\documentclass[journal]{rmaa}

\newcommand{\casitiny}{\fontsize{6}{7}\selectfont}


\def\uv{uvby-\beta \ }

\title{$\uv$ photoelectric photometry of\\ the open clusters NGC 6811 and NGC 6830\altaffilmark{1}}


\author{
J.~H. Pe\~na,\altaffilmark{2} 
L. Fox Machado,\altaffilmark{3} 
H. Garc\'ia,\altaffilmark{4} 
A. Renter\'ia,\altaffilmark{2} 
S. Skinner,\altaffilmark{2,5} 
A. Espinosa,\altaffilmark{2} 
and E. Romero\altaffilmark{2}}

\altaffiltext{1}{Based on observations collected at the San Pedro M\'artir Observatory, Mexico.} 
\altaffiltext{2}{Instituto de Astronom\'ia, Universidad Nacional Aut\'onoma de
M\'exico, Mexico.}
\altaffiltext{3}{Observatorio Astron\'omico Nacional, Instituto de Astronom\'ia, Ensenada, Mexico.}
\altaffiltext{4}{Observatorio Astron\'omico de la Universidad Nacional Aut\'onoma de Nicaragua, Nicaragua.}
\altaffiltext{5}{Universidad Nacional de Panam\'a, Panama.}


\shortauthor{Pe\~na et al.} 

\shorttitle{Study of NGC 6811 and NGC 6830}


\listofauthors{J.~H.~Pe\~na, L.~Fox~Machado, H.~Garc\'ia, A.~Renter\'ia, S.~Skinner, A.~Espinosa, \& E.~Romero}

\indexauthor{Pe\~na, J.~H.}
\indexauthor{Fox Machado, L.}
\indexauthor{Garc\'ia, H.}
\indexauthor{Renter\'ia, A.}
\indexauthor{Skinner, S.}
\indexauthor{Espinosa, A.}
\indexauthor{Romero, E.}


\fulladdresses{ 
\item A. Espinosa, J.~H. Pe\~na,  A. Renter\'ia, E. Romero, and S. Skinner: Instituto de Astronom\'ia, Universidad Nacional Aut\'onoma de 
M\'exico, Apdo. Postal 70-264, M\'exico, D. F. Mexico (jhpena@astroscu.unam.mx).
\item  L. Fox Machado: Observatorio Astron\'omico Nacional, Instituto de Astronom\'ia, Universidad Nacional Aut\'onoma de M\'exico, 
Apdo. Postal 877, 22800, Ensenada, B. C., Mexico (lfox@astrosen.unam.mx).
\item  H. Garc\'ia: Observatorio Astron\'omico de la Universidad Nacional Aut\'onoma de Nicaragua, Nicaragua.}


\ReceivedDate{2010 October 27}
\AcceptedDate{2011 June 15}
\SetYear{2011}


\resumen{A partir de la fotometr\'ia fotoel\'ectrica $\uv$ de los c\'umulos abiertos NGC 6811 (75 estrellas) y NGC 6830 (19 estrellas) realizamos la 
determinaci\'on de distancias y, por ende, la pertenencia de las estrellas a cada c\'umulo. Asimismo, se determinaron la edad y el enrojecimiento 
de cada uno. Dado que recientemente se han determinado estrellas variables para el primero, realizamos un estudio de dichas variables.}

\abstract{From $\uv$ photometry of the open clusters NGC 6811 (75 stars), and NGC 6830 (19 stars) we were able to determine membership of the stars 
to each cluster, and fix the age and reddening for each. Since several short period stars have recently been found, we have carried out a study of 
these variables.\smallskip}


\addkeyword{open clusters and associations: individual (NGC 6811, NGC 6830)}
\addkeyword{techniques: photometric}


\begin{document}


\maketitle


\section{Introduction}

The study of open clusters and their short period variable stars is fundamental in  stellar evolution. Because the cluster members are formed in 
almost the same physical conditions, they share similar stellar  properties, such as age and chemical composition. The assumption of common age, 
metallicity and distance imposes strong constraints  when modeling  an ensemble of short period pulsators belonging to open clusters (e.g., Fox 
Machado et al. 2001, 2006). Thus,  observational studies involving  variable stars in open clusters have attracted more and more attention (e.g., 
Fox Machado et al. 2002; Li et al. 2002, 2004).

A series of papers (see Pe\~na \& Peniche 1994; Pe\~na et al. 1998, 2003; Pe\~na, Fox Machado, \& Garrido 2007) study the physical nature of the 
short period variable stars in open clusters  by means of Str\"omgren photometry, since, once their membership to the cluster has been established, 
their physical quantities can be unambiguously derived. In particular, the determination of physical parameters of cluster member stars from $\uv$ 
photometry  can be done through a comparison with theoretical models (Lester, Gray, \& Kurucz 1986, hereinafter LGK86).

As a continuation of our study, we now present observations of the open clusters NGC 6811 and NGC 6830. Both clusters have no previous published 
$\uv$ data.


%%%%%% TABLA 1

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabnotewidth}{0.8\textwidth}
%\setlength{\tabcolsep}{1.25\tabcolsep}
\tablecols{5}
\caption{Log of the observing seasons}
\label{log}
\begin{tabular}{lcccc}
\toprule
\multicolumn{1}{c}{Epoch} & Cluster  & Initial date  &  Final date  & Observers\\
                          &          & year mo day   &  year mo day &          \\
\midrule
2009 June   & NGC 6811, NGC 6830  &  2009 06 24 & 2010 06 29 & jhp, hg, arl\\
2010 August & NGC 6811            &  2010 08 03 & 2010 08 06 & jhp, ss, er, ae\\
\bottomrule
\tabnotetext{}{Observers: jhp, J. H. Pe\~na; hg, H. Garc\'ia; arl, A. Renter\'ia; ss,  S. Skinner;  er, E. Romero; ae, A. Espinosa.}
\end{tabular}
\vspace{0.3cm}
\end{table*}

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


Very recently, Luo et al. (2009) carried out a search for variable stars in the direction of NGC 6811 with CCD photometry in the $B$, and $V$ bands. 
They detected a total of sixteen variable stars. Among these variables, twelve were catalogued as $\delta$ Scuti stars, while  no variability type 
was assigned to the remaining stars. They claim that the twelve $\delta$ Scuti stars are all very likely members of the cluster, which makes this 
cluster an interesting target for asteroseismological studies. Moreover, NGC 6811 has been selected as a asteroseismic target of the Kepler space 
mission (Borucki et al. 1997). Therefore, deriving accurate physical parameters for the pulsating star members is very important.

For NGC 6811 Luo et al. (2009) estimated an age of $\log(t)=8.76 \pm 0.009$ from theoretical isochrone fitting to the color magnitude diagram (CMD 
hereafter) and assuming a metallicity of $Z=0.019$. They determined the distance modulus and color excess as $10.59 \pm 0.09$ and $0.12 \pm 0.05$, 
respectively.

To the best of our knowledge, no $\delta$ Scuti variable stars have been reported in NGC 6830 to date.

According to the compilation of data of open clusters in Paunzen \& Mermilliod (2007, WEBDA), NGC 6811 has a distance [pc] of 1215; a reddening [mag] 
of 0.160; a distance modulus [mag] of 10.92; a log age 8.799 and no data on metallicity reported. NGC 6830 has the following: distance [pc] 1639; 
reddening [mag] 0.501; distance modulus [mag] 12.63; log age 7.572 with no determined metallicity.


%%%%% TABLA 2

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{Transformation coefficients obtained\\ for the two observing seasons}
\begin{tabular}{lccccccc}
\toprule
Season  &  B  &   D  &   F  &   J  &  H   &   I  &   L\\
\midrule
2009     & $-$0.005  & 0.975 & 1.002 & 0.037 & 1.008  & $-$0.067 & $-$1.397\\
$\sigma$ &  ~~0.051  & 0.032 & 0.045 & 0.033 & 0.049  &  ~~0.067 &  ~~0.031\\
\noalign{\smallskip}
2010     &  ~~0.002  & 0.962 & 1.021 & 0.025 & 0.991  & $-$0.006 & $-$1.309\\
$\sigma$ &  ~~0.013  & 0.003 & 0.034 & 0.002 & 0.042  &  ~~0.145 &  ~~0.021\\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table*}

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


\section{Observations}

These were all taken at the Observatorio Astron\'omico Nacional, Mexico in two different seasons, those of 2009 and 2010. The dates are listed in 
Table~1. The 1.5~m telescope to which a spectrophotometer was attached was utilized at all times. The first observing season was carried out over 
six nights from June--July 2009. The ID charts utilized were those of WEBDA. When the NGC 6811 data were reduced, there were several stars whose 
photometry showed large discrepancies with the literature. In view of this and due to the fact that several $\delta$ Scuti stars were recently 
discovered in this cluster (Luo et al. 2009), a second observing season was planned in 2010 to measure all of these stars in the $uvby-\beta$ system.


\subsection{Data acquisition}

The following procedure was utilized during all nights: each measurement consisted of at least five ten-second integrations of each star and one 
ten-second integration of the sky for the $uvby$ filters and the narrow and wide filters that define H$\beta$. Individual uncertainties were determined 
by calculating the standard deviations of the fluxes in each filter for each star. The percent error in each measurement is, of course, a function 
of both the spectral type and the brightness of each star, but they were observed long enough to secure sufficient photons to get a S/N ratio of accuracy 
of $N/\sqrt{(N)}$ of 0.01~mag in most cases. Each night a series of standard stars was also observed to transform the data into the standard system. The 
reduction procedure was done with the numerical packages NABAPHOT (Arellano-Ferro \& Parrao 1988) which reduce the data into a standard system, although 
some data were also taken from the \textit{Astronomical Almanac} (2006) for the standard bright stars. The chosen system was that defined by the standard 
values of Olsen (1983) and the transformation equations are those defined by Gr\"onbech, Olsen, \& Str\"omgren (1976) and by Crawford \& Mander (1966). 
In these equations, the coefficients D, F, H and L are the slope coefficients for $(b-y)$, $m_1$, $c_1$ and $\beta$, respectively. The coefficients B, J 
and I are the color terms of $V$, $m_1$, and $c_1$. The averaged transformation coefficients of each season determined from the mean of all nights are 
listed in Table~2 along with their standard deviations. Errors of the season were evaluated by means of the standard stars observed. These uncertainties 
were calculated through the differences in magnitude and colors, for ($V$, $b-y$, $m_1$, $c_1$ and $\beta$) as (0.020, 0.017, 0.011, 0.031, 0.011) respectively, 
which provide a numerical evaluation of our uncertainties. Emphasis is made on the large range of the standard stars in the magnitude and color values: 
$V$:(5.4, 8.7); $(b-y)$:(0.02, 0.80); $m_1$:(0.09, 0.67); $c_1$:(0.06, 1.12) and $\beta$:(2.53, 2.89).


%%%%% TABLA 3

\setcounter{table}{2}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{14}
\setlength{\tabcolsep}{1.2\tabcolsep}
\caption{$\uv$ photoelectric photometry of the open cluster NGC 6811}
\renewcommand{\arraystretch}{0.99999999999}
\casitiny
\begin{tabular}{rccccccccccccc}
\toprule
WBD & V & $(b-y)$ & $m_1$ & $c_1$ & bt & sV & sby & sm$_1$ & sc$_1$ & sbt & N &\multicolumn{2}{c}{Spectral Type}\\
    &   &         &       &       &    &    &     &       &        &     &   & Photometry & WBD \\
\midrule
~~4 & 12.681 & 0.259 & 0.127 & 0.861 & 2.706 &       &       &       &       &       & ~1 & A3V & A7\\
~~5 & 11.795 & 0.168 & 0.185 & 0.950 & 2.770 & 0.067 & 0.028 & 0.015 & 0.029 & 0.062 & 28 & A5V & A2\\
~~6 & 14.463 & 0.786 & 0.291 & 0.554 & 2.538 & 0.076 & 0.111 & 0.108 & 0.226 & 0.071 & ~3 & $>$G &\\
~~7 & 14.381 & 0.399 & 0.125 & 0.388 & 2.588 & 0.201 & 0.071 & 0.221 & 0.104 & 0.020 & ~3 & F7V &\\
~~8 & 14.110 & 0.356 & 0.142 & 0.498 & 2.630 & 0.150 & 0.053 & 0.153 & 0.115 & 0.055 & ~3 & F7V &\\
~~9 & 12.081 & 0.166 & 0.218 & 0.959 & 2.790 & 0.080 & 0.015 & 0.029 & 0.067 & 0.077 & ~3 & Ap & A1\\
~10 & 14.234 & 0.339 & 0.223 & 0.346 & 2.525 & 0.283 & 0.073 & 0.065 & 0.153 & 0.180 & ~3 & G2V &\\
~12 & 14.363 & 0.455 & 0.148 & 0.387 & 2.540 & 0.098 & 0.067 & 0.057 & 0.142 & 0.094 & ~3 & G0V &\\
~13 & 15.055 & 0.567 & 0.058 & 0.542 & 2.585 & 0.264 & 0.158 & 0.164 & 0.277 & 0.037 & ~2 & F7V &\\
~14 & 13.672 & 0.765 & 0.399 & 0.174 & 2.510 & 0.182 & 0.029 & 0.041 & 0.022 & 0.040 & ~2 & $>$G &\\
~16 & 12.196 & 0.235 & 0.165 & 0.927 & 2.781 &       &       &       &       &       & ~1 & A5V & A4\\
~18 & 12.118 & 0.236 & 0.144 & 0.966 & 2.806 &       &       &       &       &       & ~1 & A5V & A4\\
~22 & 13.034 & 0.522 & 0.267 & 0.230 & 2.529 & 0.019 & 0.018 & 0.005 & 0.023 & 0.039 & ~2 & K0V &\\
~23 & 13.981 & 0.558 & 0.227 & 0.185 & 2.655 &       &       &       &       &       & ~1 & $>$G &\\
~24 & 11.245 & 0.613 & 0.327 & 0.318 & 2.564 & 0.044 & 0.020 & 0.012 & 0.052 & 0.019 & ~2 & $>$G & G8\\
~26 & 11.414 & 0.197 & 0.186 & 0.985 & 2.795 &       &       &       &       &       & ~1 & A5V &\\
~31 & 13.308 & 0.327 & 0.131 & 0.635 & 2.760 &       &       &       &       &       & ~1 & F5V &\\
~32 & 11.351 & 0.640 & 0.349 & 0.322 & 2.583 &       &       &       &       &       & ~1 & $>$G & G\\
~33 & 11.917 & 0.232 & 0.149 & 0.950 & 2.771 &       &       &       &       &       & ~1 & A5V & A2\\
~34 & 11.623 & 0.204 & 0.204 & 0.956 & 2.829 &       &       &       &       &       & ~1 & A5p & B9\\
~35 & 13.859 & 0.325 & 0.206 & 0.406 & 2.559 & 0.084 & 0.071 & 0.052 & 0.071 & 0.020 & ~2 & G2V &\\
~36 & 13.221 & 0.283 & 0.180 & 0.561 & 2.614 & 0.065 & 0.062 & 0.049 & 0.009 & 0.052 & ~2 & G0V &\\
~37 & 11.113 & 0.182 & 0.181 & 0.933 & 2.766 & 0.034 & 0.013 & 0.006 & 0.023 & 0.040 & 29 & A5V-F5Ib\\
~38 & 13.206 & 0.662 & 0.382 & 0.330 & 2.535 & 0.052 & 0.079 & 0.013 & 0.066 & 0.128 & ~2 & $>$G &\\
~39 & 11.528 & 0.212 & 0.157 & 0.961 & 2.728 & 0.069 & 0.020 & 0.012 & 0.042 &       & 29 & A5V & A4\\
~40 & 13.070 & 0.111 & 0.147 & 0.632 & 2.673 & 0.127 & 0.062 & 0.073 & 0.100 & 0.071 & ~2  & A1V &\\
~41 & 12.014 & 0.148 & 0.195 & 0.956 & 2.741 & 0.100 & 0.035 & 0.017 & 0.037 &       & 29 & A5V &\\
~42 & 12.568 & 0.190 & 0.184 & 0.829 & 2.698 & 0.172 & 0.055 & 0.028 & 0.049 & 0.059 & 29 & A8V &\\
~43 & 12.743 & 0.268 & 0.176 & 0.785 & 2.658 & 0.023 & 0.000 & 0.001 & 0.049 & 0.030 & ~2  & A8V &\\
~44 & 12.046 & 0.169 & 0.182 & 0.935 & 2.757 & 0.082 & 0.033 & 0.016 & 0.032 & 0.029 & 29 & A5V &\\
~45 & 12.705 & 0.204 & 0.194 & 0.831 & 2.735 & 0.142 & 0.027 & 0.015 & 0.040 & 0.039 & ~3 & A8V & A5\\
~46 & 12.958 & 0.329 & 0.116 & 0.533 & 2.645 & 0.058 & 0.006 & 0.017 & 0.047 & 0.043 & ~3 & F5V &\\
~47 & 13.649 & 0.383 & 0.099 & 0.389 & 2.613 & 0.136 & 0.020 & 0.046 & 0.065 & 0.083 & ~3 & F5V &\\
~49 & 12.422 & 0.218 & 0.142 & 0.978 & 2.822 &       &       &       &       &       & ~1 & A0V & A5\\
~51 & 13.418 & 0.269 & 0.139 & 0.592 & 2.590 & 0.076 & 0.094 & 0.115 & 0.125 & 0.035 & ~2 & F5V &\\
~53 & 12.754 & 0.178 & 0.191 & 0.898 & 2.774 & 0.076 & 0.020 & 0.030 & 0.045 & 0.085 & ~3 & A5V &\\
~54 & 12.356 & 0.266 & 0.136 & 0.757 & 2.713 & 0.027 & 0.025 & 0.029 & 0.027 & 0.078 & ~3 & A8V &\\
~56 & 12.160 & 0.247 & 0.149 & 0.787 & 2.691 & 0.013 & 0.025 & 0.024 & 0.055 & 0.037 & ~2 & A8V &\\
~57 & 14.039 & 0.439 & 0.161 & 0.357 & 2.670 & 0.149 & 0.196 & 0.161 & 0.114 & 0.073 & ~4 & G0V &\\
~58 & 14.350 & 0.622 & 0.219 & 0.151 & 2.650 & 0.187 & 0.231 & 0.122 & 0.256 & 0.132 & ~3 & K0V &\\
~62 & 12.846 & 0.224 & 0.163 & 0.728 & 2.714 &       &       &       &       &       & ~2 & A8V &\\
~63 & 15.234 & 0.979 & 0.846 & 0.714 &       & 0.193 & 0.569 & 0.401 & 0.677 & 0.294 & ~2 & $>$G &\\
~64 & 13.609 & 0.352 & 0.088 & 0.557 & 2.897 & 0.041 & 0.016 & 0.056 & 0.021 & 0.366 & ~2 & F2V &\\
~65 & 14.450 & 0.460 & 0.199 & 0.217 & 2.510 & 0.087 & 0.164 & 0.106 & 0.057 & 0.103 & ~2 & G2V &\\
~68 & 10.850 & 0.272 & 0.152 & 0.869 & 2.737 &       &       &       &       &       & ~1 & A8V & A2\\
~70 & 10.925 & 0.298 & 0.139 & 0.876 & 2.713 &       &       &       &       &       & ~1 & A5V & A4\\
~71 & 13.716 & 0.388 & 0.154 & 0.473 & 2.551 &       &       &       &       &       & ~1 & G0V & A2\\
~73 &  9.851 & 0.992 & 0.830 & 0.166 & 2.551 &       &       &       &       &       & ~1 & $>$G & K5\\
~74 & 12.322 & 0.415 & 0.171 & 0.305 & 2.568 & 0.078 & 0.007 & 0.003 & 0.028 & 0.008 & ~2 & G0V\\
~77 & 13.860 & 0.257 & 0.206 & 0.461 & 2.650 & 0.120 & 0.040 & 0.041 & 0.028 & 0.025 & ~2 & G0V\\
~78 & 13.664 & 0.270 & 0.167 & 0.567 & 2.676 & 0.070 & 0.023 & 0.011 & 0.040 & 0.037 & ~2 & F7V\\
~79 & 10.393 & 0.935 & 0.719 & 0.146 & 2.519 &       &       &       &       &       & ~1 & $>$G \\
~82 & 13.025 & 0.705 & 0.341 & 0.333 & 2.546 &       &       &       &       &       & ~1 & $>$G \\
~85 & 12.860 & 0.308 & 0.134 & 0.545 & 2.684 &       &       &       &       &       & ~1 & F5V\\
~86 & 13.389 & 0.334 & 0.106 & 0.490 & 2.662 &       &       &       &       &       & ~1 & F2V\\
~87 & 12.622 & 0.380 & 0.206 & 0.399 & 2.617 &       &       &       &       &       & ~1 & G2V\\
~92 & 12.260 & 0.221 & 0.166 & 0.722 & 2.704 &       &       &       &       &       & ~1 & A8V\\
~99 & 11.962 & 0.168 & 0.184 & 0.957 & 2.817 & 0.036 & 0.036 & 0.028 & 0.028 & 0.078 & ~2 & A5V & B9\\
101 & 10.682 & 0.671 & 0.393 & 0.333 & 2.569 &       &       &       &       &       & ~1 & $>$G &\\
102 & 12.882 & 0.586 & 0.221 & 0.287 & 2.562 &       &       &       &       &       & ~1 & K0V &\\
105 & 12.419 & 0.230 & 0.241 & 0.850 & 2.802 &       &       & &  &  & ~1 & Ap & A7\\
106 & 11.379 & 0.301 & 0.138 & 0.796 & 2.713 &       &       &  &  &  & ~1 & A8V & A3\\
107 & 12.726 & 0.419 & 0.123 & 0.414 & 2.640 &       &  &  &  &  & ~1 & F7V &\\
112 & 12.825 & 0.372 & 0.146 & 0.412 & 2.663 &       &  &  &  &  & ~1 & F9V &\\
113 & 11.471 & 0.233 & 0.144 & 0.990 & 2.767 &       &  &  &  &  & ~1 & A5V & A4\\
114 & 12.145 & 0.229 & 0.141 & 0.967 & 2.786 & 0.020 & 0.033 & 0.019 & 0.053 & 0.035 & ~3 & A5V & B7\\
115 & 11.551 & 0.220 & 0.169 & 0.787 & 2.759 & 0.135 & 0.040 & 0.023 & 0.076 & 0.025 & ~3 & A3V & A1\\
118 & 12.352 & 0.469 & 0.174 & 0.399 & 2.548 &       &  &  &  &  & ~1 & G2V &\\
122 & 12.825 & 0.372 & 0.146 & 0.412 & 2.663 &       &  &  &  &  & ~1 & F9V &\\
123 & 13.970 & 0.648 & 0.689 & 0.386 & 2.579 &       & &  &  &  & ~1 & $>$G &\\
133 & 12.069 & 0.576 & 0.346 & 0.230 & 2.510 &       &  &  &  &  & ~1 & $>$G & G2\\
139 & 13.197 & 0.358 & 0.082 & 0.569 & 2.646 &  &  &  &  &  & ~1 & F2V &\\
146 & 12.504 & 0.353 & 0.151 & 0.475 & 2.650 &  &  &  &  &  & ~1 & F9V &\\
147 & 12.129 & 0.168 & 0.200 & 0.972 & 2.847 &  &  &  &  &  & ~1 & A5V & A4\\
178 &  9.909 & 1.039 & 0.839 & 0.225 & 2.835 &  &  &  &  &  & ~1 & $>$G &\\
218 & 12.087 & 0.194 & 0.157 & 0.982 & 2.858 &  &  &  &  &  & ~1 & A5V & A5\\
489 & 11.000 & 0.252 & 0.179 & 0.855 & 2.748 &  & &  &  &  & ~1 & A5V &\\
491 & 13.681 & 0.240 & 0.241 & 0.857 & 2.889 &  &  &  &  &  & ~1 & Ap &\\
V17 & 15.009 & 0.560 & 0.067 & 0.157 & 2.468 &  &  &  &  &  & ~1 & F9V & \\
\bottomrule
\end{tabular}
\end{table*}

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


The transformation equations used in the work have the following forms in which `inst' stands for instrumental values and `std' for photometric values 
in the standard system:
\begin{eqnarray}
V & = & \mathrm{A} + \mathrm{B}~(b-y)(\mathrm{inst}) + y~(\mathrm{inst}), \nonumber \\
(b-y)~(\mathrm{std}) & = & \mathrm{C} + \mathrm{D}~(b-y)(\mathrm{inst}), \nonumber \\
m_1(\mathrm{std}) & = &  \mathrm{E} + \mathrm{F}~m_1(\mathrm{inst}) + \mathrm{J}~(b-y)(\mathrm{inst}), \nonumber \\
c_1(\mathrm{std}) & = & \mathrm{G} + \mathrm{H}~c_1(\mathrm{inst}) + \mathrm{I}~(b-y)(\mathrm{inst}), \nonumber \\
\beta~(\mathrm{std}) & = & \mathrm{K} + \mathrm{L}~\beta~(\mathrm{inst}). \nonumber 
\end{eqnarray}
Table~3 lists the photometric values of the observed stars for the NGC 6811 cluster. In this table we list the following: Column~1, the ID number 
as in WEBDA, which follows Lindoff's nomenclature; Columns~2 to 6 the measured photometric values (N denotes the times each star was measured) the 
next five columns list the standard deviations from our photometry and the final columns, the spectral type for each star, determined from the 
[$m1$] [$c1$] diagram and from WEBDA and Becker (1947). The agreement between the spectral types deduced from the photometry with that reported by 
spectroscopic methods is interesting to note. Although there is consistency among the three values, there also is some disagreement among them. For 
example, W113 has spectroscopic types A4 and A8 from WEBDA and Becker (1947), respectively and there are some stars (W16 and W37) that are defined 
as early type stars from the spectroscopy and as later types from the photometry. Nevertheless, we note that, in general, the spectral types are 
coincident within the three mentioned sources. The remaining stars we classified do not have reported spectral classes. Table~4 lists in Column~1 
the ID of WEBDA, Columns~2 to 6 the photometric values, Column~7 the spectral type derived from the photometry and Columns~8 and 9 the spectral 
types listed by WEBDA which are, respectively, Hoag \& Applequist (1965) and Turner (1976).


\subsection{Comparison with other photometries}

Since no $\uv$ has been previously obtained for these clusters, a comparison of our values was made with the available $UBV$ photometry reported in WEBDA.

NGC 6811. We compared our 2009 season photometry with that reported by WEBDA. The intersection of both sets is constituted of seventy five stars, some of 
them (four) showing a large difference, greater than 0.5~mag in $V$. There were some others (six) with differences larger than 0.1~mag. In view of this we 
planned and carried out a second campaign in 2010. Table~3 reports the mean values of the two observing campaigns; N indicates the number of 
measurements for each star. Among the stars with large differences found in the 2009 season and WEBDA, five were measured in both observational campaigns 
showing small differences between them. Hence, with high probability, the discrepancies cannot be attributed to our measurements because (i) these stars were 
measured in two different seasons one year apart by different observers and (ii) the measured standard stars show reasonable values when compared to the 
standard literature values. Hence, the differences can be due to either a misidentification of the star by previous authors or a variable nature of these 
stars. Despite these differences, a linear fit between both sets yields the equation $V_\mathrm{(pp)}=0.82 + 0.97~V_\mathrm{(WEBDA)}$ with a correlation coefficient 
of 0.97 and a standard deviation of 0.25. The color relationship yields $(b-y)=0.06+0.57~(B-V)$ with a correlation coefficient of 0.92 and a standard deviation 
of 0.09.


%%%%% TABLA 4

\setcounter{table}{3} 
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabcolsep}{1.3\tabcolsep}
\caption{$\uv$ photoelectric photometry of the open cluster NGC 6830}
\begin{tabular}{rccrccccc}
\toprule
\multicolumn{1}{c}{ID} & $V$ & $(b-y)$ & \multicolumn{1}{c}{~~$ m_1$} & $c_1$ & $\beta$ & SpTyp &      & sptp \\
\midrule 
                       &     &         &                            &       &         & Phe   & Spc  &     \\
\midrule
5    & ~9.849&0.266 &    0.013&0.554      & 2.721& B6V & B7 V  & B5 III \\
7    & 11.176&0.353 &    0.007&0.822      & 2.689& B8V & A0 V  & B7 III \\
8    & 11.540&0.373 & $-$0.018&0.716      & 2.616& B7V & B7 IV & \\
49   & 10.956&0.456 &    0.103&0.875      & 2.751& AV5 &       &\\
4    & 12.623&0.600 & $-$0.100&0.471      & 2.685& B3V &       & \\
2258 & 13.003&0.546 &    0.086&0.484      & 2.721& F9V &       &\\
2257 & 12.166&0.390 & $-$0.008&0.584      & 2.706& B7V &       & \\
26   & 12.309&0.564 &    0.160&0.255      & 2.661& G1V &       &\\
164  & 12.240&0.460 &    0.093&0.819      & 2.766& A8V &       &\\
25   & 12.465&0.333 &    0.012&0.661      & 2.718& B8V &       &\\
24   & 11.644&0.391 & $-$0.034&0.612      & 2.635& B5V & B6 V  & B6 IV \\
2    & 10.625&0.329 & $-$0.017&0.606      & 2.603& B5V &       &\\
3    & 12.888&1.620 &    0.383&0.256      & 2.569& K G &       & \\
39   & 11.192&0.386 & $-$0.051&0.681      & 2.668& B8I & B5 IV & \\
2275 & 11.909&1.160 &    0.306&$-$0.047~~ & 2.576& B7V &       &\\
13   & 12.787&0.767 &    0.134&0.380      & 2.605& K0V &       &\\
14   & 11.995&0.348 &    0.017&0.532      & 2.714& B6V & B6 V  & B6 IV \\
15   & 12.659&0.407 & $-$0.035&0.646      & 2.681& B6V &       &\\
16   & 12.456&0.408 &    0.108&0.807      & 2.794& K   &       &\\
\bottomrule
\end{tabular}
\vspace{0.935cm}
\end{table*}

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


NGC 6830. This cluster was compared with those $UBV$ values reported by WEBDA for a set constituted of only seven stars. The linear fit between both 
sets gave the equation $V_\mathrm{(pp)}=0.477+0.958 \times V_\mathrm{(WEBDA)}$ with a correlation coefficient of 0.997 and a standard deviation of 0.080. 
The relationship in $B-V$ and $b-y$ gave $(b-y)=0.117+0.573 \times (B-V)$ with a correlation coefficient of 0.922 and a standard deviation of 0.022.


%%%%% TABLA 5

\setcounter{table}{4}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{12}
\setlength{\tabcolsep}{1.25\tabcolsep}
\caption{Reddening, unreddened parameters and distance for the open cluster NGC 6811}
\footnotesize
\begin{tabular}{rccccccccccc}
\toprule
\multicolumn{1}{c}{~~~ID} & $E(b-y)$ & $(b-y)_0$ & $m_0$ & $c_0$ & $\beta$ & $V_0$ & $M_V$ & DM & DST & [Fe/H] & Memb \\
\midrule
 112  & 0.082 & 0.290 & 0.171 & 0.396 & 2.663 & 12.47 & 3.82 & ~8.7 & ~537 &    0.1 & NM\\
 122  & 0.082 & 0.290 & 0.171 & 0.396 & 2.663 & 12.47 & 3.82 & ~8.7 & ~537 &    0.1 & NM\\
 107  & 0.108 & 0.311 & 0.155 & 0.392 & 2.640 & 12.26 & 3.47 & ~8.8 & ~574 & $-$0.2~~ & NM\\
  31  & 0.134 & 0.193 & 0.171 & 0.608 & 2.760 & 12.73 & 3.47 & ~9.3 & ~713 &        & M\\
 489  & 0.072 & 0.180 & 0.201 & 0.841 & 2.748 & 10.69 & 1.32 & ~9.4 & ~749 &        & M\\
 146  & 0.052 & 0.301 & 0.167 & 0.465 & 2.650 & 12.28 & 2.82 & ~9.5 & ~780 &    0.0 & M\\
  68  & 0.085 & 0.187 & 0.177 & 0.852 & 2.737 & 10.48 & 1.01 & ~9.5 & ~786 &        & M\\
  34  & 0.099 & 0.105 & 0.234 & 0.936 & 2.829 & 11.20 & 1.57 & ~9.6 & ~842 &        & M\\
 105  & 0.093 & 0.137 & 0.269 & 0.831 & 2.802 & 12.02 & 2.16 & ~9.9 & ~938 &        & M\\
  85  & 0.055 & 0.253 & 0.150 & 0.534 & 2.684 & 12.63 & 2.71 & ~9.9 & ~964 & $-$0.1~~   & M\\
 218  & 0.116 & 0.078 & 0.192 & 0.959 & 2.858 & 11.59 & 1.65 & ~9.9 & ~973 &     & M\\
 106  & 0.088 & 0.213 & 0.164 & 0.778 & 2.713 & 11.00 & 1.06 & ~9.9 & ~973 & 0.0 & M\\
  47  & 0.060 & 0.323 & 0.117 & 0.377 & 2.613 & 13.39 & 3.42 & 10.0 & ~985 & $-$0.7~~ & M\\
  37  & 0.024 & 0.158 & 0.188 & 0.928 & 2.766 & 11.01 & 0.87 & 10.1 & 1065 &     & M\\
 147  & 0.080 & 0.088 & 0.224 & 0.956 & 2.847 & 11.79 & 1.62 & 10.2 & 1080 &     & M\\
  70  & 0.089 & 0.209 & 0.166 & 0.858 & 2.713 & 10.54 & 0.31 & 10.2 & 1112 & 0.0 & M\\
  86  & 0.061 & 0.273 & 0.124 & 0.478 & 2.662 & 13.13 & 2.88 & 10.3 & 1120 & $-$0.5~~ & M\\
  26  & 0.067 & 0.130 & 0.206 & 0.972 & 2.795 & 11.12 & 0.84 & 10.3 & 1140 &     & M\\
  99  & 0.053 & 0.115 & 0.200 & 0.946 & 2.817 & 11.73 & 1.42 & 10.3 & 1154 &     & M\\
  18  & 0.113 & 0.123 & 0.178 & 0.943 & 2.806 & 11.63 & 1.18 & 10.5 & 1233 &     & M\\
115B  & 0.261 & $-$0.041 & 0.247 & 0.737 & 2.759 & 10.43 & $-$0.22~~ & 10.6 & 1345 &     & M\\
  16  & 0.088 & 0.147 & 0.192 & 0.909 & 2.781 & 11.82 & 1.15 & 10.7 & 1357 &     & M\\
  54  & 0.052 & 0.214 & 0.152 & 0.747 & 2.713 & 12.13 & 1.43 & 10.7 & 1384 & $-$0.2~~ & M\\
 113  & 0.082 & 0.151 & 0.168 & 0.974 & 2.767 & 11.12 & 0.37 & 10.8 & 1409 &  & M\\
  92  & 0.000 & 0.226 & 0.166 & 0.722 & 2.704 & 12.26 & 1.49 & 10.8 & 1423 & 0.0 & M\\
  46  & 0.040 & 0.289 & 0.128 & 0.525 & 2.645 & 12.79 & 2.01 & 10.8 & 1431 & $-$0.5~~ & M\\
  33  & 0.080 & 0.152 & 0.173 & 0.934 & 2.771 & 11.57 & 0.79 & 10.8 & 1431 &  & M\\
 114  & 0.090 &    0.139 & 0.168 & 0.949 & 2.786 & 11.76 & 0.87 & 10.9 & 1506 &  & M\\
049B  & 0.244 & $-$0.026 & 0.215 & 0.932 & 2.822 & 11.37 & 0.48 & 10.9 & 1513 &  & M\\
  5  & 0.015 &    0.153 & 0.189 & 0.947 & 2.770 & 11.73 & 0.78 & 11.0 & 1549 &  & M\\
  9  & 0.030 &    0.136 & 0.227 & 0.953 & 2.790 & 11.95 & 1.00 & 11.0 & 1551 &  & M\\
 62  & 0.008 &    0.216 & 0.165 & 0.726 & 2.714 & 12.81 & 1.72 & 11.1 & 1650 & 0.0 & M\\
139  & 0.080 & 0.278 & 0.106 & 0.553 & 2.646 & 12.85 & 1.57 & 11.3 & 1808 & $-$0.7~~ & M\\
 44  & 0.004 & 0.165 & 0.183 & 0.934 & 2.757 & 12.03 & 0.72 & 11.3 & 1824 &  & M\\
 53  & 0.023 & 0.155 & 0.198 & 0.893 & 2.774 & 12.66 & 1.31 & 11.4 & 1860 &  & M\\
 45  & 0.012 & 0.192 & 0.198 & 0.829 & 2.735 & 12.65 & 1.30 & 11.4 & 1863 &  & M\\
 78  & 0.004 & 0.266 & 0.168 & 0.566 & 2.676 & 13.65 & 2.27 & 11.4 & 1882 & 0.1 & M:\\
 39  & 0.028 & 0.184 & 0.165 & 0.955 & 2.728 & 11.41 &$-$0.03~~ & 11.4 & 1938 &  & NM\\
 41  & 0.000 & 0.176 & 0.195 & 0.956 & 2.741 & 12.01 & 0.31 & 11.7 & 2192 &  & NM\\
  8  & 0.039 & 0.317 & 0.154 & 0.490 & 2.630 & 13.94 & 2.20 & 11.7 & 2230 & $-$0.3~~ & NM\\
 56  & 0.013 & 0.234 & 0.153 & 0.784 & 2.691 & 12.11 & 0.36 & 11.8 & 2238 & $-$0.1~~ & NM\\
 36  & 0.000 & 0.344 & 0.180 & 0.561 & 2.614 & 13.22 & 0.98 & 12.2 & 2805 & $-$0.1~~ & NM\\
 42  & 0.000 & 0.231 & 0.184 & 0.829 & 2.698 & 12.57 & 0.22 & 12.4 & 2952 & 0.3 & NM\\
004B & 0.296 &$-$0.037 & 0.216 & 0.805 & 2.706 & 11.41 & $-$1.33~~ & 12.7 & 3532 &  & NM\\
 51  & 0.000 & 0.342 & 0.139 & 0.592 & 2.590 & 13.42 & $-$0.09~~ & 13.5 & 5033 & $-$0.6~~ & NM\\
 43  & 0.000 & 0.279 & 0.176 & 0.785 & 2.658 & 12.74 & $-$0.77~~ & 13.5 & 5041 & 0.1 & NM\\
040B & 0.161 &$-$0.050 & 0.195 & 0.601 & 2.673 & 12.38 & $-$1.76~~ & 14.1 & 6728 &  & NM\\
\noalign{\smallskip}
Mean value     & 0.074 &       &       &       &       &       &      & 10.42 & 1258 & $-$0.3~~\\
$\sigma$ & 0.057 &       &       &       &       &       &      & ~0.61 & ~339 & 0.3 & \\
\bottomrule
\end{tabular}
\vspace{0.8cm}
\end{table*}

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


%%%%% TABLA 6

\setcounter{table}{5} 
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabcolsep}{1.22\tabcolsep}
\caption{Reddening, unreddened parameters and distance for the open cluster NGC 6830}
\begin{tabular}{rcrccccrcccc}
\toprule
\multicolumn{1}{c}{ID} & $E(b-y)$ & \multicolumn{1}{c}{~~$(b-y)_0$} & $ m_0$ & $c_0$ & $\beta$ & $V_0$ 
& \multicolumn{1}{c}{~~$M_V$} & DM & DST & [Fe/H] & Mbr \\
\midrule
~~26 & 0.244 &  0.320   & 0.233 & 0.206 & 2.661 & 11.26 &  5.67   & ~5.59 & ~131 & 0.85 & nm\\
2258 & 0.310 &  0.236   & 0.179 & 0.422 & 2.721 & 11.67 &  4.10   & ~7.57 & ~327 &      & nm\\
~~13 & 0.371 &  0.396   & 0.245 & 0.306 & 2.605 & 11.19 &  3.43   & ~7.76 & ~357 & 0.46 & nm\\
~164 & 0.291 &  0.169   & 0.180 & 0.761 & 2.766 & 10.99 &  1.90   & ~9.09 & ~658 &      & nm\\
~~~5 & 0.326 & $-$0.060 & 0.111 & 0.492 & 2.721 & ~8.45 & $-$0.65 & ~9.10 & ~661 &      & m:\\
~~~4 & 0.677 & $-$0.077 & 0.103 & 0.342 & 2.685 & ~9.71 & $-$1.25 & 10.96 & 1559 &      & m\\
~~14 & 0.412 & $-$0.064 & 0.141 & 0.454 & 2.714 & 10.22 & $-$0.76 & 10.98 & 1571 &      & m\\
~~~7 & 0.394 & $-$0.041 & 0.125 & 0.747 & 2.689 & ~9.48 & $-$1.64 & 11.12 & 1676 &      & m\\
2257 & 0.449 & $-$0.059 & 0.127 & 0.499 & 2.706 & 10.23 & $-$0.91 & 11.14 & 1692 &      & m\\
~~39 & 0.436 & $-$0.050 & 0.080 & 0.598 & 2.668 & ~9.32 & $-$1.89 & 11.21 & 1745 &      & m\\
~~25 & 0.384 & $-$0.051 & 0.127 & 0.588 & 2.718 & 10.81 & $-$0.76 & 11.57 & 2063 &      & m\\
~~15 & 0.461 & $-$0.054 & 0.103 & 0.558 & 2.681 & 10.68 & $-$1.49 & 12.16 & 2709 &      & m\\
~~24 & 0.447 & $-$0.056 & 0.100 & 0.527 & 2.635 & ~9.72 & $-$2.81 & 12.53 & 3200 &      & m\\
~~~2 & 0.385 & $-$0.056 & 0.098 & 0.533 & 2.603 & ~8.97 & $-$4.40 & 13.37 & 4719 &      & nm\\
~~~8 & 0.420 & $-$0.047 & 0.108 & 0.636 & 2.616 & ~9.73 & $-$4.08 & 13.81 & 5785 &      & nm\\
\bottomrule
\end{tabular}
\vspace{0.55cm}
\end{table*}

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


\vspace{0.2cm}

\section{Methodology}

In order to determine the physical characteristics of the stars in each cluster this procedure was followed.

The evaluation of the reddening was done by first establishing, as was stated above, to which spectral class the stars belonged: early (B and early A) or 
late (late A and F stars) types; the later class stars (later than G) were not considered in the analysis since no reddening determination calibration has 
yet been developed for MS stars. In order to determine the spectral type of each star, the location of the stars in the $[m_1]-[c_1]$ diagram was employed 
as a primary criteron. In Tables~3 and 4 the photometrically determined spectral class has been indicated. The determined spectral types compiled in the 
literature are also presented.

The reddening determination was obtained from the spectral types through Str\"omgren photometry. The application of the calibrations developed for each 
spectral type (Shobbrook 1984 for O and early A types and Nissen 1988 for late A and F stars) were considered. No determination of reddening was calculated 
for G and later spectral types. The results of applying such calibrations are shown in Tables~5 and 6 for NGC 6811 and NGC 6830, respectively. In Table~5, 
the following columns are presented: Column~1 the ID (WEBDA) for each star; Column~2, the reddening $E(b-y)$; Columns~3 to 5, the unreddened indexes 
$(b-y)_0$, $m_0$, and $c_0$; Column~6 the H$\beta$ value; Columns~7 and 8 $V_0$, and the absolute magnitude, respectively. Columns~9 and 10 show the distance 
modulus and the distance in parsecs. The metallicity is presented in Column~11 and, finally, Column~12 lists the membership to the cluster, denoted by M 
(member) or NM (non-member). The membership was determined from the distance modulus or distance histograms. A Gaussian fit with a bin size of one was done 
to the bars in the histogram to all the stars and the obtained fit is presented, along with the uncertainties in each figure. Membership then was established 
from the above mentioned fit. Stars within a standard deviation value from the mean were considered to be members. Those with standard deviation values 
slightly larger than one sigma are considered to be stars with marginal membership. In the table, those stars that are considered to be members of the 
cluster are denoted by an `m'. Marginal membership is indicated by a semi-colon, `m:', those that were non-members are denoted by `nm'. Table~6 is analogous. 
Probable members are denoted by a semicolon.


%%%%% FIGURA 1

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{jpenafig1}
\caption{Histogram of the distance modulus ($X$ axis, in magnitudes) found for the 
B, A and F stars in the direction of NGC 6811 (top) and NGC 6830 (bottom).}
\vspace{0.4cm}
\end{figure}

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


\section{Analysis}

In order to gain some insight into the clusters we must first find out which stars belong to each one. As was already mentioned, this is accomplished by 
constructing a histogram of the deduced distances. From the results listed in Tables~5 and 6 and shown in Figure~1, we can establish that NGC 6811 has a 
distinctive accumulation of thirty-seven stars at a distance modulus of $10.5 \pm 1.0$~mag, whereas NGC~6830 is merely an association of eight early type 
stars at DM $11.1 \pm 1.6$~mag, although emphasis should be made on the fact that we merely observed a small sample of stars in the direction of this 
cluster: nineteen of the brightest stars. According to the study of Netopil et al. (2007)  four CP stars in NGC 6830 were found. Since Str\"omgren photometry 
is most suitable for this topic, we checked our measured stars for the Ap determination. Unfortunately, none of our measured stars lay in the regions 
defined by the boxes in the $m_0$, and $c_0$ diagram where the Ap stars should be, as in Golay's (1974, Figure 124). Hence, we cannot corroborate, nor 
discard the findings by Netopil et al. (2007). For NGC 6811 we determined four stars belonging to the Ap category, namely W9, W34, W105 and W491, all to 
the Sr-Cr-Eu class.

Age is fixed for the two determined clusters once we measured the hottest and hence the brightest stars for each one. The effective temperature of these 
hottest stars was determined by plotting the location of all stars on the theoretical grids of LGK86, once we evaluated the unreddened colors (Figure~2) 
for a solar chemical composition. We considered this metallicity  based on the thirteen F type stars for which we determined the metallicity [Fe/H]; a 
mean value of $-0.18 \pm 0.30$ was found. In the related figures, LGK86 in the upper left corner indicates that the grids were taken from the mentioned 
reference of LGK86 and the specified metalicity. We have utilized the $(b-y)$ vs. $c_0$ diagrams which allow the determination of the temperatures with 
an accuracy of a few hundreds of degrees. However, for NGC~6811, as can be seen in Figure~2, the stars are clustered together and the effective temperature 
cannot be easily determined. To measure the temperature with more accuracy, a plot of $(b-y)$ vs. $\beta$ was constructed and compared with the theoretical 
grids of LGK86, Figure~3. The temperature for the hottest stars is around 11,700~K for NGC 6811, whereas for NGC~6830 it is much hotter (17,000~K). Once 
membership has been established, age is determined after calculating the effective temperature through the calibrations of Meynet, Mermilliod, \& Maeder 
(1993) for open clusters; a log age of 8.266 ($1.845 \times 10^{8}$~yr) is found from the relation $-3.611 \log \log T_{\rm eff}+22.956$ valid in the range 
$\log \log T_{\rm eff}$ within the limits [3.98, 4.25] for NGC~6811; whereas for NGC 6830 the relation log(age) = $-3.499 \log \log T_{\rm eff}+22.476$ valid 
in the range [4.25, 4.56] yields log(age) of 7.69 ($4.89 \times 10^{7}$~yr).

These determinations are confirmed by constructing the color-magnitude diagram of NGC 6811 and NGC 6830 which are shown in Figures~4 and 5, respectively. 
The unreddened magnitudes  [$(b-y)_{0},~M_{V}$] of cluster members taken from Tables~5 (NGC 6811) and 6 (NGC 6830) are shown with filled circles. In each 
plot two theoretical isochrones  in the Str\"omgren photometric system are shown with solid and dashed lines. The metallicity and  ages are indicated in 
the figures. The theoretical isochrones were obtained from the Padova database (Girardi et al. 2003). As can be seen, the isochrones match the observed 
color-magnitude diagram with the ages and distance derived in the present paper.


%%%%%% FIGURA 2

\begin{figure}[!t]
\vspace{0.05cm}
\centering
\includegraphics[clip,width=0.99\columnwidth]{jpenafig2.eps}
\caption{Location of the unreddened points of the two clusters on the LGK86 grids. 
Squares: NGC~6811; dots: NGC 6830.}
\vspace{0.5cm}
\end{figure}

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


%%%%% FIGURA 3

\begin{figure}[!t]
\centering
\includegraphics[clip,width=0.99\columnwidth]{jpenafig3.eps}
\caption{Location of the unreddened points of the hot stars in the NGC 6811 cluster 
on the LGK86 grids.}
\vspace{0.4cm}
\end{figure}

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


%%%%% FIGURA 4

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{jpenafig4}
\caption{Color-magnitude diagram of the NGC 6811 cluster considering only the cluster 
members. The target stars are represented by filled circles. Theoretical isochrones for 
100~Myr (dashed line) and 200~Myr (solid line) computed with $Z=0.019$ are shown.}
\vspace{0.15cm}
\end{figure}

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


\section{Variable stars in NGC 6811}

As was stated in the introduction, Luo et al. (2009) performed time-series photometric observations of the open cluster NGC 6811 to search for variable 
stars. These observations were carried out during five nights from June 6 to July 24, 2008 utilizing the 85~cm telescope of the Xonglong Station of the 
National Astronomical Observatories of the Chinese Academy of Sciences. The instrumentation they used was a $1024 \times 1024$ CCD camera with a field of 
view of $16.5' \times 16.5'$ with standard Johnson-Cousin-Bessell filters in $B$ and $V$ bands, with which they obtained 750 CCD frames in each band. Sixteen 
certain variable stars were detected or confirmed from that survey, namely V1--V7 and V10--V18 following the variable name list of van Cauteren et al. 
(2005) (see Table~1 by Luo et al. 2009). Among these, twelve stars were catalogued as Delta Scuti variables based upon the light curves (V1--V7 and 
V10--V14). The omitted variables, V8 and V9, were outside of their field-of-view. In particular, Luo et al. (2009) discovered variability in V10--V18; 
four of them (V10, V12, V15, V16) had been just reported  as suspected variables by Rose \& Hintz (2007), while the variability of V1--V7 was discovered 
by van Cauteren et al. (2005). On the other hand, nine stars reported as variables by Rose \& Hintz (2007) were not confirmed by Luo et al. (2009). One 
explanation provided for this inconsistency was that the amplitude of light variations was too low to be detected. Luo et al. 2009 also determined the 
membership probabilities of twelve variables (V1--V5 and V10--V16) through the proper-motion membership probabilities (PMP) listed by Sanders (1971). 
From these values they claim that with high probability all of the twelve stars (V1--V3, V5, V10--V16) are cluster members, except for V4. For the the 
stars without PMP data, namely V6, V7, V17 and V18, based on their position in the CMD diagram, they concluded that the first two  are most likely members 
of the cluster whereas the last two are probably field stars.


%%%%% FIGURA 5

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{jpenafig5}
\caption{Color-magnitude diagram of the NGC 6830 cluster considering only the cluster 
members. The target stars are represented by filled circles. Theoretical isochrones for 
40~Myr (dashed line) and 100~Myr (solid line) computed with $Z=0.019$ are shown.}
\vspace{0.3cm}
\end{figure}

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


On the night of  August 6, 2010 (UT) we carried out a very short span of observations in differential photometric mode. The variables we considered were 
chosen due to their nearness and were, in the notation of Luo et al. (2009): V2, V4, V11 and V14 with W5 and W99 as reference and check stars. Although 
the time span we observed was too short to detect long period variation, the only star which showed a clear variation was V4, with two clearly discernible 
peaks of relatively large amplitude of variation, 0.188~mag, and a period of 0.025~d.

From our cluster membership determinations on a star-to-star basis, the conclusion we reach is slightly different from the previous assertions regarding 
variability. Memberships are determined for V1, V3, V4, V5, V10, V11, V13 and V16. Marginal membership for V12 and V14, non-membership for V15 and we were 
unable to determine membership  for the remaining stars mainly because they do not belong to the spectral classes B, A or F but belong to a latter spectral 
type which makes them unlikely to be $\delta$ Scuti type variables. From the location of these variables in the theoretical grids of LGK86, Figures~6 and 7, 
we determine their temperatures.


%%%%% FIGURA 6

\begin{figure}[!t]
\centering
\includegraphics[clip,width=0.99\columnwidth]{jpenafig6}
\caption{Location of the $\delta$ Scuti stars of NGC 6811 on the theoretical grids of LGK86.}
\vspace{0.5cm}
\end{figure}

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


\section{Confidence of the results}

As has been said in previous sections, the high accuracy of each observed star was attained by multiply observing each star in sequences of five 
10~sec integrations. Hence, mean values and standard deviations were calculated to determine the signal/noise ratio. In all cases, enough star 
counts were secured to attain a signal to noise ratio large enough to achieve an accuracy better than 0.01~mag. Nevertheless, it is obvious that 
the brighter stars were more accurately observed than the fainter ones. Quoting Nissen (1988) ``as expected from photon statistics considerations 
the average mean errors increase as we go to fainter magnitudes''. Unfortunately, since the aim of this project was to observe as many stars as 
possible, most of them were observed only twice, and a few, only once. The uncertainties of the season were determined from the differences between 
the derived magnitude of the standard stars vs. reported values in the literature. The average values of such differences are 
$\Delta (V,~b-y,~m_1,~c_1)=(0.008,~0.005,~-0.004,~0.012)$; on most nights at least ten standard stars were observed but this figure increased to 
15 on some nights. The number of the whole sample of standards data points, due to the large time span of the season, was considerable, adding up 
to 80 points of standard stars.

To calculate the propagation of errors for the reddening (in Nissen's 1988 work, \S~3), the intrinsic color index $(b-y)_0$ has served to determine 
the individual color excess, $E(b-y)=(b-y)-(b-y)_0$ and, as in his paper, assuming the photometric mean errors given for our observations, although 
larger than the work by Nissen (1988), we do expect a mean error $E(b-y)$ close to that derived by Nissen of 0.011 for F stars and of 0.009 for 
A stars, since our errors are not exceedingly different.


%%%%% FIGURA 7

\begin{figure}[!t]
\includegraphics[clip,width=0.99\columnwidth]{jpenafig7.eps}
\caption{Location of the hot variable stars of NGC 6811 on the theoretical grids of LGK86.}
\vspace{0.4cm}
\end{figure}

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



%%%%% TABLA 7

\setcounter{table}{6}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabcolsep}{1.2\tabcolsep}
\caption{Compiled characteristics for NGC 6830 and NGC 6811}
%\small
\begin{tabular}{clcccc}
\toprule
Cluster & \multicolumn{1}{c}{Source} & log age  & Reddening $E(B-V)$ & Distance & Metallicity  \\
        &                            &          & [mag]              & [kpc]    &             \\
\midrule
NGC 6830 & Barkhatova (1957)             & --   & --    & 1.68 & --   \\
         & Hoag \& Applequist (1965)     & --   & 0.51  & 1.38 & --   \\
         & Becker \& Fenkart (1971)      & --   & 0.58  & 1.47 & --   \\
         & Moffat (1972)                 & 8.0~ & 0.56  & 1.70 & --   \\
         & Glushkova et al. (1999)       & --   & 0.12  & 1.24 & --   \\
         & Dias et al. (2002)            & 7.57 & 0.50  & 1.64 & --   \\
         & Kharchenko et al. (2005)      & 7.52 & 0.50  & 1.64 & --   \\
         & Paunzen \& Mermilliod (2007)  & 7.57 & 0.50  & 1.64 & --   \\
         & PP                            & 7.69 & 0.63  & 1.88 & +0.13\\
NGC 6811 & Luo et al. (2009)             & 8.76 & 0.12  & 1.31 & +0.02\\
         & Paunzen \& Mermilliod (2007)  & 8.80 & 0.16  & 1.22 & --   \\
         & PP                            & 8.27 & 0.14  & 1.64 & $-$0.02\\
\bottomrule
\end{tabular}
\vspace{0.5cm}
\end{table*}

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


%%%%% TABLA 8

\setcounter{table}{7}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{11}
\caption{Cross ID and membership probabilities for the open cluster NGC 6811}
\renewcommand{\arraystretch}{0.99999999999}
\casitiny
\begin{tabular}{rcccccccccc}
\toprule
\multicolumn{1}{c}{WBD} & Luo et al.  & Sanders & \multicolumn{1}{c}{Becker} & Barkhatova et al. & Kharchenko & Prob (Sanders) 
& \multicolumn{3}{c}{Prob (Kharchenko)} & mbr \\ 
                        & (2009)      & (1971)  & \multicolumn{1}{c}{(1947)} & (1978)            & (2005)     &                & Pkin & Pph & Psp &     \\
\midrule
112 &    &~177 & ~51 & 1136 &    & ~0 &        &        &   & nm\\
122 &    &     &     &      &    &    &        &        &   & nm\\
107 &    &~183 & ~48 &      &    & 96 &        &        &   & nm\\
 31 &    &~102 & ~15 & 1057 &    & 97 &        &        &   & m\\
489 & ~6 &~205 &     & 2080 &    & 89 &        &        &   & m\\
146 &    &~187 & ~42 & 1143 &    & ~0 &        &        &   & m\\
 68 &    &~110 & ~86 & 1065 & 78 & 97 & 0.9272 & 1      & 1 & m\\
 34 &    &~121 & ~22 & 1084 &    & 96 &        &        &   & m\\
105 &    &~185 & ~47 & 1141 &    & 25 &        &        &   & m\\
 85 &    &~~94 & ~~4 & 1041 &    & 95 &        &        &   & m\\
218 &    &~192 &     & 1154 &    & 92 &        &        &   & m\\
106 &    &~172 & ~49 & 1133 &    & 97 &        &        &   & m\\
 47 &    &~158 & ~35 & 1121 &    & 96 &        &        &   & m\\
 37 & ~2 &~136 & ~26 & 1104 &    & 96 &        &        &   & m\\
147 &    &~189 & ~43 & 1146 &    & 97 &        &        &   & m\\
 70 & ~3 &~108 & ~82 & 1063 & 76 & 96 & 0.9837 & 1      & 1 & m\\
 86 &    &~~98 & ~~5 & 1050 &    & 89 &        &        &   & m\\
 26 &    &~~86 & ~10 & 1038 & 69 & 97 & 0.4193 & 1      & 1 & m\\
 99 &    &~159 & ~29 & 1122 &    & 97 &        &        &   & m\\
 18 & ~1 &~~97 & ~85 & 1049 & 73 & 97 & 0.0016 & 1      & 1 & m\\
115 &    &~149 & ~65 &      &    & 95 &        &        &   & m\\
 16 &    &~103 & ~81 & 1059 &    & 90 &        &        &   & m\\
 54 &    &~147 & ~68 & 1114 &    & 97 &        &        &   & m\\
113 & ~5 &~166 & ~60 & 1126 & 98 & 93 & 0.8128 & 1      & 1 & m\\
 92 &    &~115 & ~20 & 1071 &    & ~0 &        &        &   & m\\
 46 &    &~160 & ~36 & 1124 &    & 96 &        &        &   & m\\
 33 & 13 &~113 & ~19 & 1066 & 79 & 95 & 0.9765 & 0.9971 & 1 & m\\
114 &    &~146 & ~66 &      &    & 96 &        &        &   & m\\
 49 &    &~165 & ~46 & 1125 & 97 & 93 & 0.7504 & 1      & 1 & m\\
  5 &    &~127 & ~25 & 1092 & 83 & 93 & 0.9227 & 0.7357 & 1 & m\\
  9 & 16 &~134 & ~71 & 1101 & 86 & 88 & 0.9565 & 1      & 1 & m\\
 62 &    &~123 & ~77 & 1087 &    & 97 &        &        &   & m\\
139 &    &~131 &     & 1096 &    & 95 &        &        &   & m\\
 44 & 11 &~157 & ~33 & 1120 & 95 & 96 & 0.9137 & 1      & 1 & m\\
 53 & 10 &~135 & ~69 & 1105 &    & 94 &        &        &   & m\\
 45 &    &~155 & ~34 & 1118 & 94 & 97 & 0.0001 & 0.6244 & 1 & m\\
 78 &    &~~72 & ~11 & 1023 &    & 95 &        &        &   & m:\\
 39 & ~4 &~144 & ~30 & 1112 &    & 54 &        &        &   & nm\\
 41 &    &~154 & ~28 & 1117 &    & ~0 &        &        &   & nm\\
  8 &    &     &     & 1106 &    &    &        &        &   & nm\\
 56 &    &~138 & ~67 & 1108 & 89 & ~0 & 0.7463 & 0.9707 & 1 & nm\\
 36 &    &~132 &     & 1099 &    & 97 &        &        &   & nm\\
 42 & 14 &~143 & ~31 & 1111 &    & 90 &        &        &   & nm\\
  4 & 12 &~119 & ~23 & 1077 &    & 95 &        &        &   & nm\\
 51 & 15 &~137 & ~70 & 1109 &    & 97 &        &        &   & nm\\
 43 &    &~142 & ~32 & 1110 &    & 96 &        &        &   & nm\\
 40 &    &     &     &      &    &    &        &        &   & nm\\
  6 &    &     &     & 1093 &    &    &        &        &   & und\\
  7 &    &     &     & 1102 &    &    &        &        &   & und\\
 10 &    &     &     & 1085 &    &    &        &        &   & und\\
 12 &    &     &     & 1078 &    &    &        &        &   & und\\
 13 &    &     &     & 1082 &    &    &        &        &   & und\\
 14 &    &~114 & ~80 & 1067 &    & ~0 &        &        &   & und\\
 22 &    &~~84 & ~18 & 1029 &    & ~0 &        &        &   & und\\
 23 & 18 &     & ~17 & 1053 &    &    &        &        &   & und\\
 24 &    &~~95 & ~14 & 1047 & 72 & 97 & 0.8117 & 1      & 1 & und\\
 32 &    &~106 & ~16 & 1061 &    & 97 &        &        &   & und\\
 35 &    &~128 &     & 1095 &    & 80 &        &        &   & und\\
 38 &    &~150 & ~27 & 1115 &    & ~0 &        &        &   & und\\
 57 &    &~129 & ~72 & 1097 &    & 79 &        &        &   & und\\
 58 &    &~130 & ~73 & 1098 &    & 71 &        &        &   & und\\
 63 &    &     &     &      &    &    &        &        &   & und\\
 64 &    &     &     &      &    &    &        &        &   & und\\
 65 &    &~120 & ~78 & 1081 &    & 96 &        &        &   & und\\
 71 &    &~~77 & 100 & 1026 & 66 & 97 & 0.5865 & 1      & 1 & und\\
 73 &    &~~64 & 101 & 1016 & 61 & ~0 & 0.0646 & 1      & 1 & und\\
 74 &    &~~74 & ~13 &      &    & ~0 &        &        &   & und\\
 77 &    &~~67 & ~12 & 1018 &    & 97 &        &        &   & und\\
 79 &    &~~85 & ~~1 & 1031 & 68 & ~0 & 0.4112 & 1      & 1 & und\\
 82 &    &~~89 & ~~3 & 1036 &    & 27 &        &        &   & und\\
 87 &    &~100 & ~~7 & 1054 &    & 57 &        &        &   & und\\
101 &    &~170 & ~38 & 1131 & 87 & 97 & 0.8326 & 1      & 1 & und\\
102 &    &~179 & ~40 & 1137 &    & ~0 &        &        &   & und\\ 
145 & 64 &1113 &     & 0    &    &    &        &        &   & und\\
123 &    &     &     & 1051 &    &    &        &        &   & und\\
133 &    &~~92 & ~~2 & 1039 & 71 & 94 & 0.8766 & 1      & 1 & und\\
178 &    &~~76 & ~99 & 1025 & 65 & 96 & 0.8519 & 0.9999 & 1 & und\\
491 & ~7 &~209 &     &      &    & ~0 &        &        &   & und\\
v17 &    &     &     &      &    &    &        &        &   & und\\
\bottomrule
\end{tabular}
\vspace{0.3cm}
\end{table*}

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


\section{Discussion}

New $\uv$ photoelectric photometry has been acquired and is presented for the brightest stars in the direction of two open clusters NGC 6811 and 
NGC 6830. From the observed stars in the field, some were determined to be early type stars, either B or A. Using the calibrations to determine 
reddening and distance for these stars, distances for the clusters have been obtained. Unreddened indexes in the LGK86 grids allowed us to 
determine the effective temperature of the hottest stars and hence, the age of the cluster.

A brief discussion of each cluster is presented. Table~7 lists the previous  knowledge and the newly determined characteristics of the clusters.

\vspace{0.15cm}

NGC 6811. Considering the classical $UBV$ photometry compiled for this cluster, very little can be deduced about its properties. No clear distinction 
in the color-color diagram $B-V$ vs $U-B$ can be drawn; the same conclusion is reached from its HR diagram. From our results we have determined that 
37 stars belong to the cluster. Since they are the brightest, the conclusion on the age, which agree with that previously determined, is also correct. 
We have found that the cluster is farther, its extinction is less and it is younger than previously assumed. The goodness of our method has been 
previously tested, as in the case of the open cluster Alpha Per (Pe\~na \& Sareyan 2006) against several sources which consider proper motion 
studies as well as results from the Hipparcos and Tycho data bases. Hence, we feel that our results throw new light regarding membership to this cluster.

\vspace{0.15cm}

There have been several previous works in which membership probabilities were considered. Table~8 lists the identification numbers from several 
studies, namely those of WEBDA, Luo et al. (2009), Sanders (1971), Becker (1947), Barkhatova, Zakharova, \& Shashkina (1978) and more recently, the 
compilation by Kharchenko et al. (2005). We have repeated part of the information on  the distance 
provided in Table~8 in order to support the conclusions based on the last columns of the table, which present the membership probability obtained 
in the present paper (PP), that of Sanders (1971) and those reported by the compilation of Kharchenko et al. (2005) based on studies of proper 
motion, photometry and position of the stars. Membership probabilities, if compared with those of Sanders' (1971), are in rough agreement: all but 
two stars (W92 and W146) that we assign cluster membership are not assigned as members according to Sanders' probabilities, but it is equally true 
that those which we define as non-members are determined to be members by Sanders (1971). When the comparison is done with those probabilities of 
the compilation of Kharchenko et al. (2005) the conclusions are equally in agreement. There are two stars, W18 and W45 we define as members that 
Kharchenko et al. (2005) find to be non-members from the proper motion studies but members with the other two criteria. In conclusion, the comparison 
of our results with the others support our findings particularly because the results obtained from $\uv$ photometry are more accurate.

The DM and reddening determined from our photometry, although discordant from those derived from $UBV$ photometry, is in agreement with that of 
Glushkhova, Batyrshinova, \& Ibragimov (1999) who, from radial velocity measurements for 60 late-type stars and $UBVRI$ photoelectric photometry 
refined the distance modulus of the cluster to be $10.47 \pm 0.08$~mag and $E(B-V)$ of $0.12 \pm 0.02$, in agreement with the values we derived. 

We were able to determine membership to the NGC 6811 open cluster of several variable stars. We found that six stars V1, V4, V10, V11, V13 and V16 
are cluster members. On the contrary, V12, V14 and V15 are definitely non-member stars. For the rest not much can be said. Accurate temperature 
determination was done for each star.

NGC 6830. Again, since no previous $\uv$ exists, knowledge of the cluster rests on $UBV$ photometry. Both the color-color and the color-magnitude 
diagrams do not show a clear main sequence which make the distance, age and reddening determinations ambiguous. We only measured nineteen stars, 
but with this small sample we determined some clustering of stars. Our findings coincide, within the uncertainties, with the previous distance, 
reddening and age determinations. Of course, many more data are needed to unambiguously establish the true nature of this cluster, but we emphasize 
that, since we observed all the bright stars, our conclusions are correct.


\acknowledgments

We would like to thank the staff of the OAN and E. Romero for their assistance in securing the observations. This work was partially supported 
by PAPIIT IN110102 and IN114309. HG, ER, SS, AE and ARL thank the IA- Universidad Nacional Aut\'onoma de M\'exico, for the opportunity to carry 
out the observations. JHP thanks the hospitality of the UNAN. Typing and proofreading were done by J. Orta, and J. Miller, respectively. C. Guzm\'an, 
F. Ruiz and A. D\'iaz assisted us in the computing. This research has made use of the Simbad databases operated at CDS, Strasbourg, France and 
NASA ADS Astronomy Query Form.


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\end{document}

