\sigma$ 
level with this prediction,\footnote{They are, of course, even more inconsistent with the relative velocity of 40~km~s$^{-1}$ obtained in the detached 
clump scenario assuming a sound speed of 10~km~s$^{-1}$ (see \S~2.1).} and show that PV Cep is in fact very nearly stationary relative to NGC~7023 
both in right ascension and declination. If anything, the Hipparcos value suggests a marginal motion of PV Cep {\it toward} NGC~7023. We conclude 
that PV Cep is very unlikely to have been ejected from NGC~7023 about $10^5$~yr ago.

Strictly speaking, the analysis of GA2004 does not require PV Cep to be moving away from NGC~7023 at 22~km~s$^{-1}$. It only requires PV Cep to be 
moving at that speed relative to its surrounding gas. The morphology of the jet driven by PV Cep could still be explained by the model proposed by 
GA2004 if the gas cloud in which PV Cep is embedded were moving at 22~km~s$^{-1}$ {\em toward the east} relative to both PV Cep and NGC~7023. We 
consider this possibility very unlikely, however, because (i) as mentioned in \S~1, the radial velocities of the gas associated with NGC~7023 and with 
PV Cep are very similar, and (ii) it is not clear what physical mechanism could accelerate an entire molecular cloud to 22~km~s$^{-1}$, particularly 
without also accelerating the stars that formed within it.


\section{Discussion}

Given that a relative velocity of 22~km~s$^{-1}$ between PV Cep and its surroundings appears to be inconsistent with the present observations, one 
must seek a different interpretation of the systematic east-ward shift of the bisectors of successive HH pairs along the flow driven by PV Cep. One 
obvious alternative possibility is provided by the continuous jet model presented in \S~2.2. In that scenario, a relative velocity between PV Cep 
and NGC~7023 of a few km~s$^{-1}$ would be sufficient to explain the bisector data, and such a small relative velocity would be fully consistent with 
the astrometry presented in \S~3. We note, indeed, that continuous jet models have been used to explain the curved morphologies of other young stellar 
flows. Of particular relevance is the case of the jet driven by HH 30 (L\'opez et al. 1995) whose curved shape was interpreted by Cant\'o \&amp; Raga (1995) 
in terms of such a continuous flow in a sidewind.

It is important to note, however, that the flow driven by PV Cep does show clear signs of strong variability (GA2004, and references therein). A 
steady jet is clearly present in the system, but the knots considered by GA2004 in their bisector analysis have likely been created during episodes 
of significantly increased mass-loss.\footnote{Note that the flow in HH 30 appears overall more continuous than that in PV Cep, and does lend itself 
more naturally to a treatment based on the hypothesis of a steady jet.} To completely describe that situation, one should consider a steady, low-level 
(i.e., moderate mass-loss rate) underlying jet, periodically undergoing episodes of enhanced mass-loss. This is a case intermediate between the two 
idealized descriptions provided in \S~2, so numerical simulations would in principle be needed to treat it in general. However, since the periodic 
mass-loss enhancements undergone by PV Cep seem particularly strong, the correct description for that specific source is almost certainly more similar 
to the case of detached bullets than to that of a continuous jet. In this situation, a relative velocity between PV Cep and its surroundings of at 
least 20~km~s$^{-1}$ would be needed to explain the bisector results of GA2004, and that appears to be inconsistent with our new measurements. 


%%%%% FIGURA 3

\begin{figure*}[!t]
\centering
\includegraphics[angle=-90,width=0.96\textwidth]{lloinardfigura3.ps}
\caption{Distribution of groups of HH knots around PV Cep. The three groups towards the north-west are 
labelled A, B, and C, and the three groups toward the south-east are D, E, and F. The positions are taken 
from G\'omez et al. (1997). (a) Model based on a symmetric precessing jet following G\'omez et al. (1997) 
with the parameters given in the text (solid black line). Lines joining the expected positions along the 
jet at times 6000, 7000, and 8000~yr are shown. (b) Model based on an asymmetric precessing jet with the 
parameters given in the text (solid black line). Lines joining the expected positions along the jet at 
4900 and 6900~yr are shown. They intercept the positions of the bisectors of the B-E and C-F pairs (shown 
as blue and red squares).}
\label{fig:precess}
\vspace{0.35cm}
\end{figure*} 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  


Another alternative interpretation of the bisector results of GA2004 would be to invoke asymmetries. The basic assumption behind the argumentation of 
GA2004 is that pairs of clumps ejected from a stationary star propagate symmetrically away from it, in such a way that the bisectors of such ejecta 
pairs intercept the driving source. This assumption would be violated, however, if the ejecta on the two sides of the star moved away at different 
speeds and/or not exactly in opposite directions, either because of an intrinsic asymmetry in the jet launching mechanism or because of an asymmetry 
in the density of the circumstellar material. Several jets (e.g., HH 1--2, Cepheus A, or HH 80; Rodr\'iguez et al. 2000; Mart\'i, Rodr\'iguez, \&amp; 
Reipurth 1998; Curiel et al. 2006) are known to exhibit this kind of asymmetries. Arguably the clearest case is that of the very young low-mass protostar 
IRAS~16293-2422 (Pech et al. 2010). In this object, a bipolar pair of clumps has been ejected just a few years ago, and each clump has now moved (in 
projection) about 60 AU away from the central source. Multi-epoch radio observations have shown that the projected speed of the southern clump is two 
to three times larger than that of the northern clump and that --in at least one of the observations-- the line joining the ejecta does not pass through 
the position of the driving source (Pech et al. 2010, particularly their Figure~2). In addition, the large-scale molecular outflow powered by that jet 
system is known to be highly asymmetric (e.g., Castets et al. 2001; Hirano et al. 2001), the northern lobe being much more conspicuous, massive, and 
extended that its southern equivalent. Interestingly, the molecular outflow in PV Cep happens to be equally asymmetric (e.g., Arce \&amp; Goodman 2002a) 
with a northern lobe about 2.5 times more massive and 1.5 times more extended than its southern counterpart. Could an asymmetry similar to that in 
IRAS~16293-2422 be at the origin of the PV Cep bisector results of GA2004?

Three pairs of HH groups have been identified along the jet driven by PV Cep: HH~315 A, B, and C towards the north-west, and HH~315 D, E, and F toward 
the south-east (e.g., G\'omez et al. 1997, see Figure~3). They are believed to have been created during three episodes of enhanced accretion/ejection 
(G\'omez et al. 1997; GA2004; Arce \&amp; Goodman 2002a). Moreover, these HH groups are not distributed along a straight line, but along an S-shaped 
structure, clearly resulting from precession in the underlying jet (Figure~3). A simple precessing jet model that reasonably accounts for that structure 
has been proposed by G\'omez et al. (1997) and is reproduced in Figure~3a. This model (e.g., Hjellming \&amp; Johnston 1981) assumes that the jet axis 
precesses on the surface of a cone of opening angle $\theta$, inclined by an angle $i$ from the line of sight. The jet has constant ejection velocity 
$v_e$ and precession velocity $\omega$, and the position angle of the precession axis is $\phi$. The black line on Figure~3a corresponds to $\theta=22.5^{\circ}$, 
$i=80^{\circ}$, $\omega=1.5$~arcmin~yr$^{-1}$, $v=180$~km~s$^{-1}$, and $\phi=-36.5^{\circ}$ (G\'omez et al. 1997). As discussed by G\'omez et al. (1997), 
this model shows that successive episodes of enhanced mass-loss occurred in PV Cep roughly every 2000 years. 

An asymmetry in the distribution of the HH groups is immediately apparent in Figure~3a. For instance, while the C-F pair is expected to have been 
created during the same enhanced mass-loss episode, the symmetric model shown in Figure~3a would ascribe to them ages differing by about 1000~yr. A 
similar situation occurs for the B-E pair. Of course, this age inconsistency is simply a different way of re-expressing the bisector conclusions 
of GA2004. Because of the asymmetry in the distribution of the HH groups, the segments joining C to F and B to E do not pass through the current 
position of the driving source. The situation can be significantly improved by relaxing slightly the symmetry of the jet. As an example, we show 
in Figure~3b a model identical to that of G\'omez et al. (1997) for the northern part of the flow, but slightly different for the southern counterpart. 
Specifically, the velocity of the southern jet is 10\% larger than that of the northern jet, and the southern half of the jet precesses around an 
axis misaligned by 10$^\circ$ relative to the symmetry axis of the northern jet. Such a model represents a somewhat better fit to the positions of 
the southern HH groups, and ascribes the same age to the B and E groups (4900~yr) and to the C and F groups (6900~yr). Moreover, the bisector of 
segments joining pairs of same-age positions on either sides of the jet are progressively displaced towards the east as larger ages are considered. 
In particular, the bisectors at ages 4900~yr and 6900~yr are very nearly coincident with the measured bisectors of the B-E and C-F pairs (Figure~3b).

The model shown in Figure~3b certainly represents an oversimplification of the true structure of the jet in PV Cep, and is clearly not unique. It 
does demonstrate, however, that a slightly asymmetric jet can provide a better description of the structure of the flow than a symmetric one, and 
could readily explain the bisector results of GA2004 with no need for a large stellar velocity. It would be interesting to investigate more realistic 
numerical models of bipolar jets encountering asymmetric surroundings. In particular, it would be useful to know in what domain of the parameter 
space they can produce bisector results similar to those found in PV Cep by GA2004. 

It is worth mentioning that the gas immediately south of PV Cep appears to be significantly denser than the gas immediately north of it (Arce \&amp; 
Goodman 2002a,b). Thus, one might expect the southern lobe to be slower than the northern lobe and not the other way around, as our asymmetric model 
would suggest. The distribution of the gas surrounding PV Cep, however, is likely to be quite asymmetric. For instance, knot C (to the north) is 
known to entrain a massive molecular gas shell, whereas no entrained gas is associated with its southern counterpart knot F (Arce \&amp; Goodman 2002a,b). 
This suggests that, on large scales, the density of molecular material north of PV Cep might be higher that south of it. This is reversed compared 
to the density distribution in the immediate surroundings of PV Cep. 

In addition to their bisector results, GA2004 mention two pieces of evidence supporting the idea that PV Cep might be a runaway star. The first one 
is the existence of a tail of red-shifted gas located to the east of PV Cep. The second is the wiggling of the southern jet seen at small scales. These 
two effects have not been reported in other outflow systems, and it is unclear if they have a direct relation to the asymmetry of the jet in PV Cep. 
It certainly would be worthwhile to search for these effects in other outflow systems (symmetric or not) and to investigate numerically in what kind 
of situation they would tend to develop.


\section{Conclusions}

Comparing two VLA observations separated by 10.5~years, we have measured the proper motion of the young star PV Cep. This measurement shows that PV Cep 
is essentially stationary with respect to its surroundings, and is not a fast-moving runaway star, as suggested by GA2004. The jet morphological 
characteristics that led GA2004 to conclude that PV Cep might be a runaway star might instead result from an asymmetry in the jet itself. GA2004 
had built a case against PV Cep reflected in the title of their paper: ``PV Cephei: young star caught speeding?'' Given the new evidence presented 
here, that accusation is now under question.

\vspace{0.1cm}

\acknowledgments 

LFR, LL, JC and ACR acknowledge the support of DGAPA, Universidad Nacional Aut\'onoma de M\'exico, and of Conacyt (Mexico).  L. G. was supported for 
this research through a stipend from the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn 
and Cologne. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

%\vspace{0.1cm}

\begin{thebibliography}

\renewcommand\baselinestretch{0.98}\small

\bibitem[Arce \&amp; Goodman(2002a)]{2002ApJ...575..928A} Arce, H.~G., \&amp; Goodman, A.~A. 2002a, \apj, 575, 928 

\bibitem[Arce \&amp; Goodman(2002b)]{2002ApJ...575..911A} \ibidrule 2002b, \apj, 575, 911 

\bibitem{ca95} Cant\'o, J., \&amp; Raga, A.~C. 1995, MNRAS, 277, 1120

\bibitem{ca08} Cant\'o, J., Raga, A.~C., Loinard, L., \&amp; Rodr\'iguez, L.~F. 2008, RexMexAA, 44, 381

\bibitem[Castets et al.(2001)]{2001A&amp;A...375...40C} Castets, A., Ceccarelli, C., Loinard, L., Caux, E., \&amp; Lefloch, B. 2001, \aap, 375, 40 

\bibitem[Cohen et al.(1981)]{1981ApJ...245..920C} Cohen, M., Kuhi, L.~V., Spinrad, H., \&amp; Harlan, E.~A. 1981, \apj, 245, 920 

\bibitem[Curiel et al.(2006)]{2006ApJ...638..878C} Curiel, S., et al. 2006, \apj, 638, 878 

\bibitem{du05} Ducourant, C., Teixeira, R., P\'eri\'e, J.~P., Lecampion, J.~F., Guibert, J., \&amp; Sartori, M.~J. 2005, A\&amp;A, 438, 769

\bibitem{e100} Eisl\"offel, J., Mundt, R., Ray, T.~P., \&amp; Rodr\'iguez, L.~F. 2000, in Protostars and Planets IV, ed. V. Mannings, A.~P. Boss, 
\&amp; S.~S. Russell (Tucson: Univ. Arizona Press), 815

\bibitem{GA2004} Galv\'an-Madrid, R., \'Avila, R., \&amp; Rodr\'iguez, L.~F. 2004, RevMexAA, 40, 31

\adjustfinalcols

\bibitem[G\'omez et al.(2005)]{2005ApJ...635.1166G} G\'omez, L., Rodr\'iguez, L.~F., Loinard, L., Lizano, S., Poveda, A., \&amp; Allen, C. 2005, \apj, 635, 1166 

\renewcommand\baselinestretch{0.993}\small

\bibitem[G\'omez et al.(2008)]{2008apj} \ibidrule 2008, \apj, 685, 333

\bibitem[G\'omez et al.(1997)]{1997AJ....114.1138G} G\'omez, M., Whitney, B.~A., \&amp; Kenyon, S.~J. 1997, \aj, 114, 1138 

\bibitem[Goodman \&amp; Arce(2004)]{2004ApJ...608..831G} Goodman, A.~A., \&amp; Arce, H.~G. 2004, \apj, 608, 831 (GA2004)

\bibitem[Greisen(2003)]{Gre03} Greisen, E.~W. 2003, in Information Handling in Astronomy: Historical Vistas, ed. A. Heck (Dordrecht: Kluwer), 109

\bibitem{he60} Herbig, G. 1960, ApJS, 4, 337 

\bibitem[Hirano et al.(2001)]{2001ApJ...547..899H} Hirano, N., Mikami, H., Umemoto, T., Yamamoto, S., \&amp; Taniguchi, Y. 2001, \apj, 547, 899 

\bibitem[Hjellming \&amp; Johnston(1981)]{1981ApJ...246L.141H} Hjellming, R.~M., \&amp; Johnston, K.~J. 1981, \apjl, 246, L141 

\bibitem{le74} Lepine, J. R. D., \&amp; Rieu, N. Q. 1974, A\&amp;A 36, 469

\bibitem[Li et al.(1994)]{1994ApJ...433..199L} Li, W., Evans, N.~J., II, Harvey, P.~M., \&amp; Colome, C. 1994, \apj, 433, 199 

\bibitem{bb} Loinard, L., Chandler, C.~J., Rodr\'iguez, L.~F., D'Alessio, P., Brogan, C., Wilner, D., \&amp; Ho, P. 2007, ApJ, 670, 1353

\bibitem{gg} Loinard, L., Rodr\'iguez, L.~F., \&amp; Rodr\'iguez, M.~I. 2003, ApJ, 587, L47

\bibitem[Lopez et al.(1995)]{1995MNRAS.274L..19L} L\'opez, R., Raga, A., Riera, A., Anglada, G., \&amp; Estalella, R. 1995, \mnras, 274, L19 

\bibitem[Marti et al.(1998)]{1998ApJ...502..337M} Mart\'i, J., Rodr\'iguez, L.~F., \&amp; Reipurth, B. 1998, \apj, 502, 337 

\bibitem[Masciadri \&amp; Raga(2001)]{2001AJ....121..408M} Masciadri, E., \&amp; Raga, A.~C. 2001, \aj, 121, 408 

\bibitem{dd} Marvel, K.~B. 2005, AJ, 130, 2732 

\bibitem[Pech et al.(2010)]{2010ApJ...712.1403P} Pech, G., et al. 2010, \apj, 712, 1403 

\bibitem[Perryman et al.(1997)]{1997AA...323L..49P} Perryman, M.~A.~C., et al. 1997, \aap, 323, L49

\bibitem[Poveda et al.(1967)]{1967BOTT....4...86P} Poveda, A., Ruiz, J., \&amp; Allen, C. 1967, Bol. Obs. Tonantzintla y Tacubaya, 4, 86 

\bibitem[Reipurth(2000)]{2000AJ1203177R} Reipurth, B. 2000, \aj, 120, 3177 

\bibitem[Reipurth et al.(1997)]{1997AJ....114.2708R} Reipurth, B., Bally, J., \&amp; Devine, D. 1997, \aj, 114, 2708 

\bibitem[Rodr\'iguez et al.(2005)]{2005ApJ...627L..65R} Rodr\'iguez, L.~F., Poveda, A., Lizano, S., \&amp; Allen, C. 2005, \apjl, 627, L65 

\bibitem[Rodr\'iguez et al.(2000)]{2000AJ....119..882R} Rodr\'iguez, L.~F., et al. 2000, \aj, 119, 882 

\bibitem[Valtonen \&amp; Mikkola(1991)]{1991ARAA299V} Valtonen, M., \&amp; Mikkola, S. 1991, \araa, 29, 9 

\bibitem[Zapata et al.(2009)]{2009ApJ...704L..45Z} Zapata, L.~A., Schmid-Burgk, J., Ho, P.~T.~P., Rodr\'iguez, L.~F., \&amp; Menten, K.~M. 2009, \apjl, 704, L45 


\end{thebibliography}


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