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The Leonard E Parker Center for Gravitation, Cosmology and Astrophysics is supported by NASA, the National Science Foundation, UW-Milwaukee College of Letters and Science, and UW-Milwaukee Graduate School. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations.
The first eclipsing double white dwarf system was recently discovered (Steinfadt et al, 2010) and observations of this system, NLTT 11748, yielded one of the earliest ground-based measurements of the relativistic beaming effect. It is the first beaming observation for a binary white dwarf system.
Relativistic beaming is one of three effects that can be seen in light curves of binary systems. Because specific intensity is not a relativistic invariant, relativistic beaming of the emitted light (aka Doppler boosting) occurs when an object moves relative to an observer. If the object is part of a binary system, then its radial velocity is periodically modulated, causing a periodic sinusoidal variation in the observed flux. The other two observable effects are the ellipsoidal effect, when a member of the binary system is tidally affected by the gravitational pull of its companion, and the reflection effect, when light originating from one component is reflected by the other.
Few observations of the beaming effect have been reported, but until this work, none had ever been reported in a binary white dwarf system. NLTT 11748 contains two eclipsing, non-interacting white dwarfs. Upon its discovery it was considered an excellent candidate for ground-based observations of the beaming effect. This is because it has a large radial velocity (270 km/s) and the orbital period (5.6 hr) is short enough to be covered within a single night of observing. Additionally, the two white dwarfs have a high mass ratio and low luminosity ratio, which increase the beaming amplitude.
The relatively large beaming amplitude in non-interacting double white dwarf binaries originates from the unique white dwarf mass-radius, or mass-luminosity relation. In these binary systems the photometric primary is a helium (He) core white dwarf, a few times smaller in mass, but larger in radius and luminosity than the photometric secondary, a carbon/oxygen (C/O) core white dwarf. The observed beaming effect is the weighted difference between the individual beaming effects of the two binary components, shifted by a phase of 0.5. However, the larger mass and smaller luminosity of the C/O white dwarf make its own beaming effect much smaller, and even negligible, relative to that of the He white dwarf. Assuming a blackbody spectrum, the beaming amplitude is expected to be at the level of 10-3, and therefore detectable from the ground, while the ellipsoidal and reflection amplitudes are smaller by an order of magnitude.
NLTT 11748 was observed for about 4 hours each during three nights in February 2010. Observations were done at the LCOGT 2.0m Faulkes Telescope North in Hawaii. After analyzing the data and modeling the beaming effect as a sine modulation at the orbital period, the fitted beaming relative amplitude is 3.0 x 10-3, showing that the beaming effect is detected with a significance of greater than 7 sigma. Neither the ellipsoidal or reflection effects were detected by this ground-based observation, and that agrees with expectations that sufficient accuracy requires space-based observations.
Five similar binary systems have recently been discovered and can be used for further studies. Binary white dwarf systems where both the (photometric) beaming amplitude and (spectroscopic) radial velocity amplitude can be measured are a valuable tool for testing the relation between these two quantities, which is currently approximated using theoretical assumptions. Additionally, the evolution of a low-mass He white dwarf requires it to have a binary companion. Therefore, once a He white dwarf is identified, the beaming effect can be used to look for a binary companion photometrically.