The KAGRA science overview (Akutsu et al., PTEP 2020) states that the successor upgrade of the cryogenic underground gravitational-wave detector KAGRA — 'KAGRA+' — has no fixed design: the balance among a low-frequency option, a high-frequency option, heavier 40 kg test-mass mirrors, frequency-dependent squeezing, and their combination remains open and technology-dependent, while the science each option would deliver is blocked by uncertain inputs — intermediate-mass black hole and intermediate-mass-ratio inspiral event rates, binary-neutron-star tidal and post-merger waveform systematics, and unclarified core-collapse-supernova spectral evolution. The open problem is the quantitative, uncertainty-aware mapping from the named design options to detection and parameter-estimation capability for the named source classes, together with quantification of which input (rate, waveform modeling, supernova physics) binds each science case.

Background

Ground-based gravitational-wave (GW) detectors — the laser interferometers LIGO and Virgo (surface, 3–4 km arms) and KAGRA (underground in the Kamioka mine, 3 km arms, cryogenic sapphire mirrors) — measure strain by monitoring differential arm length with laser interferometry; they observe the coalescence of compact binaries and, prospectively, bursts from core-collapse supernovae (CCSN). Detection capability is set by the amplitude spectral density of the detector noise versus frequency: better sensitivity at low frequency (roughly 10–50 Hz) increases the number of observable cycles, the precision of source-parameter estimation, and access to more massive systems such as intermediate-mass black holes (IMBHs, roughly 10210^2–10510^5 solar masses), while high-frequency sensitivity (kilohertz band) governs binary-neutron-star (BNS) post-merger science. Quantum noise — photon shot noise at high frequency and radiation-pressure noise at low frequency — can be beaten down by injecting squeezed states of light into the antisymmetric port; frequency-dependent squeezing (FDS), implemented with a filter cavity, raises the squeezing angle with frequency so that both bands improve simultaneously rather than trading one against the other. The KAGRA science overview (Akutsu et al., Prog. Theor. Exp. Phys. 2020, DOI 10.1093/ptep/ptaa120) states that the concrete KAGRA+ upgrade plan 'has not been decided officially yet' and considers four options plus a combination: a low-frequency option (improving roughly the 10–50 Hz band), a high-frequency option (roughly 300 Hz–5 kHz), heavier 40 kg test-mass mirrors (mirror mass increased from 22.8 kg to 40 kg), and frequency-dependent squeezing; the quantitative noise curves for these options come from Michimura et al. (Phys. Rev. D 102, 022008 (2020)). For the science each option enables, the overview identifies three source-class limitations: (i) intermediate-mass-ratio inspirals (IMRIs — binaries whose component-mass ratio lies between the equal-mass and extreme-ratio regimes, e.g. a stellar-mass compact object inspiralling into an IMBH) and IMBH binaries, whose detection prospects hinge on coalescence rates that are 'still highly uncertain' (the overview quotes roughly 1–30 events per year for IMRIs) and on low-frequency sensitivity; (ii) BNS science, where tidal deformability (the induced quadrupole moment of a neutron star in its companion's tidal field, encoding the neutron-star equation of state) and post-merger kilohertz emission are limited by waveform systematics — numerical-relativity-calibrated waveform models carry systematic error significant relative to statistical error at current signal-to-noise ratios, and the post-merger phase is 'less reliable than those of the inspiral' because simulations must resolve shocks, turbulence, magnetic fields, and neutrino cooling; and (iii) CCSN bursts, whose spectral evolution 'has not been completely clarified yet' and depends on the details of supernova modeling, so the overview judges it 'too early to make a quantitative discussion about the best-suited sensitivity curves for KAGRA+'. The problem posed is therefore the coupled question: which design choices buy which science, given these uncertainties — a question the overview leaves open in a specific sense: it explicitly declares the design decision undecided and judges quantitative CCSN discussion premature.

Problem Statement

Construct the quantitative, uncertainty-aware mapping from the named KAGRA+ design options — low-frequency upgrade (roughly the 10–50 Hz band), high-frequency upgrade (roughly 300 Hz–5 kHz), heavier 40 kg test-mass mirrors, frequency-dependent squeezing, and their combination, with noise curves as specified by Michimura et al. (2020) — to detection and parameter-estimation capability of the KAGRA detector within the LIGO–Virgo–KAGRA network, for the source classes named in the KAGRA science overview: (a) intermediate-mass black hole binaries and intermediate-mass-ratio inspirals, whose reach is governed by low-frequency sensitivity and whose prospects are conditional on the still highly uncertain (roughly 1–30 events per year at the time of the overview) event rates; (b) binary neutron stars, both inspiral tidal and equation-of-state inference and kilohertz post-merger emission, where the answer must be stated with waveform-systematics errors treated as comparable to or larger than statistical errors, and with numerical-relativity post-merger phase treated as unreliable; and (c) core-collapse supernova bursts, whose spectral evolution is not yet clarified by supernova modeling. Construct the mapping so that, for each of the four single-technology options and for every source class, it yields the detection horizons (with the detection threshold and distance convention used), the parameter-estimation precision (with the parameters whose precision is reported), and the quantified strength of the binding input — the degree to which rate uncertainty, waveform systematics, or supernova-model dependence limits that science case — with their combination treated at whatever level the science requires, with the rate-dependent conclusions stated conditionally on a single explicit rate prior or scenario within the overview's still uncertain (roughly 1–30 events per year) range, or on accumulated observations, since the rates are empirical inputs that analysis alone cannot close, and with the core-collapse-supernova outputs stated conditionally on a single named supernova model family, since the spectral evolution is not yet clarified by supernova modeling. The final cross-class weighing of options involves a collaboration-level strategic science weighting; the scientifically reviewable completion boundary is the per-source-class quantitative mapping with its binding inputs quantified, not that strategic choice.

References

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