\documentclass[journal]{rmaa}


\usepackage[latin1]{inputenc}


\title{The Absolute Parameters for NSVS\,11868841\altaffilmark{1} and the Oversized Stars in Low-Mass Eclipsing Binaries} 

\author{
\"{O}. \c{C}ak{\i}rl{\i},\altaffilmark{2,3} 
C.~\.{I}bano\v{g}lu,\altaffilmark{2} 
and A. Dervi{\c s}o{\v g}lu\altaffilmark{2}}


\altaffiltext{1}{Based on spectroscopic observations collected at T\"{U}B\.{I}TAK National Observatory, Turkey.} 
\altaffiltext{2}{Ege University, Science Faculty, \.{I}zmir, Turkey.}
\altaffiltext{3}{T{\"u}b{\.i}tak National Observatory, Akdeniz University Campus, Turkey.}


\shortauthor{\c{C}akirli, \.{I}bano\v{g}lu, \& Dervi{\c s}o{\v g}lu}

\shorttitle{Absolute Parameters for NSVS\,11868841}


\fulladdresses{
\item \"{O}. \c{C}ak{\i}rl{\i}, C.~\.{I}bano\v{g}lu, and A. Dervi{\c s}o{\v g}lu: Ege University, Science Faculty, 
Astronomy and Space Sciences Dept., 35100 Bornova, \.{I}zmir, Turkey (omur.cakirli@ege.edu.tr).}


\listofauthors{\"{O}.~\c{C}ak{\i}rl{\i}, C.~\.{I}bano\v{g}lu, \& A.~Dervi{\c s}o{\v g}lu}

\indexauthor{\c{C}ak{\i}rl{\i}, \"{O}}
\indexauthor{\.{I}bano\v{g}lu, C.}
\indexauthor{Dervi{\c s}o{\v g}lu, A.}

\SetYear{2010}
\SetVolume{46}
\ReceivedDate{2010 April 12}
\AcceptedDate{2010 July 29}


\resumen{Se han realizado observaciones espectrosc\'opicas de la binaria eclipsante de baja masa NSV\,11868841, y se han derivado las 
velocidades radiales de ambas componentes. Las masas y radios dererminados son $M_1=0.870\pm0.074~M_{\odot}$, $M_2=0.607\pm0.053~M_{\odot}$, 
$R_1=0.983\pm0.030~R_{\odot}$, $R_2=0.901\pm0.026~R_{\odot}$. Los radios de ambas componentes son, respectivamente, 10\% y 57\% mayores que 
los que corresponden a estrellas de la secuencia principal de edad cero y de las mismas masas. Esta discrepancia puede deberse a que ambas 
estrellas tienen una gran cobertura por manchas. Hemos reunido par\'ametros absolutos para 21 binarias eclipsantes de doble l\'inea y de 
baja masa, para comparar sus posiciones en los diagramas masa-radio y masa-temperatura efectiva. Los valores altos de los radios y las 
bajas temperaturas efectivas encontradas no son debidos a diferencias en metalicidad o en longitud de mezcla. Las discrepancias encontradas 
para estrellas de baja masa pueden deberse a campos magn\'eticos que inhiben el transporte convectivo, lo cual propicia una gran cobertura 
de la superficie estelar por manchas magn\'eticas.}

\abstract{Spectroscopic observations of the low-mass eclipsing binary NSVS\,11868841 have been obtained and the radial velocities 
were derived for both components. The masses and radii determined for the components are $M_1=0.870\pm0.074~M_{\odot}$, $M_2=0.607\pm0.053~M_{\odot}$ 
and $R_1=0.983\pm0.030~R_{\odot}$, $R_2=0.901\pm0.026~R_{\odot}$. Both the primary and secondary stars' radii are 10\% and 57\% larger 
than those of zero-age-main-sequence stars with the same masses. This discrepancy may arise from the large spot coverage of both 
stars. We collected absolute parameters of 21 low mass double-lined eclipsing binaries and compared their positions  in the mass-radius 
and mass-effective temperature panels.  The large radii and lower effective temperatures found for NSV\,11868841 are solved neither with 
differences in metallicity nor in mixing length parameters. These discrepancies for low mass stars may be due to magnetic fields inhibiting 
the convective energy transport, which lead to a large magnetic spot coverage of the surface of such low mass stars.}


\addkeyword{binaries: eclipsing}
\addkeyword{stars: activity}
\addkeyword{stars: fundamental parameters}
\addkeyword{stars: low-mass}


\begin{document}


\maketitle


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

Eclipsing binaries are the best laboratories for determining the fundamental physical properties of stars. Detached, double-lined eclipsing 
binaries yield direct and accurate measures of the masses and radii of the component stars. Measuring these quantities has always been 
observationally challenging. Large-scale surveys, providing imaging and photometric catalogues for substantial fractions of the celestial 
sphere, are now available at a wide range of wavelengths. Over the last few years, these surveys have become invaluable research tools for 
investigating the properties of intrinsically rare objects. These surveys have proven most useful in searches for low-mass stars. Stars with 
masses less than $1~M_{\odot}$ are regarded as low-mass stars  and have late spectral types, namely G, K or M. We cannot vary the conditions 
prevalent on an individual star, but observations of many individual stars can be combined to build up a picture of how stars of different mass 
and composition evolve. Since the  intermediate- and high-mass stars are intrinsically bright sources, most studies have centered on them, with 
little consideration of M dwarfs with masses below $0.6~M_{\odot}$. This reflects the availability of more precise observational constraints, 
and also greater analytic tractability in modelling higher-mass stars. Recently, however, the lower main-sequence has attracted more attention, 
with a series of detailed models extending past the hydrogen-burning limit to the boundary between low-mass brown dwarfs and giant planets. 
Understanding the structure and evolution of stars is a basic goal of stellar astronomy. Critical tests of the evolution theory for stars can 
be made on a small set of eclipsing binary stars  (Baraffe et al. 1998; Girardi et al. 2002; Siess, Forestini, \& Dougados 1997; Chabrier, 
Gallardo, \& Baraffe 2007).  While the results of stellar evolution models compare favorably to data for main-sequence stars with masses greater 
than that of the Sun, evidence has been growing that the models for stars on the lower main-sequence have problems when confronted with precise 
masses and radii from double-lined eclipsing binaries.  As shown by Torres \& Ribas (2002) the evolutionary models underestimate the radii 
and overestimate the effective temperatures of the low-mass stars. These discrepancies were confirmed in subsequent studies by Ribas (2003), 
Lopez-Morales \& Ribas (2005), Torres et al. (2006), Morales et al. (2009a), Morales et al. (2009b), and others. Hints of the radius discrepancies 
have also been described by Popper (1997),  Clausen, Hett, \& Olsen (1999), and others. Recently,  Mullan \& MacDonald (2001),  Torres et al. 
(2006), Morales, Ribas, \& Jordi (2008) proposed a hypothesis based upon the effects of stellar activity to explain the discrepancies. Furthermore 
Stassun et al. (2009) called attention to the fact that low-mass stars appear older or younger in the mass-radius diagram depending on whether 
post- or pre-main-sequence models are used. As the number of low-mass eclipsing binaries studied carefully, both photometrically and spectroscopically, 
increases, a better comparison with the theoretical models can be made. 
   
Light variability of NSVS\,11868841 ($\alpha=23^h17^m58^s$, $\delta=+19\arcdeg17\arcmin 03\arcsec$ (J2000), hereafter NSVS\,1186) was detected 
by Wozniak et al. (2004) from data of the {\it Northern Sky Variability Survey}. They classified it as a detached eclipsing binary with combined 
median magnitude $V=14^m.084\pm0.076$ and an orbital period of 0.60179 days. High-precision light curves in the Johnson $V$-, $R$-, and $I$-bandpass 
were obtained by Coughlin \& Shaw (2007). Since the radial velocities of the components were not available they determined the radii of the stars 
by analyzing the $V$- and $R$-bandpass light curves. In this study we present the first radial velocities obtained for the components of the 
double-lined, short-period eclipsing binary NSVS\,1186 and the physical parameters derived from the analyses of the radial velocities and the light 
curves. Both components show high level chromospheric  activity, evidenced by H$\alpha$ emission lines in their spectra. We discuss the properties 
of the binary and their relation to the discrepancies between empirical and theoretical mass-radius and mass-effective temperature relations for 
low-mass stars.


\section{Spectroscopic Observations}
\subsection{Spectroscopy}

Since wide-band light curves of NSVS\,1186 are available we observed the star spectroscopically. Optical spectroscopic observations were 
obtained with the Turkish Faint Object Spectrograph Camera (TFOSC) attached to the 1.5 m telescope,\footnote{Further details on the telescope 
and the spectrograph can be found at \url{http://www.tug.tubitak.gov.tr}.} on  August 23, 24, and 25, 2008 under good seeing conditions. The 
wavelength coverage of each spectrum was 4100--8100~\AA\ in 11 orders, with a resolving power of $\lambda$/$\Delta \lambda \approx 7000$ at 
6563~\AA\ and an average signal-to-noise ratio (S/N) of $\sim 150$. We also obtained a high S/N spectrum of the M dwarfs GJ\,740 (M0 V) and 
GJ\,623 (M1.5 V) for use as templates in the derivation of the radial velocities (Nidever et al. 2002). 

The electronic bias was removed from each image and we used the {\sc crreject} option for cosmic ray removal. The echelle spectra were extracted 
and wavelength calibrated using a Fe-Ar lamp source with help of the IRAF {\sc echelle} package. The stability of the instrument was checked 
by cross correlating the spectra of the standard star against each other using the {\sc fxcor} task in IRAF. The standard deviation of the 
differences between the velocities measured using {\sc fxcor} and the velocities in Nidever et al. (2002) was about 1.1~km~s$^{-1}$.


\subsubsection{Spectral Types and Temperature Estimates}

We have used the spectra to reveal the spectral type of the primary component of NSVS\,1186. For this purpose we have degraded the spectral 
resolution from 7000 to 3000, in order to use the calibrations by Hern\'andez et al. (2004) by convolving the data with a Gaussian kernel of the 
appropriate width, and we have measured the equivalent widths (EW) of photospheric absorption lines for the spectral classification. We 
have followed the procedures described by Hern\'andez et al. (2004), choosing metallic lines in the blue-wavelength region, where the contribution 
of the primary component is considerably larger than that of the secondary. From several spectra we measured equivalent widths of some spectral 
lines assuming the light contribution of the primary star is 0.6, as given in Table~1.


%%%%% TABLA 1

\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{Equivalent widths of the selected lines in the spectra}
\label{Table 1.}
\begin{tabular}{lcc}
\toprule
\multicolumn{1}{c}{Spectral lines} & EW$_\mathrm{p}$ (\AA)  & EW$_\mathrm{s}$ (\AA)  \\
\midrule
Ca \sc i $\lambda$ 4226			&2.13$\pm$0.11 	& 1.39$\pm$0.12	\\
Fe \sc i $\lambda$ 5329			&1.11$\pm$0.11 	& 0.99$\pm$0.12	\\
Fe \sc i $\lambda$ 4271			&1.44$\pm$0.13 	& 1.41$\pm$0.12	\\
Ca {\sc i}+Fe {\sc i} $\lambda$ 5270	&2.91$\pm$0.21 	& 2.11$\pm$0.21	\\
Ca \sc i $\lambda$ 6162			&1.99$\pm$0.42 	& 1.11$\pm$0.09	\\
Fe \sc i $\lambda$ 5079  		&0.79$\pm$0.07 	& 0.47$\pm$0.11	\\
\bottomrule
\end{tabular}
\vspace{0.2cm}
\end{table}

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


From the calibration relations of EW-Spectral-type given by Hern\'andez et al. (2004), we have derived a spectral type of G9$\pm$1 for the 
primary component. The effective temperature deduced from the calibrations of Drilling \& Landolt (2000), de Jager \& Nieuwenhuijzen (1987) 
and Popper (1980) is, respectively, 5230$\pm$80, 5230$\pm$80, and 5330$\pm$141~K for the primary component. The mean effective temperature of 
the primary component deduced from the spectra is 5250$\pm$95~K . 
  
NSVS\,1186 is listed in several large photometric databases consolidated in the {\it Naval Observatory Merged Astronomical Dataset} (NOMAD-1.0, 
Zacharias et al. 2004), which provides optical magnitudes of $B=14^m.77\pm0^m.02$, $V=13^m.87\pm0^m.01$, $R=13^m.94\pm0^m.01$, $I=12^m.74\pm0^m.02$. 
Since the magnitudes collected from photographic measurements and the colors are inconsistent no attempt has been made to calculate the effective 
temperatures of the components. The infrared magnitudes are taken from 2MASS (Cutri et al. 2003) catalog as $J=12^m.518\pm0^m.023$, 
$H=12^m.069\pm0^m.021$, and $K=11^m.995\pm0^m.019$. The observed infrared colours $J-H=0^m.449\pm0^m.031$ and $H-K=0^m.074\pm0^m.028$ correspond 
to a combined spectral type of G9$\pm$2, in a good agreement with that we derived by spectral lines alone. Using the depth of the eclipses 
in three bands we estimate the light contribution  of the primary component as 0.60, 0.57, 0.55 and 0.56 in the $V$, $J$, $H$ and $K$ bands, 
respectively. Hence, the  $V-K$, $J-H$ and $H-K$ colors of the primary component correspond to a spectral type of G9$\pm$2. We estimate a temperature 
of 5240$\pm$230~K from the calibrations of Tokunaga (2000). The temperature uncertainty of the primary component results from considerations of 
spectral type uncertainties, and calibration differences. The effective temperature of the primary star that we derived from infrared photometric 
measurements is in a good agreement with that we estimated from the spectra alone. The weighted mean of the effective temperature of the primary 
component is 5250$\pm$135~K. 


\subsubsection{Rotational Velocities of the Components}

The width of the cross-correlation profile is a good tool for the measurement of $v \sin i$ (see e.g., Queloz et al. 1998). The rotational 
velocities ($v \sin i$) of the two components were obtained by measuring the FWHM of the CCF peaks in nine high-S/N spectra of NSVS\,1186 
acquired close to the quadratures, where the spectral lines have the largest Doppler-shifts. In order to construct a calibration curve 
FWHM-$v \sin i$, we used an average spectrum of HD\,27962, acquired with the same instrumentation. Since the rotational velocity of 
HD\,27962 is very low, but not zero ($v \sin i \simeq 11$~km~s$^{-1}$, e.g., Royer, Zorec, \& G\'omez 2004, and references therein), it could 
be considered as a useful template for low-mass stars rotating faster than $v \sin i \simeq 10$~km~s$^{-1}$. The spectrum of HD\,27962 was 
synthetically broadened by convolution with rotational profiles of increasing $v \sin i$ in steps of 5~km~s$^{-1}$, and the cross-correlation 
with the original one was performed at each step. The FWHM of the CCF peak was measured and the FWHM-$v \sin i$ calibration was established. 
The $v \sin i$ values of the two components of NSVS\,1186 were derived from the FWHM of their CCF peaks and the aforementioned calibration 
relations, for few wavelength regions and for the best spectra. As a result, a projected rotational velocity of $77\pm3$~km~s$^{-1}$ for the 
primary star and of $62\pm4$~km~s$^{-1}$ for the secondary star were estimated. However, note that the spectral lines of the components could 
not be separated even at quadrature. Thus, the projected rotational velocities estimated in this way should involve larger uncertainties 
than those  given here. 


%%%%% FIGURA 1

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig1.ps}
\caption{Sample of cross correlation functions (CCFs) between NSVS\,1186 and the radial velocity template spectrum around first and second quadrature.}
\label{Figure 1.}
\vspace{0.2cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5


\section{Analysis}
\subsection{The Orbital Configuration}

To derive the radial velocities for the components of binary system, the 16 TFOSC spectra of the eclipsing binary were cross-correlated against 
the spectrum of GJ\,740, a single-lined M0V star, on an order-by-order basis using the {\sc fxcor} package in IRAF\footnote{IRAF is distributed 
by the National Optical Observatory, which is operated by the Association of the Universities for Research in Astronomy, inc. (AURA) under 
cooperative agreement with the National Science Foundation.}. The majority of the spectra showed two distinct cross-correlation peaks in quadrature, 
one for each component of the binary. Thus, to measure the velocity and errors of the individual components both peaks were fitted independently 
in quadrature with a Gaussian profile. If the two peaks appeared blended, a double Gaussian was applied to the combined profile 
using {\sc de-blend} function in the task. For each of the 16 observations we then determined a weighted-average radial velocity for each star 
from all orders without significant contamination by telluric absorption features. Here we used as weights the inverse of the variance of the 
radial velocity measurements in each order, as reported by {\sc fxcor}. In these data, we find no evidence for a third component, since the 
cross-correlation function showed only two distinct peaks. We adopted a two-Gaussian fit algorithm to resolve cross-correlation peaks near the 
first and second quadratures when spectral lines are visible separately. Figure~1 shows examples of cross-correlations obtained by using the 
largest FWHM at nearly first and second quadratures. The two peaks, non-blended, correspond to each component of NSVS\,1186. The stronger peaks 
in each CCF correspond to the more luminous component, which has a larger weight into the observed spectrum. 


%%%%% TABLA 2

\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{Heliocentric radial velocities of NSVS\,1186\tabnotemark{a}}
\label{Table 2.}
\setlength{\tabnotewidth}{0.99\columnwidth}
\tablecols{6}
\setlength{\tabcolsep}{0.995\tabcolsep}
\footnotesize
\begin{tabular}{ccrrcc}
\toprule
HJD 2400000+ & Phase & \multicolumn{2}{c}{Star 1}  & \multicolumn{2}{c}{Star 2}  \\
             &       & $V_\mathrm{p}$ & $\sigma$  & $V_\mathrm{s}$ & $\sigma$ \\
\midrule
55069.4412\tabnotemark{*}  & 0.0536 &$-$120.0 &14.3 &   \nodata   &  \nodata   \\		  
55069.4855  & 0.1272 &$-$162.0 & 9.2 &   \nodata   &  \nodata   \\		   
55069.5284  & 0.1985 &$-$193.6 & 4.3 &  ~80.6  &  ~4.2  \\	   
55069.5727  & 0.2721 &$-$198.1 & 3.9 &  ~85.6  &  ~6.3  \\	   
55068.3810  & 0.2918 &$-$183.7 & 3.2 &  ~80.0  &  ~8.4  \\	   
55068.4258  & 0.3663 &$-$171.6 & 3.0 &  ~47.2  &  ~8.6  \\	   
55068.4707  & 0.4409 &$-$128.7 &13.2 &   \nodata   &  \nodata   \\		  
55068.5134  & 0.5119 & $-$68.2 &14.9 &   \nodata   &  \nodata   \\		  
55068.5578  & 0.5857 & $-$28.6 &11.1 &   \nodata   &  \nodata   \\		  
55067.3674  & 0.6076 &  $-$6.0 & 7.3 &$-$184.6  & 19.7  \\		  
55068.6006  & 0.6568 &  19.2 & 3.3 &$-$214.3  & 12.6  \\		  
55067.4122  & 0.6820 &  28.3 & 3.1 &$-$235.1  & 10.2  \\		  
55067.4552  & 0.7534 &  40.0 & 1.4 &$-$244.3  & 13.3  \\		  
55067.4976  & 0.8240 &  19.9 & 9.2 &$-$230.6  & ~5.2  \\	   
55067.5419  & 0.8975 &   1.1 & 2.4 &   \nodata   &  \nodata   \\		  
55067.5846\tabnotemark{*}  & 0.9684 & $-$56.5 &15.5 &   \nodata   &  \nodata   \\		  
\bottomrule
\tabnotetext{a}{The columns give the heliocentric Julian date, the orbital phase, the radial velocities 
of the two components and the corresponding standard deviations.}
\tabnotetext{*}{These data were not used in the RV analysis.} 
\end{tabular}
\vspace{0.2cm}
\end{table}

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


The heliocentric radial velocities for the primary ($V_\mathrm{p}$) and the secondary ($V_\mathrm{s}$) components are listed in Table~2, along 
with the dates of observation and the corresponding orbital phases computed with the ephemerides given by Coughlin \& Shaw (2007). The velocities 
in this table have been corrected to the heliocentric reference system by adopting a radial velocity of 9.5~km~s$^{-1}$ for the template star 
GJ\,740. The radial velocities listed in Table~2 are the weighted averages of the values obtained from the cross-correlation of orders \#4, 
\#5, \#6 and \#7 of the target spectra with the corresponding order of the standard star's spectrum. A weight $W_i=1/\sigma_i^2$ has been 
given to each measurement. The standard errors of the weighted means have been calculated on the basis of the errors ($\sigma_i$) of the radial 
velocity values for each order according to the usual formula (e.g., Topping 1972). The $\sigma_i$ values are computed by {\sc fxcor} according 
to the fitted peak height, as described by Tonry \& Davis (1979).

First we analysed the radial velocities given in Table~2 for the initial orbital parameters. We held fixed the orbital period and computed 
the eccentricity of the orbit, the systemic velocity and the semi-amplitudes of the radial velocities. The results of the analysis performed with 
{\sc phoebe} are as follows: $e=0.002\pm0.001$, i.e. formally consistent with a circular orbit, $\gamma=-80\pm3$~km~s$^{-1}$, $K_1=118\pm5$ and 
$K_2=169\pm6$~km~s$^{-1}$. Using these values we estimated the projected orbital semi-major axis and the mass ratio as: $a\sin i=3.412\pm0.093~R_{\odot}$ 
and $q={M_2}/{M_1}=0.70\pm0.04$. The observed and calculated radial velocities of  both components are plotted in Figure~2 for comparison.


%%%%% FIGURA 2

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig2.eps}
\caption{Radial velocity curve folded on an orbital period of 0.601790 days, where phase zero is defined to 
be at primary mid-eclipse. Symbols with error bars show the RV measurements for two components of the system 
(primary:  circles, secondary: squares).  Open circles were excluded from the RV analysis.}
\label{Figure 2.}
\vspace{0.2cm}
\end{figure}

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


\subsection{Modelling the Light Curves}

As we mentioned in \S~1 the $V$-, $R$- and $I$-bandpass light curves were obtained by Coughlin \& Shaw (2007). The differential magnitudes 
and orbital phases were read out carefully by the method of {\sc dexter}\footnote{\url{http://dc.zah.uni-heidelberg.de/sdexter}.}. We used 
the most recent version of the eclipsing binary light curve modelling algorithm of Wilson \& Devinney (1971, with updates), as implemented 
in the {\sc phoebe} code of Pr{\v s}a \& Zwitter (2005). The code needs some input parameters, which depend upon the physical structures 
of the component stars. In the light curve solution we fixed some parameters whose values can be estimated from global stellar properties, 
such as effective temperature of the primary component and mass ratio. The weighted mean of the effective temperature has been estimated to 
be  5250$\pm$135~K and the mass ratio 0.70$\pm$0.04. Using these values we adopted the linear limb-darkening coefficients from van Hamme 
(1993) as 0.39 and 0.28 for the primary and secondary components, respectively; the bolometric albedos from Lucy (1967) as 0.5, typical for 
a convective stellar envelope, the gravity brightening coefficients as 0.32 for the both components. The components are assumed to be in 
synchronous rotation. We start with the adjustable parameters: the orbital inclination, $i$, the effective temperature of 
the less massive star, $T_\mathrm{eff_2}$, the potential of the components, $\Omega_1$ and $\Omega_2$, and the monochromatic  luminosity of the 
more massive star, $L_{1}$. Assuming it is a detached binary we used {\sc Mode-2} of the DC program for the individual solution. First we determined 
the preliminary elements and compared them with the observed light curves. Since the observed light curves show distortions we started with the 
two-spot solution, one on the primary and the other on the secondary component. The initial spot parameters were adopted from Coughlin \& Shaw 
(2007). A best fit was obtained for each light curve using the same spots, and the corresponding parameters are given in Table~3. The parameter 
presented in the last column is the weighted mean of the parameters obtained from the individual light curves. The light curves along with the 
best-fitting solutions are shown in Figure 3. 


%%%%% FIGURA 3

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig3.eps}
\label{Figure 3.}
\caption{The phase folded $V$-, $R$- and $I$-bandpass light curves for NSVS\,1186. The best fitting solutions 
represented by the solid lines are also plotted for comparison (see text).}
\vspace{0.2cm}
\end{figure}

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


%%%%% TABLA 3

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{Results of the $V$-, $R$- and $I$-bandpass light curve\\ analysis for NSVS\,1186\tabnotemark{a}} 
\setlength{\tabnotewidth}{0.65\textwidth}
\tablecols{5}
%\setlength{\tabcolsep}{0.95\tabcolsep}
\small
\begin{tabular}{lcccc}
\toprule
\multicolumn{1}{c}{Parameters} & $V$ & $R$ & $I$ & Adopted  \\
\midrule
$i^{\circ}$	      & 87.0$\pm$0.5    & 88.6$\pm$0.2      & 88.3$\pm$0.2     & 88.0$\pm$0.4	\\
T$_\mathrm{eff_1}$ (K)  & 5250[Fix]       & 5250[Fix]        & 5250[Fix]         & 5250[Fix]	\\
T$_\mathrm{eff_2}$ (K)  & 5040$\pm$12     & 4990$\pm$14      & 5110$\pm$34       & 5020$\pm$16	\\
$\Omega_1$            & 4.242$\pm$0.049  & 4.274$\pm$0.049  & 4.260$\pm$0.072   & 4.262$\pm$0.052\\
$\Omega_2$            & 3.810$\pm$0.026  & 3.739$\pm$0.020  & 3.989$\pm$0.054   & 3.790$\pm$0.026\\				
r$_1$                 & 0.289$\pm$0.004  & 0.288$\pm$0.004  & 0.286$\pm$0.006   & 0.288$\pm$0.004\\
r$_2$                 & 0.263$\pm$0.003  & 0.267$\pm$0.002  & 0.250$\pm$0.005   & 0.264$\pm$0.003\\
${L_{1}}/{(L_{1}+L_{2})}$  & 0.604$\pm$0.009  & 0.586$\pm$0.009  & 0.591$\pm$0.013  & \nodata \\
$\sum(W(O-C)^2) $     & 0.041            & 0.026            & 0.131             & \nodata \\
Weight                & 3                & 5                & 1                 & \nodata \\		
\bottomrule
\tabnotetext{a}{The adopted values are the weighted means of the values determined from the individual light curves.}
\end{tabular}
\vspace{0.58cm}
\end{table*}

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


Coughlin \& Shaw (2007) analyzed only $V$- and $R$-light curves. Our analysis gives very different parameters when compared with those obtained 
by them. They estimate very low effective temperatures for the components with respect to their predicted masses. The fractional radii for the 
primary and secondary stars obtained by them are 15\% and 20\% smaller than those obtained by us using the same light curves. In contrast, the 
absolute radii are 5\% and 3\% larger than we found. The main difference is the location of the spots on the surface of the stars. The spot 
parameters given by them for the stars should be interchanged. One spot on the south pole of the primary and one spot on the north pole of the 
secondary represent well the three-color light curves.  The spot coverage on the surface of the stars is about 8\%. 


\subsection{Absolute Parameters}

Combining the parameters obtained by radial velocity and light curve analyses we calculated the physical parameters of the components 
as listed in Table~4. We compared the locations of the components in the effective temperature-luminosity diagram, i.e., Hertzsprung-Russell 
diagram (Figure~4). While the location of the more massive primary star agrees well with that of a star having its mass, the secondary 
component appears to be more luminous, probably due to a larger effective temperature and radius. We also computed the  radii of the 
components as $R_1=0.983\pm0.030~R_{\odot}$ and $R_2=0.901\pm0.026~R_{\odot}$ for the primary and secondary stars, respectively.

We computed the luminosities of the components using these radii and effective temperatures as $L_1=0.649\pm0.069~L_{\odot}$ and 
$L_2=0.456\pm0.049~L_{\odot}$ for the primary and secondary stars, respectively. We compared the positions of the components in the $L-T_e$ 
diagram with evolutionary tracks of  pre- and post- main sequence evolution and as well as with the ZAMS, as shown in Figure~4. 
For constructing the solar metallicity ZAMS and evolutionary tracks, we used the Cambridge version of the  the {\sc stars} code which was 
originally developed by Eggleton (1971) and substantially updated by Eldridge \& Tout (2004). The current version is also capable of 
accounting for molecular contributions in the equation of state according to the Marigo (2002) approximation, which may be crucial for low 
mass stars. The less massive component seems to be hotter and more luminous with respect to the models. The physical parameters determined 
by us are very different from those obtained by Coughlin \& Shaw (2007). While they estimate effective temperatures between 4370 and 
5250~K from the observed colours they adopted an effective temperature of 3970~K for the more massive star. The masses of the components 
were estimated to be $0.94~M_\odot$ and $0.87~M_\odot$, the radii $1.03~R_\odot$ and $0.93~R_\odot$, and the effective temperature 3750 K for 
the secondary star. The locations of the component stars in the HR diagram correspond to stars having masses below $0.4~M_{\odot}$. The 
$J$-,$H$-, and $K$- band extinctions in the direction of the variable were taken from Schlegel, Finkbeiner, \& Davis (1998) as $A_J=0.046$, 
$A_H=0.030$ and $A_K=0.019$ magnitudes. We computed the absolute magnitudes as $M_J=3.96\pm0.10$, $M_H=3.50\pm0.07$ and $M_K=3.46\pm0.07$ for
 the primary star. Then using the $JHK$ magnitudes given in \S~2.1.1 we estimate the distance to the variable as 668$\pm$25, 689$\pm$24 and 
678$\pm$22 parsec in the $J$, $H$, and $K$ bands, respectively.


%%%%% FIGURA 4

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig4.eps}
\caption{Comparison between evolutionary models and the physical parameters of NSVS 1186 in the effective 
temperature-luminosity diagram with the luminosities determined from the light and radial velocity curves. 
Theoretical evolutionary tracks, both pre- and post- main sequence, for masses of $0.870~M_{\odot}$ (dotted 
line) and $0.607~M_{\odot}$ (dashed line) and ZAMS (solid line) with solar abundance were calculated with the 
{\sc stars} code. The circle and square denote the primary and secondary stars.}
\label{Figure X.}
\vspace{0.2cm}
\end{figure}

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


\section{Oversized Stars in Low-Mass Eclipsing Binaries}

Abt (1963) and Duquennoy, Mayor, \& Halbwachs (1991) report that binary stars are more common than single stars at masses 
above that of the Sun. In contrast, Reid \& Gizis (1997) and Delfosse et al. (1999) suggest that binaries are not very 
common among low-mass stars, although approximately 75\% of all stars in our Galaxy are low-mass dwarfs with masses smaller 
than $0.7~M_{\odot}$. Due to the low binary fractions and their faintness very few low-mass eclipsing binary systems have been 
observed so far both photometrically and spectroscopically, yielding accurate physical parameters. Recently, in a pioneer 
study, Ribas (2003, 2006) collected the available masses and radii of the low-mass stars and compared with those obtained by 
stellar evolution models. Despite the small numbers of the sample, a total of eight double-lined eclipsing binaries with masses 
and radii determined with an accuracy of better than 3\%, the comparison evidently revealed that the observed radii are 
systematically larger than those predicted by the models. However, the effective temperatures are cooler than in the theoretical 
calculations, the luminosities being in agreement with those of single stars of the same mass. This discrepancy between the 
models and observations has been explained by Mullan \& MacDonald (2001), Torres et al. (2006), Ribas (2006) and Lopez-Morales 
(2007) and others by the high level magnetic activity in low-mass stars. They suggest that stellar activity may be responsible 
for the observed discrepancy through inhibition of convection or effects of a significant spot coverage. However, Berger et al. 
(2006) compared the interferometric radii of low-mass stars with those estimated from theory and found a correlation between an 
increase in metallicity and a larger-than-expected radius, i.e. the larger radii seem to be caused by differences in metallicity. 


%%%%% TABLA 4  

\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{Fundamental parameters of the system}
\label{parameters}
\setlength{\tabcolsep}{0.98\tabcolsep} 
\footnotesize
\begin{tabular}{lcc}
\toprule
\multicolumn{1}{c}{Parameter}  & Primary  & Secondary \\
\midrule
Mass ($M_{\odot}$)                        & 0.870$\pm$0.074   & 0.607$\pm$0.053  \\
Radius ($R_{\odot}$)                      & 0.983$\pm$0.030   & 0.901$\pm$0.026  \\
$\log~g$ (cgs)                           & 4.392$\pm$0.019   & 4.311$\pm$0.021  \\
$T_\mathrm{eff}$ (K)                      & 5250$\pm$135      & 5\,020$\pm$135  \\
$\log~(L/L_{\odot})$                      & $-0.188\pm0.045$  & $-0.341\pm0.046$  \\
$(v \sin~i)_\mathrm{obs}$ (km~s$^{-1}$)    & 77$\pm$3          & 62$\pm$4  \\
$(v \sin~i)_\mathrm{calc}$ (km~s$^{-1}$)   & 83$\pm$3          & 76$\pm$2  \\
\bottomrule  
\end{tabular}
\vspace{0.2cm}
\end{table}

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


The number of double-lined low-mass eclipsing binaries having precise photometric and spectroscopic observations is now 21, 
as far as the authors know. Combining the results of the analysis of both photometric and spectroscopic observations accurate 
masses, radii, effective temperatures and luminosities  of the components have been obtained. In Table~5 we list absolute 
parameters for the low-mass stars with their standard deviations. In Figure~5 we plot the radii of the low-mass stars in 
eclipsing binary systems as a function of mass. Theoretical mass-radius ($M-R$) diagrams for the zero-age main-sequence stars 
with solar abundance taken from the {\sc stars} code and Siess, Dufour, \& Forestini (2000) are also plotted for comparison.


%%%%% FIGURA 5

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig5.eps}
\caption{Locations of the low-mass stars in the mass-radius diagram. The components of NSVS\,1186 are 
shown by triangles. The solid and dashed lines represent the ZAMS models taken from the {\sc stars} code 
and Siess et al. (2000), respectively, with solar abundance.}
\label{Figure x.}
\vspace{0.2cm}
\end{figure}

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

 
The stars below $0.3~M_{\odot}$ appear to trace the theoretical $M-R$ diagram. However, larger mass stars, above $0.3~M_{\odot}$, 
significantly deviate from the theoretical $M-R$ digram. We also computed projected rotational velocities of the components 
using their radii and orbital periods. Since the orbital periods are generally short, we assumed spin-orbit synchronization. 
The rotational velocities are plotted in Figure~6 as a function of the radius difference calculated as 
$(R_\mathrm{obs}-R_\mathrm{zams})/R_\mathrm{zams}$. This plot shows that as the rotational velocity increases, the difference 
in  radius, gets larger for the stars given in Table~5.

A low-mass star has a convective atmosphere with a radiative core. The depth of the convective zone is about $0.28~R$ for 
a star of mass of about $0.9~M_{\odot}$, and gradually increases to about $0.41~R$ for a star with a mass of about $0.4~M_{\odot}$. 
Stars are thought to be fully convective below about $0.35~M_{\odot}$. Therefore, the internal structure of such a low-mass 
star with a deep convective zone is tightly dependent on the mixing length parameter, $\alpha$. In Figure~7a and b we compare 
locations of the low-mass stars in the $M-R$ and $M-T_\mathrm{eff}$ diagrams with the theoretical calculations for various $\alpha$ 
parameters. Convection is modelled by mixing length theory (B{\"o}hm-Vitense 1958) with the ratio of mixing length to pressure 
scale height (i.e., $\alpha=l/H_\mathrm{p}$). Theoretical models show that there is no significant separation in the $M-R$ relation 
for the stars below about $0.6~M_{\odot}$, depending on the mixing length parameter. For masses above this value a separation 
is revealed. However, as the $\alpha$ parameter increases the computed effective temperature also increases. A separation is 
clearly seen even for the masses below $0.6~M_{\odot}$. We also plotted empirical parameters for the low-mass stars in these diagrams. 
This comparison clearly exposes that the discrepancies in radii and effective temperatures could not be explained only by changing 
the $\alpha$ parameter as it is obvious in the $M-R$ and $M-T_\mathrm{eff}$ plots represented in Figure~7. On the other hand, Demory et al. (2009) 
showed that there is no significant correlation between metallicity and radius for the single, low-mass stars. An alternative 
explanation appears to be the magnetic activity responsible for the observed larger radii but cooler effective temperatures. As 
demonstrated by D'Antona, Ventura, \& Mazzitelli (2000), Mullan \& MacDonald (2001) and Chabrier et al. (2007) magnetic fields change the evolution 
of low-mass stars. Due to the high magnetic activity in fast-rotating dwarfs their surfaces are covered by dark spots. Spot 
coverage in active dwarfs yields larger radii and lower effective temperatures.


%%%%% TABLA 5

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\setlength{\tabnotewidth}{0.99\textwidth}
\tablecols{7}
\setlength{\tabcolsep}{1.5\tabcolsep} 
\caption{Mass, radius, effective temperature and orbital period of\\ the low-mass stars in double-lined eclipsing binaries}
\label{parameters2}
\scriptsize
\begin{tabular}{lcccccc}
\toprule
\multicolumn{1}{c}{Object}  & Star  & Mass/$M_{\odot}$  & Radius/$R_{\odot}$  & $T_{\rm eff}$/K  & $P_{\rm orb}/\rm day$  & Refs \\
\midrule
CM Dra	&A	& 0.2310$\pm$0.0009  & 0.2534$\pm$0.0019  & 3130$\pm$70  & 1.276  & 1 \\
	&B	& 0.2141$\pm$0.0008  & 0.2398$\pm$0.0018  & 3120$\pm$70  &        &   \\
YY Gem	&A	& 0.5992$\pm$0.0047  & 0.6194$\pm$0.0057  & 3820$\pm$100 & 0.820  & 2 \\
	&B	& 0.5992$\pm$0.0047  & 0.6194$\pm$0.0057  & 3820$\pm$100 &        &   \\
CU Cnc	&A	& 0.4349$\pm$0.0012  & 0.4323$\pm$0.0055  & 3160$\pm$150 & 2.794  & 3 \\
	&B	& 0.3992$\pm$0.0009  & 0.3916$\pm$0.0094  & 3125$\pm$150 &        &   \\
GU Boo	&A	& 0.6101$\pm$0.0064  & 0.6270$\pm$0.0160  & 3920$\pm$130 & 0.492  & 4 \\
	&B	& 0.5995$\pm$0.0064  & 0.6240$\pm$0.0160  & 3810$\pm$130 &        &   \\
TrES-Her0-07621	& A	& 0.4930$\pm$0.0030  & 0.4530$\pm$0.0600  & 3500$\pm$\nodata    & 1.137  & 5 \\
	&B	& 0.4890$\pm$0.0030  & 0.4520$\pm$0.0500  & 3395$\pm$\nodata  &       &   \\
2MASS J05162881+2607387	&A	& 0.7870$\pm$0.0120  & 0.7880$\pm$0.0150  & 4200$\pm$\nodata  & 2.619 & 6 \\
	&B	& 0.7700$\pm$0.0090  & 0.8170$\pm$0.0100  & 4154$\pm$\nodata  &       &   \\
UNSW-TR 2	& A  & 0.5290$\pm$0.0350  & 0.6410$\pm$0.0500  & \nodata  & 2.144  & 7 \\
	& B	& 0.5120$\pm$0.0350  & 0.6080$\pm$0.0600 & \nodata  &      &  \\
NSVS 06507557	& A  & 0.6560$\pm$0.0860  & 0.6000$\pm$0.0300  & 3960$\pm$80  & 0.520  & 8 \\
	&B	& 0.2790$\pm$0.0450  & 0.4420$\pm$0.0240  & 3365$\pm$80  &      &   \\
NSVS 02502726	&A	& 0.7140$\pm$0.0190  & 0.6740$\pm$0.0600  & 4300$\pm$200  & 0.560 & 9 \\
	&B	& 0.3470$\pm$0.0120  & 0.7630$\pm$0.0050  & 3620$\pm$205  &     &   \\
T-Lyr1-17236	&A	& 0.6795$\pm$0.0107 & 0.6340$\pm$0.0430 & 4150$\pm$\nodata  & 8.430 & 10 \\
	&B	& 0.5226$\pm$0.0061  & 0.5250$\pm$0.0520  & 3700$\pm$\nodata   &      & \\
2MASS J01542930+0053266	&A	& 0.6590$\pm$0.0310  & 0.6390$\pm$0.0830  & 3730$\pm$100 & 2.639 & 11 \\
	&B	& 0.6190$\pm$0.0280  & 0.6100$\pm$0.0930  & 3532$\pm$100  &      &   \\
GJ 3236	&A	& 0.3760$\pm$0.0170  & 0.3828$\pm$0.0072  & 3310$\pm$110  & 0.770  & 12 \\
	&B	& 0.2810$\pm$0.0150  & 0.2992$\pm$0.0075  & 3240$\pm$110  &      & \\
SDSS-MEB-1	&A	& 0.2720$\pm$0.0200  & 0.2680$\pm$0.0090  & 3320$\pm$130  & 0.410 & 13 \\
	&B	& 0.2400$\pm$0.0220  & 0.2480$\pm$0.0080  & 3300$\pm$130  &      &   \\
BD -22 5866	&A	& 0.5881$\pm$0.0029  & 0.6140$\pm$0.0450  & \nodata  & 2.211 & 14 \\
	&B	& 0.5881$\pm$0.0029  & 0.5980$\pm$0.0450  & \nodata    &     &  \\
NSVS 01031772	&A	& 0.5428$\pm$0.0027  & 0.5260$\pm$0.0028  & 3615$\pm$72  & 0.368 & 15 \\
	&B	& 0.4982$\pm$0.0025  & 0.5088$\pm$0.0030  & 3513$\pm$31  &      &   \\
NSVS 11868841	&A	& 0.8700$\pm$0.0740  & 0.9830$\pm$0.0300  & 5260$\pm$110  & 0.602  & This paper	\\
	&B	& 0.6070$\pm$0.0530  & 0.9010$\pm$0.0260  & 5020$\pm$110   &     & \\
GJ 2069A	&A	& 0.4329$\pm$0.0018  & 0.4900$\pm$0.0800  & \nodata   & 2.771  & 16 \\
	&B	& 0.3975$\pm$0.0015  & 0.3300$\pm$0.0400  & \nodata    &     &  \\
2MASS J04463285+1901432	 & A  & 0.4700$\pm$0.0500  & 0.5700$\pm$0.0200  & 3320$\pm$150  & 0.630  & 18 \\
	                 & B  & 0.1900$\pm$0.0200  & 0.2100$\pm$0.0100  & 2910$\pm$150  &        &    \\
NSVS 6550671	         & A  & 0.5100$\pm$0.0200  & 0.5500$\pm$0.0100  & 3730$\pm$60   & 0.193	 & 19 \\
	                 & B  & 0.2600$\pm$0.0200  & 0.2900$\pm$0.0100  & 3120$\pm$65   &        &    \\
IM Vir	                 & A  & 0.9810$\pm$0.0120  & 1.0610$\pm$0.0160  & 5570$\pm$100  & 1.309  & 20 \\
	                 & B  & 0.6644$\pm$0.0048  & 0.6810$\pm$0.0130  & 4250$\pm$130  &        &    \\
RXJ0239.1                & A  & 0.7300$\pm$0.0090  & 0.7410$\pm$0.0040  & 4645$\pm$20   & 2.072  & 21 \\
	                 & B  & 0.6930$\pm$0.0060  & 0.7030$\pm$0.0020  & 4275$\pm$15   &        &    \\
\bottomrule
\noalign{\smallskip}
\tabnotetext{}{References: (1) Morales et al. (2009a), (2) Torres \& Ribas (2002), (3) Ribas (2003), (4) L\'opez-Morales \& Ribas (2005), 
(5) Creevey et al. (2005), (6) Bayless \& Orosz (2006), (7) Young et al. (2006), (8) {\c C}ak{\i}rl{\i} \& Ibano{\v g}lu (2010), 
(9) {\c C}ak{\i}rl{\i}, Ibano{\v g}lu, \& G{\"u}ng{\"o}r (2009), (10) Devor et al. (2008), (11) Becker et al. (2008), (12) Irwin et al. (2009), 
(13) Blake et al. (2008), (14) Shkolnik et al. (2008), (15) L\'opez-Morales et al. (2006), (16) Delfosse et al. (1999), (17) Beatty et al. (2007), 
(18) Hebb et al. (2006), (19) Dimitrov \& Kjurkchieva (2010), (20) Morales et al. (2009b), (21) L\'opez-Morales \& Shaw (2007).}
\end{tabular}
\vspace{0.57cm}
\end{table*}

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


%%%%% FIGURA 6

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{ocakirlifig6.eps}
\caption{The rotational velocities are plotted against the radius difference from the ZAMS at the same mass.}
\label{Figure y.}
\vspace{0.2cm}
\end{figure}

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



%%%%% FIGURA 7

\begin{figure}[!t]
\centerline{\includegraphics[width=0.99\columnwidth]{ocakirlifig7a.eps}}
\vspace{0.2cm}
\centerline{\includegraphics[width=0.99\columnwidth]{ocakirlifig7b.eps}}
\caption{Mass-radius (a) and mass-effective temperature (b) relationships for zero-age main-sequence low-mass 
stars  calculated with the {\sc stars} code for values of the mixing length parameter $\alpha=4$ (dotted line), 
$\alpha=2$ (solid line), $\alpha=1$ (dashed line) and $\alpha=0.5$ (dot-dashed line). Values of the $\alpha$ 
parameter larger than 0.5 appear to affect the radius slightly for a star below $0.7~M_{\odot}$. As $\alpha$ 
increases the effective temperatures also increase.}
\label{Figure z.}
\vspace{0.2cm}
\end{figure}

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



\section{Discussion}

We obtained the radial velocity curves for the low-mass eclipsing binary NSVS\,1186. We re-analysed  the existing $V$-, $R$- 
and $I$-bandpass light curves. Since the light curves are distorted they are modelled assuming one spot located on each star. 
Then, combining the photometric and spectroscopic solutions, we derived the absolute physical parameters for both components. 
The standard deviations of the parameters have been determined using the {\sc jktabsdim} code (Southworth \& Clausen 2007). 
The less massive component appears to have a larger radius and a higher temperature than expected for its mass. On the other 
hand, the primary star seems to have a larger radius but the effective temperature is in agreement with that expected for its 
mass. We suppose that the larger radii of both components may be due to a higher activity in the system at the time that photometry 
is obtained. The locations of the components in the H-R diagram have been plotted and compared with theoretical models. The 
secondary component seems to be slightly brighter than expected for its mass.

Basic physical parameters determined from double lined low mass binaries, such as mass, radius, effective temperature and orbital 
period, are collected. The locations of the low-mass stars in the mass-radius diagram are compared with the theoretical ZAMS models. 
Since the low-mass stars evolve very slowly, we prefer a comparison with the ZAMS models. Theoretical models tend to underestimate 
the radii at a given mass in the range of 0.3 and $0.6~M_{\odot}$. Due to the evolutionary effect on the radius, we take into account 
only this mass range, preventing any confusion. Since low-mass stars have deeper convective layers in their atmospheres, we also 
computed the radii and temperatures for the above-mentioned mass range for various mixing-length parameters. We find that the 
mixing-length parameter does not significantly affect the radii; on the contrary, it changes considerably the effective temperatures 
of the stars. Comparison with the observations shows that the observed larger radii of the late K and M dwarfs cannot be represented 
with the values of mixing-length parameters. These comparisons confirm that magnetic field induced inhibition of convection in 
fast-rotating low-mass stars with deep convective zones leads to larger radii and lower effective temperatures than those expected 
from theoretical models (D'Antona et al. 2000; Mullan \& MacDonald 2001; Chabrier et al. 2007).  


\acknowledgments

The authors acknowledge generous allotments of observing time at T\"UB{\.I}TAK National Observatory (TUG) of Turkey. We also 
wish to thank the Turkish Scientific and Technical Research Council for supporting this work through grant Nr. 108T210 
and  EB{\.I}LTEM Ege University Science Foundation Project No:08/B\.{I}L/027. Dr. Esin Sipahi is acknowledged for the 
aid during the computation. We would like express our sincere gratitude to the anonymous referee, whose suggestions made 
the paper much clearer. 


\begin{thebibliography}

\bibitem{1963ApJS....8...99A} Abt, H.~A. 1963, ApJS, 8, 99 

\bibitem{} Baraffe, I., Chabrier, G., Allad, F., \& Hauschildt, P.~H. 1998, A\&A, 337, 403

\bibitem{} Bayless, A.~J., \& Orosz, J.~A. 2006, ApJ, 651, 1155 

\bibitem{} Beatty, T.~G., et al. 2007, ApJ, 663, 573 

\bibitem{} Becker, A.~C., et al. 2008, MNRAS, 386, 416

\bibitem{} Berger, D.~H., et al. 2006, ApJ, 644, 475 

\bibitem{} Blake, C.~H., Torres, G., Bloom, J.~S., \& Gaudi, B.~S. 2008, ApJ, 684, 635 

\bibitem{1958ZA.....46..108B} B{\"o}hm-Vitense, E. 1958, Zert. Astrophys., 46, 108

\bibitem{} Chabrier, G., Gallardo, J.,  \& Baraffe, I. 2007, A\&A, 472, 17

\bibitem{} Clausen, J.~V., Helt, B.~E., \& Olsen, E.~H. 1999, in ASP Conf. Ser. 173, Theory and Tests of Convection in Stellar Structure, 
ed. A. Gim\'enez, E.~F. Guinan, \& B. Montesinos (San Francisco: ASP), 321 

\bibitem{} Coughlin, J.~L., \& Shaw, J.~S. 2007, J. Southeastern Assoc. Res. Astron., 1, 7C

\bibitem{2005ApJ...625L.127C} Creevey, O.~L., et al. 2005, ApJ, 625, L127 

\bibitem{} Cutri, R.~M., et al. 2003, The IRSA 2MASS All-Sky Point Source Catalog, NASA/IPAC Infrared Science Archive (Pasadena, CA: NASA/CalTech), 
\url{http://irsa.ipac.caltech.edu/applications/Gator/} 

\bibitem{2010MNRAS.401.1141C} {\c C}ak{\i}rl{\i}, {\"O}., \& Ibano{\v g}lu, C. 2010, MNRAS, 401, 1141 

\bibitem{2009NewA...14..496C} {\c C}ak{\i}rl{\i}, {\"O}., Ibano{\v g}lu, C.,  \& G{\"u}ng{\"o}r, C. 2009, New Astron., 14, 496 

\bibitem{} D'Antona, F., Ventura, P., \&  Mazzitelli, I. 2000, ApJ, 543, L77

\bibitem{1999AA...341L..63D} Delfosse, X., Forveille, T., Mayor, M., Burnet, M., \& Perrier, C. 1999, A\&A, 341, 63 

\bibitem{} de Jager, C., \& Nieuwenhuijzen, H. 1987, A\&A, 177, 217

\bibitem{} Demory, B.-O., et al. 2009, A\&A, 505, 205 

\bibitem{} Devor, J., et al. 2008, ApJ, 687, 1253 

\bibitem{} Dimitrov, D.~P., \& Kjurkchieva, D.~P. 2010, MNRAS, 406, 2559

\bibitem{} Drilling,  J.~S., \& Landolt, A.~U. 2000, in Allen's Astrophysical Quantities, ed. A.~N. Cox (4th ed., New York: AIP/Springer), 381

\bibitem{} Duquennoy, A., Mayor, M., \& Halbwachs, J.-L. 1991, A\&AS, 88, 281 

\bibitem{1971MNRAS.151..351E} Eggleton, P.~P. 1971, MNRAS, 151, 351 

\bibitem{} Eldridge, J.~J., \& Tout, C.~A. 2004, MNRAS, 348, 201 

\bibitem{} Girardi, L., Bressan, A., Bertelli, G., \&  Chiosi, C. 2002, A\&AS, 141, 371

\bibitem{2006AJ....131..555H} Hebb, L., Wyse, R.~F.~G., Gilmore, G., \& Holtzman, J. 2006, AJ, 131, 555 

\bibitem{} Hern\'andez, J., Calvet, N., Brice\~no, C., Hartmann, L.,  \& Berlind, P. 2004, AJ, 127, 1682

\bibitem{2009ApJ...701.1436I} Irwin, J., et al. 2009, ApJ, 701, 1436 

\bibitem{2007ApJ...660..732L} L\'opez-Morales, M. 2007, ApJ, 660, 732 

\bibitem{2006astro.ph.10225L} L\'opez-Morales, M., Orosz, J.~A., Shaw, J.~S., Havelka, L., Ar\'evalo, M.~J., McIntyre, T., \& L\'azaro, C. 
2006, arXiv:astro-ph/0610225 

\bibitem{2005ApJ...631.1120L} L\'opez-Morales, M., \& Ribas, I. 2005, ApJ, 631, 1120 

\bibitem{} L\'opez-Morales, M., \& Shaw, J.~S. 2007, in ASP Conf. Ser. 362, The Seventh Pacific Rim Conference on Stellar Astrophysics, 
ed. Y.~W. Kang, H.-W. Lee, K.-C. Leung, \& K.-S. Cheng (San Francisco: ASP), 26 

\bibitem{} Lucy, L.~B. 1967, Zert. Astrophys., 65, 89

\bibitem{} Marigo, P. 2002, A\&A, 387, 507 

\bibitem{} Morales, J.~C., Ribas, I., \& Jordi, C. 2008, A\&A, 478, 507

\bibitem{} Morales, J.~C., Torres, G., Marschall, L.~A., \& Brehm, W. 2009b, ApJ, 707, 671

\adjustfinalcols

\bibitem{} Morales, J.~C., et al. 2009a, ApJ, 691, 1400 

\bibitem{} Mullan, D.~J., \&  MacDonald, J. 2001, ApJ, 559, 353 

\bibitem{} Nidever, D.~L., Marcy, G.~W., Butler, R.~P., Fischer, D.~A., \& Vogt, S.~S. 2002, ApJS, 141, 503

\bibitem{} Popper, D.~M.\ 1980, ARA\&A, 18, 115 

\bibitem{} \ibidrule  1997, AJ, 114, 1195 

\bibitem{} Pr{\v s}a, A., \& Zwitter, T. 2005, ApJ 628, 426

\bibitem{} Queloz, D., Allain, S., Mermilliod, J.-C., Bouvier, J., \& Mayor, M. 1998, A\&A, 335, 183

\bibitem{1997AJ....114.1992R} Reid, I.~N., \& Gizis, J.~E. 1997, AJ, 114, 1992 

\bibitem{} Ribas, I. 2003, A\&A, 398, 239 

\bibitem{} \ibidrule 2006, Ap\&SS, 304, 89 

\bibitem{} Royer, F., Zorec, J.,  \&  G\'omez, A. 2004, in IAU Symp. 224, The A-Star Puzzle, ed. J. Zverko, J. Ziznovsky, S.~J. Adelman, \& 
W.~W. Weiss (Cambridge: Cambridge Univ. Press), 109

\bibitem{} Schlegel, D.~J., Finkbeiner, D.~P., \& Davis, M. 1998, ApJ, 500, 525 

\bibitem{2008ApJ...682.1248S} Shkolnik, E., Liu, M.~C., Reid, I.~N., Hebb, L., Cameron, A.~C., Torres, C.~A., \& Wilson, D.~M. 2008, ApJ, 682, 1248 

\bibitem{} Siess, L., Dufour, E., \& Forestini, M. 2000, A\&A, 358, 593

\bibitem{} Siess, L., Forestini, M., \& Dougados, C. 1997, A\&A, 324, 556

\bibitem{} Southworth, J., \& Clausen, J. V. 2007, A\&A, 461, 1077

\bibitem{2009arXiv0902.2548S} Stassun, K.~G., Hebb, L., L\'opez-Morales, M., \& Pr{\v s}a, A. 2009, arXiv:0902.2548 

\bibitem{} Tokunaga, A. T. 2000, in Allen's Astrophysical Quantities, ed. A.~N. Cox (4th ed. New York: Springer), 143

\bibitem{} Tonry, J., \& Davis, M. 1979, AJ, 84, 1511

\bibitem{} Topping, J. 1972, Errors of Observation \& Their Treatment (London: Chapman \& Hall Ltd.)

\bibitem{} Torres, G., Lacy, C.~H., Marschall, L.~A., Sheets, H.~A., \& Mader, J.~A. 2006, ApJ, 640, 1018

\bibitem{2002ApJ...567.1140T} Torres, G., \& Ribas, I. 2002, ApJ, 567, 1140 

\bibitem{} van Hamme, W. 1993, AJ, 106, 2096

\bibitem{} Wilson, R.~E., \& Devinney, E.~J. 1971, ApJ, 166, 605

\bibitem{} Wozniak, P.~R., et al. 2004, AJ, 127, 2436

\bibitem{2006MNRAS.370.1529Y} Young, T.~B., Hidas, M.~G., Webb, J.~K., Ashley, M.~C.~B., Christiansen, J.~L., Derekas, A., \& Nutto, C. 2006, MNRAS, 370, 1529 

\bibitem{} Zacharias, N., Monet, D.~G., Levine, S.~E., Urban, S.~E., Gaume, R., \& Wycoff, G.~L. 2004, BAAS, 36, 1418


\end{thebibliography}


\end{document}
