3 away from the Earth, and it is demonstrated in Figure 2. It can be seen that the angular position of the source might have a maximum of 5% effect on the Shapiro delay of the considered source. Δ A ( r ) and Δ B ( r ): Here ϵ is the usual Schwarzschild term ϵ ≡ (2 GM/c $^{2}$r ) and the ϵ ∗ is the extra small parameter due to this effect, ϵ ∗ ≡ 2 v 2 $_{∗}$/c 2 where given the asymptotic rotation speed v ∗ for Milky Way ϵ ∗ is at the order of 6 × 10 − $^{7}$. Since r$_{s}$ ≈ 8 kpc the logarithm will be of order one. Looking at Eq.(2) and observing the direct proportionality of Δ t with Δ A ( r ) and Δ B ( r ), one can see that the time delay would approximately be equal to 10 − 6 times the total time of flight in flat space. But our aim is to calculate the time lag numerically, due to the difficulty of solving the Eq.(2) analytically. Us- ing the relevant parameters for the NFW density profile of the Milky Way [39], the numerical solution is depicted in Figure 1. Externally triggered search of gravitational waves is a strategy to look for possible signals around sources which might produce both GWs and other particles(external triggers). The information provided by an external trig- ger is extremely useful to impose extra requirements for a possible GW signals as well as to increase the confidence of the detection. Knowing the source direction would al- low us to look for only relevant portion of the sky. One can even infer the frequency of the possible GW signal based on the information provided by an external trigger and make a data analysis at a specific band [44]. Gamma ray bursts (GRBs) are one of the possible external triggers. A neutron star(NS) black hole or a NS-NS merger might be a good source for a GRB. A highly magnetized NS might also produce short and in- tense gamma rays, which are called as soft gamma ray Repeaters (SGRs). One sixth of short GRBs are thought to be because of SGRs, where during S5 of LIGO, electro- magnetically several hundred of them are were observed [45]. Disruption of neutron star’s crust would produce an increase in the rotation energy of a neutron star which results in increase of freqency, so called a “pulsar glitch”. This might also lead to emission of GWs. Last but not least, supernova explosions would surely produce both GWs and neutrinos. This triggered detection on the other hand, would provide us more information about neutrino mass as well as the mechanism of supernova ex- plosions. But still, there has not been a single direct detection of GWs. The search is based on the assumption that, the GW signal and the external trigger are coincident in If we look at Figure 1 we can see that the time lag for an event that is located at 100 kpc is approximately 100 days, which is 10 − 6 times 3 × 10 5 light years (the total time of flight of a photon in flat space). The time lag would surely depend on the angular po- sition of the source, since we are not the center of the Milky Way. Therefore one would like to see the effect of the direction of the position of a source in the whole sky. This was done for a source that is located up to 400 kpc FIG. 1: Shapiro delays for sources located in Milky Way. FIG. 2: The angular dependence of Shapiro delays for sources located in Milky Way. The units of RA(Right ascension) and Dec(Declination) is coverted to radians. IV. EXTERNALLY TRIGGERED SEARCHES FOR GWS TABLE I: Shapiro delays for GRB 070201 from the NFW profiles of the Milky Way and Andromeda using two different data sets. A ( r ) ≈ 1 + ϵ + ϵ ∗ , B ( r ) ≈ 1 − ϵ + ϵ ∗ ln( r r$_{s}$ ) . (6) Data Set ρ ( GeV/cm $^{3}$) M vir ( M ⊙ ) Δ t ( days ) MW − Klypin [39] 0 . 185 1 . 0 × 10 12 426 MW − Ascasibar [41] 0 . 347 1 . 0 × 10 12 421 M31 − Klypin [39] 0 . 188 1 . 6 × 10 12 634 M31 − Tempel [42] 0 . 661 1 . 0 × 10 12 383 TimeLag 0.0 0.5 1.0 1.5 2.0 RA GLYPH<Minus> 0.5 0.0 0.5 Dec 295 300 305 days 100 200 300 400 distance GLYPH<LParen1> kpc GLYPH<RParen1> 50 100 150 200 250 300 days TimeLag