You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
over the past years the dominant explanation for the large mass to light ratios inferred for galactic and meta - galactic systems , that these are embedded within massive dark matter halos , has begun to be challenged .
direct detection of the dark matter particles , in spite of decades of extensive and dedicated searches , remains lacking .
numerous alternative theories of gravity have appeared ( e.g. teves of @xcite , f(r ) theories e.g. @xcite ) mostly grounded on geometrical extensions to general relativity , and leading to laws of gravity which in the low acceleration regime , mimic the modified newtonian dynamics ( mond ) fitting formulas e.g. @xcite .
similarly , @xcite have explored mond not as a modification to newton s second law , but as a modified gravitational force law in the newtonian regime , finding a good agreement with observed dynamics across galactic scales without requiring dark matter .
recently @xcite have constructed an @xmath5 extension to general relativity which in the low velocity limit converges to the above approach .
a generic feature of all such modified gravity schemes is the appearance of an acceleration scale , @xmath2 , above which classical gravity is recovered , and below which the dark matter mimicking regime appears .
this results in a general prediction ; all systems where @xmath6 should appear as devoid of dark matter , and all systems where @xmath7 should appear as dark matter dominated .
it is interesting that no @xmath6 system has ever been detected where dark matter needs to be invoked . on the other hand
, the latter condition furnishes a testable prediction in relation to the orbits of wide binaries . for test particles in orbit around a @xmath1 star , in circular orbits of radius @xmath8
, the acceleration is expected to drop below @xmath9 for @xmath107000 au@xmath11 .
this provides a test for the dark matter / modified theories of gravity debate ; the relative velocities of components of binary stars with large physical separations should deviate from kepler s third law .
seen as an equivalent newtonian force law , beyond @xmath127000 au the gravitational force should gradually switch from the classical form of @xmath13 to @xmath14 , and the orbital velocity , @xmath15 , should no longer decrease with separation , but settle at a constant value , dependent only on the total mass of the system through @xmath16 . under modified gravity theories , binary stars with separations beyond 7000 au should exhibit `` flat rotation curves '' and a `` tully - fisher relation '' , as galactic systems in the same acceleration regime do .
we apply this test to the binaries of two recent catalogues containing relative velocities and separations .
the two catalogues are entirely independent in their approaches . the first one , @xcite , comprises 280 systems from the _ hipparcos _ satellite , while the second , @xcite , identifies 1,250 ones from the sloan digital sky survey ( sdss ) .
details can be found in @xcite .
the newtonian prediction for the relative velocities of the two components of binaries having circular orbits , when plotted against the binary physical separation , @xmath8 , is for a scaling of @xmath17 , essentially following kepler s third law , provided the range of masses involved were narrow . in a relative proper motion sample however , only two components of the relative velocity appear , as velocity along the line of sight to the binary leads to no proper motion .
thus , orbital projection plays a part , with systems having orbital planes along the line of sight sometimes appearing as having no relative proper motions .
a further effect comes from any degree of orbital ellipticity present ; it is hence clear that the trend for @xmath17 described above , will only provide an upper limit to the distribution of projected @xmath18 vs. @xmath8 expected in any real observed sample , even if only a narrow range of masses is included .
one should expect a range of measured values of projected @xmath18 at a fixed observed projected @xmath8 , all extending below the newtonian limit , which for equal mass binaries in circular orbits gives @xmath19 .
further , over time , the orbital parameters of binaries will evolve due to the effects of galactic tidal forces and dynamical encounters with other stars in the field , specially in the case of wide binaries .
to first order , one would expect little evolution for binaries tighter than the tidal limit of 1.7pc , and the eventual dissolution of wider systems .
a very detailed study of all these points has recently appeared , @xcite .
these authors numerically follow populations of 50,000 @xmath1 binaries in the galactic environment , accounting for the evolution of the orbital parameters of each due to the cumulative effects of the galactic tidal field at the solar radius . also , the effects of close and long range encounters with other stars in the field are carefully included , to yield a present day distribution of separations and relative velocities for an extensive population of wide binaries , under newtonian gravity .
it is found that when many wide binaries cross their jacobi radius , the two components remain fairly close by in both coordinate and velocity space .
thus , in any real wide binary search a number of wide pairs with separations larger than their jacobi radii will appear . finally ,
@xcite obtain the rms one - dimensional relative velocity difference , @xmath20 , projected along a line of sight , for the entire populations of binaries dynamically evolved over 10 gyr to today , as plotted against the projected separation on the sky for each pair .
the expected keplerian fall of @xmath21 for separations below 1.7 pc is obtained , followed by a slight rise in @xmath20 as wide systems cross the jacobi radius threshold .
@xmath20 then settles at rms values of @xmath22 .
this represents the best currently available estimate of how relative velocities should scale with projected separations for binary stars ( both bound and in the process of dissolving in the galactic tides ) under newtonian gravity .
we see that all we need is a large sample of relative proper motion and binary separation measurements to test the newtonian prediction for the rms values of the 1 dimensional relative velocities of @xcite , and to contrast the @xmath23 and the @xmath24 predictions for the upper envelope of the @xmath18 vs. @xmath8 distributions .
in the @xcite catalogue wide binaries are identified by assigning a probability above chance alignment to the systems by carefully comparing to the underlying background ( and its variations ) in a 5 dimensional parameter space of proper motions and spatial positions .
we keep only binaries with a probability of non - chance alignment greater than @xmath25 .
the binary search criteria used by the authors requires that the proposed binary should have no near neighbours ; the projected separation between the two components is thus always many times smaller than the typical interstellar separation .
we use the reported distances to the primaries , where errors are smallest , to calculate projected @xmath18 and projected @xmath8 from the measured @xmath26 and @xmath27 values reported .
although the use of _ hipparcos _ measurements guarantees the best available quality in the data , we have also removed all binaries for which the final signal to noise ratio in the relative velocities was lower than @xmath28 .
we are left with a sample of 280 binaries , having distances to the sun within @xmath29 in pc .
the data show a perfectly flat upper envelope in a @xmath18 vs. projected @xmath8 , @xcite .
the average signal to noise ratio for the data is 1.7 , with an average error on @xmath18 of 0.83 @xmath30 , which considering a @xmath31 factor from the top of the distribution to the real underlying upper limit for the sample , results in 3 @xmath30 as our estimate of the actual physical upper limit in @xmath18 .
the sloan low mass wide pairs catalogue ( slowpokes ) of @xcite contains a little over 1,200 wide binaries with relative proper motions for each pair , distances and angular separations .
also , extreme care was taken to include only physical binaries , with a full galactic population model used to exclude chance alignment stars using galactic coordinates and galactic velocities , resulting in an estimate of fewer than 2% of false positives .
this yields only isolated binaries with no neighbours within many times the internal binary separation .
again , we use the reported distances to the primaries to calculate projected @xmath18 and projected @xmath8 from the measured @xmath26 , @xmath27 and @xmath32 values reported by @xcite , to obtain a sample of 417 binaries .
the upper envelope of the distribution of @xmath18 from this catalogue does not comply with kepler s third law . as was the case with the _ hipparcos _ sample ,
the upper envelope describes a flat line , as expected under modified gravity schemes .
the average signal to noise in @xmath18 for the @xcite catalogue is 0.48 , with an average error on @xmath18 of 12 @xmath30 , which considering a @xmath31 factor from the top of the complete distribution to the real underlying upper limit gives the same @xmath33 as obtained for the @xcite _ hipparcos _ catalogue .
figure ( 1 ) shows the rms value of the one - dimensional relative velocity difference for both of the samples discussed .
the error bars give the error propagation on @xmath26 and @xmath32 .
we construct @xmath20 by considering only one coordinate of the two available from the relative motion on the plane of the sky .
thus , each binary can furnish two @xmath20 measurements , which statistically should not introduce any bias .
indeed , using only @xmath34 or only @xmath35 or both for each binary , yields the same mean values for the points shown .
the small solid error bars result from considering an enlarged sample where each binary contributes two @xmath36 measurements , while the larger dotted ones come from considering each binary only once , and do not change if we consider only @xmath34 or only @xmath35 .
the series of small @xmath37 interval data are for the _ hipparcos _ catalogue of @xcite , while the two broader crosses show results for the @xcite sdss sample .
the solid curve is the newtonian prediction of the full galactic evolutionary model of @xcite for binaries , both bound and in the process of dissolving .
note that the results of this simulation deviate from kepler s law for @xmath8 larger than the newtonian jacobi radius of @xmath38 , whereas the discrepancy with the observed samples also occurs at much smaller separations . even considering the large error bars , where each binary contributes only one @xmath20 value
, we see eight points lying beyond 1@xmath39 , making the probability of consistency between this prediction and the observations of less than @xmath40=@xmath41 .
we obtain a constant rms value for @xmath20 of 1 @xmath30 , in qualitative agreement with expectations from modified gravity schemes .
the vertical line marks @xmath42 ; we see the data departing from the newtonian prediction outwards of this line , and not before .
the two independent catalogues , each using different sets of selection criteria , each perhaps subject to its own independent systematics , are consistent with the same result , a constant horizontal upper envelope for the distribution of relative velocities on the plane of the sky at an intrinsic value of 3 @xmath431 @xmath30 , extending over 3 orders of magnitude in @xmath8 , with a constant rms @xmath20 value consistent with 1 @xmath430.5 @xmath30 .
this supports the interpretation of the effect detected as the generic prediction of modified gravity theories .
the solid curve gives the rms values for one dimensional projected relative velocities as a function of projected separations , for the dynamical modelling of large populations of wide binaries evolving in the galactic environment , taken from @xcite .
the same quantity for the data from the catalogues analysed is given by the points with error bars ; those with narrow @xmath37 intervals being from the _ hipparcos _ sample of @xcite , and those two with wide @xmath37 intervals coming from the sdss sample of @xcite ]
we identify a critical test in the classical gravity / modified gravity debate , using the relative velocities of wide binaries with separations in excess of 7000 au , as these occupy the @xmath0 regime .
we present a first application of this test using the best currently available data .
results show constant relative rms velocities for the binary stars in question .
this is quantitatively inconsistent with detailed predictions of newtonian dynamical models for binaries evolving in the local galactic environment .
our results are qualitatively in accordance with generic modified gravity models which explain galactic dynamics in the absence of dark matter .
bekenstein , j. , 2004 , phys .
d. , 70 , 3509
assuming newton s gravity and gr to be valid at all scales leads to the dark matter hypothesis as a requirement demanded by the observed dynamics and measured baryonic content at galactic and extragalactic scales . 
 alternatively , modified gravity scenarios where a change of regime appears at acceleration scales @xmath0 have been proposed . 
 this modified regime at @xmath0 will generically be characterised by equilibrium velocities which become independent of distance . here 
 we identify a critical test in this debate and we propose its application to samples of wide binary stars . since for @xmath1 systems the acceleration drops below @xmath2 at scales of around 7000 au , a statistical survey of wide binaries with relative velocities and separations reaching @xmath3 au and beyond should prove useful to the above debate . 
 we apply the proposed test to the best currently available data . 
 results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude , in analogy with galactic flat rotation curves in the same @xmath0 acceleration regime . 
 our results are suggestive of a breakdown of kepler s third law beyond @xmath4 scales , in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond .