\section{INTRODUCTION}

The study of galactic open clusters is of great interest in several
astrophysical aspects. Young open clusters provide information about
current star formation processes and are key objects for clarifying questions
of galactic structure, while observations of old and intermediate age open cluster
play an important role in studying the theories of stellar and galactic
 evolution.

The nucleus and the corona (extended region of the star cluster)
are two main regions in open clusters (Kholopov 1969). The nucleus of a cluster
contains relatively bright and massive ($\ge$ 3 $M_\odot$) stars whereas
corona, which contains a large number of faint and low mass ($\le$ 1 $M_\odot$)
stars, has important bearing on studies related to the mass function (MF),
the structure and the evolution of open clusters.
A detailed analysis of the structure of corona of open clusters is needed
to understand the effects of external environments like the
galactic tidal field and impulsive encounters with interstellar clouds etc.
on dynamical evolution of open clusters (Pandey et. al. 1990).
Extensive studies of the coronal regions of clusters have not been carried
 out so far mainly because of non-availability of photometry in a large field
around open star clusters.

The $2K\times2K$ CCD mounted on Schmidt
telescopes (Kiso, Japan), covering $\sim 50'\times 50'$ field
can be used to get photometry in a large field around open
star clusters. The ability to obtain improved photometry of
thousands of stars means that large-scale studies of open clusters can
be conducted to study the spatial structure and stability of galactic
open clusters. With the addition of photometry of nearby field region,
it is possible to construct luminosity
function (LF)/mass function (MF), which are useful to understand
the cluster-formation processes and the theory of star
formation in open clusters (Miller \& Scalo 1979).

Considering the importance of low mass stars in the corona of star clusters,
we have generated wide field photometric database around 9 open star clusters
with the aim to re-investigate the cluster's parameters e.g. reddening, distance,
age, their size and LF/MF using a homogeneous data base. The basic parameters of the cluster taken from
WEBDA\footnote{http://obswww.unige.ch/webda} (Mermilliod 1995) are given in Table 1.

\section{OBSERVATIONS AND DATA REDUCTIONS}

 The broad band CCD photometric observations of clusters were carried out during 2001 November 19 to
  2001 November 25 using the 105 cm Schmidt telescope of the Kiso Observatory. The CCD
   camera used a SITe 2048$\times$2048 pixel$^2$ TK2048E chip having a pixel size 24 $\mu$m.
 At the Schmidt focus (f/3.1) each pixel of CCD corresponds to $1.^{\prime\prime}5$
   and the entire chip covers a field of $\sim 50'\times 50'$ on
   sky. The read out noise and gain of the CCD are 23.2 $e^-$ and 3.4 $e^-$/ADU
   respectively.

The observations of NGC 1528, NGC 2287, NGC 2301, NGC 2323,
NGC 2420, NGC 2437 and NGC 2548 were standardized by observing
standard stars in SA95 (Landolt 1992) having brightness
$12.2<V<15.6$ and color $0.45<(B-V)<1.51$ on four nights during 2001 November 22 to 2001 November 25.
To standardize the observation of Be 62 and NGC 1960 we generated secondary standard in
the field of these two clusters by observing stars in SA95 on 2001 November 24 and 2001 November 22 respectively.
A number of bias and dome flat frames were also taken during
the observing runs. The log of observations is given in Table 2.
A number of short and deep exposure frames have been obtained for all
the clusters.

The CCD data frames were reduced using computing facilities available at
Aryabhatta Research Institute of Observational Sciences (ARIES), Nainital.
Initial processing of the data frames was done
using the IRAF\footnote{IRAF is distributed by National Optical Astronomy
Observatories, USA} and ESO-MIDAS\footnote{ ESO-MIDAS is developed and
maintained by the  European Southern Observatory.} data reduction packages. Photometry  of
cleaned frames was carried out using DAOPHOT-II software (Stetson 1987).
The PSF was obtained for each frame using several uncontaminated
stars. The FWHM of the star images varied between $3^{\prime\prime}$
to $4^{\prime\prime}$ from night to night.
When brighter stars were saturated on deep exposure frames, their
magnitude has been taken from short exposure frames.
We used DAOGROW program for construction of an aperture growth curve required for
determining the difference between aperture and profile fitting magnitude.
 Calibration of the instrumental magnitude to standard system was
done using procedure outlined by Stetson (1992). The  photometric
calibration equations used are as follow:

{\it
~~~~~~~~~~~~~~~~~~~~~~u = U + $c_1$ + $m_1$(U-B) + $k_u$X,

~~~~~~~~~~~~~~~~~~~~~~b = B + $c_2$ + $m_2$(B-V) + $k_b$X,

~~~~~~~~~~~~~~~~~~~~~~v = V + $c_3$ + $m_3$(V-I) ~+ $k_v$X,

~~~~~~~~~~~~~~~~~~~~~~r = R + $c_4$ + $m_4$(V-R) + $k_r$X,

~~~~~~~~~~~~~~~~~~~~~~i = ~I~ + $c_5$ + $m_5$(V-I) + $k_i$X, \\
}

 where {\it U,B,V,R {\rm and} I} are the standard magnitudes, {\it u,b,v,r {\rm and} i}
are the instrumental magnitudes normalized for 1 second of exposure time
and {\it X} is the air mass; the $c_1,c_2,c_3,c_4,c_5$ and
$m_1,m_2,m_3,m_4,m_5$ are zero-point constants
and color-coefficients respectively; and $k_u,k_b$, $k_v$,$k_r$,$k_i$
are extinction coefficients in {\it U,B,V,R {\rm and} I} bands respectively.
The values of zero-point constants, color coefficients and extinction coefficients in various
bands on different nights are given in Table 3.
Figure 1 shows the standardization residual, $\Delta$, between standard and transformed V magnitude
and $(U-B),(B-V),(V-R)$ and $(V-I)$ colors of standard stars. The standard deviations in
$\Delta V, \Delta (U-B), \Delta (B-V), \Delta (V-R)$ and $\Delta (V-I)$
are 0.017, 0.060, 0.028, 0.023, 0.020 mag respectively.
The typical DAOPHOT errors in magnitude and colors along with parameter $\chi$ and sharpness
as a function of $V$ magnitude in the case of clusters Be 62 and NGC 1960 are shown in Figure 2.
It can be seen that the errors become larger ($\ge$0.1 mag) for stars
fainter than $V=20$ mag, therefore the measurements below this magnitude are not reliable.

\section{ COMPARISON WITH PREVIOUS STUDIES}

We have carried out a comparison of the present data with that
 available in the literature. The difference $\Delta$ (literature -
present data) as a function of $V$ magnitude is shown in Figure 3 and
 the statistical results are given in Table 4. The comparison
indicates rather a large scatter in $\Delta$
for photographic data as compared to the $\Delta$ values for CCD photometry.
Comparison of the photometry in case of each cluster is discussed below.

Be 62:  CCD $V$ magnitude and $(B-V)$ colors obtained by Phelps \& Janes (1994) are
in good agreement with those obtained in the present work. However the photoelectric
$V$ magnitudes in the range 13-14  obtained by Forbes (1981) are brighter by $\sim$0.13 mag than
that obtained in the present work. The $(U-B)$ colors obtained in the present work
for stars having $V\sim13-16$ mag are redder than those reported by Phelps \& Janes (1994). For stars
having $V>17$ mag, the $(U-B)$ colors obtained by Phelps \& Janes (1994) show a strong variation
with $V$ magnitude and becomes redder by $\sim$ 1.2 mag at $V\sim$18-19 mag. Our $(U-B)$ colors for star
$V$=13-14 mag are in agreement with the photoelectric observations by Forbes (1981).

NGC 1528: The $V$ magnitude and $(B-V)$ colors obtained in the present work are
in agreement with those reported by Hoag et al. (1961, hereafter H61).

NGC 1960: The comparison of present CCD photometry with the available
photoelectric (Johnson \& Morgan 1953) and photographic (Barkhatova et al. 1984)
 photometry indicates a fair agreement between the different measurements.
The $V$ magnitude and $(B-V)$ colors obtained by us for stars having $V\le15$ mag
are in good agreement with those given by Sanner et al. (2000, CCD photometry),
whereas $V$ magnitude obtained by us for stars fainter than $V=15$ mag are systematically
fainter by $\sim$ 0.06 mag and $(B-V)$ color shows a trend with increasing $V$
magnitude in the sense that colors obtained by us become redder.

NGC 2287: Photoelectric $V$ magnitude by Eggen (1974) are in agreement with the present
observations whereas photoelectric $V$ magnitudes given by Harris et al. (1993),
Ianna et. al. (1987) and H61 are systematically fainter by
$\sim$ 0.05 magnitude. The $(B-V)$ colors obtained in the present work are in agreement
with those reported by Harris et al. (1993), Eggen et al. (1974) \& Ianna et al. (1987).
The $(B-V)$ colors obtained by H61 are systematically blue by $\sim$
 0.06 mag than the $(B-V)$ colors reported in the present work.

NGC 2301: The $V$ magnitude and $(B-V)$ colors obtained in the present work are in
agreement with those reported in the literature.
The $(U-B)$ colors for stars having
$V\le16$ mag by Kim et al. (2001) are in agreement with the present results, whereas stars having
$V>16$ mag show a trend in $(U-B)$ color in the sense that present colors become
 bluer with increasing $V$ magnitude. The $(U-B)$ photographic colors reported
 by Mohan \& Sagar (1988) at $V\sim$10-13 mag are systematically redder by $\sim$
0.12 mag and become further red with increasing $V$ magnitude. Whereas, photographic
$(U-B)$ colors for stars having $V$ = 13-15 mag by H61 are systematically redder by $\sim$ 0.12 mag.

NGC 2323: The comparison indicates that the $V$ magnitude obtained by us are
in general in agreement with those given in literature barring the magnitudes
given by H61. The V magnitudes reported by
H61 are fainter by $\sim$ 0.06 mag. The $(B-V)$ colors also show a fair agreement
with the values reported  in the literature excepting
$(B-V)$ colors for $V\ge13.0$ mag given by H61 which are bluer by $\sim$ 0.07 mag.
The $(U-B)$ colors given in the literature also show a fair agreement with those
obtained in the present study.

NGC 2420: The comparison of present CCD observations indicates a good agreement
with those  reported in the literature.

NGC 2437: The comparison of the present CCD photometry with the available
photographic, photoelectric and CCD photometry indicates a good agreement
between various reported observations.

NGC 2548: The photoelectric $V$ magnitude by Pesch (1961) and Oja (1976) are
systematically faint by about 0.05 magnitude.

\section{ ANALYSIS}

\subsection{ Radial stellar surface density and cluster radius }

As the area of present CCD observations is quite large,
it can be used to study the radial extent, structure (core and corona region)
and evolutionary aspects of clusters.
Since, the projected distribution of stars in a cluster follows systematic
distribution from the center to the outer region,
the center of the cluster was estimated by convolving a Gaussian
 kernel with the stellar distribution and taking the point
of maximum density as the center. This was performed for both the axis to
 get the center coordinates of the clusters.
To determine the radial surface density, the cluster was divided into
 a number of concentric rings. Projected radial stellar density in
each concentric circle was obtained by dividing the number of
stars in each annulus by its area, and the same are plotted in Figure 4
for various magnitude levels. The error bars derived assuming that the number
of stars in each annulus follows the Poisson statistics.
The extent of the cluster `$r_{cl}$' is defined as the point where the radial
density becomes constant. The horizontal dashed line
in the plots indicates the density of contaminating field stars, which
is obtained from the region outside (about 1.5 cluster radius) the cluster area.

To check whether the density distribution shown in the left panel of Figure 4
is affected by contamination due to field stars, we selected a sample of stars
near a well defined main sequence (MS) in the color-magnitude diagram (CMD)
as mentioned by Pandey et al. (2001). The radial density distribution of the MS sample
is also shown in the right panel of Figure 4. Both the samples in general show almost similar radial density profiles.

The observed radial density profile of the clusters was parametrized following the
approach by Kaluzny \& Udalski (1992) where projected radial density $\rho(r)$
is described as:
\begin{center}
$\rho (r) \propto {f_0\over \displaystyle{1+\left({r\over r_c}\right)^2}}$,
\end{center}
where the clusters core radius $`r_c$' is the radial distance at which
the value of $\rho (r)$ becomes half of the central density $f_0$.
The best fit obtained by $\chi^2$ minimization technique is shown in Figure 4.
Within uncertainties the King model (King 1962) reproduces well the radial density
profiles (RDPs) of the clusters studied in the present work.
Structural parameters obtained by fitting the King model surface density profile
to the observed radial density profile of main sequence stars having {$V<18$ mag} are given in Table 5.

Majority of the clusters indicate an increase in core radius when fainter cluster members
included in the radial density profile, however two clusters namely
NGC 1960 (log age $\sim$ 7.4) and NGC 2437 (log age $\sim$ 8.4)
yield a  smaller $r_c$ toward fainter magnitude.
Whereas clusters NGC 2301 (log age $\sim$ 8.2) and NGC 2420 ( log age $\sim$ 9.3)
do not show any significant change in core radius as a function of brightness of the
cluster stars. The radial stellar surface density profiles displayed in Figure 4 indicate that
field star contamination is not significant up to $V\sim$18 mag, however it increases
significantly at $V=20$ mag. We expect for the sample brighter than $V \sim18$ mag field star
contamination is not strong enough to smear the cluster properties and
hence will have insignificant effect in the results derived below.
Poor radial surface density profile in the case of NGC 2287 is due to lack of clustering in  the object.

Recently various authors have used Two Micron All Sky Survey (2MASS)
data to study the radial structures of open clusters (Chen et al. 2004, hereafter C04;
Bonatto \& Bica 2005, hereafter BB05). We also used 2MASS data to obtain the radial
density profile curve of the clusters studied in the present work and the same
are shown in the lowermost panels of Figure 4. The core radius `$r_c$' and extent of
the cluster `$r_{cl}$' of the target open clusters estimated from the projected
radial density profile for main-sequence band stars are given in Table 5.
Table 5 indicates that the $r_c$ and $r_{cl}$  obtained using the 2MASS data are larger, in some cases, than
that obtained from optical data. The error in $r_c$ obtained from 2MASS data
is also relatively large in comparison to that for optical data.
Various recent estimates of radii of target clusters are given in Table 6, which indicates
a fare agreement between present optical estimates and those by Nilakshi et al. (2002, hereafter N02).
To study various parameters, e.g. interstellar reddening, age, distances etc,
in detail, we considered only those stars which are inside the cluster extent as determined from radial density profile.

\subsection {Isodensity contours}

It is well known that the internal interaction of two body relaxation due to encounters
among member stars and external tidal forces due to the galactic disk or giant molecular
clouds influence the morphology of the clusters.
To study the effects of external forces on the morphology of the
clusters, we obtained isodensity contours for the sample of MS stars ($V\le18$ mag)
and the contours are shown in Figure 5.
The isodensity contours are least square fitted with ellipse to obtain the elongation
of the corona of the clusters. The elongation parameter `$e_p$' is defined as $e_p$ = b/a, where
a and b are semi-major and semi-minor axis of the ellipse. The parameter $e_p$ for each cluster
is given in Figure 5. $e_p$ = 1 indicates a spherical cluster. The fitting could not be done
in the case of Be 62 and NGC 1960. However a visual inspection of density contours of these
two clusters indicates an elongated corona of the clusters. C04 have also reported an elongated corona in the
case of NGC 1960.

Figure 5 indicates that outer region (corona) of six clusters is found to be elongated.
The elongated morphology in the case of NGC 2287,
NGC 2548 (Bergond et al. 2001, hereafter B01) and NGC 1893, Be 17, NGC 2420 (C04) have
already been reported in the literature. Present results further support the elongated
morphology of the coronal region of the clusters.

\subsection {Interstellar Extinction}

The extinction towards the clusters Be 62, NGC 1960, NGC 2301 and NGC 2323 was estimated using the $(U-B)/(B-V)$
two color diagram shown in Figure 6. We compared observed main-sequence (MS)
in the cluster region with the intrinsic MS to
estimate the value of reddening $E(B-V)$. In Figure 6, we show intrinsic MS for $Z=0.02$ by Schmidt-Kaler (1982)
shifted along the reddening vector having a normal slope of $E(U-B)/E(B-V)$ = 0.72.
The interstellar extinction
in the case of other five clusters NGC 1528, NGC 2287, NGC 2420, NGC 2437 and NGC 2548 was estimated using the $V/(B-V)$ or
$V/(V-I)$ color-magnitude diagrams (CMDs, cf. $\S$ 4.4). The estimated values of $E(B-V)$ are given in Table 7
which are in good agreement with those given in the literature. Barring the cluster Be 62, all other
clusters show a uniform reddening across the cluster region. The reddening in Be 62 varies from $E(B-V)_{min}=0.70$ mag
to $E(B-V)_{max}=1.00$ mag. The reddening for individual stars ($V_{error}\le 0.1$ mag) having spectral
type earlier than $A0$ has also been derived using the Q-method (Johnson \& Morgan 1953).

To study the nature of the extinction law in the cluster region, we used two-color diagrams (TCDs)
as described by Pandey et al. (2001, 2003).
The TCDs of the form of ($\lambda-V$) vs. ($B-V$), where ($\lambda-V$) is one of the
wavelength of the broadband filters ($R,I,J,H,K,L$) provide an effective method for
separating the influence of the normal extinction produced by the diffuse interstellar medium
from that of the abnormal extinction arising within regions having a peculiar distribution of dust sizes
(cf. Chini \& Wargan 1990, Pandey et al. 2000).
The near infrared (NIR) data have been taken from the 2MASS.
For illustration, the TCDs for the clusters Be 62, NGC 2420 and NGC 1960 are
shown in Figure 7 and slopes of the distribution, $m_{cluster}$,
in the case of these three clusters are given in Table 8.

The ${E(\lambda-V)}\over {E(B-V)}$ values in the cluster region are estimated using the
following approximate relation:
\begin{center}
${{E(\lambda-V)}\over {E(B-V)}} ={ { m_{cluster}\over m_{normal}} \times [{{{E(\lambda-V)}\over {E(B-V)}}]_{normal}}}$
\end{center}
as described by Pandey et al. (2003), where $m_{cluster}$ and $m_{normal}$ are the slope of the
distribution in the cluster region and slope of the theoretical
MS. The slopes of the theoretical MS, $m_{normal}$, obtained from the stellar models by Bertelli et al. (1994)
are also given in Table 8. The obtained slope $m_{cluster}$ indicates
that barring Be 62 and NGC 2420 all other clusters show a normal reddening law towards the cluster region.
The color excess ratio $E(\lambda-V)\over E(B-V)$ for Be 62 and NGC 2420
are smaller than the normal ones, which indicates that there may be
anomalous reddening law towards these cluster
regions. Since Be 62 shows a differential extinction indicating that the stars are still embedded in the parent
molecular gas and dust, an anomalous reddening law is expected in the cluster region. The value of $R$
towards the cluster Be 62 region estimated to be $2.95\pm0.12$. However it is quite surprising
in the case of NGC 2420 which is an old cluster having a uniform reddening across the cluster.
Keeping the large error in mind we used a normal value of $R$ for all the cluster regions in the ensuing discussions.

\subsection{Color magnitude diagrams, distance and age of the clusters}

Color magnitude diagrams (CMDs) for stars lying within cluster region as mentioned in Table 5 are
shown in Figure 8. The CMDs show a well defined MS.
Barring Be 62, other clusters manifest a uniform reddening in the cluster region and the error
in magnitude estimation is $\sim$ 0.05 mag for stars having $V\le$18.0 mag. Therefore we can conclude that the
presence of probable binaries and field stars should be the main cause for broadening of the MS in these clusters.
In the case of Be 62 variable reddening in the cluster region along with presence of probable
binaries and field stars should be the cause of broad MS.
It is difficult to separate field stars from the cluster stars, however we can reduce the contamination
due to field stars if we restrict the sample to the central portion of the cluster only.

We supplemented present CCD data for some cluster with the photoelectric photometry for bright stars available in the
literature as these bright stars were saturated even on present short exposure frames. The
distance and age of the cluster were obtained by visual fitting of isochrones by Bertelli et al. (1994)
for $Z=0.02$ to the blue envelope of the observed MS except in the case of NGC 2420 where we used
isochrones for $Z=0.008$ as Lee et al. (2002) have reported $Z=0.009$ for the cluster NGC 2420.
The fitted isochrones are shown in Figure 8.
Since extinction is uniform in clusters under study except Be 62,
we used mean value of $E(B-V)$ and following relations,
$E(U-B)/E(B-V)$=0.72, $A_V=3.1\times E(B-V)$, $E(V-R)=0.60\times E(B-V)$, $E(V-I)=1.25\times E(B-V)$
to fit the theoretical isochrones to the observations. In the case of Be 62
individual reddening for stars earlier than
$A0$ was obtained using the $Q$ method and the same was applied to get intrinsic magnitude and colors,
whereas for other stars mean reddening of the nearby stars was applied to get the intrinsic magnitude and colors.
The unreddened CMDs along with the fitted isochrones in the case of Be 62 are shown in Figure 9. The age and distance
obtained for the target clusters are given in Table 8.
The $K/(J-K)$ CMDs for the clusters obtained from 2MASS data are shown in Figure 10. The theoretical
isochrones by Bertelli et al. (1994) using the parameters obtained from the optical data (cf. Table 7)
are also plotted in Figure 10 which nicely follow the observations.
Comparison of previous estimates available in the literature with the present estimates is
given in Table 9.

\section {RESULTS}

We have determined basic parameters of 9 open clusters by analyzing the
color-color diagrams and CMDs of the clusters.
We assumed solar abundance for all the clusters except NGC 2420 where metallicity is reported to be $Z = 0.009$ by
Lee et al. (2002). The discussion on individual cluster follows, where we have compared the radii of the cluster obtained in the present study with those reported by N02, BB05, C04 and Kharchenko et al. (2005, hereafter K05).
The morphological parameters of open clusters derived by N02 and K05 are based on optical observations whereas
C04 and BB05 have used 2MASS data. In the subsequent sections we use the core radius
 `$r_c$' and cluster extent `$r_{cl}$' obtained from the present
optical photometric and 2MASS data.

\subsection {Be 62}

The reddening $E(B-V)$, distance and age for the cluster has been estimated as $0.86$ mag, $2.05\pm0.24$
kpc and 10 Myr by Forbes (1981) using the photoelectric photometry, whereas Phelps \& Janes (1994) using the
CCD observations reported $E(B-V)$=0.82 mag, distance=2.7 kpc and an age of $\sim$ 10 Myr for this cluster.

In Figure 8, $V/(B-V)$, $V/(V-R)$, $V/(V-I)$ CMDs for stars within  the cluster region i.e. $r_{cl}=10.'0$ (6.8 pc)
are presented.  The CMDs of the Be 62 shows a broad MS which should be due to variable reddening in the cluster region.
To get unreddened CMDs, the reddening $E(B-V)$ for stars having spectral type $A0$ or
earlier has been calculated using the $Q$ method and these stars
were unreddened individually. For remaining stars the average reddening of the nearby stars was applied. The
unreddened CMDs shown in Figure 9. To calculate ${\it V_O}$, the value of $R=3.1$ is assumed.
The distance and age of the cluster comes out to be 2.32 kpc and 16 Myr (log age = 7.2).
The distance obtained in the present work is in between the values 2.05 kpc and
2.70 kpc reported by Forbes (1981) and Phelps \& Janes (1994) respectively.

The core of the cluster using the optical MS data is estimated to be $\sim2.'2\pm0.'3$ ($1.5\pm0.2$ pc).
The 2MASS data  gives the value for core as $\sim2.'5\pm1.'0$ ($1.7\pm0.7$ pc).
The optical and 2MASS data yields the extents of cluster as $\sim10'$ (6.8 pc) and $\sim12'$ (8.1 pc) respectively.
The core and the coronal region of the cluster are found to be elongated.

\subsection {NGC 1528}

The radial density profile of the cluster yields its extent $r_{cl}\sim15'$ (4.8 pc)
with a core radius $r_c\sim8.'3\pm1.'5$ ($2.6\pm0.5$ pc) which is in agreement with the
value ($8.'4$) by K05, however the $r_{cl}$ obtained in the
present work ($\sim15'$) is significantly smaller than the value ($26'.4$) by K05.
The RDP obtained using the 2MASS data is quite noisy and it yields significantly
different value of $r_c$ ($\sim18.'5\pm7.'4$; $5.9\pm2.4$ pc).

 The CMDs of the cluster within $r_{cl}\sim15'$ show a well defined but broad MS.
Since the cluster has uniform reddening, the presence of binary stars
should be a probable reason for the broadening of the MS. The CMDs show the turn-off
of the MS which can be fitted nicely with a isochrones of log age = 8.6 (400 Myr) and $Z=0.02$.
The distance to the cluster comes out to be 1.09 kpc which is in agreement with those reported in the literature.
Isodensity curves shown in Figure 5 indicate that both the core and the corona have elongated morphology.

\subsection {NGC 1960 (M36)}

This cluster situated in Auriga constellation is reported to have diameter of $10^\prime$
(Lynga \& Palous 1987). Sanner et al. (2000)
reported a distance modulus $(m-M)_o = 10.6\pm0.2$ mag ($1318\pm120$ pc),
reddening $E(B-V)$ = $ 0.25\pm0.02$ mag, age = $16^{+10}_{-5}$ Myr and metallicity $Z = 0.02$ for the cluster.

The CMDs of the NGC 1960 show a well defined narrow MS. By fitting the isochrones for
log age = 7.4 (25 Myr)
to the stellar distribution in the CMDs using $E(B-V)$ = 0.22 mag, we obtained a distance modulus $(m-M)_V$ = 11.3 mag
corresponding to a true distance modulus $(m-M)_o$ = 10.62 mag,
or a distance of 1.33 kpc. The estimated age, distance and
reddening in the cluster region are in good agreement with
the values obtained in earlier studies (e.g. Sanner et al. 2000).

The core radius ($r_c\sim3.'2\pm0.'5$; $1.2\pm0.1$ pc) and cluster extent ($r_{cl}\sim14'$; 5.4 pc) obtained in
the present study are in good agreement with the values obtained by N02 ($r_c\sim3.'2$, $r_{cl}\sim15.'4$).
The core radius ($r_c\sim5.'4$) obtained by K05
is larger than the present value. The cluster extent ($r_{cl}\sim14'$) obtained in the
present work is in agreement with the value ($\sim16.'2$)
by K05 whereas it is larger than that ($\sim7.'6$) reported by C04.
From 2MASS data, we obtained $r_c \sim 3.'8\pm0.'6$ ($1.5\pm0.2$ pc)
and $r_{cl} \sim 21'$ (8.1 pc). The core of the cluster is rather spherical
symmetric whereas the outer region of the cluster clearly shows the effect of external forces.

\subsection {NGC 2287 (M41)}

Despite being a bright cluster, no CCD photometry is available for this cluster. This cluster has been studied
for proper motion (Ianna et al. 1987), radial velocities (Amieux 1988) and spectroscopic properties
(Harris et al. 1993). Battinelli et al. (1994) and B01 have reported
$R_{lim}$ = 4.0 pc ($19'$) and $R_{tidal}$ = 4.1 pc ($20.'3$) respectively for the cluster.
K05 have reported $r_c\sim9.'6$ and $r_{cl} \sim 30'$. BB05 have estimated
$R_{core}$ = 1.1 pc ($4.'7$) and $R_{lim}$ = 7.0 pc ($30.'1$). In present study we found that optical
data for brighter limiting visual magnitude
($V\sim14$ mag) and fainter limiting magnitude ($V\le18$ mag) were yielding quite different values for the morphology of the
cluster. For brighter sample we obtained $r_c\sim5'.5\pm0.'9$ ($1.1\pm0.2$ pc), $r_{cl}\sim17'$ (3.5 pc)
whereas for sample having V$\le$18 mag these
values are estimated as $\sim 1.'4\pm0.'3$ ($0.3\pm0.2$ pc) and $\sim 12'$ (2.5 pc) respectively.
The radial density profile for 2MASS data is quite noisy with $r_c\sim12.'7\pm3.'8$ ($2.6\pm0.8$ pc) and
$r_{cl}\sim 16'$ (3.3 pc). For further study of the cluster, we assumed
$r_{cl}\sim12'$ (2.5 pc). The morphology of the cluster indicates that both the
central region and outer region are elongated.
The center coordinate for the cluster reported by B01 are shifted towards
$15'$ SW of ``classical'' coordinates given in WEBDA. However, BB05 find the same coordinates for the center
as given in WEBDA, whereas in the present work we find a shifted center for the cluster
towards north of the center as given in WEBDA.

The CMDs of the clusters show a very well defined MS along with red giant clump. The distance
and age for the cluster estimated to be 0.71 kpc and 250 Myr (log age = 8.4)
which are in agreement with recent findings.

\subsection {NGC 2301}

A comparison of the theoretical isochrones with the observations yields
a distance modulus $(m-M)_V$ = 9.8 mag, which corresponds to a true distance modulus $(m-M)_0$ = 9.71 mag
or a distance of 0.87 kpc and an age of 160 Myr (log age = 8.2) for the cluster.
The age, distance and reddening towards the cluster region obtained in the present work
are in good agreement with those reported in the literature.

The estimated core radius ($r_c\sim1.'9\pm0.'3$; $0.5\pm0.1$ pc) is in good agreement with the value
($r_c\sim1.'9$; 0.5 pc) by N02 whereas it is significantly smaller than $r_c\sim4.'8$ by K05.
The extent of cluster ($\sim9'$; 2.3 pc) obtained in the present work is smaller
than that reported by N02 ($12'$; 3.0 pc) and K05 ($\sim15'$). Here
it is worthwhile to mention that the core radius ($r_c\sim4.'5\pm1.'0$; $1.1\pm0.2$ pc)
and cluster extent ($r_{cl}\sim20'$; 5.1 pc) obtained from the
2MASS data are almost double to that values obtained from the optical observations. The core and
coronal region of the cluster NGC 2301 are found to be highly elongated indicating
a strong effect of external forces on the cluster.

\subsection {NGC 2323 (M50)}

The distribution of MS stars having V$\le$18 mag yields $r_c \sim 6'.5\pm1'.5$ ($1.8\pm0.4$ pc)
and $r_{cl} \sim 17'$ (4.7 pc).
The core radius obtained in the present study is larger than that obtained by N02 ($2.'6$)
but in agreement with that obtained by K05 ($6'$).
The extent of the cluster is in agreement with that reported by N02 ($16.'7$), however it is smaller than that reported by
K05 ($\sim22'.2$). The 2MASS data yield $r_c\sim6.'7\pm1.'3$ ($1.9\pm0.4$ pc) and
$r_{cl}\sim22'$ (6.1 pc).
The radial density profile derived from optical and 2MASS data thus gives comparable core radius.
The core and the coronal region of the cluster are found to be spherical.

The cluster NGC 2323 shows a well defined MS towards the brighter end ($V\le15$ mag).
The effect of photometric error becomes significant towards the fainter end. A comparison of the observations with the
theoretical isochrones yields a distance of 0.95 kpc and age of $\sim$ 100 Myr (log age = 8.0) to the cluster.

\subsection{ NGC 2420}

The $BV$ and $VI$ CCD photometry for the cluster NGC 2420 has been carried out by
Anthony-Twarog et al. (1990) and Lee et al. (2002)
respectively. Leonard (1988), using the star counts on Palomar Sky Survey, reported a quite large
extent of $\sim20'$ for the cluster. In the present work we find that optical data
and 2MASS data indicate a radial extent of the cluster is $\sim10'$ (7.2 pc) and $\sim9'$ (6.5 pc)
respectively which is in fair agreement with that reported by C04 ($\sim11.'6$) but smaller
than that reported by N02 ($\sim13.'2$).
The core radius is estimated to be $1.'4\pm0.'1$ ($1.0\pm0.1$ pc) which is in agreement
with that obtained by N02 ($1.'5$).
2MASS data also yield nearly same core radius $\sim1.'3\pm0.'2$ ($0.9\pm0.1$ pc).
The isodensity curves indicate a rather spherical core and coronal regions of the cluster.
C04 have obtained a spherical core with an elongated coronal region of the cluster.

The CMDs within the cluster region displayed in Figure 8 show a well defined MS.
As can be seen in the CMDs, the contamination
due to field stars is almost negligible. The CMDs manifest a sequence of evolved stars which is nicely reproduced by
the theoretical isochrones for $Z=0.008$ and log age = 9.3 (2 Gyr).

The distance to the cluster is estimated to be 2.48 kpc, which is in good agreement with the values reported by
Anthony-Twarog et al. (1990), Lee at al. (2002) and West (1967)
whereas distance reported by McClure et al. (1974) is 1.9 kpc.
Because of its age and metallicity, NGC 2420 is an important object to test
theoretical stellar evolutionary models.

\subsection {NGC 2437 (M46)}

The star count peak obtained in the present work is shifted by $\sim3'$ East and $\sim1'$ south to the center
coordinates given in WEBDA.
The radial density profile obtained for optical as well as 2MASS data shows a well
defined distribution of stellar density around center of the cluster. However the extent of the cluster obtained for two distributions  differs. The $r_{cl}$ estimated to be $\sim20'$ (8.8 pc) and $25'$ (11.0 pc) for the optical
and 2MASS data while the corresponding values of $r_{c}$ are $6.'8\pm1.'0$ ($3.0\pm0.4$ pc)
and $9.'6\pm0.'6$ ($4.2\pm0.3$ pc) respectively.
The values of $r_{c}$ reported by K05 and N02 are $7.'2$ and $5.'2$ respectively.
The corresponding $r_{cl}$ values are $22.'8$ and $26.'6$ respectively.
The core of the cluster is elongated whereas the corona of the cluster
is found to have spherical symmetry.

The $V/(B-V)$ and $V/(V-I)$ CMDs for the cluster indicate a broad and well defined MS.
The effect of field star contamination and errors is clearly visible towards fainter end ($V>15$ mag).
A few stars on the red giant clump region can also be noticed. Using $E(B-V)=0.10$ mag
we obtained a distance of $\sim$ 1.51 kpc and an age $\sim250$ Myr (log age = 8.4) for the cluster. Since the cluster is of intermediate age and no indication of presence of parental molecular gas and dust, the broad
MS may be probably due to presence of binary stars.

\subsection {NGC 2548 (M48)}

The point of maximum stellar density i.e. adopted center of the cluster is found towards south ($\sim1.'6$) of
the center given in WEBDA. The center reported by BB05 is in excellent agreement with that obtained
in the present work. However, B01 obtained the center of this cluster further south of ($\sim1.'4$)
of the coordinate obtained in the present work. The extent of
the cluster is reported to be 4.8 pc ($21.'5$), 8.8 pc ($37.'8$)
by B01 and BB05 respectively. K05 have reported a significantly larger value
($43.'8$) for the cluster extent. The core radius $r_c$ is reported as $3.'9\pm0.'9$
($0.9\pm0.2$ pc) by BB05
whereas K05 reported a significantly larger value for the core as $r_c\sim15'$. In the present work
we found $r_c\sim 1.'5\pm0.'2$ ($0.3\pm0.1$ pc) and $\sim2.'4\pm1.'5$ ($0.5\pm0.3$ pc) for optical
and 2MASS data respectively,
whereas the extent of the cluster for both of the samples is found to be $\sim8'$ (1.8 pc).
The elongated morphology of the coronal region of the cluster manifests
that cluster structure has been affected by a significant amount of external forces.

The cluster shows a well defined narrow MS in the $V/(V-I)$ CMD with a few evolved stars on the giant branch.
The shape of the turn-off point is that of typical intermediate-age open cluster and can be nicely explained
by an isochrones having $Z=0.02$ and age  $\sim400$ Myr (log age = 8.6). The distance to the cluster is estimated to be 0.77 kpc.

\section {DISCUSSION AND SUMMARY}

\subsection { The evolution of core and corona of clusters}

The isodensity curves shown in Figure 5 indicate  that the coronal regions of the six clusters show an
elongated morphology. The youngest cluster of the present sample, Be 62 (log age = 7.2) has an elongated
core, whereas NGC 1960 (log age = 7.4) has somewhat spherical core.
On the other hand, the core of the cluster NGC 2548 (log age = 8.6)
shows an elongated morphology whereas the core
 of the NGC 2420, oldest cluster in the present sample (log age = 9.3) shows rather a spherical symmetry.
C04 have also reported a spherical core in the case of NGC 2420. On the basis of present small
homogeneous data sample it is not possible to establish any correlation between age and shape of the core.
However C04 found that the core tends to circularize as a star cluster ages. It seems that initial
morphology of the open cluster at the time of formation of the cluster is governed by the initial conditions
in the parent molecular clouds (cf. C04), because observed shapes of molecular cloud cores also
show highly elongated morphology (Curry 2002; Gutermuth et al. 2005).
C04 suggested that the later evolution of the cluster may be governed by both
 the internal gravitational interaction and external tidal forces.

Danilov \& Seleznev (1994) showed that the parameter $\zeta$ (=$R_1\over R_2$) and
$\mu$ (=$N_1 \over N_2$) follow the relationship
$\zeta \propto \mu^{0.35}$, where $R_1$ and $R_2$ are the radii of the cluster core and halo,
and $N_1$ and $N_2$ are numbers of star in the core and halo. This relationship may be
caused by an approximate equality between the rates of transfer of star from the core to corona
and vice-versa, as a result of stellar encounters (Danilov 1997).
In order to study the core-corona structure, we selected a mass limited sample,
since evolution of clusters, their stability
and their parameters depend on the mass of the cluster (cf. Pandey et al. 1991; BB05).
We estimated various parameters for the target clusters for mass limited sample having $M_V\le 7$ mag
and these are given in Table 10. In the case of Be 62, it is not possible to estimate the parameters for
$M_V\le 7$ mag ($V\le 21$ mag), we used parameters obtained for $V\le 20$ mag ($M_V\le 6$ mag) for further analysis.
Data for a few cluster studied earlier by us have been taken from literature
and relevant parameters for the clusters are given in Table 11.
In Figure 11 we plot ($r_c\over r_{cn}$) vs. ($n_c\over n_{cn}$) and ($r_c\over r_{cl}$) vs. ($n_c\over n_{cl}$)
diagrams for the target clusters where $r_c$, $r_{cn}$ (= $r_{cl}-r_c$) and $r_{cl}$ represents
core radius, size of corona and cluster extent respectively and $n_c$, $n_{cn}$ and $n_{cl}$
represents number of stars in the core, corona and cluster respectively.
Figure 11a indicates that clusters under study except NGC 1528 follow the relation
($r_c\over r_{cn}$) $\propto$ $({n_c\over n_{cn}})^{0.35}$ as suggested
by Danilov \& Seleznev (1994). The anomalous location of NGC 1528 in Figure 11
is probably due to large error in estimating the core radius
because of noisy radial density profile. If we take the core radius obtained from all star radial density profile
as shown in Figure 4, the cluster follows the expected relation as shown in Figure 11.
Danilov \& Seleznev (1994) have carried out simulation of isolated cluster dynamics and found that
the parameters $\zeta$ \& $\mu$ obtained from simulations also follow the relation
$\zeta \propto \mu^{0.35}$. They concluded that the evolution of the core and corona
of the clusters are mainly controlled by internal relaxation processes.

In Figure 12 we plot various structural parameters of the clusters, given in Tables 10 and 11,
which indicates that $r_c$ has a good correlation
with $r_{cn}$ and $r_{cl}$. Similarly $r_c$, $r_{cn}$ and $r_{cl}$ indicate a linear correlation with the
 number of stars in the core, corona and the entire cluster in the sense larger core, corona can accommodate
larger number of stars. The central density $f_0$ decreases exponentially
with increase in core radius.
In Figure 13, various structural parameters from Tables 10 and 11 are plotted
as a function of age which indicate that in the age range 10-1000 Myr,
the core and extent of the cluster seems to shrink with age. In the case of less massive
clusters, the work of BB05 (their Figure $7g$) also indicates a similar correlation
between age and core radius for the cluster having age $\le1000$ Myr. Because of the above correlation between
age and core/corona radius, the projected surface density in core ($\rho_c$) and corona ($\rho_{cn}$) is higher for
intermediate/old age (100-1000 Myr) clusters as compared to younger clusters. The same trend can be
noticed in Figure {7\it i} and Figure {7\it l} of BB05 for less massive clusters.
The concentration parameter $r_{cl}/r_c$ is plotted as a function of age in Figure 13
which indicates no trend with age. N02 have also concluded the same.

Figure 13 also indicates that the core and corona of two oldest open clusters in the
present sample (age $> 10^9$ yr), namely NGC 2420 ($r_c$ = 1.0 pc, $r_{cl}$ = 10 pc)
and Be 20 ($r_c$ = 1.6 pc, $r_{cl}$ = 6.6 pc), are found to be relatively larger
than the expected value of $r_c$ ($\sim$ 0.5 pc) and $r_{cl}$ ($\sim$ 2 pc) at age
$\sim10^9$ yr. These clusters are located at large distances (NGC 2420; $z$ = 844 pc \&
Be 20; $z$ = -2700 pc) from the galactic plane. The large corona of NGC 2420 and Be 20
probably indicates that these clusters may be in process of disintegration as suggested by C04.

Dependence of cluster sizes on the galactocentric distances $R_G$ is displayed in Figure 14.
A vertical dashed line is drawn to delineate the sample of clusters having $R_G<10$ kpc
and $R_G>10$ kpc. The figure indicates
that in the range $9<R_G<10$ kpc, the core, corona and total cluster size increase with the
galactocentric distance. The study of N02 also indicates a similar correlation between cluster size and $R_G$
in the range $R_G>9$ kpc.

\subsection{Summary}

This paper analyzes homogeneous wide field CCD data of nine open cluster (ages in the range 16 Myr to
2 Gyr) taken from Kiso Schmidt telescope. Based on the well defined $(U-B)/(B-V)$ two color diagram and CMDs,
we estimated the reddening towards the cluster region, the distance and age of the target clusters. The
structural parameter for target clusters were obtained using the projected radial density profile.
Most of the clusters show an increase in core radius when faint cluster members included in the sample.
The radial structure of all clusters can be well explained by King's empirical model (1962).
The target clusters sample indicate an elongated core for young (Be 62, log age = 7.2) as well as for intermediate
age open clusters (NGC 2548, log age = 8.6). C04 mentioned that the
clusters have tendency towards spherical shaping away from the disk, in particular in the case of old systems
due to internal dynamical relaxation. However we find that relatively young cluster NGC 1960 (log age = 7.4, $z$ = 24 pc)
has a rather spherical core.

Present sample of the clusters follows the relation ${r_c\over r_{cn} }\propto{ ({n_c\over n_{cn}})^{0.35}} $
as suggested by Danilov \& Seleznev (1994). It is found that the core radius and corona size/cluster
radius are linearly correlated. It is also found that in the age range 10-1000 Myr, the core
and corona of the cluster shrink with age. In the galactocentric distance range 9-10 kpc, the core
and corona/cluster extent of the clusters increase with galactocentric distance.

\acknowledgments
We would like to thank the anonymous referee for his constructive comments.
This work is partly supported by the Department of Science and Technology (DST) India
and Japan Society for the Promotion of Science (JSPS) Japan. AKP is thankful to the staff
of KISO observatory for their help during his stay there.

\newpage


\section{Introduction}
CEDAR is the communications and security library used in the Condor
\cite{condor-hunter, condorgrid}
High-Throughput Computing software.  CEDAR is a multi-platform C++
TCP and UDP network socket representation that
offers several important features essential in a distributed
environment.  The cross-platform implementation allows a wide variety of
architectures to easily communicate over a network while maintaining a very
strong focus on security.
CEDAR offers several improvements to overcome
shortcomings with traditional UDP datagrams, and makes timeout management and
error propagation first-class citizens which is essential in distributed
computing.  In this section we briefly introduce the salient CEDAR feature
set.

\subsection{Cross-platform Capabilities}
Basic communication principals are provided for sending integers, floating
point values, strings, ClassAds \cite{mms}, and even files, all in an
architecture-independent representation which allows for differing sizes of
core data types like integers and floating point values.  Integers on different
platforms may be different sizes, such as 32 vs. 64-bit, and so are padded and
sign-extended.  Also, CEDAR is aware of different byte ordering on different
platforms and automatically translates from one to another when necessary.
Furthermore,
floating point values are translated between single and double precision.  The
ability to send and receive ClassAds as first-class entities is vital to
CEDAR's use in Condor as ClassAds are the lingua franca of the Condor HTC
system \cite{gridbook-htc}, and allows for great flexibility in wire protocols.

\subsection{UDP Capabilities}
Traditional UDP datagrams have many shortcomings that are addressed by CEDAR to
increase UDP's usefulness in a typical distributed environment.  CEDAR does not
rely on the kernel to do packet fragmentation and reassembly, which has several
advantages.  Doing fragmentation and reassembly in user-space avoids using
precious system kernel memory which is often a fixed size and relatively
limited resource, thus allowing a higher volume of UDP traffic without dropping
packets.  Furthermore, it allows for datagrams greater than 64 kilobytes
(KB) in size, a
UDP
limitation that is easily exceeded by today's workloads.  For example, a single
ClassAd representing a job's environment could easily exceed 64 KB in size.
Another advantage to CEDAR's packet fragmentation is that CEDAR can optimize
the size of the fragments and introduce delays when sending them, which  we
have observed on many
operating systems results in fewer lost packets.  Finally, CEDAR adds
security capabilities to UDP traffic, including authentication, encryption, and
integrity checks, which for UDP are often overlooked in other security layer
implementations such as SSL \cite{ssl}.

\subsection{Timeout Management}
In a distributed system where many components are communicating with one
another, it is essential that the amount of time spent blocking on I/O
operations is minimized, particularly if some of the connections are
established over Wide Area Networks (WANs) as is typical in a grid environment.
For this reason, CEDAR allows for carefully managing the timeouts for all I/O
operations so that one process is never stuck indefinitely waiting for another.
CEDAR does use non-blocking connects to avoid having processes sit idle, but to
avoid having one component of the system wreak havoc in other parts, timeouts
are used to break out of blocking I/O reads and writes in the event that one
component has failed or is lagging behind for any reason.

\subsection{Error Stack}
Because a single failure at a low level can often cause a cascade of error
conditions, CEDAR keeps an \emph{error stack} instead of a single integer
\emph{errno} which is the conventional approach, thereby
providing a richer method of propagating and reporting failures.  This
allows very detailed information on the root cause of the problem to be kept
while each layer chooses to either handle the error and continue, or to add its
own information to the error stack and propagate the stack to the next layer.
Ultimately, this leads to a more detailed and hopefully more informative message that
makes understanding both the high-level problem and low-level problem clear.

As an example, suppose a user was trying to query a Condor daemon and the
security settings are setup to require GSI \cite{globus-security} authentication.  However, the user
does not have a valid proxy.  Instead of a single ``111 -- connection refused''
error, the user would get something more like:
\begin{quote}
	111  -- connection refused\\
	1003 -- authentication failed\\
	5003 -- GSI: unable to acquire credential\\
	851968 -- GLOBUS: no valid proxy file
\end{quote}

Also, if an error is recoverable, any layer may pop the error off the stack,
take corrective action, and continue.

\subsection{Basic Security Features}
Many basic security features essential for a distributed system are provided by CEDAR, including
authentication, encryption, and integrity checks.  There is also a layer for
the negotiation of which security features are available and allowed for a
given connection.  Finally, there is a layer which maps users from their native
credential to a canonical Condor identity and allows for authorization based on
this identity.  Currently in CEDAR the available authentication methods include
authentication using the local file system, SSPI \cite{sspi} (for Windows),
password, Kerberos \cite{kerberos} (via Active Directory on Windows), GSI
\cite{globus-security}, and OpenSSL \cite{openssl}.  This
variety of mechanisms allows strong authentication even between wildly different
operating systems such as Linux and Windows.  Integrity checks can by done with
MD5 \cite{md5} while encryption can be done with either 3DES \cite{3des} or
Blowfish \cite{blowfish}.  Current development efforts are adding AES and SHA-1
support.

When negotiating security features for a connection, it is the server (the side
which receives the incoming connection) who has final say over which features
are allowed and what the order of preference is.  It is also the server's
responsibility to perform the mapping from a security credential to
canonical identity (user name), and
inform the client who it ultimately was authenticated as.

\section{Importance of Session Management}

Capable network session management is critical to a highly scalable
distributed system that needs secure connections.  To understand why,
consider OpenSSL and GSI.  Both are authentication systems that make use of X.509
certificates, based on public-key infrastructure (PKI) technology.  While
they offer a cryptographically
strong authentication, there are two significant drawbacks to using these
methods exclusively: CPU overhead and network latency.  The first has
minimal impact with today's processors, but even a modest amount of CPU usage can become a bottleneck
as the scale of a distributed system increases.  For the
\emph{condor\_collector} service,
which handles incoming connections from all compute nodes in a cluster,
performing GSI authentication for many thousands of incoming connections can
overwhelm a server.  The latter concern of latency is a bigger issue, as quite
often the network connections in a grid environment are established across a
WAN.  Authentication using GSI or OpenSSL requires several round
trips across the network, which when combined with typical latencies over a WAN
can result in delays on the order of 1/10 to 1/4 of a second.

Kerberos is another authentication protocol supported by Condor, but it also
has potential bottlenecks.  Kerberos relies on network connectivity to the
centralized KDC service \cite{kerberos},
which again will introduce latency and even worse, can become overloaded due to
too many authentications happening.  Therefore, we need to minimize the number
of actual authentications performed in order to enable a reasonable level of
scalability.

This can be done by using a session management layer, which allows for a
semi-permanent information exchange that is explicitly set up and torn down.
The authentication is performed only once during the setup part, during which
secret keys are also securely distributed to both the server and the client.
These keys are then used to resume the session in the future, thus allowing the
high cost of authentication to be paid only once for the duration of the
conversation.

\subsection{CEDAR Sessions}

CEDAR implements its own session management layer, because of the delegation
opportunities enabled with this approach (see below), and because we found session
handling in other security libraries to be lacking.  For instance, OpenSSL
also provides session management, but cannot support sessions established
via authentication mechanisms other than SSL.  In addition, OpenSSL alone
also does not address the authentication of UDP packets and the ability to
use sessions over UDP.  Finally, OpenSSL sessions do not store as much state
as Condor would like, such as the mapped canonical name and the
authorization policy used to establish the connection.

The CEDAR session management layer is highly stateful and records several
important pieces of information about the session, including who the connection
claims to be, where it originated from, how it was authenticated, which
canonical user that credential maps to, how that user was authorized, and which
types of encryption and integrity checks will be used for the connection.
Using this extra data, many optimizations can be made, allowing the same
session to be used for other purposes as long as the new purpose is also
authorized by the policy used to create the original session.  This further
reduces the number of authentications and improves scalability.

After two entities make initial contact and authenticate each other with
whatever method was negotiated, a session is created and an internal 192-bit
session key is generated and distributed securely to each entity.  It is the
knowledge of this key that allows sessions to be resumed quickly and securely
without re-authenticating each time.  The keys have expiration dates after which
the session is torn down and a new one must be created.  The default lifetime
for a session varies depending on the purpose of the connection, but is also
configurable, and adjusting the session lifetime can impact the memory
footprint of a running daemon by limiting the number of sessions cached in
memory at any given point.  A shorter lifetime will cause fewer sessions to be
cached, which reduces the memory footprint but also increases the number of
authentications performed to periodically reestablish new sessions.

\subsection{Resuming a Session}
Condor's session management is optimized for the common case of resuming an
already established session.  When resuming a session, Condor sends the session
ID (and not the key itself of course) as part of the initial contact.  Each
entity looks up the session key using the session ID.  The sending party uses
the secret key to encrypt either the entire stream or at the very least the MD5
sum.  The ability of the receiving side to decrypt the stream or MD5 sum proves
they share the same secret key and therefore authenticates the resumed
connection.  Condor does not wait for confirmation that the session ID is
valid, as this would require a network round trip.  By optimizing for the
common case, there are no additional round trips in resuming a session, and
eliminating the round trip means there is no additional latency.  This makes
resuming a session very efficient, which is extremely important in constructing
a scalable distributed system where the network connections are potentially
made over a WAN with relatively high latency.

\subsection{Invalid Sessions}
Because Condor is optimized for the common case, in the event of an invalid
session being resumed the server must notify the client out-of-band that the
session is no longer valid.  This instructs the client to destroy the invalid
session and create a new one.  This could happen for instance if the server was
restarted for some reason (thus clearing the server's soft-state session cache) and the
client is not.  This message to invalidate a session is sent using TCP by
default since UDP packets are unreliable, but delivery of this information is
critical.

\section{Delegated Sessions}

An important characteristic of CEDAR's session layer is the clean seperation
between network authentication and the establishment of a security session.  In
CEDAR, the authentication process results in the creation of a security
session.  This session contains all state required to perform secure
communications.  Furthermore, this session state is serializable and
transferable.  By transfering the session state from one service to another
that have established a trust relationship, a system using CEDAR is able to
establish a secure communication channel between two entities that had not
previously communicated.

For example, when the Condor system is matching jobs from a submit node to an
execute node, the centralized Condor directory service must already communicate
with both the nodes to perform matchmaking.  By delegating
the security session through these existing secure connections, Condor can establish a
secure channel between the submit and execute nodes even though they have not
previously authenticated to each other directly.  This then allows them to
communicate by resuming an existing session, the optimized common case, and
avoid performing the expensive authentication.  This is especially helpful
because the queueing service on the submit node is typically where scalability
is limited, and the limiting factor was often high-latency network
authentications and somewhat heavy CPU utilization due to PKI.  Delegating
sessions enables this cost to be offloaded to a third-party machine.

Another advantage to delegating trust relationships in this manner is it
allows two daemons to establish a secure channel even if they do not share a
common authentication mechanism between them.  For instance, GSI has not yet
been implemented on Windows despite GSI being widely deployed on world-wide
physics grids.  By having the central directory service delegate sessions to
the submit and execute nodes, systems with no common authentication methods can
still be part of the same grid.

\subsection{Advantages for UDP}
Most common communication libraries overlook the implementation of security
features for UDP datagrams.  Enabling security features via UDP can be a
challenge because it is connectionless and also has no delivery guarantees.
However, because of CEDAR's flexible session management, a session set up on
one connection can be reused for another connection, which allows CEDAR to
provide the ability to send and receive secure UDP datagrams.  A session must
first be established using TCP, since that is the only way many authentication
mechanisms can operate.  If a session already exists between two communicating
entities, there is then no additional overhead to using secure UDP.  If one
does not exist, CEDAR will automatically establish a session using TCP,
incurring only the minimal overhead of a single authentication and secure key
exchange.  After establishing a session, CEDAR can then use the session to send
secure UDP messages using the shared secret key in exactly the same way as a
TCP session is resumed and authenticated.  This technique adds no additional
round trips on the network and thus sending a UDP datagram remains a one-way
operation.

\subsection{Experimental Results}
The US CMS collaboration is using Condor glideins\cite{glideinwms} to harvest
Grid resources; the Condor collector and schedd are kept in a central location,
while the Condor startds are sent to the Grid resources to create a
virtual-private Condor pool.  GSI authentication is used for all inter-daemon
communication.

The initial deployments used Grid resources located in the same region as the
central services and the results were very good; Condor could easily handle
10000 glideins, with a 1 Hz global glidein turnaround rate (equal to the global
glidein startup rate).  However, when testing the scalability on Grid resources
spread world-wide, Condor failed to scale beyond a few hundred glideins. The
network latencies were determined to be the root cause; Condor did not yet
support the delegated sessions at that time.

Tests were performed over the wide area network, compared to the loopback
device, and the following results were obtained (all times are in seconds):

\begin{center}
\begin{tabular}{ l | l | l }
\hline \hline
                    &   WAN  & loopback \\
\hline
ping time               &   0.15 & 0.00006 \\
bare GSI authentication (client)    &   0.43 & 0.15 \\
bare GSI authentication (server)    &   0.74 & 0.15 \\
CEDAR session setup with GSI (client)   &   1.0  & 0.15 \\
CEDAR session setup with GSI (server)   &   1.2  & 0.16 \\
   \hline
\end{tabular}
\end{center}

The network latencies are a performance killer for single threaded products
like the Condor daemons.

The first obvious bottleneck is the Condor daemon that keeps the state of the
resource pool (the collector), since it does a lot of communication.  In the US
CMS setup, each glidein initiates four sessions at startup.  US CMS mitigated
the collector scalability problem by deploying multiple daemons, which worked
great since collectors can be arranged in a tree fashion.  Using a tree of 1+70
collectors the system was able to handle first 10000 and then 25000 glideins
over a WAN, with a global glidein turnaround rate of up to 2.5Hz.

The other Condor daemon that is connection-intensive is the schedd, as it has
to handle the connections with the startds when the jobs start and end.  While
the schedds can also be replicated, they cannot be arranged in a tree
structure; each schedd has to be independent.  As such, from the usability
point of view, it is desirable to use a single schedd.

The schedd scalability problem was addressed by using the delegated sessions.
In this setup, only the collector needs to fully authenticate the parties (i.e
the schedd and startds) and establish a security session. The schedd is then
given the security session of the matched startd during the matchmaking
process, thus making communication between the schedd and the startd very
efficient.  With this setup, the schedd easily handled 25000 running jobs in
the above mentioned test.

\section{Conclusion}

This paper demonstrated how thoughtful network session management can
enhance the performance of a large-scale distributed system.  The
demands of establishing and resuming a secure channel across
administrative domains, multiple distributed services, and wide-area networks
created the challenges that motivated the development of CEDAR.  The
mechanisms in CEDAR's design, outlined in this paper, have played a key
role in allowing the Condor High Throughput Computing system to meet the
large and dynamic workload of the US CMS experiment.

\section*{References}