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the movement of a light - emitting object relative to an observer causes relativistic beaming of the light ( aka doppler boosting ) since the specific intensity is not a relativistic invariant . when the object s radial velocity ( rv ) is periodically modulated , as is the case in binary systems , a periodic sinusoidal variation in the observed flux is induced . this effect is one of three that can be seen in light curves  of binary systems , not necessarily eclipsing . the other two 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 . the three effects were discussed in the context of planet - host stars by @xcite , and main sequence stellar binaries by @xcite . both studies addressed binary systems with orbital periods much longer than a day , finding that the required photometric accuracy necessitates space - based observations . observational detections of the beaming effect are rare . @xcite noted that the beaming effect is likely to be seen in their ground - based data of a sdb star + wd binary system with a period of @xmath2=2.28 hr , although the effect s amplitude was not measured and the light curve  is dominated by the ellipsoidal effect . @xcite measured the beaming and ellipsoidal effects in a _ kepler _ light curve  of an a - type star + low - mass wd binary system with @xmath2=5.19 d @xcite , and in fact used these measurements to resolve the puzzling nature of the system ( see also * ? ? ? @xcite identified the beaming and ellipsoidal effects in _ corot _ data of a brown dwarf host star ( corot-3 ; @xmath2=4.26 d ) , and @xcite observed all three effects with _ kepler _ in a 9.69 hr sdb + wd binary . we show here that for high mass ratio detached , non - interacting double white dwarf ( wd ) binaries the relative beaming amplitude is above the 10@xmath3 level , while the ellipsoidal and reflection amplitudes are smaller by an order of magnitude or more . therefore , these systems represent an excellent opportunity to measure the beaming effect using ground - based telescopes .    following the discovery of the first eclipsing detached double wd binary nltt  11748  by @xcite we immediately noticed it is an excellent candidate for ground - based observations of the beaming effect . the observed rv amplitude is large ( @xmath4270 km s@xmath5 ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , while the secondary is @xmath430 times fainter than the primary @xcite . in addition , the orbital period is short enough to be covered within a single night . nltt  11748  and similar systems where both the ( photometric ) beaming amplitude and the ( spectroscopic ) rv amplitude can be measured are a valuable tool for testing the relation between these two quantities , which is currently approximated using theoretical assumptions ( e.g. , * ? ? ? * ; * ? ? ? we discuss the beaming effect in non - interacting double wd systems in . our observations and data analysis are described in . we present the results in where we also test them and compare our findings to theoretical expectations . in we summarize our results and give our conclusions . the relatively large beaming amplitude in non - interacting double wd binaries originates from the unique wd mass - radius , or mass - luminosity relation . in those binary systems the photometric primary ( hereafter , the primary ) is a helium core wd , a few times smaller in mass but larger in radius and luminosity than the photometric secondary ( hereafter , the secondary ) , a c / o core wd ( see also table 1 in @xcite ) . as shown by @xcite 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 wd make its own beaming effect much smaller , and even negligible relative to that of the he wd . this can be seen by assuming both stars radiate as blackbodies and rewriting equation  ( 6 ) of @xcite as : @xmath6 where @xmath7 is the radial velocity amplitude of the primary , @xmath8 the speed of light , @xmath9 ( @xmath10 ) is the mass of the primary ( secondary ) and @xmath11 ( @xmath12 ) is the flux from the primary ( secondary ) . @xmath13 relates to the spectral index @xmath14 as : @xmath15 where @xmath16 and @xmath17 ( @xmath18 ) is the effective temperature of the primary ( secondary ) .    for a high mass ratio non - interacting double wd binary the term @xmath19 in eq . ( [ eq : beamamp1 ] ) right hand side becomes of order unity . this follows from the mass ratio and the flux ratio of the two stars , and also from the fact that @xmath20 is itself close to unity for the expected effective temperatures of the two stars . therefore eq . ( [ eq : beamamp1 ] ) reduces to : @xmath21 or in physical parameters : @xmath22 where @xmath23 the orbital inclination angle . the approximation neglects the contribution of the secondary and assumes a blackbody spectrum and a circular orbit . since @xmath24 has a value of a few in the optical for the typical temperatures of he wds ( e.g. , * ? ? ? * ) , the equation above shows that the beaming amplitude is expected to be at the few 10@xmath3 level , and therefore detectable from the ground . we note that this is not the accuracy required from a single measurement but the overall relative sinusoidal variability amplitude along the entire orbit . [ fig : beamamp2 ] shows the expected sdss-@xmath0 beaming amplitude versus orbital period , for nltt  11748-like systems ( solid line ) . also plotted ( dashed line ) is the expected amplitude for a system with an inclination angle of @xmath25 degrees . the figure shows that systems similar to nltt  11748 , but with longer periods and/or lower inclinations are also expected to show a beaming amplitude above the 10@xmath3 level . we observed nltt  11748  for 3.54.0 hr during each of the three nights of 2010 february 7 , 9 & 12 ut , obtaining data over all orbital phases . most orbital phases were observed during two different nights . our observations were done at the lcogt 2.0 m faulkes telescope north ( ftn ) , located at the haleakala observatory , hawaii . we used the spectral instruments 600 series camera and the sdss-@xmath0 filter . the camera has a 4k @xmath26 4k back - illuminated fairchild imaging ccd with a @xmath27 field of view ( fov ) . we used the default @xmath28 pixel binning mode , with an effective pixel scale of @xmath29 . the telescope pointing was adjusted to have the guiding camera fov include a suitable guide star . our observations were done while defocusing the telescope , spreading the stellar psf over more pixels and increasing the overall open shutter time relative to the camera dead time , mostly ccd readout time . the exposure time was 120 s , resulting in a median cycle time of 143 s.    data taken during each night was processed the same way . preliminary reduction , including bias and flat - field corrections was done using standard iraf routines . we applied aperture photometry using iraf / phot by using a few aperture sizes and eventually choosing a radius of 10 pixels ( @xmath30 ) , resulting in the smallest scatter in the final light curves  of the target and similar brightness stars , within 1 mag from that of the target . the target s light curve  was calibrated by dividing it by a comparison light curve   a weighted average light curve  of four comparison stars showing no variability , whether inter- or intra - night . this calibration included propagation of the errors of both the target and comparison light curves .    out of the total of 286 exposures seven were taken completely or partially during the 3 min eclipses @xcite , and were ignored in our analysis . two additional clear outliers in the target s light curve  were visually verified to result from a cosmic ray hitting within the photometric aperture . therefore , a total of 277 exposures were used in our analysis . the error estimates of the calibrated light curve  were directly based on the results of iraf / phot . we rescaled these errors to better reflect the true noise in the data , by fitting a 3rd degree polynomial to the flux ratio light curves  of each night , and inflating the error bars to make the reduced @xmath31 equal one . the derived scaling factors were 1.83 , 1.37 & 1.53 for the three nights , feb .  7 , 9 & 12 , respectively . we note that this polynomial fit was done only for the purpose of rescaling the error bars . the target s airmass varied from @xmath41 to @xmath42 during our observations , which is expected to affect the resulting light curve , depending on the difference in color between the target and comparison light curves . we removed these trends by taking the data from all three nights together and fitting a 2nd degree polynomial to the target s relative flux versus airmass , and dividing by the fit . this step resulted in the final light curve , shown in fig . [ fig : lcnight ] .    in order to look for the beaming effect in the final light curve  we simultaneously fitted for the three known effects ( beaming , reflection and ellipsoidal ) . in our modeling we took the beaming effect to be a _ sine _ modulation at the orbital period . the reflection effect has the same period but is lagging in phase by @xmath32 , hence it is a _ cosine _ modulation at the orbital period . the ellipsoidal effect has half the orbital period but the same phase as the reflection effect , so it is a cosine modulation at the first harmonic of the period . we used the ephemeris of @xcite and fitted the phase folded light curve  with a 5-parameter model @xcite , including a sine and cosine terms for the orbital period and its first harmonic : @xmath33 where @xmath34 , time subtracted the mid primary eclipse time . the ephemeris of @xcite is based on observations done during 1.5 months prior to the observations presented here . this resulted in a negligible uncertainty in the phase during our observations , smaller than 20 seconds , or 10@xmath3 of the period , justifying keeping the phase fixed in our fit . results for the fitted coefficients are listed in the middle column of . the fitted beaming relative amplitude is @xmath35 , showing that the beaming signal is detected with a significance of @xmath36 . the other three fitted coefficients were found to be consistent with zero . the @xmath31 statistics of the fitted model was 283.9 , and the reduced @xmath31 was @xmath37 for the 272 degrees of freedom , indicating a good estimate of the errors . fig . [ fig : lccomb ] presents the phase folded light curve  and the fitted model is overplotted . we have tested our results in order to verify they are not a statistical fluctuation , and that the beaming signal was not accidently injected into the data by our analysis .    assuming the light curve  is non - variable ( equivalent to fitting a constant value equal to the weighted average ) results in @xmath38 for 276 degrees of freedom , and @xmath39 , clearly rejecting the no variability hypothesis . a bootstrap analysis , done by randomly permuting the light curve  points in time showed that the probability of the measured beaming signal being a random one is smaller than 10@xmath40 . both these tests show , in addition to the amplitude s high s / n , that the detected variability has a high statistical significance .    it could be that the way we accounted for the airmass induced variation has injected the sine signal into the data . we tested this in two ways . first , we changed the polynomial degree used in fitting the relative flux versus airmass . using a degree of 1 gave a 0.5@xmath41 increase in the fitted beaming amplitude and increasing the polynomial degree up to 6 decreased the amplitude by @xmath42 . in all these fits the other three fitted amplitudes were found to be consistent with zero . second , we examined the light curves  of similar color stars in the field , with a @xmath43 term within 0.1 mag from that of nltt  11748 . for those stars @xmath44 was similar at the 0.01 level to that of a non - variable model , indicating they show no significant variability , and that the way we accounted for the airmass variation during our observations did not induce the detected variability . another possibility is that the detected signal originated from a variability in one of the four comparison stars . we checked this in two ways . first , we repeated our analysis four times while excluding one of the four comparison stars , using only the other three . this changed the fitted coefficients by less than 1@xmath41 and resulted in similar @xmath31 values . second , we applied the same analysis for each comparison star , using only the other three as comparisons . as in the case of the similar color stars described above , for all four comparison stars this resulted in a similar @xmath31 when fitting the 5-parameter model and a non - variable model , and the fitted beaming amplitude was consistent with zero . these two tests show that the variability identified in the target did not originate from the comparison stars . we repeated our analysis three times using data from only two of the three nights . we were able to detect the beaming amplitude in each of the three analyzes , although with a lower significance , but still higher than 4@xmath41 . in each of those three analyzes the other three coefficients were found to be consistent with zero .    finally , we fitted the data also with a simpler , 2-parameter model , including a zero point and only the sine component corresponding to the beaming amplitude ( @xmath45 ) . the result was the same as in the original 5-parameter model , and is listed on the second column from the right in .      for estimating the expected amplitude of the beaming effect in our data we first calculated it as a function of wavelength assuming a blackbody spectrum , using eq . ( [ eq : beamamp2 ] ) . this function is plotted as a solid black line in fig . [ fig : beamamp ] . we then weighted it by the sdss-@xmath0 filter transmission curve and the ccd qe . the final estimates for each band are marked as filled circles in fig . [ fig : beamamp ] where the error bars due to the uncertainties in @xmath17 and @xmath7 are comparable to the size of the markers . fig . [ fig : beamamp ] also justifies our choice to observe in sdss-@xmath0 , as the beaming amplitude increases towards the blue , but observations in sdss-@xmath46 are difficult at ftn . the expected sdss-@xmath0 amplitude is ( @xmath47 , which is within 1@xmath41 from the measured amplitude of ( @xmath48 , marked by a diamond in fig . [ fig : beamamp ] . therefore , the measured amplitude for the beaming effect is consistent with the expected value assuming a blackbody spectrum . another way to estimate the expected beaming amplitude , in a more direct manner and without the need to assume a blackbody spectrum is to integrate over a measured spectrum of the system using eq .  2 of @xcite . for that end we used the ntt / efosc2 spectrum obtained by @xcite , which covers the sdss-@xmath0 band . this resulted in an expected amplitude of @xmath49 , less than 2@xmath41 away from the measured amplitude . however , we caution that the uncertainty on this result is difficult to estimate . this low resolution spectrum was derived from two 20 min exposures , and was affected by the doppler shift variation during the exposure , and by the rv difference between the two exposures , which could have been at the @xmath5050 km s@xmath5 level , depending on the exact orbital phases they were taken at . we estimate the amplitude of the ellipsoidal effect following @xcite to be about @xmath51 , where @xmath52 is the orbital semi - major axis , @xmath53 the radius of the primary , and we have ignored an order to unity coefficient ( see also * ? ? ? * ; * ? ? ? this expression is @xmath54 for nltt  11748 . although it is only a rough estimate and a more accurate one can be derived for this system , we use it only to show that the ellipsoidal effect is too small to be detected in our data . for the reflection effect we use @xmath55 as an upper limit , which is @xmath56 for nltt  11748 . therefore , both the ellipsoidal and reflection effects are not expected to be detected from the ground , in agreement with our results . we have presented a ground - based measurement , carried out with a 2.0 m telescope , of the relativistic beaming effect in the high mass ratio wd binary nltt  11748  @xcite . we showed that the measured amplitude , of @xmath1 , is within 1@xmath41 from an approximated theoretical estimate , and within 2@xmath41 from a more direct estimate using a low resolution spectrum of the system . the ellipsoidal and reflection effects were not detected in our data , in agreement with theoretical expectations . to our knowledge this is the first ground - based measurement of the relativistic beaming effect . our measurement is a first step in testing the relation between the beaming and rv amplitudes in systems similar to nltt  11748 , and it suggests it can be approximated by assuming a blackbody spectrum . although we were not able to obtain a high precision measurement of the beaming amplitude , it is identified at a high significance , of more than 7@xmath41 . although short period detached he + c / o wd binaries are rare , their discovery rate is increasing . five such systems were recently discovered @xcite by rv monitoring , and are expected to show beaming amplitudes of @xmath57 in the optical . all five have orbital periods of only a few hours , shorter than that of nltt  11748 , so they can be used to further test the relation between the rv amplitude and the beaming amplitude , and also the wavelength dependency of the latter , shown in fig . [ fig : beamamp ] for nltt  11748 . the evolution of a low - mass he wd requires it to have a binary companion ( e.g. , * ? ? ? therefore , once a he wd is identified the beaming effect can be used to look for a binary companion photometrically , in a very similar way to spectroscopic monitoring . since in this case the light curve  becomes analogous to the rv curve , high precision photometry can in principle be used to model the orbit and measure the mass ratio of the two components . the authors warmly thank marten van kerkwijk and shai zucker for helpful discussions . this paper uses observations obtained with facilities of the las cumbres observatory global telescope . dlk was supported by nasa through hubble fellowship grant # 01207.01-a awarded by the stsci which is operated by aura , inc . , for nasa , under contract nas 5 - 26555 . this work was supported by the national science foundation under grants phy 05 - 51164 and ast 07 - 07633 .                                                 expected beaming amplitude according to eq . ( [ eq : beamamp3 ] ) , for an nltt  11748-like system as a function of orbital period in the sdss-@xmath0 band . the plot was produced using the masses of the two wds in nltt  11748  and the effective temperature of the primary . the solid line corresponds to a completely edge - on system , close to nltt  11748  inclination of @xmath66 degrees , while the dashed line corresponds to a similar system with @xmath23=60 degrees . the black filled circle marks the expected nltt  11748  position . the plot clearly shows that similar systems to nltt  11748 , with a longer period and a lower inclination are also expected to show a beaming amplitude above the 10@xmath3 level , marked with a horizontal dotted line . ] nightly light curves  of nltt  11748 , observed at ftn on the nights of ( from left to right ) 2010 february 7 , 9 & 12 ut . the overplotted solid line is the fitted model . although the scatter in the data is relatively large , the small variability can be seen in the data . ] nltt  11748  light curve  phase folded with the known ephemeris . phase zero is time of primary eclipse . data from different nights are marked by different colors ( top light curve ) . the bottom light curve  was generated by binning the points in phase , using 0.04 phase bins , and was shifted downward for clarity . the binned light curve  is shown for visualization only , and was not used in our analysis . overplotted solid line ( black ) is the fitted 5-parameter model , constructed from the coefficients listed in . ] amplitude of the expected relativistic beaming effect for nltt  11748  as a function of wavelength ( black solid line ) , assuming a blackbody spectrum . the filled circles are the calculated amplitudes in each filter , accounting for the ccd qe and filter transmission curves . the plotted colored curves account for both the ccd qe and filter transmission . the sdss-@xmath0 beaming amplitude measured here is marked by a diamond , along with error bars ( green ) . ]
we report on the first ground - based measurement of the relativistic beaming effect ( aka doppler boosting ) . 
 we observed the beaming effect in the detached , non - interacting eclipsing double white dwarf ( wd ) binary nltt  11748 . 
 our observations were motivated by the system s high mass ratio and low luminosity ratio , leading to a large beaming - induced variability amplitude at the orbital period of 5.6 hr . 
 we observed the system during 3 nights at the 2.0 m faulkes telescope north with the sdss-@xmath0 filter , and fitted the data simultaneously for the beaming , ellipsoidal and reflection effects . 
 our fitted relative beaming amplitude is @xmath1 , consistent with the expected amplitude from a blackbody spectrum given the photometric primary radial velocity amplitude and effective temperature . 
 this result is a first step in testing the relation between the photometric beaming amplitude and the spectroscopic radial velocity amplitude in nltt  11748  and similar systems . 
 we did not identify any variability due to the ellipsoidal or reflection effects , consistent with their expected undetectable amplitude for this system . 
 low - mass , helium - core wds are expected to reside in binary systems where in some of those systems the binary companion is a faint c / o wd and the two stars are detached and non - interacting , as in the case of nltt  11748 . 
 the beaming effect can be used to search for the faint binary companion in those systems using wide - band photometry .