\documentclass[journal]{rmaa}


\title{Space reddenings for fifteen Galactic Cepheids}

\author{
D.~G. Turner,\altaffilmark{1} 
R.~F. MacLellan,\altaffilmark{2}
A.~A. Henden,\altaffilmark{3}
and L.~N. Berdnikov\altaffilmark{4}}

\altaffiltext{1}{Saint Mary's University, Halifax, Nova Scotia, Canada.}
\altaffiltext{2}{Queen's University, Kingston, Ontario, Canada.}
\altaffiltext{3}{AAVSO, Cambridge, Massachusetts, USA.}
\altaffiltext{4}{Sternberg Astronomical Institute, Moscow, Russia.}


\shortauthor{Turner et al.} 

\shorttitle{Space reddenings for fifteen Galactic Cepheids}


\fulladdresses{
\item D.~G. Turner: Department of Astronomy and Physics, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada (turner@ap.smu.ca).
\item R.~F. MacLellan, Department of Physics and Engineering Physics, Queen's University, Kingston, ON K7L 3N6 Canada (rmaclellan@bama.ua.edu).
\item A.~A. Henden, American Association of Variable Star Observers, 49 Bay State Road, Cambridge, MA 02138, U.S.A. (arne@aavso.org)
\item L.~N. Berdnikov, Sternberg Astronomical Institute, 13 Universitetskij prosp., Moscow 119992, Russia (leonid.berdnikov@gmail.com).}

\listofauthors{D.~G. Turner, R.~F. MacLellan, A.~A. Henden, \& L.~N. Berdnikov}

\indexauthor{Turner, D.~G.}
\indexauthor{MacLellan, R.~F.}
\indexauthor{Henden, A.~A.}
\indexauthor{Berdnikov, L.~N.}


\ReceivedDate{2011 February 24}
\AcceptedDate{2011 June 27}
\SetYear{2011}


\resumen{Derivamos enrojecimientos espaciales para 15 Cefeidas gal\'{a}cticas a partir de datos CCD {\it BV(RI)}$_C$ desenrojecidos para 
estrellas tipo AF en las vecindades inmediatas de esas variables, en conjunci\'{o}n con enrojecimientos 2MASS de estrellas tipo BAF en los 
mismos campos. Analizamos las soluciones potenciales de enrojecimiento utilizando el m\'{e}todo de extinci\'{o}n variable para identificar 
estrellas con distancias y enrojecimientos similares a las de las Cefeidas, muchas de las cuales presentan excesos de color. Hemos modificado 
ligeramente la relaci\'on de color intr\'{i}nseco {\it BV(RI)}$_C$ para enanas AF en nuestro an\'{a}lisis, de tal forma que los colores 
observados para estrellas no enrojecidas en la muestra queden descritos de forma apropiada.}

\abstract{Space reddenings are derived for 15 Galactic Cepheids from dereddening CCD {\it BV(RI)}$_C$ data for AF-type stars in the immediate 
vicinities of the variables, in conjunction with 2MASS reddenings for BAF-type stars in the same fields. Potential reddening solutions were 
analyzed using the variable-extinction method to identify stars sharing potentially similar distances and reddenings to the Cepheids, several 
of which have large color excesses. The intrinsic {\it BV(RI)}$_C$ color relation for AF dwarfs was modified slightly in the analysis in order 
to describe better the colors observed for unreddened stars in the samples.}


\addkeyword{methods: observational} 
\addkeyword{stars: variable: Cepheids} 
\addkeyword{ISM: dust, extinction}


\begin{document}


\maketitle


\section{INTRODUCTION}

Because of the deleterious effects of interstellar reddening and extinction, it is difficult to establish an empirical picture of the Cepheid 
instability strip based entirely upon observations of Milky Way Cepheids. The use of extragalactic Cepheids is not necessarily a practical 
solution to the problem, since the available data for Milky Way Cepheids are generally more extensive and of greater precision, and the effects 
of internal reddening within other galaxies are not as well established as they are locally. Such considerations justify the continued use of 
the Galactic sample in studies aimed at establishing reliable intrinsic properties of classical Cepheid variables.

The determination of accurate reddenings for Cepheids has traditionally followed three different routes: (i) from field reddenings of specific 
objects (e.g., binary, cluster, association, or isolated Cepheids) based upon the analysis of photometric data for early-type stars sharing the 
same lines of sight, (ii) from observations mainly of bright Cepheids involving photometric parameters designed to be independent of interstellar 
reddening, and (iii) from using standard reddening laws and a calibrated intrinsic color relation (either observational or model generated) to 
deredden photometric observations for large samples of Cepheids. Methods (i) and (ii) are the most reliable means of establishing reddenings for 
individual Cepheids since method (iii) may entail use of period-color relations \citep[e.g.,][]{fe90a,fe90b}, which do not account for the intrinsic 
spread in effective temperature of the Cepheid instability strip and may generate erroneous results \citep[see][]{tu95}.

For method (ii), spectroscopic indices related to stellar effective temperature and designed to be independent, or relatively independent, of 
interstellar and atmospheric extinction include the $\Gamma$-index \citep{kr60,sj89}, which measures the depression of the {\it G}-band of CH 
($\lambda$4305) relative to the local continuum, the $\beta$-index, which samples the strength of the H$\beta$ Balmer line of hydrogen relative 
to the surrounding continuum, and the {\it KHG}-index of Brigham Young University (McNamara \& Potter 1969; McNamara, Helm, \& Wilcken 1970; 
Feltz 1972), which measures the strengths of Ca {\sc II} K ($\lambda$3933), Balmer H$\delta$ ($\lambda$4101), and the {\it G}-band through narrow 
band interference filters in a manner independent of extinction. A more recent technique \citep{sl90} involves the use of line depth ratios between 
C {\sc I} and Si {\sc II} lying on the Brackett continuum near 10728 \AA. A similar technique was used by \citet{kr98} using spectral lines falling 
in the red region of Cepheid spectra. \citet{ko08} have taken the technique to its ultimate level of sophistication by using high resolution optical 
spectra of Cepheids throughout their cycles, in conjunction with stellar atmosphere models, to track their changes in effective temperature, and thus 
intrinsic broad band color. 

The use of close neighbours to deduce reddenings for Cepheids appears to date from its application to the blue companion of $\delta$ Cep by \citet{eg51}; 
it has also been used recently for Cepheids studied with the {\it Hubble Space Telescope} \citep{be07}. But the existing sample includes only $\sim$40 
Cepheids of known space reddening \citep{lc07}. This study presents new space reddenings for 15 Galactic Cepheids derived from CCD {\it BV(RI)}$_C$ 
photometry for stars in the immediate fields of the variables. The goal is to test the feasibility of deriving Cepheid reddenings based upon only 
{\it BV(RI)}$_C$ observations for stars in the fields of the Cepheids, as well as to augment the limited sample of Cepheids with space reddenings. 
As demonstrated here, the methodology appears to provide useful results that extend the sample of Cepheids with independently derived reddenings.

\vspace{0.2cm}

\section{OBSERVATIONAL DATA}

The input data for the present study consist of observations of 15 Cepheid fields obtained with the 1.0~m Ritchey-Chr\'{e}tien telescope of the U.S. 
Naval Observatory, Flagstaff Station. A Tektronix/SITe, 1024 $\times$ 1024 pixel, thinned CCD was used with Johnson system {\it BV} and Kron-Cousins 
system {\it (RI)}$_C$ filters to image the fields \citep[e.g.,][]{hm00}. Several deep images were obtained for each field, from which average 
{\it BV(RI)}$_C$ magnitudes and colors, with typical uncertainties smaller than $\pm0^m.01$, were extracted for all detectable stars using DAOPHOT 
\citep{st87}. Since no {\it U}-band observations or spectral types are available for the stars in the survey fields, it was necessary to deduce 
individual reddenings from photometric analyses of two-color diagrams constructed from the {\it BV(RI)}$_C$ data. The data are available electronically 
from A.A.H. via ftp from the American Association of Variable Star Observers website\footnote{\url{ftp://www.aavso.org/public/calib/}.}.

An often-ignored feature of interstellar reddening is that no single relationship accurately describes it over all regions of the Galaxy 
\citep{wa61,wa62,ma90,tu76a,tu76b,tu89,tu94}. Regional variations in the reddening law depend directly upon direction viewed through the Milky Way, 
vary slowly with Galactic longitude, and are tied to differences in the distribution of particle sizes for dust lying along different lines of sight. 
The resulting Galactic longitude and latitude dependence of the extinction law affects interstellar reddening studies that implicitly use a relationship 
of fixed parameterization to describe the extinction in a particular color system, and should be most important for stars of large reddening. Several 
of the Cepheids in the present sample are heavily reddened, so the extinction laws for the fields of each object were established prior to the analysis 
by taking advantage of existing studies for regions reasonably close to the program objects \citep[e.g.,][as well as other published studies by the lead 
author]{jo68,tu76b,tu89}.

Specifically, a reddening slope $E_{U-B}/E_{B-V}$ for the field of each program Cepheid was established from studies by \citet{tu76b,tu89} for adjacent 
regions, and was linked to specific reddening slopes $E_{V-I}/E_{B-V}$ and $E_{R-I}/E_{B-V}$ on the Johnson system using regional reddening curves from 
\citet{jo68}. Those were then converted to reddening slopes $E_{V-I}/E_{B-V}$ and $E_{R-I}/E_{B-V}$ on the Kron-Cousins system using the results of 
\citet{fe83} and \citet{ca93}. To illustrate the methodology, the results for specific fields studied by \citet{jo68} and exhibiting a range of color 
excess ratios $E_{U-B}/E_{B-V}$ are shown in Figure~\ref{fig1}, where it can be noted that the {\it I--}band $E_{V-I}/E_{B-V}$ reddening ratios appear to 
display no significant dependence on visible reddening slope $E_{U-B}/E_{B-V}$. The Cepheids studied here all lie in fields where the reddening slope 
does not vary significantly from the locally observed Galactic mean, so specifying the exact reddening ratio for each field proved to be only a minor 
concern.


%%%%% FIGURA 1

\begin{figure}[!t]
\vspace{0.2cm}
\centering
\includegraphics[width=0.99\columnwidth]{dturnerfig1.eps}
\caption{Derived Johnson system (filled symbols) and Kron-Cousins system (open symbols) reddening 
ratios $E_{V-R}/E_{B-V}$ (circles, lower) and $E_{V-I}/E_{B-V}$ (squares, upper) for fields studied by 
Johnson (1968). Gray lines denote the implied dependences on reddening slope $E_{U-B}/E_{B-V}$.}
\label{fig1}
\vspace{0.3cm}
\end{figure}

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

 
\section{METHOD OF ANALYSIS}

This study presents new space reddenings for 15 Galactic Cepheids derived from two-color diagrams, {\it V--I}$_C$ versus {\it B--V} and {\it (R--I)}$_C$ 
versus {\it B--V}, constructed from CCD {\it BV(RI)}$_C$ photometry for stars in the fields of the variables. Reddening lines appropriate for each 
field were adopted as indicated above, specifically the adopted reddening slopes $E_{U-B}/E_{B-V}$ were 0.73 for VY Sgr, AY Sgr, and V1882 Sgr, 0.75 
for HZ Per and OT Per, 0.76 for FO Cas, IO Cas, EW Aur, YZ CMa, CN CMa, BD Pup, BE Pup, and LR Pup, and 0.77 for UY Mon and AC Mon. The reddening 
slopes $E_{V-I}/E_{B-V}$ and $E_{R-I}/E_{B-V}$ were next obtained through interpolation and computation with the data of Figure~\ref{fig1}, resulting 
in values on the Kron-Cousins system of $E_{V-I}/E_{B-V}  = 1.257$ for all fields and values of $E_{R-I}/E_{B-V}$ of 0.689, 0.677, 0.670, and 0.664, 
respectively, for the Cepheid fields listed above. Examples are shown in Figure~\ref{fig2}, where the derived reddening slopes for UY Mon and AC Mon 
are $E_{V-I}/E_{B-V} = 1.257$ and $E_{R-I}/E_{B-V} = 0.664$ according to the inferred reddening ratio $E_{U-B}/E_{B-V} = 0.73$. Note that the adopted field 
reddening lines are unchanging for $E_{V-I}/E_{B-V}$ and exhibit only small variations for $E_{R-I}/E_{B-V}$.


%%%%% FIGURA 2

\begin{figure}[!t]
\vspace{0.2cm}
\centerline{\includegraphics[width=0.49\columnwidth]{dturnerfig2a.eps}%
\hspace{0.02\columnwidth}%
\includegraphics[width=0.49\columnwidth]{dturnerfig2b.eps}}
\caption{Two-color diagrams, {\it V--I}$_C$ versus {\it B--V} for the field of UY Mon (left), and 
{\it (R--I)}$_C$ versus {\it B--V} for the field of AC Mon (right), showing the intrinsic color 
relations adopted (solid curves). Reddening lines specific for the fields are shown separately in 
red for $E_{B-V} = 1.0$, with arrows denoting the direction of increasing reddening. The color figure 
can be viewed online.}
\label{fig2}
\vspace{0.3cm}
\end{figure}

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


Initial tests with two-color diagrams using intrinsic {\it BV(RI)}$_C$ colors for dwarfs from \citet{ca93} revealed small anomalies in the inferred 
$E_{B-V}$ reddenings derived from the two diagrams, as well as an overabundance of unreddened and negatively-reddened stars relative to the intrinsic 
relation, not explainable as luminosity effects \citep{ca93}. Such non-physical results suggested the need for slight corrections to the intrinsic 
colors used with the present data sets, which are normalized to the Kron-Cousins system. Small adjustments to the intrinsic relations for late B-type 
and A-type dwarfs to make them bluer were therefore tried, using alternative intrinsic colors from \citet{jo66} adjusted to the Cape system \citep{fe83}. 
That produced greater consistency in the derived reddenings and better agreement for unreddened stars, and was adopted throughout the remainder of 
the study. The intrinsic colors corresponding to such changes are presented in Table~\ref{tab1} for reference purposes, where they are compared with 
the \citet[][SAAO]{ca93} colors for dwarfs, which were adopted for all other stars. Given that the analysis was restricted to stars that dereddened 
uniquely to the AF-dwarf relation, the modification affects the resulting space reddenings, but only to a minor extent. Likely B-type stars in the 
field of each Cepheid were only used when analyzing 2MASS colors for the stars.


%%%%% TABLA 1

\setcounter{table}{0}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption[]{Intrinsic {\it BV(RI)}$_C$ Colors for Dwarfs}
\label{tab1}
\footnotesize
\begin{tabular}{ccccccccccc}
\toprule 
{\it (B--V)}$_0$ &({\it V--I})$_0$ &({\it V--I})$_0$ &({\it R--I})$_0$ &({\it R--I})$_0$ & &{\it (B--V)}$_0$ &({\it V--I})$_0$ &({\it V--I})$_0$ &({\it R--I})$_0$ &({\it R--I})$_0$ \\
& &SAAO & &SAAO & & & &SAAO & &SAAO \\
\cmidrule{1-5}
\cmidrule{7-11}
$-0.24$ &$-0.259$ &$-0.237$ &$-0.157$ &$-0.158$ & &$+0.04$ &$+0.055$ &$+0.037$ &$+0.040$ &$+0.021$ \\
$-0.23$ &$-0.248$ &$-0.221$ &$-0.150$ &$-0.146$ & &$+0.05$ &$+0.066$ &$+0.048$ &$+0.046$ &$+0.026$ \\
$-0.22$ &$-0.236$ &$-0.206$ &$-0.143$ &$-0.134$ & &$+0.06$ &$+0.077$ &$+0.059$ &$+0.053$ &$+0.032$ \\
$-0.21$ &$-0.225$ &$-0.193$ &$-0.136$ &$-0.123$ & &$+0.07$ &$+0.088$ &$+0.070$ &$+0.059$ &$+0.038$ \\
$-0.20$ &$-0.214$ &$-0.181$ &$-0.129$ &$-0.114$ & &$+0.08$ &$+0.100$ &$+0.081$ &$+0.066$ &$+0.043$ \\
$-0.19$ &$-0.203$ &$-0.170$ &$-0.121$ &$-0.105$ & &$+0.09$ &$+0.111$ &$+0.093$ &$+0.072$ &$+0.049$ \\
$-0.18$ &$-0.192$ &$-0.159$ &$-0.114$ &$-0.097$ & &$+0.10$ &$+0.122$ &$+0.105$ &$+0.078$ &$+0.055$ \\
$-0.17$ &$-0.180$ &$-0.149$ &$-0.107$ &$-0.089$ & &$+0.11$ &$+0.133$ &$+0.117$ &$+0.084$ &$+0.061$ \\
$-0.16$ &$-0.169$ &$-0.140$ &$-0.100$ &$-0.082$ & &$+0.12$ &$+0.144$ &$+0.129$ &$+0.090$ &$+0.068$ \\
$-0.15$ &$-0.158$ &$-0.131$ &$-0.092$ &$-0.076$ & &$+0.13$ &$+0.156$ &$+0.141$ &$+0.095$ &$+0.074$ \\
$-0.14$ &$-0.147$ &$-0.122$ &$-0.085$ &$-0.070$ & &$+0.14$ &$+0.167$ &$+0.153$ &$+0.101$ &$+0.080$ \\
$-0.13$ &$-0.136$ &$-0.114$ &$-0.078$ &$-0.064$ & &$+0.15$ &$+0.178$ &$+0.166$ &$+0.106$ &$+0.086$ \\
$-0.12$ &$-0.124$ &$-0.106$ &$-0.071$ &$-0.059$ & &$+0.16$ &$+0.189$ &$+0.179$ &$+0.112$ &$+0.093$ \\
$-0.11$ &$-0.113$ &$-0.098$ &$-0.064$ &$-0.053$ & &$+0.17$ &$+0.200$ &$+0.191$ &$+0.117$ &$+0.099$ \\
$-0.10$ &$-0.102$ &$-0.090$ &$-0.056$ &$-0.048$ & &$+0.18$ &$+0.212$ &$+0.204$ &$+0.122$ &$+0.106$ \\
$-0.09$ &$-0.091$ &$-0.082$ &$-0.049$ &$-0.043$ & &$+0.19$ &$+0.223$ &$+0.217$ &$+0.127$ &$+0.112$ \\
$-0.08$ &$-0.080$ &$-0.074$ &$-0.042$ &$-0.039$ & &$+0.20$ &$+0.234$ &$+0.230$ &$+0.133$ &$+0.119$ \\
$-0.07$ &$-0.068$ &$-0.066$ &$-0.035$ &$-0.034$ & &$+0.21$ &\nodata  &$+0.243$ &$+0.138$ &$+0.125$ \\
$-0.06$ &$-0.057$ &$-0.057$ &$-0.028$ &$-0.029$ & &$+0.22$ &\nodata  &$+0.256$ &$+0.143$ &$+0.132$ \\
$-0.05$ &$-0.046$ &$-0.049$ &$-0.020$ &$-0.024$ & &$+0.23$ &\nodata  &$+0.269$ &$+0.148$ &$+0.138$ \\
$-0.04$ &$-0.035$ &$-0.040$ &$-0.013$ &$-0.020$ & &$+0.24$ &\nodata  &$+0.281$ &$+0.154$ &$+0.144$ \\
$-0.03$ &$-0.024$ &$-0.031$ &$-0.006$ &$-0.015$ & &$+0.25$ &\nodata  &$+0.294$ &$+0.159$ &$+0.151$ \\
$-0.02$ &$-0.012$ &$-0.022$ &$+0.001$ &$-0.010$ & &$+0.26$ &\nodata  &$+0.307$ &$+0.164$ &$+0.157$ \\
$-0.01$ &$-0.001$ &$-0.013$ &$+0.008$ &$-0.005$ & &$+0.27$ &\nodata  &$+0.320$ &$+0.170$ &$+0.164$ \\
$+0.00$ &$+0.010$ &$-0.004$ &$+0.015$ &$+0.000$ & &$+0.28$ &\nodata  &$+0.332$ &$+0.175$ &$+0.170$ \\
$+0.01$ &$+0.021$ &$+0.006$ &$+0.021$ &$+0.005$ & &$+0.29$ &\nodata  &$+0.345$ &$+0.180$ &$+0.176$ \\
$+0.02$ &$+0.032$ &$+0.016$ &$+0.027$ &$+0.010$ & &$+0.30$ &\nodata  &$+0.357$ &$+0.185$ &$+0.182$ \\
$+0.03$ &$+0.043$ &$+0.026$ &$+0.033$ &$+0.016$ \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table*}

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


Reddening lines run nearly parallel to the intrinsic relations for B-dwarfs and KM-dwarfs, particularly in {\it V--I}$_C$ versus {\it B--V} diagrams, 
which is why the analysis was restricted to stars indicated to be likely AF-dwarfs, which are reasonably plentiful in each field. The slope of the 
intrinsic relation for AF-dwarfs relative to the effects of interstellar reddening in the {\it BV(RI)}$_C$ system results in sufficient separation, 
particularly in {\it (R--I)}$_C$ relative to {\it B--V}, to produce unique photometric dereddening solutions for each star, and the use of two separate 
color-color diagrams provides independent estimates for the intrinsic color of each star, although greater precision is obtained with solutions from 
the {\it (R--I)}$_C$ versus {\it B--V} diagram alone, because the angle between the intrinsic relation and typical reddening lines is larger. Infrared 
{\it JHK}$_{\rm s}$ observations exist for most stars \citep{cu03} from the Two Micron All Sky Survey \citep[2MASS,][]{sk06}, and confirm the adopted 
reddenings from {\it BV(RI)}$_C$ data, although the scatter in 2MASS {\it JHK}$_{\rm s}$  colors tends to be rather significant, larger than in {\it UBV} 
color-color diagrams \citep{tu76a}.

Typical companions and progenitors of Cepheids are B-type stars \citep{tu84}, which are rare enough that their occurrence in the field of a Cepheid 
raises the possibility of a physical association. AF-type stars, on the other hand, are a more common constituent of Galactic star fields \citep{mc65}, 
so the possibility of their physical association with a nearby Cepheid is reduced, but not necessarily to zero. In many of our program fields some of 
the stars identified as likely AF-type may be associated with the Cepheid of interest, but that was not explored here since there are no catalogued star 
clusters in the fields, although the regions around UY Mon, BE Pup, YZ CMa, and VY Sgr appear to contain faint anonymous clusters, and BD Pup and FO Cas 
are located in bright groups of surrounding stars.

The additional scatter in Figure~\ref{fig2} illustrates some of the problems associated with dereddening stars in {\it BV(RI)}$_C$ color-color diagrams. 
Such scatter for a small proportion of stars is a common characteristic of color-color diagrams, including those in {\it UBV} and those used for 2MASS 
photometry, and is readily explained in most cases by observational error, typically one or more of the magnitudes in the observed colors falling too 
close to the survey limits. At bright magnitude limits the typical stars encountered in Galactic star fields are A dwarfs and GK giants \citep{mc65}, 
but the demographic changes as the magnitude limits increase, and faint, nearby degenerate stars and M dwarfs begin to compound the picture with their 
unusual colors and larger measuring uncertainties. Emission, binarity, overly bright stars suffering from image saturation, objects lying away from the 
main sequence \citep{ca93}, and low quality observations for faint stars all combine to generate scatter in such plots, but using two separate 
color-color diagrams and limiting the analysis to stars fainter than the bright survey limits and brighter than the faint survey limits assures that 
likely AF dwarfs are identified properly. They are the small fraction of objects that deredden uniquely to the intrinsic relation for such stars in 
Figure~\ref{fig2}, as confirmed by their {\it JHK}$_{\rm s}$ colors.


%%%%% FIGURA 3

\begin{figure*}[!t]
\vspace{0.2cm}
\centering
\includegraphics[width=15.0cm]{dturnerfig3.eps}
\caption{Variable-extinction diagrams for the fields examined in this study, identified by the 
Cepheid of interest. Filled symbols denote AF stars near each Cepheid, and red plus signs are 
``predictions'' for the Cepheid parameters. The color figure can be viewed online.}
\label{fig3}
\end{figure*}

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


The derived reddenings for stars analyzed in each field were adjusted to equivalent color excesses for a B0 star according to their inferred intrinsic 
colors and the dependence of reddening on intrinsic color summarized by \citet{fe63}. Interstellar extinction affects the effective wavelengths of 
broad band {\it BV} filters differently according to the continuum of the star being observed, such that a typical Cepheid of, say, $(B-V)_0 = 0.60$ 
reddened by $E(B-V) = 0.90$ suffers identical extinction to a B0 dwarf star of $(B-V)_0 = -0.30$ reddened by $E(B-V) = 0.97$ \citep[cf. $\eta$ factor 
of][]{fe63}. Such adjustments are necessary when comparing reddenings of stars across a wide range of intrinsic color. Zero-age main sequence (ZAMS) 
values of $M_V$ as a function of intrinsic $(B-V)_0$ color \citep{tu76a,tu79} were also assigned to each star from the photometric dereddening solutions 
in order to provide estimates, or at least underestimates, of apparent distance modulus, {\it V--M}$_V$, for the stars in each field. The stars were 
then plotted in a variable-extinction diagram, such as those for each field summarized in Figure~\ref{fig3}, as a means of assessing the likely space 
reddening of each Cepheid. Figure~\ref{fig3} represents only a portion of each variable-extinction diagram, namely the most heavily-populated regions 
associated with the expected parameters for each Cepheid.

Mean $\langle B \rangle$ and $\langle V \rangle$ magnitudes are available for each Cepheid from \citet{bd07} and the present study, and rough estimates 
of reddening and luminosity were made from older, published period-color \citep[e.g.,][]{fe90a,fe90b} and period-luminosity \citep[e.g.,][]{tu92} 
relations, which do not differ substantially from more recent results \citep{tu01,tu10}. It was then possible to establish roughly where in each 
variable-extinction diagram the parameters for the Cepheid should fall, keeping in mind that an extremely liberal interpretation of such ``predictions'' 
is essential to avoid biasing the results. Some of the sample Cepheids are suspected Type II objects or overtone pulsators, for example, which affects 
estimates of both reddening and luminosity. Generous uncertainties of $\pm0.1$ or more in $E_{B-V}$ and $\pm 1$ in $M_V$ were therefore assumed in the 
analysis. Note that the ``predictions'' for IO Cas, FO Cas, and V1882 Sgr are inconsistent with expectations for classical Cepheids (they have larger 
predicted distance moduli than those for surrounding stars of similar reddening), which means that they are potential Type II objects. The situation 
for HZ Per, BD Pup, and OT Per is more ambiguous.

All such information is needed in order to establish which stars in the field of each Cepheid are useful for deriving its space reddening. In the case 
of UY Mon, for example, the estimated distance and reddening for the Cepheid associate it with the group of slightly reddened stars at $E_{B-V} \simeq 0.1$, 
({\it V--M}$_V)_0 \simeq$ 11--12 ($d \simeq$~1.6--2.5~kpc), but less distant and less reddened than stars of $E_{B-V} \simeq 0.5$, ({\it V--M}$_V)_0 \simeq$ 12.5--13 
($d \simeq$~3--4~kpc), in its vicinity. The best match is therefore to the 4 stars within $5^\prime$ of UY Mon that are reddened by $E_{B-V} \simeq 0.1$. 
Other cases are more complex because of the patchy reddening that permeates most fields, but have been resolved by considering only stars close to each Cepheid.

What appears to be a continuous run of reddening with distance in some fields results from the patchy extinction in each field combined with 
larger-than-average uncertainties in the inferred color excesses, $E_{B-V}$. The extinction associated with most Galactic star fields is typically 
associated with individual dust clouds dispersed along the line of sight \citep{tu94}. But large uncertainties in reddening can confuse the picture.
 Figure~\ref{fig4} presents the results of a simulation of such circumstances in a field where the scatter in the color excesses is taken to be 
$\pm0.05$, with associated uncertainties in absolute magnitude of $\pm0.5$, both quantities being applied randomly to the test points. Star 
densities were assumed constant as a function of distance, and the input parameters included specific amounts of reddening and extinction arising 
in discrete dust clouds located along the line of sight at distances of 0.5~pc, 0.9~pc, and 1.1~pc, producing mean color excesses of $E_{B-V}=0.2$, 
0.5, and 0.7, respectively. An extinction law with $R=3.0$ is depicted for the last group. The parameters, in particular the adopted scatter, were 
chosen in order to produce the greatest complexity in the resulting variable-extinction diagram. The resulting scatter produces results similar 
to some of the variable-extinction diagrams of Figure~\ref{fig3}.

The large range of inferred reddenings for field stars near each Cepheid was reduced further through an analysis of 2MASS observations \citep{cu03} 
for likely BAF-type stars in the same fields, analyzed in similar fashion to that employed by \citet*{te08} and \citet{tu11}. 2MASS observations 
were used separately without combination with the {\it BV(RI)}$_C$ photometry in order to avoid potential zero-point problems. The observed {\it J--H} 
and {\it H--K}$_{\rm s}$ colors for stars lying within $5^\prime$ of each Cepheid are shown in Figure~\ref{fig5}, and were compared with the intrinsic 
relation for main-sequence stars in the 2MASS system \citep{tu11}, adjusted with a reddening slope $E_{H-K}/E_{J-H}=0.49$ from \citet{tu11}. 
Multiple solutions in some cases, e.g., UY Mon and HZ Per, were resolved with reference to the variable-extinction diagrams and ``predicted'' values, 
and best fits were made by trial and error by establishing reddenings for which likely BAF-type stars had colors distributed randomly about the reddened 
intrinsic relation.


%%%%% FIGURA 4

\begin{figure}[!t]
\vspace{0.2cm}
\centering
\includegraphics[width=0.99\columnwidth]{dturnerfig4.eps}
\caption{A simulated variable-extinction diagram for a star field where the reddening increases 
with distance according to dust clouds producing $E_{B-V}$ = 0.20, 0.50, and 0.70 located at 
distances of 0.5~kpc, 0.9~kpc, and 1.1~kpc, respectively, with associated uncertainties in 
$E_{B-V}$ of $\pm0.05$ and in $M_V$ of $\pm0.5$. The gray line denotes a standard reddening law 
of $R=A_V/E_{B-V}=3.0$ for stars at a distance of 1.1~kpc.}
\label{fig4}
\vspace{0.3cm}
\end{figure}

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


%%%%% FIGURA 5

\begin{figure*}[!t]
\vspace{0.2cm}
\centering
\includegraphics[clip,width=13cm]{dturnerfig5.eps}
\caption{2MASS color-color diagrams, {\it H--K}$_{\rm s}$ versus {\it J--H}, for stars within $5^\prime$ 
of each Cepheid, from observations by Cutri et al. (2003). The intrinsic relation for main sequence 
stars is plotted as a black line, while red lines depict the adopted reddening for stars associated with 
the Cepheids, from Column~7 of Table~\ref{tab2}. The dashed red line for UY Mon represents the alternate 
solution for that field. The color figure can be viewed online.}
\label{fig5}
\vspace{0.3cm}
\end{figure*}

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


%%%%% TABLA 2

\setcounter{table}{1}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{10}
\setlength{\tabnotewidth}{0.95\textwidth}
%\setlength{\tabcolsep}{1.35\tabcolsep}
\caption{Space Reddenings for Cepheid Fields}
\label{tab2}
\scriptsize
\begin{tabular}{lccccccccc}
\toprule
Cepheid & $\log P$ & $E_{B-V}$(B0) & $E_{B-V}$(B0) & $E_{B-V}$(B0) & $E_{B-V}$(B0) & $E_{B-V}$ & $E_{B-V}$(B0) & No. & $E_{B-V}$(C$\delta$) \\
&  & $<2^\prime$ & $<3^\prime$ & $<4^\prime$ & $<5^\prime$ & 2MASS & Adopted & Stars &  \\
\midrule
UY Mon &0.380 &\nodata &$0.09$ &$0.09$ &$0.12 \pm0.01$ &$0.07 \pm0.07$ &$0.12 \pm0.01$ &~4 &$0.11 \pm0.01$ \\
UY Mon\tabnotemark{1} &\nodata &\nodata &$0.42$ &$0.44 \pm0.03$ &$0.43 \pm0.02$ &$0.37 \pm0.07$ &$0.43 \pm0.02$ &~3 &\nodata \\
CN CMa &0.390 &$0.62 \pm0.02$ &$0.65 \pm0.02$ &$0.66 \pm0.02$ &$0.67 \pm0.02$ &$0.63 \pm0.12$ &$0.67 \pm0.02$ &11 &$0.63 \pm0.02$ \\
EW Aur &0.425 &$0.52$ &$0.63 \pm0.06$ &$0.61 \pm0.04$ &$0.61 \pm0.04$ &$0.53 \pm0.08$ &$0.61 \pm0.04$ &~6 &$0.58 \pm0.03$ \\
V1882 Sgr &0.433 &$0.60 \pm0.01$ &$0.68 \pm0.03$ &$0.70 \pm0.02$ &$0.68 \pm0.02$ &$0.69 \pm0.05$ &$0.68 \pm0.02$ &20 &$0.64 \pm0.01$ \\
BE Pup &0.458 &$0.80$ &$0.72 \pm0.04$ &$0.69 \pm0.03$ &$0.68 \pm0.02$ &$0.73 \pm0.12$ &$0.68 \pm0.02$ &20 &$0.64 \pm0.02$ \\
YZ CMa &0.499 &\nodata &$0.71 \pm0.10$ &$0.64 \pm0.09$ &$0.60 \pm0.03$ &$0.61 \pm0.07$ &$0.60 \pm0.03$ &10 &$0.56 \pm0.03$ \\
LR Pup &0.523 &$0.44$ &$0.47 \pm0.02$ &$0.46 \pm0.01$ &$0.45 \pm0.01$ &$0.37 \pm0.07$ &$0.45 \pm0.01$ &14 &$0.42 \pm0.01$ \\
BD Pup &0.593 &$0.63 \pm0.03$ &$0.71 \pm0.03$ &$0.74 \pm0.03$ &$0.72 \pm0.02$ &$0.69 \pm0.08$ &$0.72 \pm0.02$ &19 &$0.67 \pm0.02$ \\
IO Cas &0.748 &$0.74$ &$0.64 \pm0.03$ &$0.62 \pm0.03$ &$0.63 \pm0.03$ &$0.63 \pm0.08$ &$0.63 \pm0.03$ &14 &$0.59 \pm0.02$ \\
AY Sgr &0.818 &\nodata &$1.04 \pm0.02$ &$1.02 \pm0.04$ &$1.00 \pm0.03$ &$0.97 \pm0.05$ &$1.00 \pm0.03$ &~8 &$0.94 \pm0.02$ \\
FO Cas &0.832 &$0.99$ &$0.99$ &$0.83 \pm0.07$ &$0.82 \pm0.06$ &$0.78 \pm0.14$ &$0.82 \pm0.06$ &~7 &$0.76 \pm0.05$ \\
AC Mon &0.904 &\nodata &$0.61$ &$0.61 \pm0.02$ &$0.59 \pm0.02$ &$0.56 \pm0.05$ &$0.59 \pm0.02$ &~5 &$0.55 \pm0.01$ \\
HZ Per &1.052 &$1.39$ &$1.39$ &$1.48 \pm0.07$ &$1.48 \pm0.05$ &$1.42 \pm0.10$ &$1.48 \pm0.05$ &~4 &$1.36 \pm0.04$ \\
VY Sgr &1.132 &\nodata &$1.50$ &$1.41 \pm0.04$ &$1.35 \pm0.04$ &$1.24 \pm0.15$ &$1.35 \pm0.04$ &~3 &$1.24 \pm0.04$ \\
OT Per &1.416 &\nodata &$1.70$ &$1.52 \pm0.11$ &$1.52 \pm0.09$ &$1.47 \pm0.12$ &$1.52 \pm0.09$ &~5 &$1.39 \pm0.08$ \\
\bottomrule
\noalign{\smallskip}
\tabnotetext{1}{Alternate solution for stars of large reddening near UY Mon.}
\end{tabular}
\vspace{0.3cm}
\end{table*}

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


The {\it JHK}$_{\rm s}$ colors generate independent $E_{B-V}$ reddenings for the stars in the Cepheid fields, with the advantage of being more closely 
tied to B-type stars in the fields, stars that lie blueward of the ``kink'' in the intrinsic relation and that may share a common origin with the 
Cepheid. The reddenings have slightly larger uncertainties because of larger photometric scatter in the observations (by factors of 3--5 relative to 
the {\it BV(RI)}$_C$ photometry) in combination with the correction from infrared to optical reddening. They are nevertheless crucial for narrowing 
the range of potential color excesses for some of the sample Cepheids, such as IO Cas. A few objects in the sample appear to be Type II Cepheids, but 
that does not affect the results. In most cases the implied reddening near the Cepheid is fairly evident.


\section{RESULTS}

The results of the variable-extinction studies of the sample Cepheids are presented in Table~\ref{tab2}, which lists the inferred space reddening 
for each Cepheid derived from likely AF-type stars lying within different angular radii, from $2^\prime$ to $5^\prime$ distant, and the reddening 
inferred from 2MASS {\it JHK}$_{\rm s}$ colors for stars within $5^\prime$ of the Cepheid. The adopted color excess in each case, Column~8, was the 
average for all AF-type stars lying within $5^\prime$ of the Cepheid and of comparable inferred distance, and the resulting reddening, which is 
equivalent to that for a star of spectral type B0, was converted in the last column of the table to a value appropriate for the derived intrinsic 
color of the Cepheid, again using the relationship of \citet{fe63}. The number of stars used to obtain the space reddening is listed in the second 
last column of Table~\ref{tab2}. In rich fields that number is of order $\sim$10--20, whereas in more poorly populated regions or fields with a 
larger spread in reddening, less than half a dozen reference stars were available. Two solutions are presented for UY Mon, for reasons indicated 
later, although the adopted solution for the Cepheid is the first.


%%%%% FIGURA 6

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{dturnerfig6.eps}
\caption{Derived intrinsic $\langle B \rangle$--$\langle V \rangle$ colors for sample Cepheids 
(large symbols) relative to other Cepheids with derived reddenings (small symbols, Turner 2001), 
as a function of pulsation period.}
\label{fig6}
\vspace{0.2cm}
\end{figure}

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


It is worth noting that the 2MASS reddenings fall closer to the converted color excess for the Cepheid than to the B0-star reddenings. A reasonable 
explanation lies in the fact that the BAF-star reddenings in a 2MASS color-color diagram tend to be dominated by the AF stars, particularly likely 
F-type stars, since B-type stars are less common in the small fields analyzed and are potentially affected by circumstellar effects \citep{tu11}. 
The 2MASS reddenings are also important for providing confirmation of the relationship used to convert B0-star color excesses to those appropriate 
for a star with the average unreddened colors of the Cepheid, which are very similar to F-type dwarfs in the 2MASS samples.

The derived intrinsic colors are presented in Table~3, which also provides in Column~3 the variable star type designation for the object from the 
{\it General Catalogue of Variable Stars} \citep{sa04}. Type II Cepheids are designated as CWB for short period (1--8 days) BL Herculis variables, 
and CWA for longer period (8--20 days) W Virginis stars. The intrinsic $(\langle B \rangle$--$\langle V \rangle)_0$ colors are plotted in Figure~6 
relative to a set of similar intrinsic colors calibrated relative to other Cepheids with field reddenings (binary, cluster or association members) 
and Cepheids with reddenings derived using reddening-free indices \citep{tu01}.

All of the program stars studied here appear to have intrinsic colors consistent with those of classical Galactic Cepheids, despite remaining questions 
about the true population status for some of them. The spread in color at a given value of pulsation period {\it P} for the reference sample can be 
attributed to the natural width of the Cepheid instability strip, and in a few cases to erroneous reddenings. The location of individual Cepheids 
in our sample relative to the hot (blue) and cool (red) edges of the strip, if used in conjunction with light amplitude and rate of period change, 
provides useful information about what stage the Cepheids have reached in their evolution \citep*{te06}.


%%%%% FIGURA 7

\begin{figure}[!t]
\centering
\includegraphics[width=0.99\columnwidth]{dturnerfig7.eps}
\caption{Derived Johnson system ({\it R--I})$_J$ colors for sample Cepheids (filled circles) relative 
to intrinsic $(\langle B \rangle$--$\langle V \rangle)_0$ colors, with derived colors for AFGK supergiants 
from Johnson (1966) plotted for reference purposes as open circles. The line is a fitted relation for 
the supergiants. The anomalous Cepheids are V1882 Sgr and YZ CMa.}
\label{fig7}
\vspace{0.3cm}
\end{figure}

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


\vspace{0.15cm}

Figure~\ref{fig7} plots the inferred ({\it R--I})$_J$ colors for our sample Cepheids relative to their $(\langle B \rangle$--$\langle V \rangle)_0$ 
colors, transposed from ({\it R--I})$_C$ using the relationships of \citet{fe83}. Included are inferred colors for AFGK supergiants from \citet{jo66}, 
in similar fashion to the analysis of \citet*{de78}. There is good agreement of the derived intrinsic colors for sample Cepheids with the colors 
expected for supergiant stars, with the exception of V1882 Sgr and YZ CMa. Both objects have faint optical companions that may contaminate the 
{\it (RI)}$_C$ photometry, so the results of Figure~\ref{fig7} do not necessarily indicate a significant difference in color between classical and 
Type II Cepheids. The data also indicate the general success of the procedure adopted in this study. The temperature spread of the instability strip 
is less marked in intrinsic ({\it R--I})$_J$ and ({\it R--I})$_C$ colors than in $(\langle B \rangle$--$\langle V \rangle)_0$ color, as expected.

With regard to the variable star designations for specific objects in Table~\ref{tab3}, the short period Cepheids UY Mon and CN CMa are solar-metallicity 
stars according to \citet{di90}, who derived reddenings of $E_{B-V}=0.15\pm0.08$ and $0.61\pm0.10$, respectively, for the stars from Walraven photometry. 
Both values are consistent with the present results, although of lower precision. UY Mon is an s-Cepheid, its light curve being indistinguishable from 
a sine wave, many of which are overtone pulsators, yet fundamental mode pulsation provides the simplest solution to the variable-extinction study 
presented here (Figure~3), provided it is a classical Cepheid. CN CMa is a suspected Type II Cepheid because of its unusually large amplitude for a 
short-period pulsator, but that designation is not consistent with its photometric solar metallicity \citep{di90} or the variable-extinction analysis. 
Type II Cepheids are known to display a wide range of abundances, from solar to below solar \citep{ha81}, so that is not necessarily a good criterion 
to decide Population type for CN CMa. A better case for it being a classical Cepheid lies in the variable-extinction results (Figure~\ref{fig3}). Its 
{\it (RI)}$_C$ and {\it (RI)}$_J$ colors are also consistent with those of a classical Cepheid (Figure~\ref{fig7}), which is the designation preferred 
here.


%%%%% TABLA 3

\setcounter{table}{2}
\begin{table}[!t]
\vspace{0.1cm}
\centering
\tablecols{7}
\setlength{\tabnotewidth}{0.99\columnwidth}
\setlength{\tabcolsep}{0.5\tabcolsep}
\caption{Unreddened {\it BV(RI)}$_C$ Colors for Sample Cepheids}
\label{tab3}
\scriptsize
\begin{tabular}{lcccccc}
\toprule
Cepheid & $\log P$ & Type & $\langle B \rangle$--$\langle V \rangle$ & {\it V--R}$_C$ & {\it V--I}$_C$  &Deduced  \\
& & & & & & Type \\
\midrule
UY Mon &0.380 &DCEPS &+0.43 &+0.28 &+0.51 &DCEPS\tabnotemark{1} \\
CN CMa &0.390 &CWB: &+0.51 &+0.33 &+0.61 &DCEP \\
EW Aur &0.425 &DCEP &+0.49 &+0.29 &+0.54 &DCEP \\
V1882 Sgr &0.433 &CEP &+0.53 &+0.30 &+0.42 &CWB \\
BE Pup &0.458 &CWB: &+0.47 &+0.29 &+0.52 &DCEP \\
YZ CMa &0.499 &CWB: &+0.56 &+0.28 &+0.46 &CWB? \\
LR Pup &0.523 &CEP &+0.51 &+0.32 &+0.59 &DCEP \\
BD Pup &0.593 &DCEP &+0.56 &+0.36 &+0.63 &DCEP \\
IO Cas &0.748 &DCEP &+0.57 &+0.36 &+0.63 &CWB? \\
AY Sgr &0.818 &DCEP &+0.57 &+0.31 &+0.58 &DCEP \\
FO Cas &0.832 &DCEP &+0.60 &+0.44 &+0.78 &CWB? \\
AC Mon &0.904 &DCEP &+0.63 &+0.35 &+0.63 &DCEP \\
HZ Per &1.052 &DCEP &+0.77 &+0.40 &+0.73 &DCEP \\
VY Sgr &1.132 &DCEP &+0.75 &+0.43 &+0.74 &DCEP \\
OT Per &1.416 &DCEP &+0.87 &+0.49 &+0.88 &DCEP \\
\bottomrule
\noalign{\smallskip} 
\tabnotetext{1}{Fundamental mode pulsation likely.}
\end{tabular}
\vspace{0.3cm}
\end{table}

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


For four of the sample objects the field star variable-extinction data produce results indicating that the Cepheid's luminosity may have been overestimated 
in the analysis, i.e., it might be a Type II object. The Cepheids are V1882 Sgr, BE Pup, IO Cas, and FO Cas. The latter two objects are identified as 
classical Cepheids in the GCVS, so either the variable-extinction results for them are anomalous or the classification of the stars is erroneous. The 
latter possibility is suspected here, so their deduced types as Type II Cepheids in the last column of Table~\ref{tab3} reflect the results of the 
variable-extinction analysis. V1882 Sgr has the characteristic light curve of a Cepheid, but is of uncertain type. The variable-extinction results suggest 
that it is a Type II object, while its {\it V(RI)}$_C$ colors (Table~\ref{tab3}) are slightly bluer than those of classical Cepheids in the sample, which 
may indicate a metal-poor object. The ``CEP" designation for the star in the GCVS is presumably preliminary, and it appears likely to be a Type II object. 
Similarly, the variable-extinction results for BE Pup are consistent with either a classical or Type II Cepheid, while its {\it V(RI)}$_C$ colors 
(Table~\ref{tab3}) are similar to those of classical Cepheids in the sample. BE Pup is also a double-mode pulsator \citep{wo04}, which is suggestive of 
a classical Cepheid, our preferred designation.

YZ CMa is suspected to be a classical Cepheid according to the variable-extinction analysis, but its {\it V(RI)}$_C$ colors are also slightly bluer than 
those of other classical Cepheids. The ``CWB'': designation in the GCVS may therefore be correct, although further study is needed to resolve the question. 
In general, the studies summarized here consistently tend to identify most sample objects (11/15) as classical Cepheids. Two of the likely Type II objects, 
V1882 Sgr and YZ CMa, appear slightly bluer in {\it V--R}$_C$ and {\it V--I}$_C$ than other Cepheids in the sample, but the photometry for both stars may 
suffer from contamination by close companions, so their distinctive difference in color cannot be considered definitive. Detailed atmospheric abundance 
studies of both stars should help to solidify their classifications and establish if there are obvious differences in color between classical and Type II 
Cepheids.


%%%%% FIGURA 8

\begin{figure}[!t]
\vspace{0.2cm}
\centering
\includegraphics[width=0.99\columnwidth]{dturnerfig8.eps}
\caption{Comparison of derived 2MASS reddenings, with their uncertainties, for the Cepheids in our 
sample with the color-corrected broad band {\it BV(RI)}$_C$ reddenings. The gray line represents 
expectations for an exact match.}
\label{fig8}
\vspace{0.3cm}
\end{figure}

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


Figure~\ref{fig8} plots the inferred 2MASS reddenings for our sample Cepheids relative to their broad band {\it BV(RI)}$_C$ reddenings, where we have 
included the second result for the UY Mon field because of the obvious separation in Figures~\ref{fig3} and \ref{fig5} of stars of small reddening 
from those of large reddening, for which separate solutions were obtained. The close agreement of both sets of reddenings in Figure~\ref{fig8} indicates 
that the two techniques are of comparable reliability for establishing field reddenings of Galactic objects, although there is clearly greater precision 
in the {\it BV(RI)}$_C$ color excesses.


\section{DISCUSSION}
\
The present study was undertaken as a feasibility test of the use of CCD {\it BV(RI)}$_C$ photometry for studying the space reddening of Galactic Cepheids. 
The {\it BV(RI)}$_C$ data by themselves were sometimes insufficient to define the field reddenings of each Cepheid unambiguously, but the addition of 2MASS 
reddenings and initial ``predictions'' guided the process successfully. The number of Galactic Cepheids of well-established field reddening has been increased 
from 40 \citep{lc07} to 55 by this study, and the sample now includes a few Type II Cepheids, some of which appear to display slightly bluer intrinsic 
{\it (V--R)}$_C$ and {\it (V--I)}$_C$ colors relative to their classical Cepheid cousins. A comparable test using reddenings derived from 2MASS {\it JHK}$_s$ 
colors indicates that the 2MASS survey may also be suitable for the derivation of space reddenings, for a variety of stellar types and not just Cepheids. 
Further studies of that possibility have already been initiated \citep*{me08a,me08b}.

The results of this study have already been used in a preliminary mapping of the Cepheid instability strip using Cepheid reddenings tied to space reddenings 
and spectroscopic reddenings of Galactic Cepheids \citep{tu01}, the results of which can be seen in the data plotted in Figure~\ref{fig6}. The addition of 
{\it U}-band observations would have assisted the analysis considerably, but it is important to note that accurate Johnson system {\it U}-band observations 
are difficult to obtain with some CCD/filter combinations \citep[see comments by][]{tu11}. Despite that, the success of the present study using both 
{\it BV(RI)}$_C$ and {\it JHK}$_s$ photometry should spur further investigations that take advantage of existing survey photometry to study the reddening 
in interesting Galactic star fields.

\vspace{0.1cm}

\acknowledgments

The present study was supported in part by research funding awarded through the Natural Sciences and Engineering Research Council of Canada (NSERC), 
through the Russian Foundation for Basic Research (RFBR), and through the program of Support for Leading Scientific Schools of Russia. This publication 
makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing 
and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. 


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