At the left you see a real photo of a white dwarf (WD)-M star binary [1,2]: the blue component is the WD, a very hot remnant of a former star at some 10000 K with typically 0.6 solar masses — but much smaller than the Sun. Thus, a WD is very dense. A spoon of matter taken from a WD's surface has the weight of a house! The red guy on the image is just about 3200 K °cool°. Stars like that typically have low masses of ≈ 0.3 times that of the Sun. These low-mass stars are called M stars, following a historical nomenclature. Our Sun, as a comparison, has a surface temperature of about 5800 K and is a G star.
Now, the interesting thing on these binaries is that they constitute a common final stage object of stellar evolution, a WD, and the most frequent type of star: the M component. Close WD-M binaries are also progenitor candidates for cataclysmic variables (CVs) and Type Ia supernovae. WD-M binaries consist of two stars of radically different structure and evolutionary stage that originate in interstellar matter of identical composition at the same time, on cosmological scales, and in the same region of space. Many of the constituents of the systems do not only interact gravitationally, which may lead to mutual mass exchange and substantial gravitational radiation, but they also affect each other due to their magnetic fields. I studied these systems to improve the knowledge of the basic parameters of WD-M systems.
The key to the characterization of such systems is a spectral analysis. Below, you see an SDSS spectrum showing both features of a WD and an M star. In this certain case, the WD has an atmosphere mainly composed of hydogen (H), which reveals itself by the absorption lines between 3836.6 Å and 6564.7 Å. This kind of WD is called DA, which is a subtype category of WDs. There are also helium (He)-rich WDs, called DO white dwarfs, and those showing heavier elements than He. These spectral traces, the absorption lines, are a finger print of the light escaping from the WD. As the photons pass the WD's atmosphere, those with certain energies, i.e. at certain wavelengths, are absorbed by the gas of the atmosphere.
Spectrum of the WD-M star binary SDSSJ101647.21-010907.2 
At the right part of the spectrum one can see characteristics of an M star. The absorption band around 7100 Å, e.g., belongs to titan oxide (TiO), which serves as the primary spectral indicator for M stars. At 8183 Å and 8194 Å we find sodium (Na) features.
Some of those spectroscopic binaries are optically resolvable which means that they can be seperated into a red and a blue source of light on a respective photo, such as the one shown on the left. If one is able to determine the distance of the binary system from Earth one may also compute the mutual distance of the components, or rather the projection of their displacement onto a tangent to the line of sight. Depending on the system's distance from Earth, the displacement of those resolved constituents is typically of order hundreds or thousands AU and they have orbital periods of some thousands to hundred thousand years.
To derivate parameters like the surface, or 'effective' temperature (Teff), surface gravity (g), distance to Earth etc. from the stars respectively, I wrote a program (in the programming language python) that fits spectral models to the observed spectra and thus gives information about the stellar parameters. The models I used are basing on the PHOENIX code from Peter Hauschildt at the Hamburger Sternwarte. By finding the best combination of WD and M star model spectra over a reasonable parameter range of Teff, g and metallicities, we  were able to derive these basic parameters of 636 WD-M star binaries from the SDSS.
 The name of that object is SDSSJ082022.02+431411.1 . Note that 1'' = 1/3600 ° ≜ some 100 AU = some 15 000 000 000 km .
 Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org
The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.
 R. Heller, D. Homeier, S. Dreizler, R. Østensen, 2009, A&A, 496, 191 [ADS]