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Abstract KAGRA, the underground and cryogenic gravitational-wave detector, was operated for its solo observation from February 25 to March 10, 2020, and its first joint observation with the GEO 600 detector from April 7 to April 21, 2020 (O3GK). This study presents an overview of the input optics systems of the KAGRA detector, which consist of various optical systems, such as a laser source, its intensity and frequency stabilization systems, modulators, a Faraday isolator, mode-matching telescopes, and a high-power beam dump. These optics were successfully delivered to the KAGRA interferometer and operated stably during the observations. The laser frequency noise was observed to limit the detector sensitivity above a few kilohertz, whereas the laser intensity did not significantly limit the detector sensitivity. 

Abstract We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H ( z ), including its current value, the Hubble constant H 0 . Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H ( z ). The source mass distribution displays a peak around 34 M ⊙ , followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H ( z ) measurement, yielding H 0 = 68 − 8 + 12 km s − 1 Mpc − 1 (68% credible interval) when combined with the H 0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H 0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+ , statistically marginalizing over the redshifts of each event’s potential hosts. Assuming a fixed BBH population, we estimate a value of H 0 = 68 − 6 + 8 km s − 1 Mpc − 1 with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H 0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H 0 ) is the well-localized event GW190814. 

Intermediate-mass black holes (IMBHs) span the approximate mass range 100−10 5   M ⊙ , between black holes (BHs) that formed by stellar collapse and the supermassive BHs at the centers of galaxies. Mergers of IMBH binaries are the most energetic gravitational-wave sources accessible by the terrestrial detector network. Searches of the first two observing runs of Advanced LIGO and Advanced Virgo did not yield any significant IMBH binary signals. In the third observing run (O3), the increased network sensitivity enabled the detection of GW190521, a signal consistent with a binary merger of mass ∼150  M ⊙ providing direct evidence of IMBH formation. Here, we report on a dedicated search of O3 data for further IMBH binary mergers, combining both modeled (matched filter) and model-independent search methods. We find some marginal candidates, but none are sufficiently significant to indicate detection of further IMBH mergers. We quantify the sensitivity of the individual search methods and of the combined search using a suite of IMBH binary signals obtained via numerical relativity, including the effects of spins misaligned with the binary orbital axis, and present the resulting upper limits on astrophysical merger rates. Our most stringent limit is for equal mass and aligned spin BH binary of total mass 200  M ⊙ and effective aligned spin 0.8 at 0.056 Gpc −3 yr −1 (90% confidence), a factor of 3.5 more constraining than previous LIGO-Virgo limits. We also update the estimated rate of mergers similar to GW190521 to 0.08 Gpc −3 yr −1 .