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a variety of detector concepts for space - based gravitational wave interferometers have been proposed , the most well studied concept being lisa@xcite .
it was understood early on that the most numerous source class radiating in the band covered by lisa - like detectors will be the galactic population of ultra - compact binaries ( ucbs ) comprised of pairs of stellar remnants : white dwarfs , neutron stars or black holes
. the gravitational radiation from these ucbs will be the dominant signal in the frequency band covered by lisa - like detectors .
early estimates of the composite signal from the ucbs @xcite demonstrated that the signals of the vast majority of the galactic binaries will overlap and be unresolvable from one another , forming a limiting foreground ( or `` confusion noise '' ) for space - based gravitational wave detectors .
later studies based on population synthesis @xcite have borne this expectation out .
detailed data analysis studies have shown that @xmath1 individual binaries could be resolved out of the foreground by a gravitational wave observatory like lisa @xcite
.    a subset of the resolvable binaries will be detectable electromagnetically .
the purpose of this work is to assess the multi - messenger potential for different space - based detectors spanning the trade - space of future mission designs .
this builds off previous work @xcite demonstrating the feasibility of follow - up observations for high - frequency ucb sources .
we estimate the total number of multi - messenger sources by beginning with a population synthesis model of the galaxy @xcite , complete with optical magnitudes . from this
we produce a magnitude limited source catalog , then estimate how well each system will be localized on the sky by different gravitational wave detector configurations . using hundreds of monte carlo realizations over the spatial distribution of the galaxy and the ucb orientations ,
we find tens to hundreds of sources that can be observed both electromagnetically and gravitationally .
the information encoded about the ucbs in each of the two spectrums is highly complementary , enabling tests of general relativity , full measurement of the physical parameters enabling constraints on binary synthesis channels , and new methods of probing the close interaction dynamics of the compact stars @xcite .
for a gravitational wave observatory , the limiting sensitivity as a function of frequency is dominated at low frequencies by acceleration noise @xmath2 , while the `` floor '' , where the detector is most sensitive , is dominated by position measurement noise @xmath3 . table [ tbl.detectors ] contains the parameters used for the detector configurations in this study .
these parameters can be used to compute the noise power spectral density @xmath4 ,     \label{eqn.sn }    \end{aligned}\ ] ] where @xmath5 and @xmath6 is the contribution to the instrument noise from the unresolved ucb foreground  @xcite .
the configurations we will highlight correspond to the classic lisa design ( @xmath7 gm ) , as well as two shorter arm - length configurations ( @xmath8 gm and @xmath9 gm ) in order to cover a variety of plausible mission configurations . the 1 gm configuration is similar to the elisa mission being considered by the european space agency  @xcite .
we use an observation time of two years for each configuration .
this suite of detectors provides a broad palette to illustrate the observational capabilities of these instruments with regards to the ucbs .
a classic depiction of the performance for these interferometers is a plot of the average sensitivity curve in strain spectral density versus frequency @xcite , as shown in fig .
[ fig.detectorpsd ] .
the elisa concept is the only one which uses a 4-link configuration .
the doppler ranging between each spacecraft in the constellation is accomplished using two laser links .
thus the 4-link design is a single - vertex interferometer , while the 6-link designs allow for three ( coupled ) interferometers .
this difference accounts for an additional improvement in the 6-link sensitivity curves by a factor of @xmath10 at frequencies where the ucbs are found .    .
the solid lines show the sensitivity set by the measurment noise while the dashed curves include an estimate of the ucb confusion - limited foreground .
over - plotted are the brightest ucbs in our simulated catalog ( green crosses ) , and the known verification binaries ( blue stars),scaledwidth=50.0% ]    .gravitational wave detector configurations used in this study .
configuration 1 corresponds to elisa .
configuration 5 is the classic lisa design .
all simulations were for two year mission lifetimes .
[ cols=">,^,^,^,^ " , ]      we now consider how to select candidates for follow - up observations from the full gw catalog . pointing telescopes at all of the gw sources localized within the adopted threshold would be inefficient , as we find between @xmath11 and @xmath12 gw sources in the full catalog will meet the @xmath13 deg@xmath0 threshold , while @xmath14 are likely to be brighter than @xmath15 , and only @xmath16 pass the @xmath17 cut .
additional considerations need to be made to increase the efficiency of follow - up observing campaigns .
we illustrate two simple ways to isolate the gw sources that may be electromagnetically observable .
these suggestions are supported by calculations shown in table  [ tbl.strategy ] .
first , the large majority of ucb sources are confined within the galactic plane .
conversely , the magnitude limited catalogs sample the local galaxy , which is much more uniformly distributed on the celestial sphere .
therefore , as a rough cut on the gw catalog , any binaries that are well localized but out of the galactic plane are good candidates .
these are additionally attractive sources , as there will be less optical background and extinction against which the observing campaign will have to compete .
we find between @xmath18 and @xmath19 of the well - localized binaries in the 20@xmath20 to 24@xmath20 magnitude - limited catalogs have galactic latitudes @xmath21 , while that fraction is reduced to @xmath22 for the full gw catalog .
a uniform distribution of stars on the celestial sphere would have 66% of the stars with @xmath21    the other strategy for identifying optical counterparts relies on estimates of the distance to the galactic binary .
typical ucb sources will undergo very little evolution of their orbital period during a space - borne gw detector s lifetime . without measurement of the rate of change of the gravitational wave frequency @xmath23
the gw observation only constrains the overall amplitude of the signal without decoupling the chirp - mass and the luminosity distance @xmath24 @xcite . for @xmath25 of the multi - messenger sources we sufficiently constrain @xmath23 and @xmath26 to measure @xmath24 to within 20% , but astrophysical effects such as tides may impact the orbital evolution and thus bias the distance estimate . for the remaining systems in the gw catalog , we can use reasonable priors on the mass and mass ratio of white dwarf binaries to put meaningful constraints on @xmath24 from the amplitude measurement alone .
using only the amplitude , frequency and priors on the masses constructed from the population synthesis simulation , we find that the distribution of the most likely ( ml ) luminosity distances @xmath27 is strongly peaked between 0 and 8 kpc  the distance to the galactic center  for the magnitude limited catalogs .
the @xmath28 distributions for the full well - localized catalog with no magnitude cut is more uniformly distributed over a larger range .
our final consideration pertains to the expected optical light curves for ucb systems identified in the gw catalog .
the population synthesis galaxy in our study is restricted to detached white dwarf binaries , as opposed to interacting am cvn systems . without mass transferring from one star to the other in the binary ,
photometric variability is not guaranteed .
the systems in the gw catalog that are best constrained are typically those at the high - frequency end of the population .
this is to our advantage , because the shorter period binaries have a higher probability of eclipsing one another during an orbital cycle .
we can put an additional cut on our em / gw catalog by requiring the binaries to be eclipsing .
( see the right - hand panel of figs .
[ fig.numbersources1 ]  and  [ fig.numbersources10 ] ) . from simple geometrical arguments @xcite the minimum inclination angle with respect to our line of sight that will produce eclipsing light curves is @xmath29 assuming all binaries have mass @xmath30 and radius @xmath31 .
if we only consider binaries in the multimessenger catalog with inclination angle less than @xmath32 , we reduce the total number of candidates by a factor of @xmath33 .
nevertheless , we still find upwards of @xmath34 candidates for the large gw detector configurations and deep , wide field , optical surveys .
requiring eclipsing light curves significantly degrades the multimessenger potential for the 1 gm configuration using catalogs limited to 20@xmath20 magnitude and dimmer  such em follow - up surveys could come up empty .
we conclude that space - based gravitational wave detectors will be useful observatories for discovering new ucbs in the galaxy that could be observed electromagnetically , though deep , wide field , optical surveys may be required to produce large catalogs .
we reach this verdict by considering a range of plausible near - future space - based gravitational wave detector concepts , and assess their measurement capabilities for magnitude limited catalogs of ucbs .
magnitudes for the constituents of each binary were derived from the population synthesis simulations , and the gravitational wave measurement capabilities were estimated using the fisher information matrix .
any ucbs that were brighter than our chosen magnitude limits ( 18 - 24 ) and located on the sky by the gravitational wave detector to within angular resolution @xmath35 were considered multi - messenger candidates .
we estimated the multi - messenger catalog sizes for both @xmath36 and 10 deg@xmath0 .    at the pessimistic end
, we consider magnitude 18 limited catalogs , and single - vertex interferometers with 1 gm arm - lengths . the best scenario considered the classic lisa design and an optical telescope limited at @xmath37 magnitude .
the number of multi - messenger candidates was anywhere from a few to several hundreds over that range of detector capabilities .
if we put on the additional constraint that the sources must be eclipsing to allow for electromagnetic observation the counts were reduced by a factor of @xmath33 .
while most of the known verification binaries are am cvn type stars , our study only considered detached white dwarf binaries , thus providing a very complimentary catalog of ucb multi - messenger systems .
this work considered a conservative approach to finding multi - messenger ucbs , with competing criteria that strongly affect the expected population of systems detectable in both spectrums .
electromagnetic detections are most strongly affected by the magnitude limit of the detection survey , a function of telescope aperture . by contrast , the gravitational wave detection catalogs of ucbs are expected to have thousands of systems in them ; most will be too faint to be detectable by any electromagnetic survey .
however the gravitational wave localization criterion is a strong constraint on the multi - messenger catalog .
we find that wide - field surveys ( @xmath13 deg@xmath0 ) yield more candidates than more narrow fields of view ( @xmath38 deg@xmath39 ) by 50 - 100% for the full catalogs , and by a factor of 2 - 4 for the eclipsing binaries .
we have estimated the number of ucb multi - messenger candidates without considering what could be done with joint gw and em observations .
our follow - on effort will consider the science yield from joint observations of both the known verification binaries 
mostly mass - transferring systems  and the close , detached binaries that will be discovered by space - borne gravitational wave detectors .
this work was supported by nasa grants 08- atfp08 - 0126 ( tbl ) , nnx12ag30 g ( sll ) , and nnx10ah15 g ( njc ) .
gn acknowledges support from the dutch foundation for fundamental research on matter ( fom ) .
g.  nelemans maintains a wiki with the most up to date list of verification binary parameters at link:<www.astro.ru.nl/~nelemans / dokuwiki / doku.php?id = lisa_wiki>[<www.astro.ru.nl/~nelemans / dokuwiki / doku.php?id = lisa_wiki > ] ; cited 2 september 2011
space - based gravitational wave interferometers are sensitive to the galactic population of ultra - compact binaries 
 . an important subset of the ultra - compact binary population are those stars that can be individually resolved by both gravitational wave interferometers and electromagnetic telescopes . 
 the aim of this paper is to quantify the multi - messenger potential of space - based interferometers with arm - lengths between 1 and 5 gm . 
 the fisher information matrix is used to estimate the number of binaries from a model of the milky way which are localized on the sky by the gravitational wave detector to within 1 and 10 deg@xmath0 and bright enough to be detected by a magnitude limited survey . 
 we find , depending on the choice of gw detector characteristics , limiting magnitude , and observing strategy , that up to several hundred gravitational wave sources could be detected in electromagnetic follow - up observations .    
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