\documentstyle[12pt,aasms4]{article}

\begin{document}

\title{
Deep CCD Photometry of the Globular Cluster NGC~4833 in the $BVI$ bands
\footnote{Based on observations collected at the Las Campanas Observatory,
Carnegie Institution of Washington.}
}

\author{
G. Alcaino, W. Liller, and F. Alvarado}
\affil{Isaac Newton Institute, Ministry of Education of Chile, Santiago,
Chile}

\author{A. Mironov}
\affil{Sternberg Astronomical Institute and Isaac Newton Institute Moscow
Branch, Moscow, Russia}

\author{A. Ipatov, A. Piskunov, N. Samus, and O. Smirnov}
\affil{Institute of Astronomy of Russian Acad. Sci. and Isaac Newton
Institute Moscow Branch, Moscow, Russia}

\begin{abstract}
We have obtained the first deep $BVI$ CCD photometry in the globular
cluster NGC 4833 with more than 15000 stars in $V$ and $I$ bands and
a limiting magnitude of $24^m.0$ in $V$ band. Detailed comparison
with earlier photographic photometry reveals serious systematic
effects in iris-photometry magnitudes in the central parts of the
cluster. In the field of the cluster, the $E(B-V)$ color excess increases
from north to south by as much as $0^m.02$, from $0^m.385$ to $0^m.408$
within the studied area, with $E(B-V)=0^m.39$ near the cluster center.
We have derived the following parameters for
NGC 4833: [Fe/H]$=-1.97\pm0.15$ or even lower,
and $(m-M)_{V,4833}=14.97$. In the isochrone scale of Bergbusch \&
VandenBerg (1992), the age of NGC 4833 is 16 Gyr; however, unusual
position of the subgiant branch does not coincide with any theoretical
isochrone, making age determination rather uncertain.
\end{abstract}


\section{Introduction}

Three photometric studies of stars in the globular cluster NGC 4833
[$\alpha(2000)=12^h59^m35^s.0$,
$\delta(2000)={-}70^\circ52'29''$]
exist up to now. The first two color--magnitude diagrams (CMDs)
were obtained by \cite{alc71} and by \cite{men72} from photographic data.
Numerous field stars in the dense foreground of the Milky Way
make it difficult to isolate the cluster's CMD sequences; still, the first
diagrams showed NGC 4833 to be a low-metallicity cluster, with a rather
large color excess in $B-V$ towards the cluster (at least,
$0^m.3$). The apparent distance modulus of the cluster, as determined
by Menzies, was 15.5$\pm$0.04; Alcaino found a lower value, $m-M=14.9$,
for $E(B-V)=0.4$. Both studies used traditional technique of photographic
photometry: plates were measured with an iris photometer and calibrated
through a photoelectric sequence in the same field. Alcaino obtained
photometry in $B$ and $V$ bands, and Menzies, in $U$, $B$, and $V$ bands. In
both studies, the limiting magnitude was about $17^m$ in $V$.

Later, \cite{MirSam74} concluded from its low metallicity and the shape
of its horizontal branch that the cluster was comparatively old
and that it belonged to the Galaxy's group of old clusters (M13 type).

In the course of several decades, investigators arrived at quite
different values of reddening and metallicity for NGC 4833. Some of
these values are summarized in Table 1.

The study of \cite{mcc92}
showed that the interstellar linear polarization in the field of NGC 4833
systematically increased from the northern to the southern part of the
cluster, with considerable variations from star to star. From the standard
relation between the linear polarization and the interstellar reddening,
$E(B-V) \ge P/9$ (\cite{smf75}), the range of their polarization values (from
1.5\% to 2.6\%) corresponds to changes of the color excess at least by
$0^m.1$.

A new photographic study of stars in NGC~4833 was published by \cite{sea95}.
This time the plates were measured with an automatic microdensitometer
with scans using pixels of $20\times20$ or $30\times30\ \mu$m size. The
limiting magnitude in visual light was about $19^m.5$, close to the
main-sequence turnoff.

The cluster parameters usually accepted currently, in accordance with
\cite{har96}, are [Fe/H]\,=\,--1.79, $E(B-V)=0.33$, $m-M=14.87$. The
cluster is at 5.9 kpc distance from the Sun, 6.9 kpc from the galactic center,
and 0.8 kpc to the south of the galactic plane.

In this study we present the first deep, accurate $BVI$ CCD
photometry in NGC 4833, resulting in much deeper and more accurate CMDs.
Here we are able to check earlier determinations of the cluster's distance
modulus, metallicity, and color excess, to obtain a reliable determination
of the position of the main-sequence turnoff point, and to verify
the cluster's large age.

\section{Observations and Reductions}

The observations reported on here were acquired on June 16/17,
17/18, and 18/19, 1994 using the $100''$ telescope of the Las
Campanas Observatory. The detector was a TEKTRONIC 5 CCD
($2048\times2048$ pixels) with a readout noise of $6.5e^-$ rms;
the pixel size was 21 $\mu$m. The center of the measured field was
approximately $3.0'$ to the south of the cluster center. The
frames covered a region of $10'\times15'$ on the sky, with the longer
side along the direction from north to south.

We used a total of 13 frames in $V$ with exposures from 10  to 1200
seconds, 13 frames in $B$ with exposures from 10 to 1500 seconds, and
13 frames in $I$ with exposures from 10  to 900 seconds.  The average
seeing estimated during observations and reductions was
$1.3''-1.4''$. The air masses during exposures varied from 1.32 to
1.76.

The reductions of CCD photometry were performed at the Institute of
Astronomy (Moscow) using the software described by us earlier
(\cite{sea_95}) which is based upon the DAOPHOT II ALLSTAR application
(\cite{ste91}), with some recent improvements (\cite{smir99}).
PSF stars, 15 to 20 per frame, bright but far from
saturation, were selected interactively among those having no neighbors
or defects within the PSF radius.

In the reductions, we used photoelectric standards from \cite{ala87}
(the finding chart and magnitudes of the standards can be found in the
cited paper).
As is usual for CCD studies of the Isaac Newton Institute, we used
a photoelectric sequence established in the cluster field itself rather
than observing distant comparison fields.

The formulae used in this study to derive magnitudes and color indices
in the standard system from DAOPHOT ALLSTAR instrumental magnitudes
for NGC~4833 are:
$$V=v-0.038(\pm0.040)(b-v)+0.055(\pm0.052),$$
$$V=v-0.033(\pm0.030)(v-i)+0.052(\pm0.043),$$
$$V=v-0.018(\pm0.017)(b-i)+0.053(\pm0.047),$$
$$B-V=1.118(\pm0.016)(b-v)-0.175(\pm0.021),$$
$$V-I=0.892(\pm0.025)(v-i)+0.179(\pm0.039).$$

Table 2 presents the results of our CCD photometry for the
photoelectric standards.

In each photometric band, we retained only stars with at least two
measurements. We rejected stars for which PSFs adopted for the
profile-fitting photometry were very poorly determined ($\chi^2>5.0$).
As a result, we obtained $B$ magnitudes for 8701 stars, $V$
magnitudes for 15554 stars, and $I$ magnitudes for 17977 stars.
All three magnitudes, $B$, $V$, and $I$, are available for 5197 stars.

Table 3 presents averages of the random r.m.s. errors dependent upon
the $V$ magnitude.

The results of our photometry are available from N.\,Samus upon
request.


\section{Comparison with photographic photometry}

It is instructive to compare our CCD photometry
with earlier magnitudes derived from photographic plates, especially
because in all three photographic studies, as well as in the present
study, stars were measured to the very center of this cluster with
relatively low central concentration.

Figure 1ab compares the photographically determined $V$ magnitudes from
\cite{alc71} and \cite{men72} with our CCD photometry. We have reliably
identified 261 stars in common with Alcaino and 779 stars in common
with Menzies.   Here we have plotted the magnitude differences against
the distance from the cluster center measured in CCD pixels.

The figure shows the existence of systematic
differences among the magnitude systems plus significant scatter.
No strong color relations are found, but clearly there is a strong
influence of background in the central part of the cluster: the
difference
$V_{pg}-V_{CCD}$ is practically constant for distances from the cluster
center exceeding 450 CCD pixels (i.e. $\approx 2'.5$), being $0^m.14$
for photometry from \cite{alc71} and $0^m.08$ for photometry from
\cite{men72}, whereas the differences systematically increase towards
the cluster center and, at last, exceed $0^m.5$.  This effect is
obviously due to nonlinear and nonadditive nature of photographic
imaging. In aperture photographic photometry, magnitudes of stars
measured close to the cluster center turned out to be brighter because
of insufficient accounting for contribution of unresolved background of
faint stars. Such stars do not appear on the plates individually: their
brightnesses are in the underexposure region of the photographic
characteristic curve, and they do not influence the background level
used in the reductions. However, if their light is added to the light
of a star in the linear region of the characteristic curve, then the
combined photographic effect is increased, and the measured star is
found brighter than in reality.

The comparison of our CCD photometry with the photographic photometry
from \cite{sea95}, based on 290 stars in common, is presented in
Fig. 2, it does not reveal a similar effect. It must be due to the
different technique of measurements and reductions when using automatic
microdensitometers. However, there exists a constant systematic
deviation (photographic magnitudes are, on average, brighter by
$0^m.09$), plus a slight brightness equation and a more noticeable
color equation. The magnitudes can be related through the formula
$$
V_{CCD}-V_{pg} = -0.1429 + 0.0096 V_{CCD} + 0.0830(B-V)_{CCD}.
$$

Faint unresolved stars of the cluster center also influence the CCD
photometry, but not in the same way as for the photographic
imaging. In PSF reductions, the background level is estimated
{\it after} the procedure of the subtraction of stars,  and this
estimate can also be biased.
A quantitative estimate of this effect requires special investigations
planned by us for the future.

\section{The color-color and color-magnitude diagrams}

\subsection{Selection of cluster members}

Figure 3 presents the $(V,\ V-I)$ diagrams.

In our photometry, 5197 stars were measured reliably in all three bands
and these can be used to plot a $(B-V,\ V-I)$ diagram.  The 2-color
diagram shown in Fig. 4 includes only brightest cluster stars, namely
those brighter than $19^mV$. The figure shows a separation into
two sequences in the interval $0.90<(V-I)<1.2$. As would be
expected, the metal-poor cluster stars have a blue excess relative to
the field stars because of weaker absorption lines. The cluster stars
appear in the lower sequence and delineate well the known evolutionary
sequences; conversely, the stars of the upper sequence scatter almost
uniformly in the $(V,\ B-V)$ plane. Similarly, most stars deviating from
the principal sequences in the $(V,\ B-V)$ diagram, in particular, those
situated to the red of the principal sequences in the
$(V,\ B-V)$ diagram, populate just the upper sequence in Fig. 4.

On these grounds, we considered those stars redder than the principal
sequences in the
($V,\ B-V$) diagram
(see Fig. 6 below) cluster nonmembers and rejected them from the further
analysis.

\subsection{Differential reddening}

Viewing the $(V,\ B-V)$ diagram attentively, we notice that, in the transition
region from turnoff to the subgiants, the diagram shows stratification into
several subsequences. To study this effect, we separated the whole studied
cluster field ($10'\times15'$) into six parts, approximately
$3'.5\times7'.5$ each, so that we divide the east--west side of the field
into three parts and the north--south side, into two parts
(Fig. 5).

For each of the six parts of the field, we plotted its $(V,\ B-V)$ diagram.
Then, similar to the analysis of the unified CMD presented below,
we used these diagrams to derive ridge lines and, from them, the turnoff
color $(B-V)_{TO}$ and magnitude $V_{+0.05}$. For each two fields,
the difference of their turnoff color indices is an estimate of the
differential reddening, $\delta E(B-V)$. We find that $(B-V)_{TO}$
varies by $\pm0^m.03$, reddening increasing from north to south,
in agreement with \cite{mcc92}.  As expected, $(B-V)_{TO}$ and
$V_{+0.05}$ values correlate: the redder $(B-V)_{TO}$, the fainter
$V_{+0.05}$.

We can estimate the interstellar reddening by another method.
Main-sequence ridge lines for the six subfields, parallel straight lines
in the first approximation, are differently positioned. If we fix
a value of $R=A_V/E(B-V)$, then the distances between the ridge-line
segments, $\delta V$ [$(B-V)$ fixed] and $\delta (B-V)$ [$V$ fixed]
can be used for an independent calculation of the color-excess
difference, $\delta E(B-V)$. We adopted the standard value $R=3.1$ and
arrived at results similar to those derived from the turnoff region.
We averaged results from the two methods. Then, for each of the six
subfields, we reduced the observed magnitudes and colors of cluster
stars [$(V,\ B-V)$ and $(V,\ V-I)$] to a unified level of interstellar
reddening, that for the zone 1.2. The resulting reddening-unified
$(V,\ B-V)$ diagram is shown in Fig. 6. Probable cluster nonmembers
are plotted as smaller symbols.

The principal sequences in Fig. 6 are well populated, and the ridge
points of these sequences are given in Table 4.

\subsection{The determination of color excesses}

After removing effects of the differential reddening, we estimated
the general color excess, $E(B-V)$.
To determine color excesses from two-color diagrams, it is necessary to
have a line of normal color indices for stars of similar metallicity.
Though many different CMDs have been published for numerous globulars,
$(V,\ B-V)$ for some clusters or $(V, \ V-I)$ for others, measurements
in more than two bands, making it possible to plot two-color diagrams,
are available for not many clusters, significant fractions of which
were observed in the programs of the Isaac Newton Institute. We
compared the sequence of NGC 4833 stars in the two-color $(B-V,\ V-I)$
diagram with a similar sequence for the low-metallicity globular
cluster M30 = NGC 7099, with reliable CCD $BVRI$ photometry available
(\cite{aea98}). The $E(B-V)$ color excess for M30 found in the cited
paper is 0.078. The diagram for M30 has sparsely populated horizontal
and red-giant brunches, but subgiants as well as the main sequence in
the range $0.6<V-I<1.0$ are traced quite reliably. We achieved a fit of
the sequences for the two clusters using a shift along the vector of
interstellar reddening, its slope for stars with [Fe/H] = --2.0 being
$E(V-I)/E(B-V)=1.30$ (\cite{GR95}). The reddening line in the $(B-V,\
V-I)$ diagram forms a narrow angle with the cluster sequence;
nevertheless, the fit is reliable for the portion of the sequence with
the following colors, in the scale of M30: $0.6<V-I<1.0$,
$0.45<V-I<0.8$ (Fig. 7). This method gives, for color excesses of
NGC~4833 relative to M30, the values $\delta E(B-V)=0.32$ and $\delta
E(V-I)=0.43$, thus resulting in absolute values $E(B-V)=0.40$ and
$E(V-I)=0.52$.

In the ($V,\ B-V$) diagram, the horizontal branch (HB) is really almost
horizontal for $0.45<(B-V)<0.60$. Stars immediately to the blue of the
instability strip have, on average, $V=15^m.51$. The red HB is not
well-developed. Thus, we adopt the above value for the magnitude of the
HB at the level of the instability strip. It is fainter than the value
$15^m.2$ given by \cite{alc71}, almost coincides with $V_{RR}=15.5$
from \cite{men72}, and does not significantly differ from the value
15.6 from \cite{sea95}.

The distribution of stars by color index along the HB is
shown in Fig. 8. From this histogram, it follows that at the HB level,
the blue edge of the instability strip is at
$(B-V)_b=0.56\pm0.01$; the red edge cannot be determined.

The maximum of the distribution comes at
$(B-V)_1=0.38\pm0.01$. It is known that the dereddened color index of
this maximum, $(B-V)_{0,1}$, correlates with the difference of apparent
(not dereddened) color indices of this maximum and of the blue edge of the
instability strip, $\Delta_{b-1}=(B-V)_1-(B-V)_b$.
This relation was found (\cite{aea98}) to be
$$
E(B-V)=(B-V)_1-(B-V)_{0,1} = (B-V)_1 - 0.154 + 1.006{}\Delta_{b-1},
$$
so, in accordance with our values for NGC 4833
[$(B-V)_1=0.38\pm0.01$,  $\Delta_{b-1}=+0.18\pm0.02$], we obtain
$E(B-V)=0.41\pm0.02$, in good agreement with the value found in
\cite{alc71} and by the color--color method.

For subsequent analysis, we adopt $E(B-V)=0.40\pm0.02$ (the reddening
value for subfield 1.2).

\subsection{The determination of metallicity}

We can estimate the metallicity of NGC 4833 using the compilation
of formulae for computation of [Fe/H] from $(B-V)_{0,g}$ and
$\Delta{}V_{1.4}$ values presented in \cite{fccfcbph}.

The color index of the RGB, at the brightness level of the HB, is
$(B-V)_g=1.065$;
thus we arrive at $(B-V)_{0,g}=0.66$ using our
adopted reddening value. The magnitude of RGB stars for the standard
dereddened color index, $(B-V)_{1.4}$ [i.e., for the reddened color
index $(B-V)=1.82$] is approximately $V_{1.4}=12.4$, and the elevation
of the RGB over the HB is $\Delta V_{1.4}=3.11$. This value is uncertain,
there is already no stars in our CMD at the corresponding level.

The results
are summarized in Table 5. Note that metallicities derived from
$(B-V)_{0,g}$ are systematically lower than those derived from
$\Delta{}V_{1.4}$.

\subsection{The determination of the distance modulus}

To determine the distance modulus of NGC 4833, we compare its
$V_{HB}$ with the similar value for the low-metallicity clusters M30
and NGC 5053. From \cite{aea98}, $V_{HB,M30}=15.20$,
$E(B-V)_{M30}=0.08$, and from the \cite{har96} catalog,
$V_{HB,M30}=15.20$, $E(B-V)_{M30}=0.03$, [Fe/H]$_{M30}=-2.12$, and
$(m-M)_{M30}=14.57$. Respectively for NGC~5053, from \cite{sm95},
$V_{HB,5053}=16.60$, and from the \cite{har96} catalog,
$V_{HB,5053}=16.65$, $E(B-V)_{5053}=0.03$, [Fe/H]$_{5053}=-2.29$,
and $(m-M)_{5053}=16.14$.

If we adopt, following Harris's catalog, the slope
$\partial M_V(RR)/\partial{\rm[Fe/H]}\approx0.20$,
and use the above values,
we then obtain for NGC~4833  $(m-M)_{V,4833}=14.97\pm0.10$.
This value agrees reasonably well with $(m-M)_{V,4833}=14.87$
derived by \cite{har96}.

\subsection{Some important CMD parameters}


From the three diagrams $(V,\ B-V)$, $(V,\ V-I)$, and $(V,\ B-I)$,
we find that the main-sequence turnoff is located, on the average, at
$V_{TO}=19.08\pm0.05$, and $V_{+0.05}=20.0\pm0.1$,
$(B-V)_{TO}=0.78\pm0.01$, $(V-I)_{TO}=0.99\pm0.005$,
$(B-I)_{TO}=1.76\pm0.01$. The separation between the turnoff point and
the HB is $\Delta{}V_{TO}^{HB}=3.57$.

From the $(V,\ V-I)$ diagram, one can determine the parameters
$(V-I)_{0,g}$ and $\Delta{}V_{1.2}$ used in Sarajedini's method
(\cite{Sj94}) for simultaneous determination of metallicity [Fe/H] and
reddening $E(V-I)$.  From our diagram, we find $(V-I)_{g}=1.33$.
Sarajedini's method gives $E(V-I)=0.41$ [corresponding to
$E(B-V)=0.31$ and [Fe/H]$=-1.70\pm0.10$]. Such values seem to us
quite unreasonable, and, in our opinion, suggest  problems with the method.

\section{Determination of age from isochrones}

For reasons discussed by us in detail elsewhere (see, for instance,
\cite{aea98}), we continue our homogeneous approach to the determinations
of ages of globular clusters, awaiting the results of the current
polemic on the controversy of globular cluster ages and the Hubble
constant, in particular, with relation to the recent HIPPARCOS results.
This controversy still has not been completely clarified. \cite{chea98}
argue that, from several methods including HIPPARCOS results, a
consistent revision of RR Lyrae absolute magnitudes follows leading
to mean age of $11.5\pm1.3$ Gyr for oldest globular clusters. However,
\cite{L98} claims that no significant revision of the distance scale
for RR Lyraes follows from HIPPARCOS data, and \cite{fs98} obtain the
distance scale for globular clusters, quite close to the traditional one,
from infrared absolute magnitudes of RR Lyrae variables; these results
tend to support ``old'' globular clusters. \cite{fea98}, on the base of
HIPPARCOS parallaxes and proper motions, derive statistical parallaxes
of RR Lyraes and obtain, for the mean age of Galactic globular clusters,
the value $17.4\pm3.0$ Gyr.

Figure 9 shows the ridge sequences of NGC 4833 (cf. Table 4) in the
$(V,\ B-V)$ diagram with superimposed oxygen enhanced isochrones
(\cite{BvdB92}). To select the isochrone best fitting the observations,
we varied  [Fe/H] from --1.78 to --2.26 and age from 12 to 18 Gyr. For
better agreement, we also allowed slight variations of the adopted
distance modulus and color excess.  Isochrones in Fig. 9 correspond to
[Fe/H] = --2.03 and three age values:  14, 16, and 18 Gyr (short-dash,
long-dash, and solid lines, respectively).  The zero age horizontal
branch shown as a solid line and HB star tracks for two masses (0.54 and
0.70 $M_{\odot}$), for the same chemical abundance,
shown as a tiny-dash line follow \cite{dor92}.

We achieved the best representation of the observed ridge line with the
theoretical isochrone, simultaneously for the main sequence, the
turnoff region, and the subgiant sequence, for the 16 Gyr isochrone
with [Fe/H] = --2.03. The isochrone was shifted exactly to our adopted
distance modulus, $m-M=14.97$, but the best-fit shift along the $B-V$
axis, due to reddening, was found to be $0^m.39$.

However, it is quite clear that no isochrone represents observations
sufficiently well in the subgiant region. The observed turnoff to subgiants
is much sharper than for the theoretical sequences. Similarly,
the transition from subgiants to giants is more abrupt than the theory
predicts. The
ridge points can deviate even from the closest (18 Gyr) isochrone by as much
as $0^m.3$. The behavior of the subgiant branch cannot be explained by
photometric errors or by uncertainties in the
fiducial points. This contradiction makes reliable age determination
impossible. The separation $\Delta (B-V)$ between color indices of
the base of the giant branch and of the turnoff point is
$0^m.22\pm0^m.01$. Calibration given by \cite{SD90} (cf.
Fig. 2 in the cited paper) leads to the cluster age equal to
13 Gyr, in the scale of new Yale isochrones.  However, for
\cite{BvdB92} isochrones it is impossible to
reconcile such an age value simultaneously
with the positions of the turnoff point, of main-sequence and giant-branch
stars for any values of distance modulus and reddening.

We tend to believe that NGC 4833 is a rather old low-metallicity cluster,
but with an unusual position of the subgiant branch.

\section{Conclusions}

From our $BVI$ CCD photometry of a large sample of stars in the
globular cluster NGC 4833, we have derived a number of important
parameters for the cluster and revealed some peculiarities.

1. In the field of the cluster, the $E(B-V)$ color excess increases
from north to south by as much as $0^m.02$, from $0^m.385$ to $0^m.408$
within the studied area, with $E(B-V)=0^m.39$ near the cluster center.

2. The cluster is rather metal-poor, with [Fe/H]$=-1.97\pm0.15$.

3. The distance modulus of NGC 4833 is $(m-M)_{V,6723}=14.97$.

4. The \cite{BvdB92} isochrones well represent the cluster's main sequence
and giant branch.

5. The \cite{dor92} theoretical sequences represent the horizontal branch
reasonably well.

6. The ridge line shape near the main-sequence turnoff and the subgiant
branch cannot be reproduced with any of \cite{BvdB92} isochrones.

7. The main sequence and the giant branch show the best agreement with the
\cite{BvdB92} isochrones for [Fe/H]$=-2.03$  and  16 Gyr age.
The anomalous behavior of the subgiant branch makes this estimate rather
uncertain.

\bigskip

Thanks are due to Mr. Oleg Lahtionov for his assistance and Dr.
Andrey Zakharov for useful discussion. This study made use of the catalog
of globular cluster parameters compiled by W. Harris (McMaster
University).

\begin{thebibliography}{}

\bibitem[Alcaino 1971]{alc71} Alcaino, G. 1971, \aap, 13, 287
\bibitem[Alcaino et al. 1987]{ala87} Alcaino, G., Liller, W., \& Alvarado, F.
1987, \aj, 93, 1464
\bibitem[Alcaino et al. 1998]{aea98} Alcaino, G., Liller, W.,
Alvarado, F. et al. 1998, \aj, 115, 1492
\bibitem[Bergbusch \& VandenBerg 1992]{BvdB92} Bergbusch, P. A. \&
VandenBerg, D. A. 1992, \apjs, 81, 163
\bibitem[Chaboyer et al. 1998]{chea98} Chaboyer, B., Demarque, P.,
Kernan, P. J., \& Krauss, L. M. 1998, \apj, 494, 96
\bibitem[Costar \& Smith 1988]{CS88} Costar, D. \& Smith, H. A. 1988, \aj,
96, 1925
\bibitem[Dorman 1992]{dor92} Dorman, B. 1992, \apjs, 81, 221
\bibitem[Fernley et al. 1998]{fea98} Fernley, J., Barnes, T. G., Skillen,
I. et al. 1998, \aap, 330, 515
\bibitem[Ferraro et al. 1996]{fccfcbph} Ferraro, F. R., Carretta, E.,
Corsi, C. E. et al., \aap, 320, 757
\bibitem[Frogel et al. 1983]{frea83} Frogel, J. A., Cohen, J. G., \& Persson,
S. E. 1983, \apj, 275, 773
\bibitem[Frolov \& Samus 1998]{fs98} Frolov, M. S. \& Samus, N. N. 1998,
Astronomy Letters, 24, 171
\bibitem[Geisler et al. 1992]{gea92} Geisler, D., Minniti, D., \& Claria,
J. J. 1992, \aj, 104, 627
\bibitem[Gratton 1987]{Gra87} Gratton, R. G. 1987, \aap, 179, 181
\bibitem[Gratton \& Ortolani 1989]{GO89} Gratton, R. G. \& Ortolani, S.
1989, \aap, 211, 41
\bibitem[Grebel \& Roberts 1995]{GR95} Grebel, E. K. \& Roberts, W. J. 1995,
\aaps, 109, 293
\bibitem[Harris 1996]{har96} Harris, W.E. 1996, \aj, 112, 1487
\bibitem[Harris and Racine 1979]{hr79} Harris, W. E. \& Racine, R. 1979,
Ann. Rev. Astron. Astrophys., Vol. 17, Palo Alto, CA: Annual Reviews, Inc.,
p. 241
\bibitem[Johnson \& Bolte 1998]{jb98} Johnson, J. A. \& Bolte, M. 1998,
\aj, 115, 693.
\bibitem[Layden 1998]{L98} Layden, A. C. 1998, in Post-Hipparcos Cosmic
Candles, Heck, A. \& Caputo, F. (eds.), Dordrecht, Boston: Kluwer
(Astrophysics and Space Science Library, Vol. 237)
\bibitem[Menzies 1972]{men72} Menzies, J. 1972, \mnras, 156, 207
\bibitem[Minniti et al. 1992]{mcc92} Minniti, D., Coyne, G. V., \& Claria,
J. J. 1992, \aj, 103, 871
\bibitem[Mironov \& Samus 1974]{MirSam74} Mironov, A. V. \& Samus, N. N.
1974, Perem. Zvyozdy (Variable Stars), 19, 337 (in Russian)
\bibitem[Pilachowski et al. 1983]{pea83} Pilachowski, C. A., Sneden, C.,
\& Wallerstein, G. 1983, \apjs, 52, 241
\bibitem[Samus et al. 1995a]{sea95} Samus, N., Kravtsov, V.,
Pavlov, M., Alcaino, G., \& Liller, W. 1995a, \aaps, 109, 479
\bibitem[Samus et al. 1995b]{sea_95} Samus, N., Ipatov, A., Smirnov, O. et
al. 1995b, \aaps, 112, 439
\bibitem[Sarajedini 1994]{Sj94} Sarajedini, A. 1994, \aj, 107, 618
\bibitem[Sarajedini \& Demarque 1990]{SD90} Sarajedini, A.
\& Demarque, P. 1990, \apj, 365, 219
\bibitem[Sarajedini \& Milone 1995]{sm95} Sarajedini, A. \& Milone, A. A. E.
1995, \aj, 109, 269
\bibitem[Seal 1986]{pseal86} Seal, P. 1986, Bull. Astron. Soc. India, 14,
168
\bibitem[Serkowski et al. 1975]{smf75} Serkowski, K., Mathewson, D.S.,
\& Ford, V.L. 1975, \apj, 196, 261
\bibitem[Smirnov 1999]{smir99} Smirnov, O. 1999, in: Astronomical Data
Analysis Software \& Systems VIII, ASP Conf. Ser., in press
\bibitem[Stetson 1991]{ste91} Stetson, P. B. 1991a, DAOPHOT II Users Manual,
Victoria: Dominion Astrophysical Observatory
\bibitem[Zinn 1980]{z80} Zinn, R. 1980, \apjs, 42, 19
\bibitem[Zinn 1985]{z85} Zinn, R. 1985, \apj, 293, 424
\bibitem[Zinn \& West 1984]{ZW84} Zinn, R. \& West, M. J. 1984, \apjs, 55, 45
\end{thebibliography}

\newpage

%1
\figcaption{Comparison of our CCD photometry in NGC 4833 with photographic
photometry from Alcaino 1971 (panel ``a'') and Menzies 1972 (panel ``b'').}

%2
\figcaption{Comparison of our CCD photometry in NCG 4833 with
photographic photometry from Samus et al. 1995.}

%3
\figcaption{ The $(V, \ V-I)$ diagram for stars in the region of the
globular cluster NGC 4833, with more than 15000 objects plotted.}

%4
\figcaption{The $(B-V,\ V-I)$ diagram for bright stars in NGC
4833.}

%5
\figcaption{The map of differential reddening in NGC 4833.}

%6
\figcaption{The $(V,\ B-V)$ diagram for NGC 4833, after reduction to
a unified reddening value, as described in the text.
}

%7
\figcaption{Ridge lines for M30 and NGC 4833 stars in the $(B-V,\ V-I)$
two-color diagram. The solid line is a part of the main sequence
and the turnoff region of M30, based upon data from Alcaino et al.
1998. The
dashed line shows all NGC 4833 sequences, from the present study.
Dots: the dashed line shifted along the vectors of the interstellar
reddening to the best fit of the  M30 line [by $\Delta(V-I)=0.36$ and
$\Delta(B-V)=0.47$]. The diamond and the open circle are, respectively,
the turnoff positions for NGC 4833 and M30. The plus sign shows the
turnoff position for NGC 4833, after accounting for the difference in
the interstellar reddening.}

%8
\figcaption{The distribution of $B-V$ color indices for NGC 4833
horizontal-branch stars. The positions of the distribution maximum [the
$(B-V)_1$ point] and of the  blue edge of the instability strip [the
$(B-V)_b$ point] are indicated.}

%9
\figcaption{The best fit of the observed ridge line in the $V,\ B-V$
diagram with the Bergbusch and VandenBerg 1992 theoretical isochrones of 14
(short dashes), 16
(long dashes) and 18 (solid line) Gyr. For other parameters of the isochrones,
see text. The ridge points are shown as pluses.
The zero age horizontal branch is shown as a solid line and HB star
tracks for two masses (0.54 and 0.70 $M_{\odot}$) are shown as
a tiny-dash line following Dorman 1992.}

\end{document}
