\documentclass[journal]{rmaa}


\title{Compact radio sources in the vicinity of the ultracompact HII region G78.4+2.6}

\author{Citlali Neria, Yolanda G\'omez, and Luis F. Rodr\'iguez 
\affil{Centro de Radioastronom\'ia y Astrof\'isica\\ Universidad Nacional Aut\'onoma de M\'exico, Morelia, Mexico}}


\fulladdresses{
\item Citlali Neria, Yolanda G\'omez, 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 (c.neria, y.gomez, l.rodriguez@crya.unam.mx).}
 

\shortauthor{Neria, G\'omez, \& Rodr\'iguez}

\shorttitle{Compact radio sources in the vicinity of G78.4+2.6}


\listofauthors{C.~Neria, Y.~G\'omez, \& L.~F.~Rodr\'iguez}

\indexauthor{Neria, C.}
\indexauthor{G\'omez, Y.}
\indexauthor{Rodr\'iguez, L.~F.}


\SetVolume{46} 
\SetYear{2010}
\ReceivedDate{2010 January 26} 
\AcceptedDate{2010 June 4} 


\resumen{Utilizando el Very Large Array (VLA) a 3.6~cm, hemos identificado cuatro nuevas fuentes compactas de radio en los alrededores de la 
regi\'on HII con morfolog\'ia cometaria G78.4+2.6 (VLA~1). Las cuatro fuentes compactas de radio (denominadas VLA~2 a 5), tienen contrapartes 
en el infrarrojo cercano, como se muestra en la imagen del Spitzer a 3.6~$\mu$m. Una de estas fuentes (VLA~5) claramente muestra evidencia de 
radio-variabilidad en una escala de tiempo de horas. Hemos explorado la posibilidad de que estas radio-fuentes est\'an asociadas con estrellas 
de pre-secuencia principal (PMS) en la vecindad de la regi\'on HII ultracompacta G78.4+2.6. Nuestros resultados favorecen una distancia corta 
de 1.7~kpc para G78.4+2.6. Adem\'as de la detecci\'on de radio-fuentes en los alrededores de G78.4+2.6, detectamos otro grupo de cinco fuentes, 
localizado aproximadamente $3'$ al noroeste de la regi\'on HII. Algunas de estas fuentes presentan emisi\'on extendida.\vspace{0.2cm}} 
 
 
\abstract{Using the Very Large Array (VLA) at 3.6~cm we identify four new compact radio sources in the vicinity of the cometary HII region 
G78.4+2.6 (VLA~1). The four compact radio sources (named VLA~2 to VLA~5), have near-infrared counterparts, as seen in the 3.6~$\mu$m Spitzer 
image. One of them (VLA~5) clearly shows evidence of radio variability in a timescale of hours. We explore the possibility that these radio 
sources are associated with pre-main sequence (PMS) stars in the vicinity of the UC HII region G78.4+2.6. Our results favor the smaller distance 
value of 1.7 kpc for G78.4+2.6. In addition to the detection of the radio sources in the vicinity of G78.4+2.6, we detected another group of 
five sources which appear located about $3'$ to the northwest of the HII region. Some of them exhibit extended emission.\vspace{0.33cm}}


\addkeyword{HII regions}
\addkeyword{ISM: individual (G78.4+2.6, IRAS~20178+4046)}
\addkeyword{radio continuum: stars}


%\RescaleTitleLengths{0.99}


\begin{document}


\maketitle


\section{Introduction}

Although our understanding of star forming regions has progressed in recent years, many aspects of the early evolution stages are still unclear. 
Observationally, pre-main sequence (PMS) stars are among the most difficult to study because they are usually heavily obscured by their parental 
molecular cloud. Observations at radio wavelengths of young clusters are of considerable relevance because a fraction of these stars appear to be 
undetectable even in the infrared. In this sense radio observations can provide unique information. Radio clusters of non-thermal PMS stars have 
been found in several star forming regions. G\'omez et al. (2000, 2002) reported centimeter wavelength observations of the GGD14 star forming region. 
In this study, they found a radio cluster of PMS stars made of eight extremely compact and faint  radio sources around a compact HII region that 
seems to be ionized by a B0.5 zero age main sequence (ZAMS) star. Similar radio clusters have been studied toward HH~124~IRS by Reipurth et al. 
(2002), NGC~2024 (Orion B) by Rodr\'iguez, G\'omez, \& Reipurth (2003) and toward the Orion Nebula (M42) by Zapata et al. (2004), among others. 
Some members of the radio clusters mentioned above are characterized by compact non-thermal emission, time variability, and in some cases circular 
polarization. All these characteristics suggest that most likely their radio emission is due to the gyrosynchrotron mechanism from an active 
magnetosphere in a PMS star (e.g. G\'omez et al. 2002).

\vspace{0.07cm}

The identification of more such PMS clusters can provide valuable information of the star forming processes. Here we present the identification 
of new members that surround the HII region G78.4+2.6. This is an ultracompact (UC) HII region whose estimated kinematic distances range from 1.7~kpc 
(Wilking et al. 1989; Schneider et al. 2006) to 3.3~kpc (Kurtz, Churchwell, \& Wood 1994). It has a cometary morphology (Kurtz et al. 1994) and it is 
associated with the IRAS source 20178+4046 with a far-infrared luminosity of $7 \times 10^4~L_\odot$ (assuming a distance of 3.3~kpc). From the radio 
continuum emission the HII region seems to be ionized by a B0--B0.5 ZAMS star (Kurtz et al. 1994; Tej et al. 2007). No maser emission of OH (6035~MHz), 
H$_2$O (22.2~GHz) or CH$_3$OH (6.7~GHz) or thermal emission of NH$_3$ (23.6--23.9~GHz) has been detected toward this region (Baudry et al. 1997; 
Codella, Felli, \& Natale 1996; Kurtz \& Hofner 2005; Sunada et al. 2007; Slysh et al. 1999). In the mid-infrared images the UC HII region appears 
single (Crowther \& Conti 2003), but the presence of a stellar group/cluster around it is clear in the near-infrared images (Tej et al. 2007). 

\vspace{0.07cm}

Recently, Tej et al. (2007) presented a multiwavelength study toward IRAS~20178+4046. They used the Giant Metrewave Radio Telescope (GMRT) 
to map the radio continuum emission at 1280 and 610~MHz. Available archival data from the Two Micron All Sky Survey (2MASS), the Midcourse 
Space Experiment (MSX), and the James Clerk Maxwell Telescope (JCMT) were used to study the complex in the near-infrared (NIR) $JHK$ bands, 
the mid-infrared at 8.3, 12.13, 14.65 and 21.34~$\mu$m and the sub-mm at 450 and 850~$\mu$m, respectively. From their analysis of the NIR 
2MASS data, they proposed the presence of nine early type sources with spectral types $\sim$ B0.5 or earlier around IRAS~20178+4046. Their 
multiwavelength study led Tej et al. (2007) to conclude that a scenario with possible different evolutionary stages of star formation is 
present toward IRAS~20178+4046 (G78.4+2.6).  

\vspace{0.07cm}

In this paper we present sensitive high resolution radio continuum observations at 3.6~cm in order to search for faint compact radio continuum 
sources around this UC HII region. 


%%%%% FIGURA 1

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{cneriafig1.eps}
\caption{Contour image of the 3.6~cm continuum emission from the UC HII region G78.4+2.6. The contours are 
--3, 3, 4, 6, 8, 10, 15, 30, 50, 70, 100, 120, 150, 180 and 200 times 10~$\mu$Jy~beam$^{-1}$, the rms noise 
of the image. The synthesized beam  ($0\rlap.{''}76 \times 0\rlap.{''}67$ with a position angle of $-79^{\circ}$) 
is shown in the bottom left corner of the image. The dynamic range achieved in the 3.6~cm image is approximately 
200. The crosses mark the peak position of the 3.6~cm radio sources VLA~1 and VLA~4. The triangles mark the 
positions of the NIR sources number 1 (bottom left) and number 2 (top right) of Tej et al. (2007).}
\label{fig1}
\vspace{0.3cm}
\end{figure}

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


%%%%%% FIGURA 2

\begin{figure*}[!t]
\centering
\includegraphics[width=13cm]{cneriafig2.eps}
\caption{The image shows the Spitzer 3.6~$\mu$m band emission in color for the region around G78.4+2.6. Color scale 
goes from $-0.15$ to 0.95~GJy~sr$^{-1}$. The contours represent the 3.6~cm continuum emission from G78.4+2.6 showing 
the four compact radio sources. The contours are --5, 5, 10, 15, 30, 50, 70 and 90 times 10~$\mu$Jy~beam$^{-1}$, the 
average rms noise of the image. The crosses mark the peak position of the 3.6~cm radio sources listed in Table~1. 
The synthesized beam is $0\rlap.{''}76 \times 0\rlap.{''}67$ with a position angle of $-79^{\circ}$.}
\label{fig2}
\vspace{0.55cm}
\end{figure*}

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


\section{Observations}

G78.4+2.6 was observed with the VLA of the NRAO\footnote{The National Radio Astronomy Observatory (NRAO) is operated by Associated Universities 
Inc. under cooperative agreement with the National Science Foundation.} at 3.6~cm (8.4~GHz) in the B configuration during 2002 August 6 and 7 
for a total on-source time of $\sim 10$ hrs. The data were taken using two IFs each with an effective bandwidth of 50~MHz and both circular 
polarizations. The flux density scale was determined from observations of the amplitude calibrator 1331+305, for which we assumed a flux density 
of 5.22 and 5.20 Jy, for IF=1 (8.4351 GHz) and IF=2 (8.4851 GHz), respectively. The source 2007+404 was used as the phase calibrator, with 
bootstrapped flux densities of $2.704 \pm 0.003$ and $2.708 \pm 0.003$~Jy for the first and second IF, respectively. The data were edited and 
calibrated using the standard procedures of the Astronomical Image Processing System (AIPS) of NRAO. The data were also self-calibrated in phase 
and for sources far away from the center we applied a primary beam correction to the images (with the task PBCOR). The synthesized beam is 
$0\rlap.{''}76 \times 0\rlap.{''}67$ with a position angle of $-79^{\circ}$, and the rms noise is 10~$\mu$Jy~beam$^{-1}$. 


%%%%% TABLA 1
  
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabnotewidth}{0.99\textwidth} 
\setlength{\tabcolsep}{0.94\tabcolsep}
\tablecols{8}
\caption{Parameters of the radio sources toward G78.4+2.6}
\small
\begin{tabular}{cccccccc}
\toprule
Source & $\alpha$(2000) & $\delta$(2000) & Flux Density\tabnotemark{a} & NIR Counterpart & \multicolumn{2}{c}{Spitzer Counterpart\tabnotemark{b}} & Time \\ 
       &                &                & (mJy)                       & (2MASS~PSC)     & $\alpha$(2000)    & $\delta$(2000)                     & Variable? \\
\midrule
VLA~1 & 20 19 39.224  & 40 56 36.53 & 62.26$\pm$0.14                 & 20193932+4056358\tabnotemark{d} & 20 19 39.12 & 40 56 37.84 & N \\
VLA~2 & 20 19 37.475  & 40 55 44.11 & ~0.06$\pm$0.02                 & 20193748+4055441~               & 20 19 37.48 & 40 55 44.14 & N \\
VLA~3 & 20 19 39.318  & 40 57 01.91 & ~0.11$\pm$0.02                 & 20193931+4057018~               & 20 19 39.34 & 40 57 01.85 & N \\
VLA~4 & 20 19 39.599  & 40 56 31.98 & ~0.48$\pm$0.02                 & 20193949+4056305\tabnotemark{e} & 20 19 39.56 & 40 56 32.18 & N \\
VLA~5 & 20 19 40.630  & 40 56 20.57 & ~~0.24$\pm$0.02\tabnotemark{c} & --                              & 20 19 40.64 & 40 56 20.19 & Y \\
\bottomrule
\noalign{\smallskip}
\tabnotetext{a}{Flux densities at 3.6~cm. The flux densities for sources VLA~2 to 5 were measured from an image where extended 
emission was suppressed using only ($u$, $v$) data with baselines larger than 100~k$\lambda$.}  
\tabnotetext{b}{Peak position associated with the 3.6~$\mu$m Spitzer image.}
\tabnotetext{c}{Time-averaged flux density.}
\tabnotetext{d}{NIR source number 2 of Tej et al. (2007).}
\tabnotetext{e}{NIR source number 1 of Tej et al. (2007).}
\label{tab:1}
\end{tabular}
\vspace{-0.1cm}
\end{table*}

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


\section{Results}

\subsection{Compact radio sources toward G78.4+2.6}

Figures~1 and 2 show the radio continuum emission at 3.6~cm toward the UC HII region G78.4+2.6. In addition to the UC HII region, which we 
hereafter call VLA~1, it is possible to identify emission from four fainter compact radio continuum sources above the $5\sigma$ level; they 
are called VLA~2 through VLA~5 by us. Figure~1 shows VLA~1 and the compact source VLA~4, which appears inside the extended emission region 
of the cometary source VLA~1. The source VLA~4 could be physically embedded in the cometary HII region. Unfortunately, our data do not have 
enough angular resolution to ascertain the nature of this radio source. Figure~2 exhibits a larger area where all the compact radio sources 
in the vicinity of VLA~1 can be identified.
 
For these compact sources, we looked for near-infrared counterparts using the Spitzer 3.6~$\mu$m band image and the 2MASS Point Source 
Catalog (PSC), within a radius of $2''$ around each VLA source. The parameters of the radio continuum sources, and their possible 
counterparts, are listed in Table~1. Of the nine NIR 2MASS sources reported by Tej et al. (2007), only one (source 2) clearly coincides 
in position with a VLA source (VLA~1). There is another NIR source reported by Tej (source number 1) that could be associated with a VLA 
source (VLA~4; within 1$\rlap.{''}$5). In Figure~1 we plot the peak position of the NIR source number 1 of Tej et al. (2007), where the 
shift in position with respect to the radio source VLA~4 is evident. Further observations at different frequencies and higher angular 
resolution are required to confirm or reject the association. Tej et al. (2007) have noted that their NIR source number 1 coincides in 
position with the source IRAS~20178+4046, one of the brightest infrared sources in the region.  


%%%%% FIGURA 3

\begin{figure}[!t]
\centering
\includegraphics[width=0.98\columnwidth]{cneriafig3.eps}
\caption{Real (top) and imaginary (bottom) components of the flux density of VLA 5 as a function of time 
(IAT = International Atomic Time).}
\label{fig3}
\vspace{0.1cm}
\end{figure}

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


To study the time-variability of the four fainter compact radio continuum sources (see Figure~2) during the approximately 12 hours of 
the total observing session (of which 10 hours were on-source), we proceeded as follows. The precise position of each source was 
determined from the image shown in Figure~2. The ($u,v$) data were then recentered at the position of the source considered and the real 
and imaginary parts of its flux density were plotted as a function of time, averaged over the ($u,v$) plane and in 10 time bins. A 
detailed description of this technique is given in the Appendix~A. To avoid contamination from extended emission, we use only ($u,v$) data 
with baselines larger than 100 k$\lambda$, suppressing emission from scales larger than $\sim 0\rlap.{''}5$. The technique did not work 
in a reliable way in the case of VLA 4, which is embedded in the much brighter UC HII (VLA 1). In the case of the remaining sources, we 
found clear evidence of variability for VLA 5. In Figure~3 we show the real and imaginary parts of its flux density as a function of time, 
where it can be appreciated that the source was very weak during the first half of the run and that, in a timescale of about an hour, it 
rose to a much stronger flux density. No evidence of variability was found for VLA 2 and VLA 3. In the last column of Table~1, we list if 
the sources were time-variable or not. 


%%%%%% FIGURA 4

\begin{figure*}[!t]
\centering
\includegraphics[width=12.32cm]{cneriafig4.eps}
\caption{Contour image overlapped on a grayscale image at 3.6~cm of VLAN~1, VLAN~2 and VLAN~3 toward the 
G78-North region. Contour levels are 3, 4, 6, 8, 10, 15, 30 and 50 times 21.8~$\mu$Jy~beam$^{-1}$, the 
average rms noise of the image. The grayscale flux goes from $-0.2$ to 0.9~mJy~beam$^{-1}$. The synthesized 
beam, after applying UVTAPER = 50 k$\lambda$ ($3\rlap.{''}26 \times 3\rlap.{''}02$ with a position angle 
of $-60^{\circ}$), is shown in the bottom right corner of the image. The crosses mark the peak position of 
the 3.6~cm radio sources listed in Table~2.}
\label{fig4}
\vspace{0.4cm}
\end{figure*}

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


The variability observed in VLA 5 has been observed in other low-mass PMS stars (e.g., G\'omez et al. 2002; Bower et al. 2003; G\'omez et 
al. 2008; Forbrich, Menten, \& Reid 2008) and it can be attributed to gyrosynchrotron emission from an active magnetosphere. For UC~HII regions or 
externally-ionized globules variability at such short time scales is not expected.


%%%%%% FIGURA 5

\begin{figure}[!t]
\centerline{\includegraphics[width=0.975\columnwidth]{cneriafig5a.eps}}
\vspace{0.3cm}
\centerline{\includegraphics[width=0.975\columnwidth]{cneriafig5b.eps}}
\caption{Contour image of the 3.6~cm continuum emission from VLAN~4 (top) and VLAN~5 (bottom) toward the 
G78-North region. The contours are $-5$, 5, 7, 9, 10, 12, 14 and 16 times 10~$\mu$Jy~beam$^{-1}$, the average 
rms noise of the image. The synthesized beam is $0\rlap.{''}76 \times 0\rlap.{''}67$, with a position angle 
of $-79^{\circ}$. The crosses mark the peak position of the 3.6~cm radio sources listed in Table~2.}
\label{fig5}
\vspace{0.2cm}
\end{figure}

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


\subsection{Other radio sources in the field}

Toward the north of the UC~HII region G78.4+2.6, we detect another cluster of five compact radio sources (designated as VLAN~1 to VLAN~5) 
above $5\sigma$ level. After we applied UVTAPER (50 k$\lambda$, resulting in a beam size of $3\rlap.{''}26 \times 3\rlap.{''}02$, 
P.A. = $-60^{\circ}$) to this image we noted that two of these sources (VLAN~2 and 3) have diffuse extended emission associated with them. 
The extended radio emission toward the east of VLAN~2 is more likely an extension of a possible jet. VLAN~1 also displays some signs of 
extended emission though the morphology is more compact. Figure~4 shows a close-up of the north region showing these three radio sources.
 The compact sources VLAN~4 and VLAN~5 were not included in this close-up, because they do not exhibit significant extended emission and 
lie far away from the main group ($> 10''$). Figure~5 shows the sources VLAN~4 and VLAN~5. As for the four fainter compact radio continuum 
sources in the vicinity of the UC HII (VLA~2 to 5), we also looked for any counterparts in order to gain understanding about 
their nature. The search in the Strasbourg Astronomical Data Center (CDS) and the Spitzer 3.6~$\mu$m band image does not show any counterpart 
within one arcsec. We also searched for 1.4~GHz radio emission using the NRAO VLA Sky Survey (NVSS), which does not show any source above 
$\sim 1.2$~mJy ($3\sigma$). The morphology of VLAN~1 to 3 resembles that of a cluster of radio galaxies, but the extended emission could 
alternatively be HII regions surrounding massive stars. Such varied morphologies of HII regions are not uncommon (e.g., Kurtz et al. 1994, 
1999). However, more observations are needed in order to clarify the nature of these sources. The main parameters of the five compact radio 
sources to the north of G78.4+2.6 are listed in Table~2.


%%%%%% TABLA 2

\begin{table}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabnotewidth}{0.99\columnwidth} 
\setlength{\tabcolsep}{0.84\tabcolsep}
\tablecols{4}
\caption{Parameters of the radio sources toward the north of G78.4+2.6}
\small
\begin{tabular}{cccc}
\toprule
Source & $\alpha$(2000) & $\delta$(2000) & Flux Density\tabnotemark{a} \\
       &                &                & (mJy) \\
\midrule
VLAN~1 & 20 19 33.457 & 40 58 53.25 & $0.57\pm0.05$ \\
VLAN~2 & 20 19 36.554 & 40 58 34.86 & $0.87\pm0.04$ \\
VLAN~3 & 20 19 36.874 & 40 58 46.14 & $0.49\pm0.04$ \\
VLAN~4 & 20 19 37.997 & 40 59 21.84 & $0.09\pm0.03$ \\
VLAN~5 & 20 19 42.030 & 40 59 22.97 & $0.28\pm0.05$ \\
\bottomrule
\noalign{\smallskip}
\tabnotetext{a}{Flux densities at 3.6~cm corrected for the primary beam response.}
\label{tab:2}
\end{tabular}
%\vspace{0.2cm}
\end{table}

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


\section{Discussion}

The high sensitivity continuum observations toward the region G78.4+2.6 (IRAS~20178+4046), have resulted in the identification of four new 
compact radio sources in the vicinity ($<$ $1'$) of the cometary HII region (VLA~1) (see Table~1). These sources could be associated with 
pre-main sequence (PMS) stars, but multiwavelength observations are required to confirm this.

Tej et al. (2007), based on the analysis of the 850~$\mu$m emission, have reported the presence of two regions at different evolutionary 
stages toward this star-forming region, the northern and southern cores. The southern core traces a later stage of evolution and is 
associated with the UC HII region, and an earlier stage of evolution is proposed for the northern core, which does not have radio or NIR 
emission. Tej et al. (2007) have analyzed the nature of the near-infrared sources detected in the 2MASS $JHK$ observations around the 
UC HII G78.4+2.6 region and, by using color-magnitude diagrams and assuming a distance of 3.3~kpc (Kurtz et al. 1994), they proposed the 
presence of nine B0.5 or earlier type candidates, all mainly located toward the southern core. However, only one (VLA~) of the five radio 
sources reported by us in this paper (Table~1) clearly coincides in position with one of the nine B0.5 or earlier type sources proposed 
by Tej et al. (2007).

The UC HII region (VLA~1) is excited at least by a B0.5 ZAMS star (see discussion below) and radio emission is clearly detected. We believe 
that if more B0.5 stars were present in the surroundings they should have been detected in our deep radio image. The non-detection of the 
rest of the NIR sources could be due to a factor already considered by Tej et al. (2007): there is considerable uncertainty in the distance 
to G78.4+2. Indeed, if instead of the large value of 3.3~kpc we consider the smaller value of 1.7 kpc (Wilking et al. 1989; Schneider et al. 
2006) then the B0.5 candidates will become less luminous stars, with no expected detectable HII region.

In the particular case of VLA~4, if it is associated with the NIR source number 1 of Tej et al. (2007), and the radio continuum reported in this 
work at 3.6~cm is produced by an optically thin homogeneous spherical HII region, following Mezger \& Henderson (1967), we can estimate the 
number of ionizing photons per second, $N_{\rm i}$, produced by the exciting star as,
$$\bigg[\frac{N_{\rm i}}{{\rm s}^{-1}}\bigg] = 7.7~\times 10^{43} \bigg[\frac{S_\nu}{{\rm mJy}}\bigg]\bigg[\frac{\nu}{{\rm GHz}}\bigg]^{0.1} \bigg[\frac{D}{{\rm kpc}}\bigg]^2,$$
where $S_\nu$ is the flux density of the compact source, $\nu$ is the observing frequency and $D$ is the distance from the Sun. Adopting a 
distance of 1.7~kpc, we estimate for VLA~4 $N_{\rm i}=1.3\times 10^{44}$~s$^{-1}$, implying an exciting star type B3 ZAMS (Panagia 1973), while 
for a distance of 3.3~kpc, $N_{\rm i}=5.0 \times 10^{44}$~s$^{-1}$, then the spectral type will be $\sim$ B2 ZAMS. In both cases the exciting star 
for the VLA~4 source should be later than a B2 ZAMS and does not reach the ionizing rate of a B0.5 ZAMS or earlier star. As mentioned above, 
Tej et al. (2007) had already pointed out that there is a discrepancy seen in their determination of the spectral types by using the NIR 
color-magnitude diagrams due to the distance uncertainty, to the possible presence of IR excess and to the 2MASS resolution limit.

It is possible to plot the ($H-K$) colors and $K$ magnitudes from our VLA sources with NIR counterparts in a color-magnitude diagram to derive 
the spectral types of the sources in the same way as was done by Tej et al. (2007). Assuming that VLA~1 is ionized by the NIR source number 2 
of Tej et al. (2007), a B0.5 ZAMS star at a distance of 1.7~kpc is needed to provide the ionization. Then, if we apply a similar distance 
correction in the color-magnitude diagram (Figure~3 of Tej et al. 2007) for all the other sources, we find that VLA~4 (source number 1 of 
Tej) is associated with a B3 ZAMS star (consistent with our previous estimate from the radio continuum flux density). VLA~2 and VLA~3 will 
correspond to a spectral type between F and G ZAMS. Only one source clearly shows evidence of fast (hours) radio variability (VLA~5), a 
physical characteristic of low-mass PMS stars. Unfortunately, this source does not have a NIR counterpart, although it does have a Spitzer 
(mid-infrared) counterpart (see Table~1). We then propose that VLA~1 is an HII region excited by a B0.5 ZAMS star, VLA~4 is possibly an HII 
region excited by a B3 ZAMS star and that the remaining three compact radio sources (VLA~2, VLA~3 and VLA~5) are low-mass PMS stars embedded 
in the star forming region.

The non-detection in our data of radio continuum counterparts to the NIR sources number 3 to 9 from Tej et al. (2007), favors the smaller 
value of 1.7~kpc fot the distance to G78.4+2.6. Also we notice that four of our radio sources are located toward the southern core, where 
radio and 3.6~$\mu$m emission is present (see Figure~2), which suggests their association with a later evolutionary stage core where massive 
stars have formed an UC HII region.

The compact radio source VLA~3 is displaced $\sim 16''$ from the center of the northern core. The northern core is traced by the submillimeter 
emission at 850~$\mu$m (see Figure~5 of Tej et al. 2007) and it is not associated with radio or NIR emission, suggesting an early stage of 
evolution (Klein et al. 2005; Tej et al. 2006, 2007). We propose that VLA~3 may be a PMS star embedded in the early evolutionary stage northern 
core. Alternatively, VLA~3 could simply be an outer component of the southern core that appears projected in the line-of-sight toward the 
northern core. If the association with the northern core is confirmed, it will support the idea that the less massive objects are among the first 
ones to form in a cluster (Klein et al. 2005; Molinari et al. 2008). 

In order to be sure that the four compact radio sources identified in this paper are new members of the PMS cluster toward G78.4+2.6 and not 
background sources, we now estimate the number count probability following Windhorst et al. (1993). The expected number of background sources 
per square arcmin, $N$, with a flux density at 8.3 GHz above $S$, is given by 
$$\bigg[\frac{N}{({\rm arcmin})^2}\bigg] = 0.0024\bigg[\frac{S}{{\rm mJy}}\bigg]^{-1.3}\,.$$
Using $S=0.05$~mJy ($5\sigma$ of the radio continuum image), within a solid angle of $1\rlap.{'}5 \times 1\rlap.{'}5$ we obtain that the expected 
number of background sources is $\sim 0.3$, which suggests that the four compact radio sources are members of the star forming region. 

Finally, following the formulation of Mezger \& Henderson (1967) and Rodr\'iguez et al. (1980) for a homogeneous and spherically symmetric 
region, we estimate the physical parameters of the UC HII region G78.4+2.6, assuming that the gas has constant electron density, an electron 
temperature of 8000~K (Tej et al. 2007) and a kinematic distance of 1.7~kpc. At 3.6~cm we measure a total flux density of $\sim 62.3$~mJy 
(see Table~1), and an angular size of $4\rlap.{''}5 \times 3\rlap.{''}5$ ($\sim$ 0.03~pc at a distance of 1.7~kpc). This flux density is in 
agreement with other radio estimates (Wilking et al. 1989; McCutcheon et al. 1991; Kurtz et al. 1994; Tej et al. 2007) in the 0.6--8.5~GHz frequency 
range, which is consistent with an optically thin region. Under these conditions we estimate an electron density  $n_{e}=6.4~ \times 10^{3}$~cm$^{-3}$, 
an ionized mass $M_\mathrm{HII}=8.5~\times~10^{-3}~M_\odot$, and an emission measure $EM$ of $1.3 \times 10^{6}$~cm$^{-6}$~pc. Using the ionizing rates 
of Panagia (1973) and assuming that the logarithm of the ionizing rate has an approximate linear behavior with the spectral subtype (Vacca, 
Garmany, \& Shull 1996), we estimate for the ionizing star of VLA~1 a spectral  type of B0.5 ZAMS (for a distance of 1.7~kpc) or of B0.3 ZAMS 
(for a distance of 3.3~kpc). The latter result is in agreement with Kurtz et al. (1994) and Tej et al. (2007) who estimated a spectral type 
for the exciting source of VLA~1 between B0 and B0.5 (assuming a distance of 3.3~kpc).


\section{Conclusions}

We present high angular resolution VLA observations at 3.6~cm toward the star-forming region G78.4+2.6. In addition to the cometary 
UC HII region VLA 1, a group of four compact radio sources was found (VLA~2 to 5). One of them (VLA~5) shows evidence of radio variability 
in a timescale of hours. The four new compact radio sources, reported by us, coincide in position with Spitzer 3.6~$\mu$m peaks. From 
the five radio sources reported at 3.6~cm, one is clearly associated with the NIR source number 2 of Tej et al. (2007) with a spectral 
type B0.5. Another VLA source (VLA~4) seems to be associated with the NIR source number 1 of Tej et al. (2007) and corresponds to a 
spectral type B3 ZAMS star. The rest of the radio sources (VLA~2, VLA~3 and VLA~5) are probably PMS stars with spectral types between 
F and G ZAMS. Our results favor the smaller distance of 1.7~kpc (Wilking et al. 1989; Schneider et al. 2006) proposed for the star forming 
region G78.4+2.6.
 
Another group of five radio sources is found about $3'$ to the NW of the HII region G78.4+2.6 whose nature is still undetermined.

\acknowledgments

We thank an anonymous referee for comments and suggestions that helped to improve this paper. CN, YG, and LR are thankful for the support 
of DGAPA, Universidad Nacional Aut\'onoma de M\'exico, and of Conacyt (Mexico). This research has made use of the SIMBAD database, operated at 
CDS, Strasbourg, France. This publication has also  made use of the Spitzer Space Telescope and NASA/IPAC Infrared Science Archive, which is 
operated by the Jet Propulsion  Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


\vspace{0.5cm}

\begin{appendix}


\setcounter{equation}{0}
\renewcommand{\theequation}{A\arabic{equation}}


\section*{APPENDIX A. MEASURING THE FLUX DENSITY AS A FUNCTION OF TIME IN\\ THE ($u,v$) PLANE}

In some cases, the observer is interested in determining the flux density of a source in the field as a function of time. This can be 
achieved by making images from data on small time intervals, but it is faster (since no images have to be made) to explore in the ($u,v$) 
plane different time intervals to search for variability at different timescales. As it is the case in the image plane $(x,y)$, it is 
possible to isolate the emission from a source also in the $(u,v)$ plane, as described below.

The visibility $V(u,v)$ for a given point $(u,v)$ is (Thompson, Moran, \& Swenson 1986):
\begin{equation}
V(u,v)=\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}I(x,y)\exp[i2\pi(ux+vy)]dxdy\,,
\end{equation}
\noindent where $V(u,v)$ is the visibility, in general a complex function, $u$ and $v$ are the projections of the baseline of a given 
antenna pair along the sky coordinates $x$ and $y$, respectively, given in units of wavelengths, and $I(x,y)$ is the intensity of the 
source or sources as a function of the position $(x,y)$ with respect to the phase center. A point source located at the phase center, 
$(x,y) = (0,0)$, can be described by
\begin{equation}
I(x,y) = S~\delta^2(x,y)\,,
\end{equation}
\noindent where $S$ is the flux density of the source and $\delta^2$ is Dirac's delta function in two dimensions. The integral of equation~(1) 
then becomes:
\begin{equation}
V(u,v) = S\,.
\end{equation}

In this case, the real, $\mathrm{Re}(u)$, and imaginary, $\mathrm{Im}(u)$, parts of the visibility are given by:
\begin{equation}
\mathrm{Re}(u,v) = S\,,
\end{equation}
\begin{equation}
\mathrm{Im}(u,v) = 0\,.
\end{equation}

Finally, the real and imaginary parts are averaged over the range of values of $u$ and $v$ for which one has measurements, $-u_{m} \leq u \leq u_{m}$, 
$-v_{m} \leq v \leq v_{m}$:
\begin{equation}
\mathrm{Re}={{1} \over {2 u_{m}}} {{1} \over {2 v_{m}}}\int_{-u_{m}}^{+u_{m}} \int_{-v_{m}}^{+v_{m}} \mathrm{Re}(u,v) du~ dv = S\,, 
\end{equation}
\begin{equation}
\mathrm{Im}={{1} \over {2 u_{m}}} {{1} \over {2 v_{m}}} \int_{-u_{m}}^{+u_{m}} \int_{-v_{m}}^{+v_{m}} \mathrm{Im}(u,v) du~ dv = 0\,. 
\end{equation}

That is, the average over $(u,v)$ of the real and imaginary components of the visibility of a point source at the phase center are simply 
$S$ and $0$, respectively.

What happens if there is an additional source in the field, that is centered at a position different from the phase center? Assuming again 
that this source is pointlike and that it is located at the point $(x,y) = (x_1,0)$, it can be described by
\begin{equation}
I(x,y) = S_1~\delta^2(x - x_1,y)\,, 
\end{equation}
\noindent where $S_1$ is its flux density. Again using equation~(1) we have that the real, $\mathrm{Re}_1(u,v)$, and imaginary, $\mathrm{Im}_1(u,v)$, 
parts of the visibility are in this case given by:
\begin{equation}
\mathrm{Re}_1(u,v) = S_1~ \cos(2 \pi u x_1)\,,~~~~ 
\end{equation}
\begin{equation}
~~~~\mathrm{Im}_1(u,v) = S_1~ \sin(2 \pi u x_1)\,.  
\end{equation}


Averaging over $(u,v)$, we obtain
\begin{eqnarray}
\mathrm{Re}_1 = {{1} \over {2 u_{m}}} {{1} \over {2 v_{m}}} \int_{-u_{m}}^{+u_{m}} \int_{-v_{m}}^{+v_{m}} \mathrm{Re}_1(u,v) du dv \nonumber \\ 
= {{1} \over {2 u_{m}}} \int_{-u_{m}}^{+u_{m}} S_1~ \cos(2 \pi u x_1) du~~~~~~~~~~~ \nonumber \\ 
= S_1~ {{\sin(2 \pi u_{m} x_1)} \over {2 \pi u_{m} x_1}} = S_1~ \mathrm{sinc}(2 \pi u_{m} x_1)\,, 
\end{eqnarray}
where $\mathrm{sinc}=(\sin~x)/x\,,$
\begin{eqnarray}
\mathrm{Im}_1 = {{1} \over {2 u_{m}}} {{1} \over {2 v_{m}}} \int_{-u_{m}}^{+u_{m}} \int_{-v_{m}}^{+v_{m}} \mathrm{Im}_1(u,v) du dv \nonumber \\ 
= {{1} \over {2 u_{m}}} \int_{-u_{m}}^{+u_{m}} S_1~ \sin(2 \pi u x_1) du = 0\,.~~~~
\end{eqnarray}

We conclude that, in this case, the average over $(u,v)$ of the imaginary component is $0$, as in the previous case of the source 
at the phase center. The real component is now the flux density of the source, multiplied by a sinc function. For a well-designed 
interferometer we can assume that $u_{m} \simeq v_{m}$, and that the angular resolution of the data is given approximately by
\begin{equation}
\theta \simeq {{1} \over {u_{m}}} \simeq {{1} \over {v_{m}}}\,. 
\end{equation}

We then conclude that as long as this source is several resolution elements away from the phase center and is not very bright, its 
contribution to the real component is small. In brief, as long as the condition
\begin{equation}
S \gg {{S_1} \over {2 \pi (x_1/\theta)}}\,, 
\end{equation}
\noindent is fulfilled, we can take the real component of the averaged visibility as dominated by the flux density of the source at 
the phase center.

In the case of the source VLA~5, we have that $S \simeq 0.1-0.3$~mJy. The other compact sources in the field of G78.4+2.6 have flux 
densities comparable to that of VLA~5 and are at angular distances of $15''$ or more away from it. Since the angular resolution of 
the data is $\theta \simeq 0\rlap.{''}7$, we have that the angular separation is $x_1 \simeq ~20~ \theta \simeq 20/u_{m}$, and that 
an upper limit to the contribution of these sources is given by
\begin{equation}
\vert \mathrm{Re}_1 \vert \leq 0.003~\mathrm{mJy}\,. 
\end{equation}

\vspace{0.1cm}

So, the other point sources in the field contribute less than 1\% to the real component measured after centering the $(u,v)$ data at the 
position of VLA~5. 

\vspace{0.1cm}

We have, however, to consider the effect of the extended source VLA~1, that is quite bright, $S_1 \simeq 60$~mJy. In this case it can be 
shown that the condition given by equation~(14) approximately becomes
\begin{equation}
S \gg \Biggl[{{\theta} \over {\theta_S}}\Biggr]^2~ {{S_1} \over {2 \pi (x_1/\theta)}}\,, 
\end{equation}
\noindent where $S_1$ is the flux density of the extended source, and $\theta_S$ is its angular diameter, $\theta_S \simeq 4''$ in the case 
of VLA~1. In this case $x_1 \simeq 20''$. Evaluating the contribution of VLA~1 at the position of VLA~5 we obtain
\begin{equation}
\vert \mathrm{Re}_1 \vert \leq ~ 0.01~\mathrm{mJy}\,,
\end{equation}
\begin{equation}
\mathrm{Im}_1 =~0\,.~~~~~~~~
\end{equation}

\vspace{0.2cm}

We then conclude that the contribution of VLA~1 at the position of VLA~5 does not affect significantly the flux density determinations 
of the latter source. The contribution of extended sources in the field is further suppressed by not including in the averaging the 
short baselines of the $(u,v)$ data, where most of the extended emission is present.

\end{appendix}

\vspace{0.4cm}

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