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The next LIGO-Virgo observing run, O3, is scheduled to start toward the end of 2018, and is expected to have a factor of ∼ 2 improvement in sensitivity over the O2 run that finished in August 2017. LIGO/Virgo are expected to complete their first

science runs at design sensitivity in the early 2020s [14]. Based on the earlier science

runs, several tens of BBH systems and a small number of NSB events [9, 21] are likely

to be detected in O3. These events will be similar to sources previously identified and so the primary challenge will be computational — the LVC will need the capability to process multiple events simultaneously, which implies a need for accurate waveform models that are as fast to generate as possible. Further in the future there are plans for

third generation ground based detectors, such as the Einstein Telescope [33] and Cosmic

Explorer [32], and a space-based GW detector, the Laser Interferometer Space Antenna

(LISA) [64]. These new detectors will observe new types of source which will pose new

modelling challenges.

7.2.1. Third-generation ground-based detectors Third generation ground-based detectors

aim to improve on advanced detectors in two ways. Firstly, they aim to have an increase in sensitivity by an order of magnitude. Secondly, they aim to improve low-frequency sensitivity, with the ultimate goal of sensitivity as low as 1Hz, compared to ∼ 30Hz for the LIGO/Virgo detectors in O2, and 10Hz at design sensitivity. For the Einstein

Telescope (ET [33]), these aims will be achieved by increasing the arm-length to 10km,

siting the detector underground and using cryogenic cooling of the mirrors. ET will also have three arms in a triangular configuration, so that it is equivalent to having two detectors at the same site.

The increase in sensitivity will increase the number of sources detected by about a factor of a thousand. Data analysis must be able to keep pace with such a high source volume, which means algorithms must run quickly. This places constraints on the computational cost of waveform models, which is discussed further below. The improvement in low frequency sensitivity significantly increases the duration of any given signal in band. At leading order, the time to coalescence of a binary scales like

f−8/3 [143]. The NSB event GW170817 was in the LIGO band for 40s, starting from

30Hz, and generated 3000 waveform cycles [21]. For a detector with low frequency cut-off

at 3Hz, the same source would be in band for ∼ 5h and generate ∼ 105 _{cycles. This}

longer duration places more stringent requirements on waveform models, since fractional errors in the waveforms will need to be small enough that the templates are accurate

to within 1 cycle of the 105 _{in band. This is mitigated partially by the fact that most}

of the additional cycles are generated in the weak field where analytic models are well understood.

Third-generation detectors also offer the prospect of detection of new classes of sources. These include higher-mass BH systems, made possible by the improved low-

frequency sensitivity [33], and possibly intermediate mass ratio inspirals (the inspirals

of stellar origin BHs into intermediate mass BHs with mass ∼ 100M) [1351, 1352].

The former do not pose additional modelling challenges, as these signals will be well represented by rescaling templates for lower mass systems. The latter, however, lie in a regime where both finite mass-ratio effects and higher-order PN effects become important. The latter require numerical techniques, but these are limited in terms of the number of cycles that can be modelled, while the former requires perturbative techniques, but are then limited by the size of mass ratio corrections. Any IMRIs observed are likely to be at very low SNR and so will only be identifiable in the data if accurate templates are

available. Initial attempts to construct hybrid IMRI models have been made [1353–1356],

but considerable work is still required.

It is also hoped that it will be possible to test GR to high precision with third-

generation ground-based detectors [33]. This requires development of models in

alternative theories. This challenge is common to space-based detectors and is discussed further in the next section.

7.2.2. The Laser Interferometer Space Antenna LISA is a space-based GW detector

that has been selected as the third large mission that ESA will launch in its current programme, with a provisional launch date of 2034. LISA will comprise three satellites, arranged in an approximately equilateral triangular formation with 2.5Mkm long arms and with laser links passing in both directions along each arm. By precisely measuring the phase of the outgoing and incoming laser light in each arm LISA can do interferometry and detect GWs. It will operate at lower frequency than the LIGO/Virgo detectors, in the range 0.1mHz–0.1Hz, with peak sensitivity around a few mHz. The lower frequency sensitivity means that the typical systems that LISA will observe have higher mass,

M ∼ 104_–107_M

. Such massive BHs (MBHs) are observed to reside in the centres of

lower mass galaxies. LISA is expected to observe mergers of binaries comprised of two such MBHs, which are expected to occur following mergers between the BH host galaxies. MBHs are typically surrounded by clusters of stars, which include BHs similar to those observed by LIGO that were formed as the endpoint of stellar evolution. LISA is also expected to observe the EMRIs of such stellar origin BHs into MBHs. In addition to these MBH sources, LISA will also observe stellar compact binaries in the Milky Way, it could detect some of the stellar origin BH binaries that LIGO will observe and may

detect sources of cosmological origin [64]. The latter sources do not pose particular

modelling challenges, but the BH sources do.

In contrast to the LIGO-Virgo network, there will be only one LISA constellation. While the three LISA arms allow, in principle, the construction of two independent data streams, there will inevitably be some correlation between noise in these channels. In addition, LISA sources are long-lived, lasting months or years in the data set, and so there will be hundreds of sources overlapping in the data. These properties make it

much more difficult to construct unmodelled source pipelines like those used in LIGO and so LISA will rely even more heavily on having models of potential signals in order to identify them in the data. Typical MBH binary signals will have SNR in the tens to hundreds, with a few as high as a thousand. This allows much more precise estimates of parameters, but places much higher demands on the fidelity of waveform models. A template accurate to a few percent is fine for characterising a source that has SNR of a few tens as is typical for LIGO/Virgo, but for an SNR of one thousand, the residual after extracting that source will have SNR in the several tens, biasing parameter estimation and contaminating the extraction of subsequent sources. Templates need to be two orders of magnitude more accurate for use in LISA. This accuracy comes coupled to the need for longer duration templates, as for the third-generation ground based detectors, since the signals are present in the data stream for months. MBH binaries detected by LISA are

additionally expected to have high spins [1357], in contrast to the observed LIGO/Virgo

sources which are all consistent with low or zero spin [3, 11, 18, 20,1358, 1359]. Finally,

MBH binaries are more likely to show precession. The likely presence of these physical effects in observed signals, coupled with the necessity of model-based searches for LISA places strong requirements on the MBH binary waveform models that must be available by the time LISA flies.

For EMRIs, expected SNRs are in the tens [672, 891], but this SNR is accumulated

over ∼ 105 cycles. This makes unmodelled EMRI searches impossible and imposes the

requirement on modelled searches that the EMRI templates match the true signals to

better than one cycle over 105_{. In addition, all of these cycles are generated in the}

strong-field where accurate modelling of the signals is more challenging. This drives the requirement for GSF EMRI models accurate to second order in the mass ratio described above. These models must include the effect of high spin in the central MBH, and

eccentricity and inclination of the orbit of the smaller BH [699, 1360]. EMRI models will

also have to be computationally efficient. Naively, to match 105 _{cycles in a parameter}

space with 8 intrinsic (and 6 extrinsic) parameters, requires (105₎8 _{∼ 10}40 _templates.

This is a crude overestimate, but illustrates the complexity of a template-based EMRI search, and the need to be able to generate large numbers of templates in a small

computational time. Semi-coherent methods have been proposed [698] that have less

stringent requirements, but still need templates accurate for 103 or more cycles.

Finally, one of LISA’s primary science objectives is to carry out high precision tests of GR, including both tests of strong-field gravity and tests of the nature of compact objects by using EMRIs to probe the gravitational field structure in the vicinity of

BHs. Many different tests have been proposed and we refer the reader to [1361] for a

comprehensive review. Several methods exist for phenomenological tests, which assess consistency of the observed signal with the predictions of GR. However, understanding the significance of any constraints that LISA places, and interpreting any deviations that are identified requires models for deviations from the predictions of GR in alternate theories. We require strong-field predictions, most likely relying on numerical simulations, to compare to the merger signals from MBH binaries, which will be observable with high

significance. We also require predictions for the sorts of deviations that might be present

in the inspiral phase of EMRIs. The latter need to be accurate to a part in 105 _{and must}

allow for confusion between gravitational effects and effects of astrophysical origin, e.g., the presence of matter in the system, perturbations from distant objects, etc.