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there has been a significant sensitivity improvement of the gravitational wave detectors since the laser interferometer gravitational wave observatory ( ligo )  @xcite and virgo observatory  @xcite started their operation . in 2007
ligo and virgo completed the two year run at sensitivity that allows detection of a merger of two neutron stars ( ns - ns ) as far as @xmath0  mpc away  @xcite . in the most recent run ( may 2009 - october 2010 )
the binary neutron star horizon distance has been increased to @xmath1  mpc . however , even at this impressive sensitivity , the anticipated detection rate with the initial ligo and virgo detectors is quite low .
a detection may be possible in the case of a rare astrophysical transient event such as a supernova explosion in our galaxy or a nearby merger of binary neutron stars .
the signal is likely to be weak and it will be difficult to prove its astrophysical origin unless it is confirmed with a coincident observation of the electromagnetic or neutrino counterpart .
for this reason the ligo and virgo collaborations are conducting a wide range of joint observations  @xcite with other astrophysical experiments including radio  @xcite , optical and x - ray telescopes  @xcite , and neutrino detectors  @xcite .
a more robust detection of gravitational waves from astrophysical sources is anticipated in the next five years as advanced ligo and advanced virgo come online .
numerous gw signals , expected to be observed by advanced detectors ( likely @xmath1 ns - ns events per year  @xcite ) , will begin our exploration of the gravitational - wave sky and start the era of the gravitational wave astronomy .
along with the advanced gw detectors , a new generation of optical telescopes will come online  @xcite , which will enable a wide and deep survey of the electromagnetic sky .
joint observations with the advanced gravitational wave detectors and electromagnetic instruments will not only increase the confidence of detection but also bring fundamentally new information about the gw sources .
they will reveal the physics and dynamic of sources , provide the identification of host galaxies and the associated redshifts , and in some cases determine luminosity distance to the source .
one of the major challenges for such joint observations is to establish unambiguous association between a gravitational wave signal and a possible electromagnetic counterpart .
it greatly depends on the ability of the gw networks to reconstruct sky coordinates of a detected gw source .
given an accurate sky location , a corresponding electromagnetic transient may be identified in a list of events obtained with the all - sky telescope surveys , or the em instruments can be guided to take images of a small area in the sky . in the second case , it is important that the sky localization is performed by gw detectors in real time with low latency .
the efficiency of the gw - em association and the choice of a partner telescope is affected by the sky localization error which should be well within the instrument s field of view ( typically less than few square degrees ) . moreover , exploring smaller area in the sky will decrease the probability of the false association .
the problem of the source localization with networks of gw detectors is in the focus of research in the gravitational wave data analysis .
there are several analytical studies  @xcite of this problem considering geometrical reconstruction of source coordinates based on the triangulation , which requires a measurement of the arrival time of a gw signal at different detectors
. however , the accurate timing of the gw signal is intimately related to the reconstruction of the signal waveforms . due to the different detector sensitivities to the gw polarizations , the waveforms recorded by individual detectors may be different and they may not have a common timing reference ( like a signal peak time ) for a direct measurement of the differences in the arrival time .
therefore , the problem of the source localization is better addressed in the framework of the coherent network analysis  @xcite , which reconstructs the waveforms and the sky coordinates simultaneously . by using both these methods ( triangulation and coherent network analysis ) , several practical source localization algorithms  @xcite have been recently developed and used during the ligo and virgo data taking runs in 2009 - 2010 .
there have been a number of studies addressing benefits of individual detectors  @xcite and various detector networks  @xcite . in this paper
we present a simulation study of the source localization and the reconstruction of gw waveforms with the networks of advanced detectors .
the study is performed with a coherent network method , called coherent waveburst  @xcite ( cwb ) , based on the likelihood analysis . in cwb the data from all detectors in the network
is processed simultaneously in order to reconstruct a common gw signal which is consistent with the recorded detector responses .
the consistency is measured by the likelihood ratio , which is a function of the source parameters ( waveforms and sky location ) .
the most probable source parameters are obtained by maximizing the likelihood ratio over the signal waveforms and sky coordinates .
the method performs reconstruction of unmodeled burst signals ( arbitrary waveforms ) and signals with a certain polarization state : elliptical , linear and circular .
the paper is organized as follows .
possible networks of advanced detectors and their fundamental properties are descussed in section  [ sec : networks ] . in sections  [ sec :
algorithm ] we describe the reconstruction algorithm . the simulation framework for this study
is presented in section  [ framework ] .
the results are reported in section  [ results ] . in sections  [ limitation ] and  [ conclusions ]
we describe main factors limiting the source reconstruction and discuss the results .
[ network ]    in 2001 - 2010 the ligo scientific collaboration ( lsc ) and the virgo collaboration operated a network of interferometric gravitational - wave detectors which are the most sensitive instruments from the first generation of the gw interferometers ( 1 g ) .
they consist of power - recycled michelson interferometers with kilometer - scale fabry - perot arms designed to detect gravitational waves with frequencies between tens of hz and several khz .
the two ligo observatories  @xcite are in hanford , washington ( 4  km and 2  km detectors ) and in livingston , louisiana ( 4  km detector ) , and the 3-km virgo detector  @xcite is located in cascina , italy .
other gravitational waves interferometers are the 300 m detector tama  @xcite in mitaka , japan , and the 600 m detector geo600  @xcite in hannover , germany . currently all 1 g interferometers are decommissioned , except virgo and geo600 , which continue to take data .
the second - generation gw detectors ( 2 g ) are currently under construction .
they include the advanced ligo detectors  @xcite , and the advanced virgo detector ( v )  @xcite which will have by an order of magnitude better sensitivity than the 1 g detectors .
all advanced ligo detectors have 4-km long arms , with one detector in livingston ( l ) and two identical co - aligned detectors in hanford ( h and h ) . also there are plans to build the large cryogenic gravitational telescope ( lcgt )  @xcite in japan ( the j detector ) and possibly move the ligo h detector to a site in australia  @xcite ( the a detector ) . figure  [ fig:2gsensitivities ] shows the design sensitivity for the listed 2 g detectors .
these , hopefully all five interferometers , compose the most advanced gw detector network which will be in operation after 2015 .
[ cols="^ " , ]      there are several factors limiting the accuracy of the coordinate and waveform reconstruction due to the cwb algorithm . for high snr events the coordinate resolution is limited by the cwb sky segmentation which is @xmath2 degrees . therefore the error angle can not be less than @xmath3 degrees .
also for the high frequency events the coordinate resolution is limited by the discrete time delays @xmath4 ( see section  [ sec : algorithm ] ) with the step of 1/16384 seconds and by the accuracy of the time delay filter ( few percent ) used in the analysis .
also in the analysis we did not use any unmodeled constraint specific for individual networks , which , in principle , may improve reconstruction .
these limitations are not fundamental and the algorithm performance can be improved in the future .
in the paper we present the results of the source localization and reconstruction of gw waveforms with the networks of gw interferometers . for a general characterization of the detector networks we introduce few fundamental network parameters , including the effective noise , and the network antenna and alignment factors .
the effective power spectral density of the network noise determines the average network snr for a given population of gw signals . for each direction in the sky
the network performance is characterized by its antenna and alignment factors .
the antenna factor describes how uniform is the network response across the sky .
the alignment factor , which strongly depends on the number of detectors and the orientation of their arms , determines the relative contribution of the two gw polarizations into the total network snr .
it requires several non - aligned detectors ( preferably more than three ) for a robust detection and reconstruction of both gw components .
the coordinate reconstruction strongly depends on the signal waveforms , network snr and the number of detector sites in the network .
the reconstruction can be significantly improved when it is constrained by the signal model .
although a crude coordinate reconstruction ( ring in the sky ) is possible with the networks of two spatially separated sites , at least three detector sites are required to perform the source localization .
the accuracy of the localization dramatically increases for networks with more than three sites , particularly for the low snr events .
for example , the lhhv and lhva networks are expected to have about the same detection rates , however , the 4-site lhva network would have much better performance for the accurate reconstruction of gw signals .
the pointing resolution required for joint observations with the electromagnetic telescopes is achievable with the networks consisting of four sites .
the lhvaj network demonstrates further improvements , both in the detection and reconstruction of gw signals , reaching a sub - degree angular resolution .
in addition , due to the limited duty cycle of the detectors , both the lcgt and the australian detectors will significantly increase the observation time when any of 4-site networks are operational .
the advanced ligo and virgo detectors are very capable of the first direct detection of gravitational waves .
however , for better reconstruction of the gw signals more detectors are required .
extra detectors introduce an important redundancy which lower the impact of limited duty cycle of the detectors , makes the coordinate reconstruction more accurate , and less dependent on the waveform morphology and calibration uncertainties .
the construction of the lcgt and the detector in australia will significantly enhance the advanced ligo - virgo network and these detectors will play a vital role in the future gw astronomy .
the authors are thankful to the ligo - australia committee members r.  weiss , p.  saulson , s.  sathyaprakash , f.  raab , p.  fritschel and s.  finn for useful discussion of the results . also the authors appreciate suggestions by l.  bildsten on better presentation of the results , particularly in figure  [ larshistograms ] .
this work was supported by the us national science foundation grants phy-0855044 and phy-0855313 to the university of florida , gainesville , florida .
coincident observations with gravitational wave ( gw ) detectors and other astronomical instruments are in the focus of the experiments with the network of ligo , virgo and geo detectors . 
 they will become a necessary part of the future gw astronomy as the next generation of advanced detectors comes online . 
 the success of such joint observations directly depends on the source localization capabilities of the gw detectors . in this paper 
 we present studies of the sky localization of transient gw sources with the future advanced detector networks and describe their fundamental properties . by reconstructing sky coordinates of ad hoc signals injected into simulated detector noise we study the accuracy of the source localization and its dependence on the strength of injected signals , waveforms and network configurations .    
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