Coherent observations of gravitational radiation with LISA and gLISA

The geosynchronous Laser Interferometer Space Antenna (gLISA) is a space-based gravitational wave (GW) mission that, for the past 5 years, has been under joint study at the Jet Propulsion Laboratory; Stanford University; the National Institute for Space Research (I.N.P.E., Brazil); and Space Systems Loral. If flown at the same time as the LISA mission, the two arrays will deliver a joint sensitivity that accounts for the best performance of both missions in their respective parts of the millihertz band. This simultaneous operation will result in an optimally combined sensitivity curve that is “white” from about $3\times {10}^{-3}\mathrm{Hz}$ to 1 Hz, making the two antennas capable of detecting, with high signal-to-noise ratios (SNRs), coalescing black-hole binaries (BHBs) with masses in the range $(10-10^8)M_{\odot }$. Their ability of jointly tracking, with enhanced SNR, signals similar to that observed by the Advanced Laser Interferometer Gravitational Wave Observatory (aLIGO) on September 14, 2015 (the GW150914 event) will result in a larger number of observable small-mass binary black holes and an improved precision of the parameters characterizing these sources. Together, LISA, gLISA and aLIGO will cover, with good sensitivity, the $({10}^{-4}-10^3)\mathrm{Hz}$ frequency band.

Figure 1

The optimal sensitivities of LISA (blue) and gLISA (red) averaged over sources randomly distributed over the sky and polarization states. Each of these curves is uniquely determined by the TDI $A$, $E$, and $T$ data combinations associated with the data from each mission. (See [19] for the derivation of the $A$, $E$, and $T$ combinations and the resulting optimal sensitivity. Also refer to [12] for the revised expressions of their noise spectra.) The dashed line (black) is the result of optimally combining the sensitivities of LISA and gLISA. As expected, in the lower part of the mHz band, LISA defines the network sensitivity; in the overlapping region the two sensitivities smoothly blend, resulting in a maximum sensitivity gain of $\sqrt{2}$. In the higher part of the accessible band gLISA defines the joint LISA-gLISA sensitivity. For completeness we have included the projected aLIGO sensitivity (green) together with the amplitude of GW150914 (magenta) as a function of the Fourier frequency $f$. Also included is a black horizontal line showing the frequency evolution of GW150914 over a 5-year period before coalescence.

Figure 2

Average luminosity distance achievable by LISA, gLISA and the LISA-gLISA network as a function of the chirp mass. The SNR of each configuration has been assumed to be equal to 10 with coalescence times equal to 5 years. The initial frequency was derived by using Eq. (4).

Figure 3

SNR for gLISA and the LISA-gLISA network as a function of the chirp mass of BHBs that are seen by LISA with a $\mathrm{SNR}=10.$ A coalescence time of 5 years was assumed, and the initial frequency was derived by using Eq. (4).