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\title{A Second Stellar Color Locus: a Bridge from White Dwarfs to M stars}

\author{Vernesa Smol\v{c}i\'{c}$^{1,2}$, \v{Z}eljko Ivezi\'{c}$^1$, Gillian
R. Knapp$^1$, Robert H. Lupton$^1$, Kre\v{s}imir Pavlovski$^2$, Sa\v{s}a Iliji\'{c}$^3$,
Peregrine M. McGehee$^4$, David Schlegel$^1$, James E. Gunn$^1$, Michael A. Strauss$^1$}
\vskip 0.1in
\affil{$^1$ Princeton University Observatory, Princeton, NJ 08544}
\affil{$^2$ University of Zagreb, Dept. of Physics, Bijeni\v{c}ka cesta 32, 
            10000 Zagreb, Croatia}
\affil{$^3$ Faculty of Electrical Engineering and Computing, Dept. of Applied Physics, 
            Unska 3, 10000 Zagreb, Croatia}
\affil{$^4$ Los Alamos National Laboratory, MS H820, Los Alamos, NM 87545;
            also at New Mexico State University, Department of Astronomy, P.O. Box
            30001, Dept 4500, Las Cruces, NM 88003}


\begin{abstract}
We report the discovery of a locus of stars in the SDSS $g-r$ vs. $u-g$ color-color
diagram that connects the colors of white dwarfs and M dwarfs. While its 
contrast with respect to the main stellar locus is only $\sim$1:2300, this 
previously unrecognized feature includes 863 stars from SDSS Data Release 1. 
The position and shape of the feature is in good agreement with predictions of
a simple binary star model that consists of a white dwarf and an M dwarf, with
the components' luminosity ratio controlling the position along this binary system 
locus. SDSS DR1 spectra for 47 of these objects strongly support this model.
\end{abstract}



\section{Introduction} 

\subsection{ Sloan Digital Sky Survey}

The Sloan Digital Sky Survey (SDSS; Azebajian et al.~2003, and references
therein) is revolutionizing stellar astronomy by providing homogeneous and deep 
($r < 22.5$) photometry in five passbands ($u$, $g$, $r$, $i$, and $z$, Gunn 
et al.~1998) accurate to 0.02 mag (Ivezi\'{c} et al.~2003); ultimately, up to 
10,000 deg$^2$ of sky in the Northern Galactic Cap will be surveyed. The survey 
sky coverage will result in photometric measurements for over 100 million stars 
and a similar number of galaxies. Astrometric positions are accurate to better 
than 0.1 arcsec per coordinate (rms) for point sources with $r<20.5^m$
(Pier et al.~2003), and the morphological information from the images
allows robust star-galaxy separation to $r \sim$ 21.5$^m$ (Lupton
et al.~2001).

Here we report the results of a color-based search for binary stars 
in the recent SDSS Data Release 1 (see www.sdss.org), which includes
53 million unique objects detected in 2099 deg$^2$ of sky.


\subsection{     The Stellar Locus in SDSS Photometric System     }

The effective temperature is the dominant parameter that determines the position 
of the majority of stars in optical color-color diagrams constructed with 
broad-band filters (Lenz et al. 1998, and references therein). The effective 
temperature range results in a well-defined locus in color-color diagrams, 
as shown in Figure 1 (for more details see  Finlator et al. 2000, and references
therein). 


\section{               The Locus of Binary Stars                 } 

An unresolved binary star may have colors that place it either inside or
outside the locus. If the luminosity of one star is much greater than that
of the other, the more luminous star determines the system colors. 
However, even if the luminosities are comparable, the system color may
still fall close to the locus of single stars in color-color diagrams where the 
locus resembles a straight line (e.g. the \iz\ vs. \ri\ diagram, see the bottom right
panel in Figure 1). Thus, to select unresolved binary systems by their 
colors, the most promising diagrams are those where the locus is curved,
such as \gr\ vs. \ug\ and \ri\ vs. \gr\ color-color diagrams. The curvature
in these diagrams is the result of saturation of the \ug\ and \gr\ colors
due to the strong molecular absorption bands which first appear at type $\sim$M0.


Figure 2 shows the \gr\ vs. \ug\ color-color diagram for $\sim$1.99 million
stars from the public SDSS Data Release 1 (DR1) database with $u<20.5$. 
This magnitude limit ensures that the accuracy of the $u$ magnitudes is 
better than 0.1 mag (for $u<18$, the photometric accuracy is 0.02 mag, 
Ivezi\'{c} et al. 2003). The most prominent feature is the stellar
locus discussed in Figure 1. Due to the large number of stars in DR1, 
we are able to demonstrate the existence of a second stellar locus,
clearly visible just above the main stellar locus. The number of stars
in this, previously unreported feature, is a factor of $\sim$2,300 smaller than in the main 
locus (using color cuts listed in the next Section). Thus, accurate multi-band 
photometry ($u$ band in particular) for a sufficiently large number of stars 
was required to detect such a low-contrast feature.

The second stellar locus is consistent with binary systems than include
an M dwarf and a white dwarf. We demonstrate that this simple model
provides a satisfactory explanation for the position of the second stellar 
locus, hereafter the ``bridge'' (from M dwarfs to white dwarfs). We also show
that the available SDSS spectra for a subsample of bridge stars support this 
interpretation.



%%%%% Fig 1 %%%%%% 
\begin{figure}
\label{SDSSall}
\plotfiddle{SDSSall.ps}{12cm}{0}{100}{100}{-310}{-260}
\caption{The SDSS color-color and color-magnitude diagrams which summarize 
photometric properties of unresolved sources, marked as dots (adopted from Finlator
et al. 2000, when SDSS photometric system was still marked by an asterisk). 
The top left panel displays the \r\ vs. \gr\ color-magnitude diagram for 
$\sim$25,000 high-latitude
objects observed in 3 deg$^2$ of sky (for more details see Finlator et al. 2000). 
The three remaining panels show color-color diagrams for objects brighter than 20$^m$ 
in each of the 3 bands used to construct each diagram (red is always towards 
the upper right corner). The locus of ``normal" stars (dominated by main sequence
stars) is clearly visible in all three diagrams, and the positions of several 
spectral types are indicated next to the locus in the \ug\ vs. \gr\ and \ri\ vs. 
\gr\ color-color diagrams. For completeness, point sources that have \ug\ and \gr\ 
colors similar to low-redshift QSOs (\ug $<$ 0.4, -0.1 $<$ \gr $<$ 0.3, \ri $<$ 0.5), and are 
brighter than the limit for quasars in the SDSS spectroscopic survey (\i $<$ 19), 
are marked by open circles.}    
\end{figure}


%%%%% Fig 2 %%%%%% 
\begin{figure}
\label{DR1ugr}
\plotfiddle{ugr_a.ps}{13cm}{0}{70}{70}{-210}{-60}
\caption{The number density, displayed on a logarithmic scale, of $\sim$1.9 million
stars with $u<20.5$ from SDSS Data Release 1 in the \gr\ vs. \ug\ color-color 
diagram (increasing from green to red to yellow; the color ranges are
-1 to 3, and -1 to 2, for \ug\ and \gr, respectively). The most prominent
features are the main stellar locus (yellow and red towards upper right)
and the clump of low-redshift quasars (red and purple towards the left edge).
The fainter feature, colored green, above and to the left from the main locus 
is the locus of $\sim$1,000 binary stars. The properties of this locus are consistent 
with a distribution of M dwarf -- white dwarf pairs with varying luminosity ratio. 
The root-mean-scatter of stars perpendicular to this locus is only $\sim$0.1 mag.}    
\end{figure}




\section{              M dwarf -- White Dwarf Model             }


%%%%% Fig 3 %%%%%% 
\begin{figure}
\plotfiddle{compareCCD_bridgeB.ps}{13.8cm}{0}{82}{82}{-240}{-50}
\caption{The comparison of a simple M dwarf -- white
dwarf pair model with the data. A representative distribution of all
stars is shown by linearly spaced isopleths. 863 stars from SDSS Data 
Release 1 selected by requiring $u < 20.5, \ug<2, \gr>0.4$ and $\ri>0.7$
are shown by dots. The model predictions are shown by lines, where each
line corresponds to different \ri\ and \iz\ colors assumed for the
M dwarf. The position along the line depends on the luminosity ratio
of the two components. There is only one line in the \gr\ vs. \ug\ 
diagram (top right) because all M dwarfs have practically same 
\ug\ and \gr\ colors. The observed data scatter around this line is 
presumably due to different white dwarf colors.}    
\end{figure}


The bridge of stars in the \gr\ vs. \ug\ color-color diagram appears
to connect the positions of M stars and hot blue stars, with MK spectral
type around $B$. In order to produce a locus of stars that is not
coincident with the main stellar locus, the luminosities of the two
components must be comparable. The possibilities are an M dwarf -- white
dwarf pair, or an M giant -- blue giant/supergiant pair. The latter systems
cannot dominate the sample because the sky density of the selected stars 
(0.40 deg$^{-2}$) is too high, given the faint magnitudes and high latitudes 
probed by SDSS (see Majewski et al. 2003 for a nearly complete census of 
M giants in the Galaxy).    

We generate model colors for binary systems by assuming SDSS colors for 
single M dwarf and white dwarf stars, and parametrize the system colors by 
the luminosity ratio of the two components (in practice, we use the $r$ band 
flux fractions). For the M dwarf we adopt ($u-g = 2.6$, $g-r=1.4$, 
$r-i = 2 (i-z)$, and $i-z=0.3$ to 0.75, with a step of 0.05), and for 
the white dwarf ($u-g=0.2$, $g-r=-0.2$, $r-i=0$, $i-z=0$). For more details 
about M dwarfs and white dwarfs discovered by SDSS please see Hawley et al. 2002, 
and Harris et al. 2000. The model predictions are compared to the data in 
Figure 3, where the dots represent 863 ``DR1 bridge stars'', selected by requiring
$u < 20.5, \ug<2, \gr>0.4$, $\ri>0.7$, and that processing flags BRIGHT,
SATUR and BLENDED are not set (the flag requirement selects unique unsaturated 
objects).

The agreement between this simple binary star model and the data is satisfactory. 
In particular, the model track closely follows the distribution of bridge stars
in the \gr\ vs. \ug\ color-color diagram, and reproduces the observed range of 
colors in other diagrams. A noteworthy point is that the implied contribution of 
the white dwarf to the total $r$ band flux is at most 50\% for practically all 
stars from the ``DR1 bridge'' sample (for equal $r$ band flux contributions, the 
model predicts $u-g=0.40$ and $g-r=0.33$).  


The models show that the white dwarf contribution to the \i\ and \z\ band fluxes 
is practically negligible. Hence, the absolute \i\ band magnitude, $M_i$,  and 
therefore distances, can be obtained using the $M_i$ vs. \iz\ color-magnitude
relation from Hawley et al. (2002). We find a median of $M_i\sim9$ for bridge
stars, with a root-mean-scatter of 1 mag. The corresponding median distance is $\sim$300 pc.
Given the distance to the system, the white dwarf luminosity can be easily
determined. Since the sample presented here is an unbiased, flux-limited sample
(with the adopted $u$ magnitude limit, the other four SDSS magnitudes for all 
stars in the sample are comfortably brighter than the corresponding SDSS completeness 
limits), it can be used to statistically determine the cooling curve for white
dwarfs (if the components are not strongly interacting). Such an analysis will be 
presented in a forthcoming publication (Knapp et al. 2003, hereafter Paper II). 



\section{  SDSS Spectra  }

While the close agreement between the data and model predictions supports
the hypothesis that the bridge stars are dominated by M dwarf -- white dwarf
pairs, further confirmation can be gained by examining the available SDSS spectra.
Stars are selected by various criteria for SDSS spectroscopic observations,
and we postpone a detailed analysis of the selection statistics to Paper II. 
Here we simply report the results of a visual examination of 47 ``bridge'' stars 
from the DR1 sample for which SDSS spectra are available. The spectra are obtained
through 3$^{\arcsec}$ fibers, and span the wavelength range 3800--9200$A$, 
with a spectral resolution of $\lambda/\Delta \lambda \sim 1800$. 


Out of 863 stars in the sample, spectra are available for 47. The visual 
inspection of spectra indicates that 45 are consistent with an M dwarf--white
dwarf interpretation (the remaining 2 are G stars; both are close to the 
boundary of color-selection boundary, and one is part of a complex blended
source). We display a representative sample of spectra in Figure 4.  
A preliminary comparison with the M dwarf spectral sequence (Hawley et al. 2002) 
indicates that M dwarfs in the binary systems discussed here are dominated by 
types M5 and earlier, as is the case for single M dwarfs in this magnitude-limited
sample. This conclusion is also supported by the distribution 
of their \ri\ and \iz\ colors (the median \ri\ color is $\sim$1.0, see the 
lower left panel in Figure 3). We note that SDSS spectra are of sufficient quality 
to allow determination of the white dwarf temperature and the M dwarf chromospheric
activity (via H$\alpha$ emission), as demonstrated by Raymond et al. (2003). 




\section{  Conclusions  }

The accurate multi-band SDSS photometry for a large number of stars allowed
the detection of a new feature in the broad-band optical color-color
diagrams: a ``bridge'' of stars, well-separated from the main stellar locus,
connects the positions of M dwarfs and white dwarfs. The bridge characteristics
are consistent with a binary system than includes an M dwarf and a white dwarf, 
with the system's position on the bridge determined by the components' luminosity 
ratio.


\begin{figure}
\plotfiddle{spectraMosaic.ps}{13.8cm}{0}{72}{72}{-220}{-35}
\caption{
SDSS spectra for a subsample of stars whose SDSS colors are consistent with 
an M dwarf -- white dwarf binary system. In all the shown systems the red 
half of the spectrum is typical of an M dwarf, while the blue half is consistent 
with a white dwarf spectrum. Note prominent H$\alpha$ emission for stars 3 and 6.
The feature at $\sim$5,577$A$ is due to the night sky.
} 
\end{figure}


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\bibitem[]{} Finlator, K. {\it et al.} 2000, AJ, 120, 2615
\bibitem[]{} Gunn, J.E., et al. 1998, AJ, 116, 3040
\bibitem[]{} Harris, H.C., et al. 2003, AJ, in press
\bibitem[]{} Hawley, S.L., et al. 2002, AJ, 123, 3409
\bibitem[]{} Ivezi\'c, \v Z., et al. 2003, astro-ph/0301400
\bibitem[]{} Knapp, G.R., et al. 2003, in preparation (Paper II)
\bibitem[]{} Lenz, D.D., Newberg, J., Rosner, R.,
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\bibitem[]{} Lupton, R.H. {\it et al.} 2001, in {\it Astronomical Data Analysis 
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\bibitem[]{} Majewski, S., {\it et al.} 2003, astro-ph/0304198
\bibitem[]{} Pier, J.R. et al. 2003, AJ, 125, 1559
\bibitem[]{} Raymond, S.N., et al. 2003, AJ 125, 2621
\end{thebibliography}

\end{document}
 
